Abstract image of a woman sitting on books and studying on a laptop

HPCL Report Final

Ramya Emandi, profile picture
Ramya Emandi

This document provides an overview of Hindustan Petroleum Corporation Limited (HPCL), an Indian state-owned oil and gas company. Some key points: - HPCL has a 16% market share in India and owns and operates two coastal refineries in Mumbai and Vishakhapatnam. - The company reported revenues of INR 1,294,757.90 million in fiscal year 2009, an increase of 16.53% over 2008. However, net profit decreased 44.48% from 2008. - Competitors include other state-owned oil companies like IOCL and BPCL as well as private companies like Reliance Industries. Analysis shows RIL is a major competitor and

1 of 76
Downloaded 25 times
1
2
Most read
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
Bond Mathematics 1 HINDUSTAN PETROLEUM COMPANY LIMITED Company profile: Fortune 500 company Mega Public Sector Undertaking Hindustan Petroleum Corporation Limited (HPCL) is an integrated oil refining and marketing companies in India. It is engaged in the oil and gas exploration and production, refining of crude oil and marketing of petroleum products. Currently, the company holds 16% market share and 10.3% of India‘s refining capacity. The company owns and operates two coastal refineries, one at Mumbai and the other in Vishakapatnam. The company also holds an equity stake of 16.95% in Mangalore Refinery & Petrochemicals Limited. The company is headquartered at Mumbai in Maharashtra, India. HPCL‘s Mumbai refinery has a capacity of 5.5 Million Metric Tons Per Annum (mmtpa) and Vishakapatnam refinery has a capacity of 7.5 mmtpa. Mangalore Refinery has a capacity of 9 mmtpa. HPCL owns and operates the largest lube refinery in India with a capacity of 335 TMT. The company reported revenues of (Rupee) INR 1,294,757.90 million during the fiscal year ended March 2009, an increase of 16.53% over 2008. The operating profit of the company was INR 10,118.40 million during the fiscal year 2009, a decrease of 28.92% from 2008. The net profit of the company was INR 7,573.90 million during the fiscal year 2009, a decrease of 44.48% from 2008. KEY DATA 2009 Sales: 1,31,802.65 Cr Major Industry: Oil Industry Sub Industry: Refineries Country: India Currency Indian Rupees Fiscal Year Ends: March Employees More than 11,245 Exchanges: NSE BSE Market Capitalization: 12092.38 Cr Weighted avg. no. of shares 33.86 crores OFFICERS Chairman & Managing Director Mr.Arun Balakrishnan Director- Marketing Mr.S.Roy Choudhury Director- Human Resources Mr.V. Vizia Saradhi Director- Finance Mr.B.Mukherjee
Bond Mathematics 2 Company description: Mission: "HPCL, along with its joint ventures, will be a fully integrated company in the hydrocarbons sector of exploration and production, refining and marketing; focusing on enhancement of productivity, quality and profitability; caring for customers and employees; caring for environment protection and cultural heritage. It will also attain scale dimensions by diversifying into other energy related fields and by taking up transnational operations." Vision: To be a World Class Energy Company known for caring and delighting the customers with high quality products and innovative services across domestic and international markets with aggressive growth and delivering superior financial performance. The Company will be a model of excellence in meeting social commitment, environment, health and safety norms and in employee welfare and relations. Table1.1 Business Units Description Refineries Present Projects:  Facilities for Euro-III & IV grade Gasoline  New FCCU project at Mumbai Refinery  Environmental facilities  Bottom Up-gradation Projects  LOBS Project  MR/VR DHT  Single Point Mooring (SPM) Project at Visakh Refinery  Modernization Project for Mounded Storage System for LPG /Propylene at Visakh Refinery Aviation Infrastructure  Aviation Service Facility: Our Facility to supply JET A1 at Indian Airports  Location of our ASFs: Aircraft Fueling Facilities of HP Aviation in India  Equipment: Our Equipment to supply Aircraft Jet Fuel in India  Modernization And Upgradation: Keeping ATF Refueling facilities up- to-date Jet Fuel Prices  Domestic Prices: Price of Jet A1 at various airports in India  International Prices: PLATTS based Pricing in India for International carriers Bulk Fuel Fuels Offered:  Bitumen  Fuels  Marine-Bunker Fuels  Marine Lubes  Special Products
Bond Mathematics 3  Superior Kerosene Oil-Non PDS LPG (HP Gas) LPG Offered:  Domestic LPG  Commercial LPG  Industrial & Bulk LPG  Auto LPG  Piped LPG  Rasoi Ghar Lubes (HP Lubes) HP Lubricants are borne out of an intense and unrelenting R & D effort, which aims at producing quality products that enhance automotive performance standards. The range of HP Lubes is comprehensive and catering to the minutest needs; from new generation cars to ploughing tractors and industrial machinery. The range conforms strictly to OEM specifications, often taking the initiative in customization of products. Retail Retail Offered:  Auto LPG  CNG  Power  Turbo Jet Trade The activities of IT&S relate to  Crude oil imports,  Petroleum Product Imports / Exports,  Shipping,  Production planning for Refineries,  Supplies for domestic Markets,  Product exchange with other Indian Oil Companies and Oil price risk management. E & P HPCL, in consortium with E&P partners companies currently has 19 nos. blocks in India, and 4 nos. overseas blocks in Oman, Australia and Egypt. HPCL intends to leverage and consolidate its current position and formulate & implement a strategy for E&P business based on opportunities both within and outside India. Currently HP E&P has presence in 4 countries including India and plans to expand its portfolio in other countries which is a main area of focus of its Strategic Investment plan mainly in Middle East, South East Asia & Africa. Ventures Till Date JV‘s:  HPCL-Mittal Energy Ltd. (HMEL)  Hindustan Colas (HINCOL)  Prize Petroleum Company Limited  South Asia LPG Co Pvt. Ltd. ( SALPG)  Bhagyanagar Gas Limited (BGL)  Aavantika Gas Limited  Petronet India Limited (PIL)  Petronet MHB Limited (PMHBL)  Mangalore Refineries and Petrochemicals Limited (MRPL)  CREDA-HPCL Biofuel Limited (CHBL)  Sushrut Hospital and Research Centre
Bond Mathematics 4 HPCL financial analysis: Figure1.1 Ratios- 2009: Asset Ratios Total assets/equity 4,39 Total liabilities/equity 3.39 Total liabilities/total assets 0.77 Sales/total assets 3.04 Liquidity Ratios Quick ratio 2.03 Current ratio 2.87 Interest cover 1.47 65,218.8 3 76,920.2 6 96,918.1 5 112,098. 27 131,803 2005 2006 2007 2008 2009 sales (in crores) sales (in crores) 2,347.52 1113.36 3000.43 2557.35 4158.17 2005 2006 2007 2008 2009 PBDIT (in crores) adjusted PBDIT 1277.33 405.63 1571.17 1134.88 574.98 2005 2006 2007 2008 2009 PAT (in crores) reported net profit 0 50 100 150 200 250 300 350 DIVIDEND EPS BOOK VALUE
Bond Mathematics 5 Turnover ratios Sales/inventory 12.96 Sales/receivables 20.26 Sales/working cap 7.91 Profitability ratios Operating margin 2.27 Pretax income margin 0.63 Return on equity 3.08 Return on fixed assets 2.05 Return on total assets 0.75 As per the sales seen, there is a constant increase in sales and volumes. The profit should also increase but there is a decline over last 2 years. This decrease is due to the negative results of stock adjustments in the P&L account, which says that HPCL‘s shares have been undervalued and the company was getting devalued. This can be clearly seen in the trend of EPS and the same is reflected in the net profits. Asset ratios show that total assets have 22.7% equity and 77.3% debt. The liabilities have been raised high against Rs.1 of equity i.e Rs.3.39, which is not a good sign. Sales/total assets is a good ratio of 3.04. HPCL is earning good sales out of this assets. Liquidity ratios of HPCL are good. The company has the ability to meet its short term debt obligations. It has very high short term solvency. There is a lot of liquidity in the company leading to opportunity costs. They can use this money in more investments. Interest cover ratio is quite fine and company earnings seem to be consistent. Turnover ratios show that sales inventory ratio is above 6.94 indicating excessive efficiency in sales performance. Similarly, sales receivable ratio of 20.26 signifies efficient debt management. However, considering the liquid nature of industry it operates, the ratio needs to be bought down below 15. Profitability ratios show that they are just touching margins.ROE should be around 12%. To improve their profits HPCL has to reduce its costs or has increase its volumes and sales or can increase its prices. But being a public company, it is not that easy to increases prices as they have to abide by the government policies and subsidiaries. Despite of these subsidy mechanisms, one can say that HPCL is gaining good profits. Growth ratios (2009) Net sales growth (%) 18.83 Core EBITDA growth (%) 37.22 EBIT growth (%) 47.02 PAT growth (%) -49.34 EPS growth (%) -49.34
Bond Mathematics 6 Competitive analysis (2009): The competitor‘s in the public sector: IOCL, BPCL and MRPL. The competitor‘s in the private sector: RIL, CPCL The competitor‘s in the MNC are: Essar, BP The major competitors amongst these would be IOCL, BPCL and RIL Figure1.2 0 50000 100000 150000 200000 250000 300000 350000 HPCL IOCL RIL BPCL sales (in crores) sales (in crores) 0 5000 10000 15000 20000 25000 30000 HPCL IOCL RIL BPCL Adjusted PBDIT (in crores) Adjusted PBDIT (in crores) 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 HPCL IOCL RIL BPCL PAT (in crores) PAT (in crores) 0 200 400 600 800 1000 1200 HPCL IOCL RIL BPCL Stock price STOCK PRICE (June 2,2010)
Bond Mathematics 7 Table1.2 Valuation Parameters HPCL IOCL RIL BPCL P/E 9.5 8.36 20.3 13.63 EV/NET SALES 0.25 0.29 2.08 0.25 EV/EBITDA 8.28 8.36 12.12 8.09 The above results clearly show that RIL is a big player and a tough competitor to HPCL. RIL market cap is high and all their valuation parameters are high, which indicates that to compete with RIL, HPCL‘s best adoption should be to expand its business and sales. IOCL is the next competitor to HPCL and BPCL is on same margins as HPCL, but all three companies are better in profits than HPCL. HPCL should adopt to better business plans and strategies to set a race with these companies. Threat of Intense segment rivalry: • Is witnessed in the holistic service offered by the retail outlet majors (IOCL,HPCL ,BPCL) If IOCL has Swagat outlets HPCL and BPCL has Club HP and Pure for Sure outlets. It is noted that most of these outlets have same facilities like Quality verification checks, Truck driver amenities etc, leading to intense segment rivalry. • However IOCL has the edge in terms of vast refining and distribution network, hence is the market leader. Threat of new entrants: • In the current INDIAN scenario, entry and exit barriers are high and profit potential is high. • But firms face more risk because poorer-performing firms stay in and fight it out. Like, IBP was facing bleak prospects till the time INDIAN OIL purchased it with a premium of over 60%. • Till the recent crude OIL spike, Reliance Retail petroleum, ESSAR OIL and SHELL gave a head-on clash (frontal attack in select locations) with OIL PSU‘s. • Adding to it newer plants come with better crude handling and therefore refinery margins are good, thus reflected in the net margins. Threat of Supplier’s growing bargaining power: • Petroleum is synonymous with OPEC cartel. • Big-wigs like Exxon-Mobil, Total, Occidental Petroleum, IOCL, and BPCL are not shielded from the vagaries of OPEC. • Though OPEC claims that it‘s the tax structure in the respective countries which makes petroleum products expensive, crude OIL price varies in in accordance with production levels of OPEC. • Today due to Global meltdown, Crude OIL prices are declining.
Bond Mathematics 8 • But OPEC has already initiated significant production cuts whose effect might be felt in the forthcoming months. Threat of Substitute Products: • Is from cleaner and efficient fuels like Compressed Natural Gas (CNG), where it was implemented on a war-footing in Delhi to control emissions. • Central Government‘s encouragement in the form of Bio-fuel purchase policy for 5% bio- fuel blended Diesel fuel. • Electric car – Reva also poses a challenge to the existing players. Threat of buyer’s growing bargaining power: • ‗Consumer is always the king ‗– is apt in the case of petroleum products in India. • Consumer‘s interests‘ are protected by the Government by not raising the fuel prices beyond a limit and indirectly consumer is exercising his bargaining power. • Also all the OIL PSU‘s offer varied services to the consumer including intangible ones like frequent quality checks and tangible ones like amenities ATM , Car care etc which was not even a moot concept in the past
Bond Mathematics 9 Oil industry Table1.3 Oil and Gas Exploration & Production The economic crisis left an impact on the oil and gas industry globally. The economic downturn that followed resulted in unprecedented demand destruction. The industry is on a path of recovery due to fiscal measures announced by various governments. The major deepwater basins of the world namely the East coast of India, Gulf of Mexico, Africa and Brazil continue to witness huge levels of activity and investment. The structural theme for investment in the sector remains valid. The world‘s insatiable need for reliable and affordable energy continues to grow unabated. This calls for substantial investments, access to resources and newer technologies to unlock resources from challenging locations. The International Energy Agency (IEA), in its World Energy Outlook 2009, estimates that by the year 2030, global energy demand is expected to increase by 49% from its current level. Oil and natural gas are expected to remain primary energy sources and are expected to meet 51% of the global demand. Increasing concern for climate change augurs well for natural gas as it is an environmentally benign fuel with carbon emissions far lower than other fossil fuels.
Bond Mathematics 10 IEA estimates that the world requires investments to the tune of $ 11 trillion in the oil and gas sector over the next 20 years implying an annual investment of over $ 500 billion. FY 2009-10 was a year of steady growth. Oil prices rose from an average of $ 46/barrel (bbl) in January 2009 to touch $ 75/bbl in December 2009. Average WTI prices remained at $ 70/bbl vis-à-vis $86/bbl for the previous year. Henry Hub natural gas price averaged at $ 4/Million Metric British Thermal Unit (MMBTU) for FY 2009-10 as against an average of $ 7.87/MMBTU in FY 2008-09. The year 2009 also saw the global oil demand slip to 84.93 MBPD, a decrease of 1.5% over 2008. IEA forecasts that the global oil demand is set to increase by 1.67 MBPD or 2.0% to 86.60 MBPD in 2010. Figure1.3 Kirirt parekh recommendations on future oil prices An experts group, headed by former Planning Commission member Kirit Parikh, submitted its much awaited report on pricing policy for four major oil products, namely, petrol, diesel, kerosene and LPG. The committee has recommended that prices of petrol and diesel to be market-determined, both at the refinery gate and retail levels, whereas the prices of kerosene and domestic LPG can be partially raised by Rs 6 per litre and Rs 100 per cylinder respectively. For kerosene and LPG, the committee has recommended linking fuel prices with per capita income and selective allocations to poorer families through smart cards linked with unique identities (UID) project. 29.6% 7.9% 10.9% 5.3% 8.0% 1.8% 1.6% 0.1% 9.2% 25.5% Refinery crude throughput, 2006 IOCL BPCL HPCL KRL CPCL BRPL NRL ONGC MRPL RIL
Bond Mathematics 11 The committee has accepted the subsidy formula proposed by Oil and Natural Gas Corporation (ONGC) aimed at reducing burden of oil companies. The formula suggests an incremental rate of taxes on higher crude oil price realization from the nomination blocks of ONGC and Oil India Ltd (OIL). The proposed subsidy sharing formula shall keep the government‘s subsidy contribution from budget in the range of Rs 19,780-23,340 crore at various crude price levels. A summary of recommendations and their impact has been provided in Annexure. According to D.R.Dogra, Managing Director & CEO , CARE Ltd. ― The impact on the oil and gas industry, if any of the recommendations by the committee is implemented, will be extremely positive‖. The complete deregulation of auto-fuels and sharp hikes in the prices of cooking fuels would help the government in reducing fiscal deficit and thus curtail its borrowings. The three public sector oil marketing companies, namely, Indian Oil Corporation, Bharat Petroleum Corporation Ltd and Hindustan Petroleum Corporation Ltd, would be able to reduce their under-recoveries considerably. However, the complete deregulation may prompt private players such as Reliance, Essar and Shell to re-open their retail fuel outlets, putting pressure on market share of public sector oil marketing companies (OMCs). In the past, the entry of private players in retail fuel market had resulted in an erosion of about 10 per cent in the market share of public sector OMCs. The proposed hike in prices of cooking fuels coupled with reduction in allocation of kerosene under the public distribution scheme (PDS) by 20 per cent would reduce under-recoveries by about Rs 16,454 crore, whereas, the auto-fuel deregulation would avert Rs 13,997 crore of under-recoveries. In the opinion of CARE Research, this is a landmark report, but implementation is the key. Although the report is in line with the wish-list of most of the market participants, implementation of the recommendations needs to be keenly watched for. ―The situation is tricky for the Government, as it needs to strike a balance between reducing the subsidy burden on the public sector oil and gas undertakings, reducing the fiscal deficit and managing the current inflationary scenario, given the economy being in the process of revival and attempting to restore its buoyancy‖ added Mr Dogra. It may be noted that similar kind of recommendations made by the Chaturvedi committee in 2008 were rejected by the government. Also, practicability of the selective allocations to poorer families through smart cards linked with UID project also needs to be evaluated by the government keeping in view the infrastructure requirement for the same. Although diesel is a major contributor to the total underrecoveries, its deregulation needs to be carefully evaluated as the agriculture sector (consuming 12 percent of diesel) and transport industry (consuming 40 per cent of diesel), the backbone of the Indian economy, are the major consumer of the fuel.
Bond Mathematics 12 Table1.4
Bond Mathematics 13 Conclusive report 2010 Looking at the financial results of the company for this year 2009-2010, company has recommended Rs 12 of dividend/share as against Rs 5.25 last year. The dividend/share has been increasing gradually which is a good significance for the shareholders. The sales/income from operations have been decreased from 136885.22 Cr in year 2008-2009 to 119453.33 Cr in year 2009-2010. The company‘s gross profits earned are 2564.29 Cr as against 2620.66 Cr. But the PAT has doubled from 757.39 Cr in 2008-2009 to 1475.15 Cr in year 2009-2010. The physical performance of market sales has increased from 25.39 million metric tonnes in 2008-2009 to 26.27 MMT in 2009-2010. The company‘s turnover has decreased from last year highest achieved turnover of 121510.39 Cr to 113163.38 Cr in this year. It is a matter of pride for the company to be ranked 311 amongst Global Fortune 500 Companies, 1002 amongst Forbes Global 2000 Companies and 111 in the list of World‘s Most Reputed Companies brought out by the Global Reputation Institute. HPCL aims to conduct our business with highest standards of corporate governance. HPCL has implemented the ―Right to Information Act (RTI)‖ in letter as well as spirit. HPCL has also implemented the Integrity Pact in liaison with ―Transparency International‖. The Integrity Pact forbids vendors from using any type of unwarranted influence for furthering their interests while in turn ensuring them fairness, transparency and equal opportunity in their association with the Corporation. 1. The Company is engaged in the following business segments: a) Downstream i.e. Refining and Marketing of Petroleum Products b) Exploration and Production of Hydrocarbons Segments have been identified taking into account the nature of activities and the nature of risks and returns. 2. Segment Revenue comprises of the following: a) Turnover (Net of Excise Duties) b) Subsidy from Government of India c) Other income (excluding interest income, dividend income and investment income) 3. There are no geographical segments.  Average Gross Refining Margins during the year ended March 2010, were US $ 2.68 per BBL as against US $ 3.97 per BBL during the corresponding previous year.  The prices of LPG (Domestic) and SKO (LPG) are subsidised as per the scheme approved by the Government of India. Subsidy amounting to Rs. 609.43 crores (2008-09 : Rs. 574.23 crores) for the year has been accounted at 1/3rd of the subsidy rates for 2002-03.  In principle approval of Government of India for Budgetary Support amounting to Rs. 5563.13 crores (2008-09 : Oil Bonds for Rs. 14,692.77 crores), has been received and the same have been accounted under ‗Recovery under Subsidy Schemes‘.  During the year, ONGC and GAIL offered discount amounting to Rs. 3247.14 crores (2008-09 : Rs. 7176.95 crores) on Crude Oil, SKO and LPG purchased from them.
Bond Mathematics 14  During the current year, investments in ―6.35% Oil Marketing Companies' GOI Special Bonds 2024‖ amounting to Rs. 4603.73 crores have been reclassified from ‗Long Term Investments‘ to ‗Current Investments‘. Consequently, an amount of Rs. 756.88 crores has been provided in the books of accounts towards diminution in the value for this investment.  The employee cost for the year 2009-10 is higher due to provision made for Rs. 318.25 crores towards revision in the salary for non-management staff, and perquisites & retiral benefits for management employees. Overall the emerging global scenario and economic slowdown has influenced HPCL to greater extent. However consistent performance of the corporation and efficient management has managed to maintain the profitability of the corporation at sustained levels. HPCL still expects a wide road to be travelled towards achievement of its goal and target.
Bond Mathematics 15 BOND MARKET IN INDIA The Bond Market in India with the liberalization has been transformed completely. The opening up of the financial market at present has influenced several foreign investors holding upto 30% of the financial in form of fixed income to invest in the bond market in India. The bond market in India has diversified to a large extent and that is a huge contributor to the stable growth of the economy. The bond market has immense potential in raising funds to support the infrastructural development undertaken by the government and expansion plans of the companies. Sometimes the unavailability of funds become one of the major problems for the large organization. The bond market in India plays an important role in fund raising for developmental ventures. Bonds are issued and sold to the public for funds. Bonds are interest bearing debt certificates. Bonds under the bond market in India may be issued by the large private organizations and government company. The bond market in India has huge opportunities for the market is still quite shallow. The equity market is more popular than the bond market in India. At present the bond market has emerged into an important financial sector. The government securities market has witnessed significant transformation in the 1990s in terms of market design. The most significant developments include introduction of auction- based price determination for government securities, development of new instruments and mechanisms for government borrowing as well as participation by new market participants, increase in information dissemination on market borrowings and secondary market transactions, screen based negotiations for trading, and the development of the yield curve for government securities for marking-to-market portfolios of banks. During the last one decade, RBI introduced the system of primary dealers (PDs) and satellite dealers (since discontinued from December 2002), introduced delivery versus payment (DvP) in securities settlement, expanded the number of players in the market with facility for non-competitive bidding in auctions, and allowed wider participation in constituent Subsidiary General Ledger (SGL) accounts. The government securities market also benefited from emergence of liquidity arrangement through the Liquidity Adjustment Facility (LAF), expansion of the repo markets, complete stoppage of automatic monetisation of deficits, and emergence of self regulatory bodies, such as, the Primary Dealers Association of India (PDAI) and the Fixed Income Money Markets and Derivatives Association (FIMMDA).Continuous reforms in the G- Sec market are being undertaken for improving market design and liquidity.
Bond Mathematics 16 To enhance liquidity and efficiency, some important initiatives have been taken in the Indian debt market such as:  introduction of repo/reverse repo operations in government securities to facilitate  participants of manage short term liquidity mismatches  operationalisation of Negotiated Dealing system (NDS), an automated electronic trading platform  establishment of Clearing Corporation of India Ltd. (CCIL) for providing an efficient and guaranteed settlement platform  introduction of G-secs in stock exchanges  introduction of Real time Gross Settlement System (RTGS) which addresses settlement risk and facilitates liquidity management,  adoption of a modified Delivery-versus-Payment mode of settlement which provides for net settlement of both funds and securities legs and  Announcement of an indicative auction calendar for Treasury Bills and Dated Securities. Central government securities: bonds and t-bills The different types of bond market in India Primary market: •Issuance of securities through autions •Issuance of securities with pre-announced coupon bonds •Issuance of securities through tap sale •Issuance of securities in conversion of maturing treasury bills/dated securities Secondary markets: •Trading on stock exchanges: NSE, BSE, OTCEI •Most of the secondary market trades in government securities are negotiated between participants (Banks, FIs, PDs, MFs) having SGL accounts with RBI. These may be negotiated directly between counter parties or negotiated through brokers. NDS of RBI provides an electronic platform for negotiating trades in government securities. If a broker is involved, the trade is reported to the concerned exchange. Trades are also executed on electronic platform of the WDM segment of NSE. WDM segment of NSE provides trading and reporting facilities for government securities •Repo and reverse repo •Wholesale debt market •Retail debt market Corporate bond market Municipal bond market Governmen t & agency bond market Funding bond market Mortgage backed & collateral debt obligation bond market
Bond Mathematics 17 Table 2.1 Market Segment Issuer Instruments Government securities Central Government Zero Coupon Bonds, Coupon Bearing Bonds, Treasury Bills, STRIPS State Governments Coupon Bearing Bonds Public sector bonds Government Agencies / Statutory Bodies Govt. Guaranteed Bonds, Debentures Public Sector Units PSU Bonds, Debentures, Commercial Paper Private sector bonds Corporates Debentures, Bonds, Commercial Paper, Floating Rate Bonds, Zero Coupon Bonds, Inter-Corporate Deposits Banks Certificates of Deposits, Debentures, Bonds Financial Institutions Certificates of Deposits, Bonds The major reforms in the bond market in India  The system of auction introduced to sell the government securities  The introduction of delivery versus payment (DvP) system by the Reserve Bank of India to nullify the risk of settlement in securities and assure the smooth functioning of the securities delivery and payment  The computerization of the SGL  The launch of innovative products such as capital indexed bonds and zero coupon bonds to attract more and more investors from the wider spectrum of the populace  Sophistication of the markets for bonds such as inflation indexed bonds  The development of the more and more primary dealers as creators of the Government of India bonds market  The establishment of the a powerful regulatory system called the trade for trade system by the Reserve Bank of India which stated that all deals are to be settled with bonds and funds  A new segment called the Wholesale Debt Market (WDM) was established at the NSE to report the trading volume of the Government of India bonds market  Issue of ad hoc treasury bills by the Government of India as a funding instrument was abolished with the introduction of the Ways And Means agreement
Bond Mathematics 18 Participants and products in debt markets: Table 2.2 Issuer Instrument Maturity Investors Central government Dated securities 2-30 years RBI, Banks, Insurance companies, Provident Funds, Mutual Funds, Individuals, PDs Central government T-Bills 91/182/364 days RBI, Banks, Insurance companies, Provident Funds, Mutual Funds, Individuals, PDs State government Dated securities 5-13 years RBI, Banks, Insurance companies, Provident Funds, Mutual Funds, Individuals, PDs PSUs Bonds, Structured Obligations 5-10 years Banks, Insurance companies, Provident Funds, Mutual Funds, Individuals, Corporate Corporate Debentures 1-12 years Banks, Corporate, Mutual Funds Corporate, PDs Commercial paper 7 days to 1 year Banks, Corporate Financial institutions, Mutual funds, Individuals, FIIs Scheduled commercial banks Certificates of deposit (CDs) 7 days to 1 year Banks, Corporations, Individuals, companies, Trusts, Funds, Associations, FIs, NRIs Financial Institutions 1 year to 3 years Scheduled commercial banks Bank Bonds 1-10 years Corporations, Individual companies, Trusts, Funds, Associations, FIs, NRIs Municipal Corporation Municipal Bonds 0-7 years Banks, Corporations, Individuals, Companies, Trusts, Funds, Associations, FIs, NRIs Securities market and financial system The securities market has two interdependent and inseparable segments, the new issues (primary market) and the stock (secondary) market. Primary market The primary market provides the channel for sale of new securities from the actual issuers to the primary investors based on their perception of the bond instrument. Primary market provides opportunity to issuers of securities; government as well as corporates, to raise resources to meet their requirements of investment and/or discharge some obligation.
Bond Mathematics 19 They may issue the securities at face value, or at a discount/premium and these securities may take a variety of forms such as equity, debt etc. They may issue the securities in domestic market and/or international market. The primary market issuance is done either through public issues or private placement. A public issue does not limit any entity in investing while in private placement, the issuance is done to select people. In terms of the Companies Act, 1956, an issue becomes public if it results in allotment to more than 50 persons. This means an issue resulting in allotment to less than 50 persons is private placement. There are two major types of issuers who issue securities. The corporate entities issue mainly debt and equity instruments (shares, debentures, etc.), while the governments (central and state governments) issue debt securities (dated securities, treasury bills). The price signals, which subsume all information about the issuer and his business including associated risk, generated in the secondary market, help the primary market in allocation of funds. Secondary market Secondary market refers to a market where securities are traded after being initially offered to the public in the primary market and/or listed on the Stock. The secondary market enables participants who hold securities to adjust their holdings in response to changes in their assessment of risk and return. They also sell securities for cash to meet their liquidity needs. The secondary market has further two components, namely the over-the-counter (OTC) market and the exchange-traded market. OTC is different from the market place provided by the Over The Counter Exchange of India Limited. OTC markets are essentially informal markets where trades are negotiated. Most of the trades in government securities are in the OTC market. All the spot trades where securities are traded for immediate delivery and payment take place in the OTC market. The exchanges do not provide facility for spot trades in a strict sense. Closest to spot market is the cash market where settlement takes place after some time. Trades taking place over a trading cycle, i.e. a day under rolling settlement, are settled together after a certain time (currently 2 working days). Trades executed on the leading exchange (National Stock Exchange of India Limited (NSE) are cleared and settled by a clearing corporation which provides novation and settlement guarantee. Nearly 100% of the trades settled by delivery are settled in demat form. NSE also provides a formal trading platform for trading of a wide range of debt securities including government securities. A variant of secondary market is the forward market, where securities are traded for future delivery and payment. Pure forward is outside the formal market. The versions of forward in formal market are futures and options. In futures market, standardised securities are traded for future delivery and settlement. These futures can be on a basket of securities like an index or an individual security. In case of options, securities are traded for conditional future delivery. There are two types of options–a put option permits the owner to sell a security to the writer of options at a predetermined price while a call option permits the owner to purchase a security from the writer of the option at a predetermined price. These options can also be on individual stocks or basket of stocks like index. Two exchanges, namely NSE and the Bombay Stock Exchange, (BSE) provide trading of derivatives of securities. The past few years in many ways have been remarkable for securities market in India. It has grown exponentially as measured in terms of amount raised from the market, number of stock exchanges and other intermediaries, the number of listed stocks, market capitalisation, trading volumes and turnover on stock exchanges, and investor population. Along with this growth, the profiles of the investors, issuers and intermediaries
Bond Mathematics 20 have change significantly. The market has witnessed fundamental institutional changes resulting in drastic reduction in transaction costs and significant improvements in efficiency, transparency and safety. Reforms in the securities market, particularly the establishment and empowerment of SEBI, market determined allocation of resources, screen based nation-wide trading, dematerialisation and electronic transfer of securities, rolling settlement and ban on deferral products, sophisticated risk management and derivatives trading, have greatly improved the regulatory framework and efficiency of trading and settlement. Indian market is now comparable to many developed markets in terms of a number of qualitative parameters. Securities market & economic development Three main sets of entities depend on securities market. While the corporate and governments raise resources from the securities market to meet their obligations, the households invest their savings in the securities. Corporate Sector: The 1990s witnessed emergence of the securities market as a major source of finance for trade and industry. A growing number of companies are accessing the securities market rather than depending on loans from FIs/banks. The corporate sector is increasingly depending on external sources for meeting its funding requirements. There appears to be growing preference for direct financing (equity and debt) to indirect financing (bank loan) within the external sources. The listing agreements have been amended recently requiring the companies to disclose shareholding pattern on a quarterly basis. As per the shareholding pattern of companies listed on NSE at end of March 2008, it is observed that on an average the promoters hold about 56.12% of total shares. Though the non-promoter holding is about 41.91%, Individuals held only 13.07% and the institutional holding (FIIs, MFs, VCFs-Indian and Foreign) accounted for 19.37%. Governments: Along with increase in fiscal deficits of the governments, the dependence on market borrowings to finance fiscal deficits has increased over the years. During the year 1990-91, the state governments and the central government financed nearly 14% and 18% respectively of their fiscal deficit by market borrowing. In percentage terms, depend ence of the state governments on market borrowing did not increase much during the decade 1991-2001. However, their dependence on market borrowing has been increasing since then to reach 38% during 2003-04. In case of central government, it increased to 73% by 2007-08, The central government and the state governments now-a-days finance about three fourth and one fourth of their fiscal deficits respectively through borrowings from the securities market. Households: According to RBI data, household sector accounted for 84.8% of gross domestic savings in Fixed Income Investment instruments during 2006-07. They invested 55.7% of financial savings in deposits, 24.2 % in insurance/provident funds, and 6.5% in securities market including government securities, units of mutual funds and other securities (out of which investment in Gilts has been 0.2%). Thus, the fixed income bearing instruments are the most preferred assets of the household sector.
Bond Mathematics 21 Trading platforms for bonds NSE National Stock Exchange of India Limited (NSE) was given recognition as a stock exchange in April 1993. Objectives:  establishing a nationwide trading facility for all types of securities,  ensuring equal access to all investors all over the country through an appropriate communication network,  providing a fair, efficient and transparent securities market using electronic trading system,  enabling shorter settlement cycles and book entry settlements, and  Meeting the international benchmarks and standards. Within a short span of life, above objectives have been realized and the Exchange has played a leading role as a change agent in transforming the Indian Capital Markets to its present form. NSE has set up infrastructure that serves as a role model for the securities industry in terms of trading systems, clearing and settlement practices and procedures. The standards set by NSE in terms of market practices, products, technology and service standards have become industry benchmarks and are being replicated by other market participants. It provides screen-based automated trading system with a high degree of transparency and equal access to investors irrespective of l;geographical location. The high level of information dissemination through on-line system has helped in integrating retail investors on a nation- wide basis. The Exchange currently operates three market segments, namely Capital Market Segment, Wholesale Debt Market Segment and Futures and Options segment. NSE has been playing the role of a catalytic agent in reforming the market in terms of microstructure and market practices. Right from its inception, the exchange has adopted the purest form of demutualised set up whereby the ownership, management and trading rights are in the hands of three different sets of people. This has completely eliminated any conflict of interest and helped NSE to aggressively pursue policies and practices within a public interest framework. It has helped in shifting the trading platform from the trading hall in the premises of the exchange to the computer terminals at the premises of the trading members located country- wide and subsequently to the personal computers in the homes of investors and even to hand held portable devices for the mobile investors. Settlement risks have been eliminated with NSE‘s innovative endeavors in the area of clearing and settlement viz., reduction of settlement cycle, professionalisation of the trading members, fine-tuned risk management system, dematerialisation and electronic transfer of securities and establishment of clearing corporation. As a consequence, the market today uses the state-of-art information technology to provide an efficient and transparent trading, clearing and settlement mechanism. NSE provides a trading platform for of all types of securities-equity and debt, corporate and government and derivatives. On its recognition as a stock exchange under the Securities Contracts (Regulation) Act, 1956 in April 1993, it commenced operations in the Wholesale Debt Market (WDM) segment in June 1994, in the Capital Market (CM) segment
Bond Mathematics 22 in November 1994, and in Futures & Options (F&O) segment in June 2000. The Exchange started providing trading in retail debt of Government Securities in January 2003. NDS The first step towards electronic bond trading in India was the introduction of the RBIs Negotiated Dealing System in February 2002. NDS, facilitates screen based negotiated dealing for secondary market transactions in government securities and money market instruments, online reporting of transactions in the instruments available on the NDS and dissemination of trade information to the market. Government Securities (including T-bills), call money, notice/term money, repos in eligible securities are available for negotiated dealing through NDS among the members. NDS members concluding deals, in the telephone market in instruments available on NDS, are required to report the deal on NDS system within 15 minutes of concluding the deal. NDS interfaces with CCIL for settlement of government securities transactions for both outright and repo trades done/reported by NDS members. Other instruments viz, call money, notice/term money, commercial paper and certificate of deposits settle as per existing settlement procedure. Table 2.3
Bond Mathematics 23 With the objective of creating a broad-based and transparent market in government securities and thereby enhancing liquidity in the system, the NDS was designed to provide:  Electronic bidding in primary market auctions (T-Bills, dated securities, state government securities) by members,  Electronic bidding for OMO of RBI including repo auctions under LAF,  Screen based negotiated dealing system for secondary market operations,  Reporting of deals in government securities done among NDS members outside the system (over telephone or using brokers of exchanges) for settlement,  Dissemination of trade information to NDS members,  Countrywide access of NDS through INFINET,  Electronic connectivity for settlement of trades in secondary market both for outright and repos either through CCIL or directly through RBI, and Creation and maintenance of basic data of instruments and members. The functional scope of the NDS relating to trading includes:  giving/receiving a Quote,  placing a call and negotiation (with or without a reference to the quote),  entering the deals successfully negotiated, setting up preferred counterparty list and exposure limits to the counterparties,  dissemination of on-line market information such as the last traded prices of securities, volume of transactions, yield curve and information on live quotes,  interface with Securities Settlement System for facilitating settlement of deals done in government securities and treasury bills  Facility for reporting on trades executed through the exchanges for information dissemination and settlement in addition to deals done through NDS. Figure 2.1 0 20 40 60 80 100 Aug/06 Nov/06 Feb/07 May/07 Aug/07 Nov/07 Feb/08 May/08 Aug/08 Nov/08 Feb/09 share of NDS call in total call volumes (%) share of NDS call in total call volumes (%)
Bond Mathematics 24 Repo and reverse repo Repo or Repurchase Agreements are short-term money market instruments. Repo is nothing but collateralized borrowing and lending through sale/purchase operations in debt instruments. Under a repo transaction, a holder of securities sells them to an investor with an agreement to repurchase at a predetermined date and rate. In a typical repo transaction, the counterparties agree to exchange securities and cash, with a simultaneous agreement to reverse the transactions after a given period. To the lender of cash, the securities lent by the borrower serves as the collateral; to the lender of securities, the cash borrowed by the lender serves as the collateral. Repo thus represents a collateralized short term lending. A reverse repo is the mirror image of a repo. Banks and dealers use repos to finance inventories, to cover short positions, to create leverage and to hedge or to speculate on interest rate movements. Investors such as mutual funds, pension funds, insurance companies and corporate treasurers use repo markets to invest surplus cash, to earn incremental returns on their portfolios or to raise cash for investments. There are three types of repo, each with different costs and benefits that are reflected in the repo rate and the haircut: Figure 2.2 •the collateral is held on the balance sheet of the cash provider, granting immediate access in the event of default on the loan. Bilateral repo: •an agent stands between the security lender and cash provider and physically controls the securities offered as collateral. Triparty repo: •the security lender continues to hold the bond on their own balance sheet in a segregated account, raising the risk to the cash provider. Hold-in-custody repo: share in money market trading volumes, 2009 repo volume call volume CBLO volume Call: Market in which brokers and dealers borrow money to satisfy their credit needs, either to finance their own inventory of securities or to cover their customers' margin accounts. CBLO: A money market instrument that represents an obligation between a borrower and a lender as to the terms and conditions of the loan. Collateralized borrowing and lending obligations (CBLOs) are used by those who have been phased out of or heavily restricted in the interbank call money market. Repo: For the party selling the security (and agreeing to repurchase it in the future) it is a repo; for the party on the other end of the transaction, (buying the security and agreeing to sell in the future) it is a reverse repurchase agreement.
Bond Mathematics 25 Wholesale Debt Market NSE accounts for nearly 70 % of the market share in capital market and 98 % market share in the derivatives market. The Wholesale Debt Market segment provides the trading platform for trading of a wide range of debt securities. Its product, which is now disseminated jointly with FIMMDA, the FIMMDA NSE MIBID/MIBOR is used as a benchmark rate for majority of deals struck for Interest Rate Swaps, Forwards Rate Agreements, Floating Rate Debentures and Term Deposits in the country. Its ‗Zero Coupon Yield Curve‘ as well as NSE-VaR for Fixed Income Securities have also become very popular for valuation of sovereign securities across all maturities irrespective of its liquidity and facilitated the pricing of corporate papers and GOI Bond Index. Figure 2.3 NSEs Capital Market segment offers a fully automated screen based trading system, known as the National Exchange for Automated Trading (NEAT) system, which operates on a strict price/time priority. It enables members from across the country to trade simultaneously with enormous ease and efficiency. Its Futures & Options segment provides trading of a wide range of derivatives like Index Futures, Index Options, Stock Options and Stock Futures. The Wholesale Debt Market segment deals in fixed income securities and is fast gaining ground in an environment that has largely focussed on equities. The Wholesale Debt Market (WDM) segment of the Exchange commenced operations on June 30, 1994. This provided the first formal screen-based trading facility for the debt market in the country. This segment provides trading facilities for a variety of debt instruments including Government Securities, Treasury Bills and Bonds issued by Public Sector Undertakings/ Corporates/ Banks like Floating Rate Bonds, Zero Coupon Bonds, Commercial Papers, Certificate of Deposits, Corporate Debentures, State Government loans, SLR and Non-SLR Bonds issued by Financial Institutions, Units of Mutual Funds and Securitized debt by banks, financial institutions, corporate bodies, trusts and others. Large investors and a high average trade value characterize this segment. Till recently, the market was purely an informal market with most of the trades directly negotiated and struck between various participants. The commencement of this segment by NSE has brought about transparency and efficiency to the debt market, along with effective monitoring and surveillance to the market.
Bond Mathematics 26 Retail Debt Market Netting factor (%) Figure 2.4 With a view to encouraging wider participation of all classes of investors across the country (including retail investors) in government securities, the Government, RBI and SEBI have introduced trading in government securities for retail investors. Trading in this retail debt market segment (RDM) on NSE has been introduced w.e.f. January 16, 2003. Main participants in the retail debt market include mutual funds, provident funds, pension funds, private trusts, state-level and district-level co-operative banks, housing finance companies, NBFCs and RNBCs, corporate treasuries, Hindu Undivided Families (HUFs), and individual investors. The reasons why the retail debt market boomed were: 1995-96 saw the worst ever liquidity crunch. The stock market plunged to its nadir, financial institutions were unable to disburse sanctioned amounts, and the GDR route failed to bring in enough funds. To raise money, industry needed a new instrument. It found one in retail debt. The old retail finance culture tilted towards equity is poised to give way to a more equitable debt-equity ratio dictated by financial prudence and market forces. Conclusion: The securities markets in India have witnessed several policy initiatives, which have refined the market micro-structure, modernised operations and broadened investment choices for the investors. The irregularities in the securities transactions in the last quarter of 2000-01, hastened the introduction and implementation of several reforms. While a Joint Parliamentary Committee was constituted to go into the irregularities and manipulations in all their ramifications in all transactions relating to securities, decisions were taken to complete the process of demutualisation and corporatisation of stock exchanges to separate ownership, funds (%) 0 20 40 60 80 100 funds (%) securities (%)
Bond Mathematics 27 management and trading rights on stock exchanges and to effect legislative changes for investor protection, and to enhance the effectiveness of SEBI as the capital market regulator. T+5 basis: introduced from July 2, 2001 T+3 basis: introduced from April 1, 2002 T+2 basis: introduced from April 1, 2003 All deferral products: banned from july2, 2002 1381 companies listed at NSE: March 2008 Derivative trading at NSE: June 12, 2000 Trading in index options: June 4, 2001 Trading in individual securities: July 2, 2001 Short term S&P CNX Nifty were introduced: January, 2008 long term S&P CNX Nifty were introduced: March 3, 2008 Due to rapid changes in volatility in the securities market from time to time, there was a need felt for a measure of market volatility in the form of an index that would help the market participants. NSE launched the India VIX, a volatility index based on the S&P CNX Nifty Index Option prices. Volatility Index is a measure of market‘s expectation of volatility over the near term. SEBI allowed the direct market access (DMA): April 3, 2008. Short sell and the facility for securities lending and borrowing scheme: April 21, 2008. The Debt markets in India have also witnessed a series of reforms, beginning in the year 2001-02 which was quite eventful for debt markets in India, with implementation of several important decisions like setting up of a clearing corporation for government securities, a negotiated dealing system to facilitate transparent electronic bidding in auctions and secondary market transactions on a real time basis and dematerialisation of debt instruments. Further, Adoption of modified Delivery-versus-Payment mode of settlement: March 2004 Securities was standardized to T+1 cycle: May 11, 2005 Order matching trading platform (NDS-OM) was introduced: August 2005 Short sale was permitted in G-secs: 2006 ‗When issued‘ (WI) trading in Central Government Securities was introduced: 2006 Ensures safe settlement with Straight through Processing (STP)
Bond Mathematics 28 Bond basic concepts Features:  Nominal, principal or face amount — the amount on which the issuer pays interest, and which, most commonly, has to be repaid at the end. Some structured bonds can have a redemption amount which is different to the face amount and can be linked to performance of particular assets such as a stock or commodity index, foreign exchange rate or a fund. This can result in an investor receiving less or more than his original investment at maturity.  Issue price — the price at which investors buy the bonds when they are first issued, which will typically be approximately equal to the nominal amount. The net proceeds that the issuer receives are thus the issue price, less issuance fees.  Maturity date — the date on which the issuer has to repay the nominal amount. As long as all payments have been made, the issuer has no more obligation to the bond holders after the maturity date. The length of time until the maturity date is often referred to as the term or tenor or maturity of a bond. The maturity can be any length of time, although debt securities with a term of less than one year are generally designated money market instruments rather than bonds. Most bonds have a term of up to thirty years. Some bonds have been issued with maturities of up to one hundred years, and some even do not mature at all. In early 2005, a market developed in euros for bonds with a maturity of fifty years. In the market for U.S. Treasury securities, there are three groups of bond maturities: o short term (bills): maturities up to one year; o medium term (notes): maturities between one and ten years; o long term (bonds): maturities greater than ten years.  Coupon — the interest rate that the issuer pays to the bond holders. Usually this rate is fixed throughout the life of the bond. It can also vary with a money market index, such as LIBOR, or it can be even more exotic. The name coupon originates from the fact that in the past, physical bonds were issued which had coupons attached to them. On coupon dates the bond holder would give the coupon to a bank in exchange for the interest payment. • Tax free bonds – public sector companies in India are sometimes permitted to issue bonds with tax- free interest. In this case bond- holder pays no tax on the interest • Trustee – when a debenture issue is made, a trustee is appointed (usually an FI / bank). The trustee is responsible to ensure that the company fulfils its contractual obligations • Trust (bond) indenture or Debenture trust deed – a complex and lengthy legal agreement between the company and the debenture trustee, stating the conditions under which a bond has been issued, rights of debenture holders, rights of the issuing company, and responsibilities of the trustee.
Bond Mathematics 29 • Debenture Redemption Reserve (DRR) – has to be created for the redemption of all debentures with a maturity period exceeding 18 months. The DRR must be equal to atleast 50% of the amount of redemption Table 3.1 Kinds of bonds: The following descriptions are not mutually exclusive, and more than one of them may apply to a particular bond.  Zero-coupon bonds pay no regular interest. They are issued at a substantial discount to par value, so that the interest is effectively rolled up to maturity (and usually taxed as such). The bondholder receives the full principal amount on the redemption date. An example of zero coupon bonds is Series E savings bonds issued by the U.S. government. Zero-coupon bonds may be created from fixed rate bonds by a financial institution separating "stripping off" the coupons from the principal. In other words, MODIFIABLE INTOPARAMETERSCLASSIFICATION BONDS coupon zero coupon treasury strips floating rate bonds other variations maturity callable bonds puttable bonds convertible bonds principal amortising sinking fund asset based securities
Bond Mathematics 30 the separated coupons and the final principal payment of the bond may be traded separately. See IO (Interest Only) and PO (Principal Only).  Strip bonds - Zero coupon bonds have a duration equal to the bond's time to maturity, which makes them sensitive to any changes in the interest rates. Investment banks or dealers may separate coupons from the principal of coupon bonds, which is known as the residue, so that different investors may receive the principal and each of the coupon payments. This creates a supply of new zero coupon bonds. The coupons and residue are sold separately to investors. Each of these investments then pays a single lump sum. This method of creating zero coupon bonds is known as stripping and the contracts are known as strip bonds. "STRIPS" stands for Separate Trading of Registered Interest and Principal Securities.  Fixed rate bonds have a coupon that remains constant throughout the life of the bond.  Floating rate notes (FRNs) have a variable coupon that is linked to a reference rate of interest, such as LIBOR or Euribor. For example the coupon may be defined as three month USD LIBOR + 0.20%. The coupon rate is recalculated periodically, typically every one or three months.  Inflation linked bonds in which the principal amount and the interest payments are indexed to inflation. The interest rate is normally lower than for fixed rate bonds with a comparable maturity. However, as the principal amount grows, the payments increase with inflation. The United Kingdom was the first sovereign issuer to issue inflation linked Gilts in the 1980s. Treasury Inflation-Protected Securities (TIPS) and I-bonds are examples of inflation linked bonds issued by the U.S. government.  Other indexed bonds, for example equity-linked notes and bonds indexed on a business indicator (income, added value) or on a country's GDP.  Callable bonds: A bond which the issuer has the right to redeem prior to its maturity date, under certain conditions. When issued, the bond will explain when it can be redeemed and what the price will be. In most cases, the price will be slightly above the par value for the bond and will increase the earlier the bond is called. A company will often call a bond if it is paying a higher coupon than the current market interest rates. Basically, the company can reissue the same bonds at a lower interest rate, saving them some amount on all the coupon payments; this process is called "refunding." Unfortunately, these are also the same circumstances in which the bonds have the highest price; interest rates have decreased since the bonds were issued, increasing the price. In many cases, the company will have the right to call the bonds at a lower price than the market price. If a bond is called, the bondholder will be notified by mail and have no choice in the matter. The bond will stop paying interest shortly after the bond is called, so there is no reason to hold on to it. Companies also typically advertise in major financial publications to notify bondholders. Generally, callable bonds will carry something called call protection. This means that there is some period of time during which the bond cannot be called. It is also called redeemable bond, opposite of irredeemable bond or non-callable bond.
Bond Mathematics 31  Puttable bond or put bond is a combination of straight bond and embedded put option. The holder of the puttable bond has the right, but not the obligation, to demand early repayment of the principal. The put option is usually exercisable on specified dates. This type of bond protects investors: if interest rates rise after bond purchase, the future value of coupon payments will become less valuable. Therefore, investors sell bonds back to the issuer and may lend proceeds elsewhere at a higher rate. Bondholders are ready to pay for such protection by accepting a lower yield relative to that of a straight bond. Of course, if an issuer has a severe liquidity crisis, it may be incapable of paying for the bonds when the investors wish. The investors also cannot sell back the bond at any time, rather specified dates. However, they would still be ahead of holders of non- puttable bonds, who may have no more right than 'timely payment of interest and principal' (which could perhaps be many years to get all their money back). The price behaviour of puttable bonds is the opposite of that of a callable bond. Since call option and put option are not mutually exclusive, a bond may have both options embedded.  A debenture in corporate finance is a medium- to long-term debt instrument used by large companies to borrow money. In some countries the term is used interchangeably with bond, loan stock or note. Debentures are generally freely transferable by the debenture holder. Debenture holders have no voting rights and the interest paid to them is a charge against profit in the company's financial statements. In the United States, debenture refers specifically to an unsecured corporate bond. However, in the United Kingdom a debenture is usually secured. In Asia, if repayment is secured by a charge over land, the loan document is called a mortgage; where repayment is secured by a charge against other assets of the company, the document is called a debenture; and where no security is involved, the document is called a note or 'unsecured deposit note'. Types: 1. Convertible debentures, which are convertible bonds or bonds that can be converted into equity shares of the issuing company after a predetermined period of time. "Convertibility" is a feature that corporations may add to the bonds they issue to make them more attractive to buyers. In other words, it is a special feature that a corporate bond may carry. As a result of the advantage a buyer gets from the ability to convert; convertible bonds typically have lower interest rates than non-convertible corporate bonds. 2. Non-convertible debentures, which are simply regular debentures, cannot be converted into equity shares of the liable company. They are debentures without the convertibility feature attached to them. As a result, they usually carry higher interest rates than their convertible counterparts. Call and Put Provision – provides an option to the issuing company to redeem the debentures at a specified price before maturity. Call price may be more than the par / face value, and this difference is called the Call Premium (In India, generally 5%). Put
Bond Mathematics 32 option is an option to the debenture holder to seek redemption at a specified time at a specified price  Sinking fund provision is just a pool of money set aside by a corporation to help repay a bond issue. Typically, bond agreements (called indentures) require a company to make periodic interest payments to bondholders throughout the life of the bond, and then repay the principal amount of the bond at the end of the bond's lifespan.  Amortising: Charges made against the interest received on a debt in order to offset a premium paid for the debt. Thus, with each periodic payment, a debtor is not only paying back interest, but also part of his or her premium. This leads to higher periodic payments than in the case when only interest is paid out. However, a payment schedule which includes premium amortization makes debt management easier, especially if the principal is large. While paying just the interest each period will lead to a low outflow of cash each month, the debtor might not save enough to pay the principal. Thus, amortizing the premium each period also reduces the credit risk of the debt, since the creditor gets some part of the principal each time period, as opposed to allowing a debtor to forfeit on all of it at the maturity of the loan. Amortization of premium is a common feature in cases when a person or company takes on a large amount of debt at one time, such as a mortgage.  Asset-backed securities are bonds whose interest and principal payments are backed by underlying cash flows from other assets. Examples of asset-backed securities are mortgage-backed securities (MBS's), collateralized mortgage obligations (CMOs) and collateralized debt obligations (CDOs).  Subordinated bonds are those that have a lower priority than other bonds of the issuer in case of liquidation. In case of bankruptcy, there is a hierarchy of creditors. First the liquidator is paid, then government taxes, etc. The first bond holders in line to be paid are those holding what is called senior bonds. After they have been paid, the subordinated bond holders are paid. As a result, the risk is higher. Therefore, subordinated bonds usually have a lower credit rating than senior bonds. The main examples of subordinated bonds can be found in bonds issued by banks, and asset- backed securities. The latter are often issued in tranches. The senior tranches get paid back first, the subordinated tranches later.  Perpetual bonds are also often called perpetuities or 'Perps'. They have no maturity date. The most famous of these are the UK Consols, which are also known as Treasury Annuities or Undated Treasuries. Some of these were issued back in 1888 and still trade today, although the amounts are now insignificant. Some ultra-long- term bonds (sometimes a bond can last centuries: West Shore Railroad issued a bond which matures in 2361 (i.e. 24th century)) are virtually perpetuities from a financial point of view, with the current value of principal near zero.  Successive bonds are those where sureties are discharged and new sureties are taken, the two sets of sureties become jointly liable for a breach of the bond which accrued before discharge, and the right of contribution exists as between co-sureties. The new bond relates back, and the two sets of sureties are jointly liable for a breach committed prior to the second execution.
Bond Mathematics 33 Pricing factors Interest rates change over time, based on a variety of factors, particularly base rates set by central bank. If the coupon on the bond is lower than the prevailing interest rate, then this pushes the price down, and conversely, high interest rates reduce the attractiveness of a given coupon, and so reduce the price. In buying a bond, one is in effect buying a set of cash flows, which are discounted according to the buyers perception of how interest and exchange rates will move over its life. Price determination in the debt markets The price of a bond in the markets is determined by the forces of demand and supply, as is the case in any market. The price of a bond also depends on the changes in:  Economic conditions  General money market conditions, including the state of money supply in the economy  Interest rates prevalent in the market and the rates of new issues  Future Interest Rate Expectations  Credit quality of the issuer Note: There is, however, a theoretical underpinning to the determination of the price of the bond based on the measure of the yield of the security. Supply and demand affect prices, especially in the case of market participants which are constrained in the set of investments they make. Insurance companies often have long term liabilities that they wish to hedge, which requires low risk, predictable cash flows, such as long dated government bonds. Bond pricing The cash flow of a fixed income product generally consists of several coupon payments over the period of the bond's life, and repayment of the principal at the time of maturity. Since these cash flows occur at several times in the future, the "Time Value of Money" approach is used to find the "Present Value" of each cash flow. The sum of all the present values of the bonds cash inflows of the bond is its theoretical value. Price–Discounted present value of debt service on an individual maturity. Debt service is calculated using the coupon and discounted at the yield. As a result, price and yield move in opposite directions.
Bond Mathematics 34 • Yield – two types: – Current yield: ratio of the annual interest payment to the CMP eg. If the market price of a 12% Rs 1000 FV debenture is Rs 750, then current yield is 120/750 ie. 16% – Yield to Maturity: takes into account the payments of interest and principal over the life of the debenture. So it is the internal rate of return of the debenture Par bonds:  Coupon equals yield  Purchase price equals principal amount Discount bonds:  Coupon less than yield  Purchase price less than principal amount Premium bonds:  Coupon greater than yield  Purchase price greater than principal amount
Bond Mathematics 35 Pricing a bond The price of a bond is the present value of its expected cash flow(s). The present value will be lower than the future value, as holding Rs100 next week is worth less than holding Rs100 now. There are a number of possible reasons for this: If inflation is high, the value will have eroded by the following week; if it remains in another person‘s possession for a further week, there is a potential credit risk; and there is no opportunity to invest the money until the following week, and therefore any potential return is delayed. The arithmetic assumes no credit risk or other (e.g. liquidity, tax) effects. It calculates the price of a risk-free bond, and therefore would need to be adjusted for other factors. Single Cash Flow Calculating the future value of an investment: - Starting from the simplest example, investing Rs100 for one period at 8% would give the following return: Return = 100 (1 + 8/100) = Rs108 In other words:- FV = PV (1 + r) where FV is the future value (i.e. cash flow expected in the future) PV is the present value r is the rate of return Assuming the same rate of return, if the investment is made for two periods, then:- FV = 100 (1 + 8/100)(1 + 8/100) In other words:- FV = PV (1 + r)2 And in general: FV = PV (1 + r)n where n is the number of periods invested, at a rate of return, r.If we want to calculate the price (i.e present value) of a bond as a function of its future value, we can rearrange this equation:- P = F/ (1+ r)n where P is the price of the bond and is the same as the ‗present value‘. The future value is the expected cash flow i.e. the payment at redemption n periods ahead. Discount Rate r is also referred to as the discount rate, i.e the rate of discount applied to the future payment in order to ascertain the current price. 1/ (1+ r)n is the value of the discount function at period n. Multiplying the discount function at period n by the cash flow expected at period n gives the value of the cash flow today. Relationship between discount rate and coupon rate: Discount rate less than the coupon rate implies that the security is traded at a premium. Discount rate greater than the coupon
Bond Mathematics 36 rate implies that the security is traded at a discount. Discount rate equal to the coupon rate implies that the security is traded at a par. Multiple Cash Flow In practice, most bonds have more than one cash flow and therefore each cash flow needs to be discounted in order to find the present value (current price). This can be seen with another simple example - a conventional bond, paying an annual coupon and the face value at maturity. The price at issue is given as follows: Where P = ‗dirty price‘ c = annual coupon r i = % rate of return which is used in the ith period to discount the cash flow (in this example, each period is one year) R = redemption payment at time n The above example shows that a different discount rate is used for each period (r r etc 1, 2, ). Whilst this seems sensible, the more common practice in bond markets is to discount using a redemption yield and discount all cash flows using this rate. In theory, each investor will have a slightly different view of the rate of return required, as the opportunity cost of not holding money now will be different, as will their views on, for example, future inflation, appetite for risk, nature of liabilities, investment time horizon etc. The required yield should, therefore, reflect these considerations. In practice, investors will determine what they consider to be a fair yield for their own circumstances. They can then compute the corresponding price and compare this to the market price before deciding whether – and how much – to buy or sell. Pricing a bond with a semi annual coupon follows the same principles as that of an annual coupon. A ten year bond with semi annual coupons will have 20 periods (each of six months maturity); and the price equation will be: where c = coupon y = Redemption Yield (in % on an annualised basis) In general, the bond maths notation for expressing the price of a bond is given by:- Where PV ( cf t) is the present value of the cash flow at time t
Bond Mathematics 37 Dirty prices and clean prices When a bond is bought or sold midway through a coupon period, a certain amount of coupon interest will have accrued. The coupon payment is always received by the person holding the bond at the time of the coupon payment (as the bond will then be registered in his name). Because he may not have held the bond throughout the coupon period, he will need to pay the previous holder some ‗compensation‘ for the amount of interest which accrued during his ownership. In order to calculate the accrued interest, we need to know the number of days in the accrued interest period, the number of days in the coupon period, and the money amount of the coupon payment. In most bond markets, accrued interest is calculated on the following basis:- Coupon interest x no. of days that have passed in coupon period total no of days in the coupon period Prices in the market are usually quoted on a clean basis (i.e. without accrued) but settled on a dirty basis (i.e. with accrued). Relationship between price and yield There is a direct relationship between the price of a bond and its yield. The price is the amount the investor will pay for the future cash flows; the yield is a measure of return o n those future cash flows. Hence price will change in the opposite direction to the change in the required yield. There are a number of different formulae for the relationship between price and yield. Looking at the price-yield relationship of a standard i.e. non-callable bond, the shape such as below is seen: Figure 3.1 As the required yield increases, the factor by which future cash flows are discounted also increases and therefore the present value of the cash flow decreases. Hence the price decreases as yield increases.
Bond Mathematics 38 Money market yields Money market yields are quoted on a different basis and therefore in order to compare short- term bonds and money market instruments it is necessary to look at them on a comparable basis. Uses of Yield Curves and Yield Curve Theories A yield curve is a graphical representation of the term structure of yields for a given market. It attempts to show, for a set of bonds that have differing maturities but otherwise similar characteristics, how the yield on a bond varies with its maturity. Yield curves are therefore constructed from (as far as possible) a homogeneous group of bonds: we would not construct a yield curve using both government and corporate securities, given the different categories of risk. Yield curves are used for a number of different purposes. For example, government securities‘ yield curves demonstrate the tightness (and expected tightness) of monetary policy; allow cross-country comparisons; assist pricing of new issues; assess relative value between bonds; allow one to derive implied forward rates; and help traders/investors understand risk. As there are a number of different types of yield curve that can be constructed, different ones are used for different purposes. There are various theories of the yield curve, which attempt to explain the shape of the curve, depending on, inter alia, investors‘ preferences/views: Preferred Habitat (again investors have a maturity preference, but will shift from their preferred maturity if the increase in yield is deemed sufficient compensation to do so). These are all demand-based; supply-based factors include government policy (fiscal position, views on risk, views on optimal portfolio etc). • risk premia increase with time so, other things being equal, one would expect to see a rising yield curve Liquidity Preference Theory • forward rates govern the curve - these are simply expectations of future spot rates and do not take into account risk premia Pure Expectations Hypothesis • the yield curve depends on supply and demand in different sectors and each sector of the yield curve is only loosely connected to others Segmented Markets Hypothesis
Bond Mathematics 39 Flat Yield This is the simplest measure of yield (also known as current yield, interest yield, income yield or running yield). It is given by:- Flat yield = Coupon rate (%) x 100 Clean price This is a very crude measure. It does not take into account accrued interest; nor does it take into account capital gain/loss (i.e. it assumes prices will not change over the holding period); nor does it recognise the time value of money. It can only sensibly be used as a measure of value when the term to maturity is very long (as coupon income will be more dominant in the total return than capital gain/loss). Simple Yield This is a slightly more sophisticated measure of return than flat yield, which takes into account capital gain, although it assumes that it accrues in a linear fashion over the life of the bond. However, it does not allow for compounding of interest; nor does it take into account accrued interest as it uses the clean price in the calculation. Simple Yield = [Coupon Rate + (100 - clean price) x 100] x clean price Years to maturity Obviously a bond in its final coupon period is, in terms of its cash flows, directly comparable with a money market instrument. In this case simple interest yield calculations are used (ie no need to discount at a compounded rate). Redemption Yield (Yield to Maturity) A redemption yield is that rate of interest at which the total discounted values of future payments of income and capital equate to its price in the market. Where P = dirty price (ie including accrued interest) c = coupon R = redemption payment n = no of periods y = redemption yield It is also referred to as the Internal Rate of Return or the Yield to Maturity. When quoting a yield for a bond, it is the redemption yield that is normally used, as all the factors contributing to the return can be captured in a single number. The redemption yield takes into account the time value of money by using the discount function: each cash flow is discounted to give its net present value. Obviously a near coupon is worth more than a far coupon because it can be reinvested but also, in nearly all cases (except for negative interest rates), the real coupon amount will be greater the sooner it is received.
Bond Mathematics 40 However, this measure gives only the potential return. The limitations of using the redemption yield to discount future cash flows are:  The redemption yield assumes that a bond is held to maturity. (i.e. the redemption yield is only achieved if a bond is held to maturity);  It discounts each cash flow at the same rate;  It assumes a bondholder can reinvest all coupons received at the same rate i.e. the redemption yield rate (i.e. assumes a flat yield curve), whereas in reality coupons will be reinvested at the market rate prevailing at the time they are received;  The discount rate used for a cash flow in, say, three years‘ time from a 5 year bond will be different from the rate used to discount the three year payment on a 10 year bond. The redemption yield curve suffers from these limitations. The curve is used for simple analysis, and can also be used when there are insufficient bonds available to construct a more sophisticated yield curve. Net redemption yields The above equation has looked at gross returns, but bond investors are likely to be subject to tax: possibly both on income and capital gain. The net redemption yield, if taxed on both coupon and redemption payments, is given by:- P = Dirty price c = Coupon R = Redemption payment r net = net redemption yield This is a simple example. In practice, if withholding tax is imposed the equation is not so simple as a percentage of tax will be imposed at source with the remainder being accounted for after the payment has been received. As tax rules can materially affect the price of bonds, their effects need to be taken into account in any yield curve modelling process in order to avoid distortions in the estimated yield curve. Spot rate: Each spot rate is the specific zero coupon yield related to that maturity and therefore gives a more accurate rate of discount at that maturity than the redemption yield. It also means that assumptions on reinvestment rates are not necessary. Spot rates take into account current spot rates, expectations of future spot rates, expected inflation, liquidity premia and risk premia.
Bond Mathematics 41 Various curves Zero coupon curve Forward zero coupon yield Par yield P = Price (dirty) c = Coupons n = Number of periods f i = ith period forward rate for one further period (i.e. the one-year rate in i years‘ time) y is the par yield z i is the rate of return at maturity i (i.e. the spot rates at maturity i) R is the redemption payment zero coupon curve •The curve resulting from the zero coupon (spot) rates is often referred to as the ‘Term Structure of Interest Rates’; the plot of spot rates of varying maturities against those maturities. This curve gives an unambiguous relationship between yield and maturity. •advantages: 1.finding relatively misvalued bonds, valuing swap portfolios and valuing new bonds at auction. 2. it discounts all payments at the appropriate rate, provides accurate present values and does not need to make reinvestment rate assumptions. forward zero coupon yield •the forward rate is such that an investor will be indifferent to investing for two years or investing for one year and then rolling over the proceeds for a further year. •(1+r1)(1+f1,2)=(1+r2)2 •advantages: 1. the implied forward rate equals the spot rate that prevails in the future. 2. the liquidity premium hypothesis suggests that the implied forward rate equals the expected future spot rate plus a risk premium. •real implied forward rates: (1+ nominal forward) = (1+ real forward)[(1+ inflation forward)] •Nominal forward = real forward + inflation forward par yield •The par yield is a hypothetical yield. It is the coupon that a bond would have in order to be priced at par, using the zero coupon rates in the discount function. This can be seen from the following equation.
Bond Mathematics 42 Relationship between curves The par, zero and forward curves are related. Figure 3.2 In an environment of upward sloping yield curves, the zero curve will sit above the par curve because the yield on a coupon bearing bond is affected by the fact that some income is received before the maturity date, and the rate used to discount these payments will be lower than the rate used to discount the payment at maturity. Also, as the forward curve gives marginal rates derived from the zero curve, it will be above the zero curve. The opposite is true in a downward sloping yield curve environment.
Bond Mathematics 43 Debt management products (calculations) Treasury bill Treasury bills are short term discount instruments (usually of less than one year maturity) and therefore are useful funding instruments in the early stages of a debt market when investors do not want to lock in to long maturities. They are issued at a discount to their face value and have one payment on redemption. The advantages of Treasury bills are that they are simple, tradeable in the secondary market and are government credit risk. However, because of their short maturities they need to be rolled over frequently, meaning that the future cost of debt servicing is uncertain. Also, shorter maturities result in a very short government yield curve: a longer yield curve is obviously beneficial to developing financial markets as it provides information and allows pricing of new products. There are a number of issues to take into account before issuing Treasury bills. For example, how will they be issued and to whom? If the government wishes to reach a wide range of investors, including the retail sector, then this could mean that the government is a competitor to the banking system, which could actually stifle market development (although this will, of course, provide the private sector with a benchmark). Also, if issuing to the retail investor, an auction process may prove difficult to understand and to price correctly. The government may need to think of other distribution channels (e.g. banks themselves, although they may charge a fee for this, making issuance expensive). A further consideration is minimum denomination (smaller if the retail investor is to be attracted) and whether to set a minimum price. In more developed countries, Treasury bills are also used for monetary management purposes. The increase (decrease) of Treasury bill issuance will affect the liquidity position of banks by withdrawing (increasing) liquidity from the market. Calculation of Treasury bill yield/price The discount rate is described as the return on a discount instrument compared with its redemption value (also referred to as par or face value) in the future. It is given by the following formula: Treasury bills Conventi onal bonds Converti ble bonds Floating rate bonds Zero coupon bonds & strips
Bond Mathematics 44 For the yield and price on a treasury bill, the following formulae are used: Or, simply, face value minus discount. It is important to note that the discount rate (often referred to as the rate of interest) and the yield on a Treasury bill are not the same. The discount rate is a market convention. Using the discount rate gave an easy calculation from rate to price and a fairly close approximation to true yield. Conventional bonds A 'conventional' bond is one that has a series of fixed coupons and a redemption payment at maturity. Coupons are usually paid annually or semi-annually. A conventional bond, e.g. ‗6% 2005‘, is a bond that has a 6% coupon and a repayment date in 2005. The prospectus will detail the terms and conditions applied to the bond, including the dates of the coupon payments and the final maturity of the bond. For example, if the above bond has semi-annual coupon payments, then for each Rs100 of the bond purchased, the holder will receive Rs3 coupon payment every six months up to the maturity of the bond. This is a ‗standard‘ bond issued by governments, although it does not necessarily suit all investors, not least because the receipt of regular coupon payments introduces reinvestment risk, as coupons need to be re-invested at rates of interest that are uncertain at the time of purchasing the bond. The conventional bond can be thought of as offering a nominal yield that takes into account the real yield and anticipated inflation. The real yield required can be thought of as the sum of two components: a real return and a risk premium reflecting the uncertainty of inflation12. This can be written as: where N is the nominal return R is the real yield Pe is the expected inflation rate over the period the bond is held RP is the risk premium The risk premium is the amount the market demands for unanticipated inflation. It is difficult to exactly price the risk premium, but if we know the market‘s view of inflation expectations then it is possible to have some idea of the size of the risk premium, by looking at the difference between nominal and real rates in the market. Obviously in countries with high inflation, the risk premium will be greater, given the uncertainty. But the very act of issuing index-linked debt (suggesting that the government is confident of reducing inflation) may help reduce the risk premium built into conventional debt. In countries where inflation has been low and stable, investors will feel more certain that the value of their investment will not be eroded and therefore will demand a lower risk premium.
Bond Mathematics 45 Floating Rate Bonds A floating rate bond (―floater‖) has a coupon linked to some short-term reference rate e.g. an interbank rate. It is usually issued at a margin (or spread) above this reference rate. This ensures that the investor gets a current rate of return, whilst (usually) locking in his investment for a longer period than this. The price of a floater depends on the spread above or below the reference rate and any restrictions that may be imposed on the resetting of the coupon (e.g. if it has caps or floors) plus the usual credit and liquidity considerations. The rate is usually a market rate. An obvious measure of value to the issuer is the return given above or below the market index or benchmark rate (i.e. LIBID, in the UK‘s case). These margin values (if below market norm) indicate the better credit quality of government issuance. Corporates also issue floaters and may pay a small margin over a reference rate, depending on their credit quality. Because the value of the coupon in the future is not known, it is not possible to determine the future cash flows. This means that a redemption yield measure cannot be calculated for a floating-rate bond. simple margin The simple margin uses a comparison with the 'index' and calculates it throughout the life of the bond. However, it does not take into account the current yield effect on the price of the floater, since coupon payments received are given the same weight if the price is above or below par. Also, the discount/premium of the bond is amortised to par in a straight line over the life of the floater rather than discounted at a constantly compounded rate. To overcome these drawbacks, one can use a discounted margin. discount margin This measure attempts to discount all cash flows and to therefore give some idea of the Net Present Value of each cash flow. However, it makes an assumption that LIBOR will remain the same throughout the life of the bond. A more sophisticated technique would be to construct a projected LIBOR curve, and therefore discount at a more accurate rate. However, as the maturity of the floater is usually short term (and that this method also necessitates some form of assumption) it is not usually employed.
Bond Mathematics 46 Convertible bonds Some governments have issued convertible bonds. These normally offer the investor the option of converting from one type of security to another, e.g. short to long-term or vice versa, fixed to floating or indexed. In issuing them the government hopes that the investor will pay a premium for the option, and that this premium will more than offset the cost to the government if the option is exercised. Equity-convertible bonds may be useful if the government is planning to privatise certain assets, such as state-owned enterprises, and wishes to obtain some of the value of the privatisation proceeds early. For instance, a security convertible into an equity could be sold for 100, redeemable in 2 years time or convertible at the investor‘s option into, say, 10 shares of a certain enterprise which is to be privatised. If the estimated market value of that enterprise rises during the period, the investor will exercise his option and convert; and if its value has risen much faster than expected, the opportunity cost to the government - through selling the option to buy at a fixed price - may outweigh the premium received for selling the option. If the enterprise‘s estimated value falls, the investor will buy the shares more cheaply in the market and not exercise the option. If it turns out, for whatever reason, that the enterprise is not privatised, some compensation may need to be paid to the investor. Zero coupon bonds and strips A zero coupon bond has only one (redemption) payment and is sold at a discount to its face value. In pricing the bond, it will be discounted at its spot rate i.e. the rate of discount specific to that maturity. The price of a zero coupon bond is therefore given by:- Where R is the redemption payment Zi is the spot rate relating to period i: (the maturity of the bond) The discount rate used (Zi ) can be thought as the redemption yield of a zero-coupon bond. The zero coupon bond has a number of advantages over its conventional counterpart. The zero coupon bond consists of a single point cash flow and therefore, by purchasing a selection of such bonds, the investor can build up the cash flows he wants, rather than receiving - and possibly needing to reinvest - frequent coupons. This allows far more efficient asset/liability management and eliminates reinvestment risk. Zero coupon bonds can therefore be used as building blocks from which to construct financial instruments such as annuities or deferred payment bonds. A zero coupon bond also has greater duration (for the same maturity) and greater convexity (for the same duration) than coupon bonds. This makes them potentially attractive to a large part of the market; for example, traders, who trade on risk and are looking for increased volatility; investors who want long duration assets; fund managers who are seeking to match the duration of their portfolios and have, for example, long duration pension liabilities.
Bond Mathematics 47 Strips A strip is a zero coupon bond, derived from separating a standard coupon-bearing bond into its constituent interest and principal payments that can then be separately held or traded as zero-coupon bonds22. For example, a 5-year bond with an annual coupon could be separated into six zero-coupon bonds, five representing the cash flows arising from coupons and one relating to the principal repayment. For Rs100 nominal worth of this bond with, say, a 6% coupon paying on 1 June each year the following cash flow would result from stripping:- Figure 3.3 Thus, stripping would leave five zero coupon bonds of Rs6.00 (nominal), maturing on 1 June each year and one zero coupon bond of Rs100 (nominal) maturing on 1 June in five years time. As most strip markets trade on yield rather than price, it follows that a standard yield formula should be used to calculate settlement value, to avoid any disputes. where: P = Price per Rs100 nominal of the strip y = Gross redemption yield (decimal) ie if the yield is 8% then y = 0.08 r = Exact number of days from the settlement/issue date to the next quasi coupon date (the quasi coupon date is a date on which a coupon would be due were the bond coupon bearing than the shortest strip) s = Exact number of days in the quasi-coupon period in which the settlement date falls n = Number of remaining quasi-coupon period after the current period So far we have seen the relationship between various factors for determination of the bond price. These factors plat eminent role in decision making process of bond management. The Objective of the project ―Effective bond management‖ requires us to have basic concept of the above discussed aspects to understand its impact on the bond prices thereby the effective bond management.
Bond Mathematics 48 Measures of risk and return Duration Duration is a measure of:  Duration is a measure of interest rate risk exposure of a financial asset and it measures the sensitivity of a security‘s price to interest rate.  It is the approximate percentage change in the value of a fixed income security that will result from a 1% change in interest rates.  There were various ways of measuring the ‗riskiness‘ of the bond, and perhaps the most common was the time to maturity. All other things being equal, the longer the bond the greater the volatility of its price (risk). However, this measure only takes into account the final payment (not any other cash flows), does not take into account the time value of money and therefore does not give an accurate comparison of relative ‗riskiness‘ across bonds.  Duration is a weighted average of the maturity of all the income streams from a bond or portfolio of bonds. It allows us to compare the riskiness of bonds with different maturities, coupons etc.  Investors use duration to measure the volatility of the bond. The higher the duration (the longer an investor needs to wait for the bulk of the payments), the more its price will drop as interest rates go up.  It can be said that duration is how long it would take for you to get your money back if a rise in interest rates causes your bond portfolio to drop in value.  A zero coupon bond duration equals maturity. When there are interim payments, duration will be less than maturity. For a deep discount bond, a point is reached at which duration actually decreases as maturity increases. a • the approximate sensitivity of a bond's value to interest rate changes b • a bond's lifetime that accounts for the entire pattern of cash flows over the life of the bond (i.e the weighted average time to recovery of all interest payemnts plus principal) c • the number of years needed to fully recover the purchase price of a bond given the present value of its cash flows d • the price volatility of a zero coupon bond with that number of years to maturity e • the number for each bond that summarizes 3 key factorsthat affect the sensitivity of a bond's price to a change in interest rates: maturity, coupon and YTM
Bond Mathematics 49 In mathematical terms, this is expressed as:- Macauley Duration = Where D= duration of the bond CF= interest or principal payment at time t t= time period in which principal or coupon interest is paid n= number of periods to maturity i= the yield to maturity (market rate interest rate) Modified duration For a 5-year bond with a 10% annual coupon, imagine that the shaded area represents the net present value of each cash flow; and that the shaded areas are weights along a seesaw. The Macauley duration is the point at which the seesaw balances. The relation between Macauley duration, price and yield is given by: (1) Where, ΔP / Δy = Proportional change in price with respect to change in yield P = price y/fc = yield/frequency of coupon payments per annum D = Macauley duration From Macauley duration, we can express Modified Duration, which is a measure of the price sensitivity of a bond: Substituting Modified Duration into equation (1) above and slightly rearranging gives:- Figure 4.1
Bond Mathematics 50 Modified Duration describes the sensitivity of a price of a bond to small changes in its yield – and is often referred to as the volatility of the bond. It captures, in a single number, how a bond‘s maturity and coupon affect its exposure to interest rate risk. It provides a measure of percentage price volatility, not absolute price volatility and is a measure of the percentage price volatility of the full (i.e. dirty) price. For any small change in yield, the resulting percentage change in price can be found by multiplying yield change by Modified Duration as shown below:- % change in price = - (Modified Duration) x yield change (in basis points) (3) The negative sign in the equation is, of course, necessary as price moves in the opposite direction to yield. Figure 4.2 However, there are limitations in using Modified Duration in predicting the price/yield relationship. It is only valid for small changes in yield; for parallel shifts in the yield curve; and for small time horizons. The reasons for these limitations can be more clearly seen from the graph below. The price/yield relationship estimated from the Modified Duration of a bond is linear (shown by the tangent to the curve at Po) whilst the actual price/yield relationship is a curve. There is therefore an error when using Modified Duration to estimate price movements Duration is used as a way to ensure that a goal to be met in the future will not be affected by interest rate changes. The ―duration gap‖ is a well respected subject among banks. DG = DA – (MVL/MVA)* DL DG = duration gap (which you want it to be zero if you are duration matching) DA = duration of the assets MVL = market value of the liabilities MVA = market value of the assets DL = duration of the liabilities
Bond Mathematics 51 Table 4.1 Convexity duration α 1/coupon • higher coupon lead to quicker recovery of the bond's value, resulting inshorter duration duration α 1/YTM • higher yields produce lower present values of cash receipts received far out in time, thereby diminishing their relative value duration α maturity • duration expands with time to maturity but at a decreasing rate percentage price change • the percentage change in a bond's price is approximately equal to negative modified duration times the change in yield price change • the change in a bond's price is approximately equal to percentage change in prices times the original price estimated price • the estimated bond's price is approximately equal to percentage changes in prices times original price plus the original price a • Convexity is a measure of the sensitivity of a bond‘s price to changes in yield. b •It is also a measure of the degree to which a bond‘s price-yield curve departs from a straight line. This characteristic affects the estimates of a bond‘s price volatility. c •Modified Duration indicates how the price of a bond varies for small changes in yield. However, for large changes in yield, two bonds that have the same yield and the same Modified Duration can behave quite differently. This is due to the ‗error‘ in using modified duration. This error is explained by convexity d •It is the second derivative of a bond‘s price with respect to yield. The convexity of a bond is a measure of the curvature of its price/yield relationship.
Bond Mathematics 52 where, C= cash flow at time t t= period when the cash flow is expected to be received T= number of periods until maturity m= number of periods per year r= discount rate per period The approximate percentage price change due to convexity is:- % price change = ½ x convexity x (percentage yield change)2 Figure 4.3 The diagram shows the modified duration line relating to bonds AB and CD (i.e. a tangent to the price/yield curve at point P1). The price/yield curve for bond CD is clearly more convex than that for bond AB. This means that, at this point, for any given change of yield, bond CD will outperform AB. However, over time, the price yield curves will shift and therefore bond CD will not always outperform. Table 4.2 convexity α 1/coupon • the curvature relationship betwen yield and prices is greater for lower yields convexity α 1/YTM • the curavture is flatter for higher coupon bonds than lower coupon bonds convexity α duration • the curavture is greater for longer maturity bonds and therefore for long duration bonds
Bond Mathematics 53 Comparison of two bonds Figure 4.4  Bond 1 is more convex than Bond 2  Price falls at a slower rate as yield increases  Bond Convexity is defined formally as the degree to which the duration changes when the yield to maturity changes. It can be used to account for the inaccuracies of the Modified Duration approximation. On top of that, if we assume two bonds will provide the same duration and yield then the bond with the greater convexity will be less affected by interest rate change. This can be easily visualized from the diagram above where the greater the "curvature", the lesser the price drop when interest rate increase.  But at the same time, if the interest rate increases, the expected yield increases and it can be observed in the above diagram that higher the convexity higher the price increases than the lesser convexity.  This shows that convexity has double advantage because when interest rates fall, bond prices rise very high comparatively when interest rates rise, the prices fall less. percentage price change •the percentage change in a bond's price associated with the convexity is approximately equal to the product of negative modified duration and change in yield plus the product of 1/2, convexity and change in yield price change • the change in a bond's price is approximately equal to percentage change in prices times price for both duration and convexity estimated price • the change in a bond's price is approximately equal to percentage change in prices times price for both duration and convexity plus original price Bond 1 _________ Bond 2 ------------
Bond Mathematics 54 Immunization It is the strategy of protecting a portfolio against interest rate risk (i.e both price and reinvestment risk).  Zero coupon bond immunization: buy zero coupon bonds that match the desired future cash flows. (prefect immunization)  Coupon bond immunization: the process of balancing bond holdings such that price and reinvestment risks cancel out. (approximate immunization) Components of interest rate risk  Price risk: risk resulting from the inverse relationship between bond prices and required rates of return  Reinvestment rate risk: risk resulting from the uncertainty about the rate at which future coupon income can be reinvested. The two components of interest rate risk move in opposite directions. Hence, the strategy would be to purchase a bond with duration equal to the investment horizon.
Bond Mathematics 55 Exposure of bonds to HPCL Background of bonds in HPCL HPCL issues NCD‘s (Debentures) and receives oil bonds. Bonds is a way to finance long term money requirements for the new projects. It is obligatory for HPCL to receive oil bonds from the government. As government subsidises oil prices, public sector companies have to face losses. Instead of paying back the losses to the company in cash, government issues oil bonds. Now, it is the company‘s task to manage these bonds for profits ( selling and issueing). Also called management of baond portfolio. This can be done in a very efficeint manner by implementing a tool called bond mathematics (which we have studied so far). Balance sheet 2008 – 2009 Table 5.1
Bond Mathematics 56 As seen from the above investments, the modes of investments of HPCL are coupon bonds, convertible debentures, equity shares and NCDs. HPCL received 3 oil special bonds of 8108.35 Cr from the government of India which are mandatory. It bought convertible debenture from Prize Petroleum Co. Limited of 15 Cr. Also bought debentures from Shell MRPL Aviation Fuels and from Petronet India ltd of 18.54 Cr. As seen in the current investments, HPCL has been continuously been compensated by oil bonds in form of subsidy financing by GOI. In the year 2008-09 total outstanding oil bonds in hand of HPCL stood at 4594.64 Cr against 10 special oil bonds of 5682.39 Cr in year 2007- 08. This shows that the oil prices in 2009 have been sold by HPCL in the market to manage working capital requirement. All these bonds in this year have been discussed in detail below. But as an overall picture, HPCL has made huge investments of 12827.38 Cr in 2009 as against 5869.17 Cr in 2008. Most of their investments are bond based which are secured and gives fixed income. They are playing safe and hence their returns might be low due to low risk but their volumes are high this year comparitively.
Bond Mathematics 57 Analysis MTM statement of oil bonds issued by govt. Of India as on 01-June -2009 7.47 % Oil Marketing Companies' GOI Special Bonds, 2012 Face value Issue date Maturity date coupon rate Yield Year to maturity 100 07-Mar- 2006 07-Mar-12 7.74% 7.5648% 6 All these calculations have been performed on HPCL. Yield, price, duration of the bonds can be calculated directly on excel. It has inbuilt formulae: PRICE(seetlement, maturity, rate, yld, redemption, frequency, [basis]); YIELD(settlement, maturity, rate, pr, redemption, frequency, [basis]); DURATION(settlement, maturity, coupon, yld,frequency, [basis]); But for calculation of convexity, there is no inbuilt formula, hence the following method as the formula for convexity is 1/(P(1+y)2 ) ∑ [CF/(1+y)2 (t2 +t)] A B Period CF Discounted flows t^2 + t a*b 1 7.74 3.72 2 7.45 2 7.74 3.86 6 23.18 3 7.74 3.86 12 46.43 4 7.74 3.86 20 77.39 5 7.74 3.86 30 116.09 6 107.74 53.86 42 2262.53 Sum 2533.12 1/(P((1+y)^2)) 0.0086 Convexity 21.89 Duration 4.91 % change in bond price 6.03 for 1% change in yield
Bond Mathematics 58 The percentage change in bond price is calculated by (-D x Δy) + (o.5 x convexity x Δy2 ). The rupee change in bond price can be calculate by multiplying current bond price with the percentage change in bond price. As seen from the above bond, the yield is just above coupon rate, hence the bond price is trading at discount price of Rs99.75. The curve has less curvature which indicates less sensitivity in the bond prices due to the yield changes. Hence the observed convexity and the duration is also less. There is only 6.03% change in prices for 1% change in yield. This is obvious as the time to maturity is just 6 years which is the major factor for price volatility. 0 50 100 150 0 5 10 15 price yield curve price yield curve
Bond Mathematics 59 7.61 % Oil Marketing Companies' GOI Special Bonds, 2015 Face value Issue date Maturity date coupon rate Yield time to maturity 100 07-Mar- 2006 07-Mar-15 7.61% 8.1467% 9 A B Period CF Discounted flows t^2 + t a*b 1 7.61 3.65 2 7.31 2 7.61 3.79 6 22.79 3 7.61 3.80 12 45.65 4 7.61 3.80 20 76.09 5 7.61 3.80 30 114.14 6 7.61 3.80 42 159.80 7 7.61 3.80 56 213.08 8 7.61 3.80 72 273.96 9 107.61 53.80 90 4842.45 sum 5755.31 % change in bond price 17.97 for 1% change in yield 1/(P((1+y)^2)) 0.0086 convexity 49.21 Duration 6.62 0 50 100 150 200 0 5 10 15 price yield curve price yield curve
Bond Mathematics 60 The above bond is better than the previous bond in terms of yield or returns, hence the bond is traded at a discount price of Rs 97.55. The good curvature to the price yield curve, average duration and moderate convexity. For 1% change in yield, the price of this bond fluctuates to 17.97%.
Bond Mathematics 61 6.35 % Oil Marketing Companies' GOI Special Bonds, 2024 Face value Issue date Maturity date coupon rate Yield time to maturity 100 23-Dec- 2008 07-Mar-15 6.35% 6.3495% 16 A B Period CF Discounted flows t^2 + t a*b 1 6.35 3.07 2 6.15 2 6.35 3.17 6 19.03 3 6.35 3.17 12 38.09 4 6.35 3.17 20 63.49 5 6.35 3.17 30 95.24 6 6.35 3.17 42 133.34 7 6.35 3.175 56 177.8 8 6.35 3.175 72 228.6 9 6.35 3.175 90 285.75 10 6.35 3.175 110 349.25 11 6.35 3.175 132 419.1 12 6.35 3.175 156 495.3 13 6.35 3.175 182 577.85 14 6.35 3.175 210 666.75 15 6.35 3.175 240 762 16 106.35 53.175 272 14463.6 Sum 18781.38
Bond Mathematics 62 1/(P((1+y)^2)) 0.0088 convexity 166.06 duration 5.13 This bond has maturity of 16 years but its yield being almost equal to the coupon rate, the price in the market remains same. The curavture is less and but its duration convexity is high and hence for 1% change in yield there is 77.9% change in prices. 0 50 100 150 0 5 10 15 price yield curve price yield curve % change in bond price 77.90 for 1% change in yield
Bond Mathematics 63 a b Period CF Discounted flows t^2 + t a*b 1 6.90 3.33 2 6.66 2 6.90 3.44 6 20.67 3 6.90 3.44 12 41.39 4 6.90 3.44 20 68.99 5 6.90 3.44 30 103.49 6 6.90 3.44 42 144.89 7 6.90 3.45 56 193.2 8 6.90 3.45 72 248.4 9 6.90 3.45 90 310.5 10 6.90 3.45 110 379.5 11 6.90 3.45 132 455.4 12 6.90 3.45 156 538.2 13 6.90 3.45 182 627.9 14 6.90 3.45 210 724.5 15 6.90 3.45 240 828 16 6.90 3.45 272 938.4 17 106.90 53.45 306 16355.7 sum 21985.84 6.90 % Oil Marketing Companies' GOI Special Bonds, 2026 Face value Issue date Maturity date coupon rate Yield time to maturity 100 04-Feb- 2009 04-Feb-26 6.90% 6.8986% 17
Bond Mathematics 64 1/(P((1+y)^2)) 0.0088 convexity 192.40 duration 10.26 This bond has very good curvature and time to maturity and hence has high duration and convexity. Therefore, the change in yield by 1%, has 85.94% change in its prices. It is very sensitive. 0 50 100 150 200 250 0 5 10 15 price yield curve price yield curve % change in bond price 85.94 for 1% change in yield
Bond Mathematics 65 8.00 % Oil Marketing Companies' GOI Special Bonds, 2026 Face value Issue date Maturity date coupon rate Yield time to maturity 100 23-Mar- 2009 23-Mar-26 8.00% 7.9980% 17 a b Period CF Discounted flows t^2 + t a*b 1 8.00 3.84 2 7.69 2 8.00 3.99 6 23.96 3 8.00 3.99 12 47.99 4 8.00 3.99 20 79.99 5 8.00 3.99 30 119.99 6 8.00 3.99 42 167.99 7 8.00 3.99 56 224 8 8.00 4 72 288 9 8.00 4 90 360 10 8.00 4 110 440 11 8.00 4 132 528 12 8.00 4 156 624 13 8.00 4 182 728 14 8.00 4 210 840 15 8.00 4 240 960 16 8.00 4 272 1088 17 108.00 54 306 16524 sum 23051.65
Bond Mathematics 66 1/(P((1+y)^2)) 0.0086 Convexity 197.64 Duration 9.57 This bond too has high curvature and high time to maturity due to which its convexity and duration are high making it sensitive. Change in yield by 1% has impact on prices by 89.24%. As on June 1. 2009, the yield being equal to the coupon rate, the bond price remains same as the face value. 0 50 100 150 200 250 0 5 10 15 price yield curve price yield curve % change in bond price 89.24 for 1% change in yield
Bond Mathematics 67 8.20 % Oil Marketing Companies' GOI Special Bonds, 2024 Face value Issue date Maturity date coupon rate Yield time to maturity 100 15-Sep- 2009 15-Sep-24 8.20% 8.1977% 15 a b Period CF Discounted flows t^2 + t a*b 1 8.20 3.93 2 7.87 2 8.20 4.09 6 24.55 3 8.20 4.09 12 49.19 4 8.20 4.09 20 81.99 5 8.20 4.09 30 122.99 6 8.20 4.09 42 172.19 7 8.20 4.09 56 229.6 8 8.20 4.1 72 295.2 9 8.20 4.1 90 369 10 8.20 4.1 110 451 11 8.20 4.1 132 541.2 12 8.20 4.1 156 639.6 13 8.20 4.1 182 746.2 14 8.20 4.1 210 861 15 108.20 54.1 240 12984 sum 17575.63
Bond Mathematics 68 This bond too has good curvature and time to maturity and hence good convexity and duration. It is sensitive for about 66.17% in prices for a change in 1% of yield. The yield on june 1, 2009 remains the same as coupon, hence the bond price is neither discounted nor premium. Convexity of all bonds Figure 5.1 Comparing convexity of all the bonds, it can be said that bonds with coupon rates 6.9%, 8% and 8.2% have high curavature indicating high sensitivity. In these bonds, if the yield decreases, the prices increase highly but at the same time if the yield increases, the prices decrease less comparitively. HPCL being the investor, this is an advantage to it. 0 50 100 150 200 250 0 5 10 15 price yield curve price yield curve 0 25 50 75 100 125 150 175 200 225 0 5 10 15 7.47%, 2012 7.61%, 2015 6.35%, 2024 6.9%, 2026 8%, 2026 8.2%, 2024 % change in bond price 66.17 for 1% change in yield 1/(P((1+y)^2)) 0.0085 Convexity 150.13 Duration 8.89
Bond Mathematics 69 HPCL has lately started issuing NCDs in the market. The present bonds in the market are discussed below: HINDUSTAN PETROLEUM CORP LTD N/A S&P 12-Apr-2010 ISIN:INE094A07038, LOCAL CODE:PTHPCL137.70% Oil and Gas - Oil and Gas Fixed:Plain Vanilla Fixed Coupon Issuance Details Bond Issued Issue Date / Price / Yield 12-Apr-2010 Issue Spread: -- (--) Original Issue Amount: 10,00,00,00,000 INR Total Issue Amount: 10,00,00,00,000 INR Total Price to Public: INR Announcement Date: 12-Apr-2010 Auction Date: -- MTN: No Underwriters: Name Type Amount CITIBANK NA Joint Lead Manager AXIS BANK LTD Joint Lead Manager SBI CAPITAL MARKETS LTD Joint Lead Manager STANDARD CHARTERED BANK (INDIA BRANCH) Joint Lead Manager Principal / Coupon Information Maturity Date: 12-Apr-2013 100 Principal / Coupon Currency: INR / INR Amount Outstanding: 10,000,000,000 INR Coupon Type / Frequency: Fixed:Plain Vanilla Fixed Coupon / Annually Current Coupon / Next Pay Date: 7.7000 12-Apr-2011 Coupon Formula: -- Dated / First / Final Coupon: 12-Apr-2010 12-Apr-2011 12-Apr-2012 Irregular Coupon: None Cumulative Dividend: -- Ratings Rating Source Date Rating Watch Code Credit Information Svce of India 12-Apr-2010 AAA -- Moody's Long-term Issue Credit Rating 12-Apr-2010 N/A -- Standard & Poor's 12-Apr-2010 N/A -- 7.7 % fixed plain vanilla bond, HPCL 2013
Bond Mathematics 70 Face value Issue date Maturity date coupon rate Yield Year to maturity 100 12-Apr-2010 12-Apr-13 7.70% 7.5333% 3 A B Period CF Discounted flows t^2 + t a*b 1 7.70 3.71 2 7.42 2 7.70 3.84 6 23.06 3 107.70 53.84 12 646.16 Sum 676.65 1/(P((1+y)^2)) 0.0086 Convexity 5.85 Duration 2.73 As seen the yield is 7.533, less than the coupon rate 7.7. It is an advantage to HPCL as it has to pay less interest rate to the receiver of the bond. The time to maturity is just 3 years and hence its duration and convexity are low. For a change in yield by 1%, there is only 0.19% change in price. Hence an advantage as an issuer. 0 20 40 60 80 100 120 140 0 5 10 15 price yield curve price yield curve % change in bond price 0.19 for 1% change in yield
Bond Mathematics 71 7.35 % fixed plain vanilla bond, HPCL 2012 HINDUSTAN PETROLEUM CORP LTD N/A S&P 04-Dec-2009 ISIN:INE094A07020, LOCAL CODE:PTHPCL127.35 Oil and Gas - Oil and Gas Fixed:Plain Vanilla Fixed Coupon Issuance Details Asset Backed Security Issued Issue Date / Price / Yield 04-Dec-2009 Issue Spread: -- (--) Original Issue Amount: 5,00,00,00,000 INR Total Issue Amount: 5,00,00,00,000 INR Total Price to Public: INR Announcement Date: -- Auction Date: -- MTN: No Underwriters: Name Type Amount CITIBANK NA Lead Underwriter or Manager SBI CAPITAL MARKETS LTD Joint Lead Manager STANDARD CHARTERED BANK (INDIA BRANCH) Bookrunner Principal / Coupon Information Maturity Date: 04-Dec-2012 100 Principal / Coupon Currency: INR / INR Amount Outstanding: 5,000,000,000 INR Coupon Type / Frequency: Fixed:Plain Vanilla Fixed Coupon / Semiannually Current Coupon / Next Pay Date: 7.3500 Coupon Formula: -- Dated / First / Final Coupon: 04-Dec-2009 04-Jun-2010 04-Jun-2011 Irregular Coupon: Last Cumulative Dividend: -- Ratings Rating Source Date Rating Watch Code Credit Information Svce of India 04-Dec-2009 AAA -- Moody's Long-term Issue Credit Rating 04-Dec-2009 N/A -- Standard & Poor's 04-Dec-2009 N/A -- Face value Issue date Maturity date coupon rate Yield Year to maturity 100 04-Dec-2009 04-Dec-12 7.35% 7.2454% 3
Bond Mathematics 72 A B Period CF Discounted flows t^2 + t a*b 1 7.35 3.54 2 7.09 2 7.35 3.67 6 22.02 3 107.35 53.67 12 644.06 Sum 673.18 1/(P((1+y)^2)) 0.0087 convexity 5.85 duration 2.74 Even this NCD has low yield of 7.2454 adding an advantage to the issuer. The curvature is less depicting less convexity. Duration is ought to be low as the time to maturity is just 3 years. 0 20 40 60 80 100 120 140 0 5 10 15 price yield curve price yield curve % change in bond price 0.18 for 1% change in yield
Bond Mathematics 73 Study of yield: for NCD/ Oil bond We have seen oil bonds and NCDs have 3 basic elements, irrespective of the issuer and the investor. i.e 1. Coupon 2. Tenor 3. Face value To consider the appriopriate time of sale and issuance, the issuer has to understand the relation between above three components. The price of bond (oil bond) from the side of issuer depends on the yield expectation of the market. So, to ensure appriopriate time for sale of oil bond , the study of yield takes utmost importance. The yields are determined by similar government securities of same tenor and relevant spreads are added as per the market appetite and interest. For the study of appriopriate timing for sale of oil bond and its yield discovery, we have taken following bond: 8.00 % Oil Marketing Companies' GOI Special Bonds, 2026 Face value Issue date Maturity date coupon rate Yield time to maturity 100 23-Mar- 2009 23-Mar-26 8.00% 17 Indicative yields of G-secs 14 years G-sec with maturity of 22-jun-2024 with yield of 8.265 15 years G-sec with maturity of 02-aug-2027 with yield of 8.232 Interpolating the above G-sec: 8.265+ (8.232-8.265)/38* 22= 8.246 so we have derived equivalent yield from the relevant benchmark and considering the market expectations spreads are added to the benchmark yield to get the price. For similar bond, spread cn be presumed at 50 basis point. So effective yield becomes 8.746. To ensure accurate timing of the sale, we have to predict the movement of benchmarks. The recent movement of benchmarks is as shown below:
Bond Mathematics 74 Figure5.2 Based on our above study the price of above bond comes to Rs96.39. Studying the graph and selling the same at appriopriate time at a yield of 7.4%, the price should come to Rs99.87. The technical analysis shows that it has an upward but has a tendency to fall due to following reasons. During this quarter, 7.4% seems to be dropped the least and this area has to be tapped for good profits. As seen, the maximum peaks touched are 8.2%, 8% and 7.8% in the recent quarter. So keeping this in mind, we can estimate that yields would not rise too high unless extreme market conditions. 7.4% is the best yield for the sale of bond only for this quarter. According to me, this is not the right time for sale, HPCL should wait for the next quarter as the yields might fall further to make the necessary decision.
Bond Mathematics 75 Determination of Benchmark Table 5.2 Observing the indicative yields of the above G- sec, the following yields of the bonds can be predicted: Table 5.3 Description of Oil Bonds Issue Date Maturity Date Nearest G- sec considered Interpolation Benchm ark 7.47 % Oil Marketing Companies' GOI Special Bonds, 2012 07-Mar- 2006 07-Mar-12 2 jun, 11 : 5.699 3 sep, 12: 6.816 5.699 + (6.816- 5.699)/14*9 6.417 7.61 % Oil Marketing Companies' GOI Special Bonds, 2015 07-Mar- 2006 07-Mar-15 20 oct, 14: 7.166 14 jun, 15: 7.37 7.166 + (7.37- 7.166)/8*5 7.2935 6.35 % Oil Marketing Companies' GOI Special Bonds, 2024 23-Dec- 2008 23-Dec-24 22 jun, 24: 8.265 02 aug, 27: 8.232 8.265 + (8.232- 8.265)/38*22 8.246 6.90 % Oil Marketing Companies' GOI Special Bonds, 2026 04-Feb- 2009 04-Feb-26 22 jun, 24: 8.265 02 aug, 27: 8.232 8.265 + (8.232- 8.265)/38*22 8.246 8.00 % Oil Marketing Companies' GOI Special Bonds, 2026 23-Mar- 2009 23-Mar-26 22 jun, 24: 8.265 02 aug, 27: 8.232 8.265 + (8.232- 8.265)/38*22 8.246 8.20 % Oil Marketing Companies' GOI Special Bonds, 2024 15-Sep- 2009 15-Sep-24 22 jun, 24: 8.265 02 aug, 27: 8.232 8.265 + (8.232- 8.265)/38*22 8.246
Bond Mathematics 76 We have seen all oil bonds are benchmarked to G- secs for determination of its yield. Since, the maturity of G- secs are not same as of oil bonds, we use mathematical tools to interpolate G- secs of nearer maturity to get benchmark for similar oil bonds. Specimen of the benchmark of government securities as on 19-07-10 is shown in table 5.2. Based on the same principle we have calculated the indicative yiled for al ol bonds. Spread factors are market determined and to be considered based on the market indications. Conclusion We have seen HPCL, a fortune 500 company has wide presence in bond market in form of Oil Bonds and Non Convertible debentures. The investments of HPCL have major impact on the financials of the corporation. Hence it is of top most priority to manage the fixed income securities effectively. As seen, bonds play a major role in funding projects and a good source of income. Hence, most of the companies opt for bond portfolios and its management. HPCL is no different and it has also entered into bond management. Managing, analysing and predicting bonds is not a difficult task. Bonds can be very well managed with the tool ‗bond mathematics‘. Mathematics is one of the keys to understanding the bond market. Grasping the concepts that underlie the bond market is the crucial task. Bond market maths can be reduced to a few key concepts: compounding and discounting; accrued interest; running yields; redemption yields; and spreads. Armed with knowledge of these concept and hefty amount of common sense, finding an undervalued bond in which to invest becomes less of a lottery. Studying bond yields, maturity, duration and convexity gives a clearer picture whether to buy that particular bond or not. At same time, what is the appropriate timing for the sale of bonds and the price at which it should be sold can also be determined. Such factors are crucial to make profits and to gain smart income. Research Methodology: An in-depth investigation of the industry conventions for calculating price and yield applied to plain vanilla bonds, including the exploration of implicit assumptions and interpretation of resulting numbers. We have further seen that bonds are sensitive to various market factors and its effective management can increase the profitability of the corporations. The advanced mathematical tools provide effective methods to systematically analyse the bonds and times its sale or issuance in the primary as well as secondary market.

More Related Content

DOC
IOCL summer internship report
sagarmehra
 
DOCX
HPCL Summer internship report
Veraat Bharat
 
DOCX
hindustan petroleum 2018 report
sachin kumar sharma
 
DOCX
A Project Report on Management Information Systems of Hindustan Petroleum Cor...
Chandan Pahelwani
 
DOCX
SUMMER INTERNSHIP PROJECT
GAURAV SHUKLA
 
PPTX
Indian oil
RAKESH BAGRECHA
 
DOC
201109017 project-report-on-hpcl-collegeprojects1-blogspot-in
homeworkping4
 
PPTX
Hpcl ppt .
Papu Nanda
 
IOCL summer internship report
sagarmehra
 
HPCL Summer internship report
Veraat Bharat
 
hindustan petroleum 2018 report
sachin kumar sharma
 
A Project Report on Management Information Systems of Hindustan Petroleum Cor...
Chandan Pahelwani
 
SUMMER INTERNSHIP PROJECT
GAURAV SHUKLA
 
Indian oil
RAKESH BAGRECHA
 
201109017 project-report-on-hpcl-collegeprojects1-blogspot-in
homeworkping4
 
Hpcl ppt .
Papu Nanda
 

What's hot (20)

DOCX
INDIAN OIL CORPORATION LIMITED
ANAND PRASAD
 
PPTX
Sip hpcl ppt
Hindustan Petroleum
 
PDF
IOCL(Gujarat Refinary) vocatational training report (Mechanical Department)
Parth Rana
 
PPTX
HPCL PPT
Veraat Bharat
 
DOCX
Indian oil
Siddharth Gupta
 
PDF
IOCL PERFORMANCE ANALYSIS
Kangan Deka
 
PDF
My mba project_iocl
buddhadev karmakar
 
PPTX
Hpcl concept of management
sofiar rahaman
 
DOC
Hpcl Operations Mgmt
DEEPAK DODDAMANI
 
DOC
Summer Training Project Report On BPC Ltd.
Peush Prabhakar
 
PPTX
Hpcl pwrpoint presentetion
Shamim Hossain
 
DOC
ongc project
Amit Gandhi
 
PPTX
Ongc ppt
palak jha
 
PPTX
Iocl barauni presentation ppt.
M4UBIHARI
 
PDF
Industrial training at Indian Oil Corporation Limited (IOCL) Noonmati
Priyam Jyoti Borah
 
DOC
45312185 maruti-suzuki-project-report
AADARSH ABHISHEK
 
PPTX
Indias petroleum and there supply chain network
Brandix India Apparel City Pvt Ltd.
 
PDF
HPCL "Market penetration of HP-Gas"
Rushikesh Kale
 
PPT
FMCG sector presentation
sujit kumar
 
PPTX
Hul
Niyati Mehta
 
INDIAN OIL CORPORATION LIMITED
ANAND PRASAD
 
Sip hpcl ppt
Hindustan Petroleum
 
IOCL(Gujarat Refinary) vocatational training report (Mechanical Department)
Parth Rana
 
HPCL PPT
Veraat Bharat
 
Indian oil
Siddharth Gupta
 
IOCL PERFORMANCE ANALYSIS
Kangan Deka
 
My mba project_iocl
buddhadev karmakar
 
Hpcl concept of management
sofiar rahaman
 
Hpcl Operations Mgmt
DEEPAK DODDAMANI
 
Summer Training Project Report On BPC Ltd.
Peush Prabhakar
 
Hpcl pwrpoint presentetion
Shamim Hossain
 
ongc project
Amit Gandhi
 
Ongc ppt
palak jha
 
Iocl barauni presentation ppt.
M4UBIHARI
 
Industrial training at Indian Oil Corporation Limited (IOCL) Noonmati
Priyam Jyoti Borah
 
45312185 maruti-suzuki-project-report
AADARSH ABHISHEK
 
Indias petroleum and there supply chain network
Brandix India Apparel City Pvt Ltd.
 
HPCL "Market penetration of HP-Gas"
Rushikesh Kale
 
FMCG sector presentation
sujit kumar
 
Hul
Niyati Mehta
 
Ad

Viewers also liked (17)

DOCX
Project report Kshitij Agarwal (1) (1) (1)
Kshitij Agarwal
 
PDF
Employee effective hpcl
Bodke Varun Kumar
 
PPTX
Presentation on Management Information System of HPCL
Chandan Pahelwani
 
DOC
A project report on benchmarking of hr practices
Projects Kart
 
PPT
Industrial Revolution 7th Grade
EMS
 
PDF
Market based cash balance plans
Jim van Iwaarden
 
PPT
Dka 1
guesta8d955
 
PPT
An update on psychopharmacology part i 22 june 2007 fountain house
Pk Doctors
 
PPTX
Elements of arts and manuella
gzorskas
 
PPT
E C G Part 4
Pk Doctors
 
PPTX
Manuella elements
gzorskas
 
PPTX
PHP from soup to nuts Course Deck
rICh morrow
 
PDF
Market based cash balance plans
Jim van Iwaarden
 
PPT
P1121340296
Ashraf Aboshosha
 
PPT
Major_Proj_Ramya
Ramya Emandi
 
PPT
Carol A Johnson Culture
carol_johnson
 
PDF
Matrixbrochure Web
toddzaugg
 
Project report Kshitij Agarwal (1) (1) (1)
Kshitij Agarwal
 
Employee effective hpcl
Bodke Varun Kumar
 
Presentation on Management Information System of HPCL
Chandan Pahelwani
 
A project report on benchmarking of hr practices
Projects Kart
 
Industrial Revolution 7th Grade
EMS
 
Market based cash balance plans
Jim van Iwaarden
 
Dka 1
guesta8d955
 
An update on psychopharmacology part i 22 june 2007 fountain house
Pk Doctors
 
Elements of arts and manuella
gzorskas
 
E C G Part 4
Pk Doctors
 
Manuella elements
gzorskas
 
PHP from soup to nuts Course Deck
rICh morrow
 
Market based cash balance plans
Jim van Iwaarden
 
P1121340296
Ashraf Aboshosha
 
Major_Proj_Ramya
Ramya Emandi
 
Carol A Johnson Culture
carol_johnson
 
Matrixbrochure Web
toddzaugg
 
Ad

Similar to HPCL Report Final (20)

PDF
Investor-Presentation-Q4-FY-2023-24-10052024.pdf
icicidirectbusinessp
 
PDF
Customer overview of retail outlets hpcl vs. reliance
Supa Buoy
 
PDF
Project on BPCL by md sajid
Md Sajid
 
PPTX
FULL PPT ON BPCL-NK&NK
NK92_06
 
PPTX
Bpcl Strategies
Kunal Goyal
 
PDF
Investorpresentation q4
Bharat Petroleum Corporation Limited
 
PPTX
Bpcl & hpcl
PranayAlva
 
PDF
Beacon June 2014
SIMCON (SIMSREE Consulting Club)
 
DOCX
Corporate Strategy Case: Haldia Petro Chemicals
Ramamurthy Prakash
 
PDF
Investor presentation q4 fy13
Bharat Petroleum
 
PDF
Investor Presentation Q4 2012
Bharat Petroleum Corporation Limited
 
PDF
toaz.info-a-project-report-on-management-information-systems-of-hindustan-pet...
gauravkumar4594
 
PDF
Investor_presentation_Q4FY13.pdf
AnkitGupta676436
 
PDF
Investor Presentation Q4 - June 2011
Bharat Petroleum Corporation Limited
 
PPTX
Petroleum bsp presentation
Simran Kaushik
 
PDF
LIVE PROJECT ON “TRAINING AND DEVELOPMENT AT HINDUSTAN PETROLEUM CORPORATION...
NISHIGANDHA BATWAL
 
PPTX
Hpc lppt1
Vaibhav Godse
 
PDF
Investor Presentation Q4 2013
Bharat Petroleum Corporation Limited
 
PPTX
INDUSTRY ppt
Anurag Chowdhury
 
PPTX
Cpcl business plan
Manav T Mehta
 
Investor-Presentation-Q4-FY-2023-24-10052024.pdf
icicidirectbusinessp
 
Customer overview of retail outlets hpcl vs. reliance
Supa Buoy
 
Project on BPCL by md sajid
Md Sajid
 
FULL PPT ON BPCL-NK&NK
NK92_06
 
Bpcl Strategies
Kunal Goyal
 
Investorpresentation q4
Bharat Petroleum Corporation Limited
 
Bpcl & hpcl
PranayAlva
 
Beacon June 2014
SIMCON (SIMSREE Consulting Club)
 
Corporate Strategy Case: Haldia Petro Chemicals
Ramamurthy Prakash
 
Investor presentation q4 fy13
Bharat Petroleum
 
Investor Presentation Q4 2012
Bharat Petroleum Corporation Limited
 
toaz.info-a-project-report-on-management-information-systems-of-hindustan-pet...
gauravkumar4594
 
Investor_presentation_Q4FY13.pdf
AnkitGupta676436
 
Investor Presentation Q4 - June 2011
Bharat Petroleum Corporation Limited
 
Petroleum bsp presentation
Simran Kaushik
 
LIVE PROJECT ON “TRAINING AND DEVELOPMENT AT HINDUSTAN PETROLEUM CORPORATION...
NISHIGANDHA BATWAL
 
Hpc lppt1
Vaibhav Godse
 
Investor Presentation Q4 2013
Bharat Petroleum Corporation Limited
 
INDUSTRY ppt
Anurag Chowdhury
 
Cpcl business plan
Manav T Mehta
 

HPCL Report Final

  • 1. Bond Mathematics 1 HINDUSTAN PETROLEUM COMPANY LIMITED Company profile: Fortune 500 company Mega Public Sector Undertaking Hindustan Petroleum Corporation Limited (HPCL) is an integrated oil refining and marketing companies in India. It is engaged in the oil and gas exploration and production, refining of crude oil and marketing of petroleum products. Currently, the company holds 16% market share and 10.3% of India‘s refining capacity. The company owns and operates two coastal refineries, one at Mumbai and the other in Vishakapatnam. The company also holds an equity stake of 16.95% in Mangalore Refinery & Petrochemicals Limited. The company is headquartered at Mumbai in Maharashtra, India. HPCL‘s Mumbai refinery has a capacity of 5.5 Million Metric Tons Per Annum (mmtpa) and Vishakapatnam refinery has a capacity of 7.5 mmtpa. Mangalore Refinery has a capacity of 9 mmtpa. HPCL owns and operates the largest lube refinery in India with a capacity of 335 TMT. The company reported revenues of (Rupee) INR 1,294,757.90 million during the fiscal year ended March 2009, an increase of 16.53% over 2008. The operating profit of the company was INR 10,118.40 million during the fiscal year 2009, a decrease of 28.92% from 2008. The net profit of the company was INR 7,573.90 million during the fiscal year 2009, a decrease of 44.48% from 2008. KEY DATA 2009 Sales: 1,31,802.65 Cr Major Industry: Oil Industry Sub Industry: Refineries Country: India Currency Indian Rupees Fiscal Year Ends: March Employees More than 11,245 Exchanges: NSE BSE Market Capitalization: 12092.38 Cr Weighted avg. no. of shares 33.86 crores OFFICERS Chairman & Managing Director Mr.Arun Balakrishnan Director- Marketing Mr.S.Roy Choudhury Director- Human Resources Mr.V. Vizia Saradhi Director- Finance Mr.B.Mukherjee
  • 2. Bond Mathematics 2 Company description: Mission: "HPCL, along with its joint ventures, will be a fully integrated company in the hydrocarbons sector of exploration and production, refining and marketing; focusing on enhancement of productivity, quality and profitability; caring for customers and employees; caring for environment protection and cultural heritage. It will also attain scale dimensions by diversifying into other energy related fields and by taking up transnational operations." Vision: To be a World Class Energy Company known for caring and delighting the customers with high quality products and innovative services across domestic and international markets with aggressive growth and delivering superior financial performance. The Company will be a model of excellence in meeting social commitment, environment, health and safety norms and in employee welfare and relations. Table1.1 Business Units Description Refineries Present Projects:  Facilities for Euro-III & IV grade Gasoline  New FCCU project at Mumbai Refinery  Environmental facilities  Bottom Up-gradation Projects  LOBS Project  MR/VR DHT  Single Point Mooring (SPM) Project at Visakh Refinery  Modernization Project for Mounded Storage System for LPG /Propylene at Visakh Refinery Aviation Infrastructure  Aviation Service Facility: Our Facility to supply JET A1 at Indian Airports  Location of our ASFs: Aircraft Fueling Facilities of HP Aviation in India  Equipment: Our Equipment to supply Aircraft Jet Fuel in India  Modernization And Upgradation: Keeping ATF Refueling facilities up- to-date Jet Fuel Prices  Domestic Prices: Price of Jet A1 at various airports in India  International Prices: PLATTS based Pricing in India for International carriers Bulk Fuel Fuels Offered:  Bitumen  Fuels  Marine-Bunker Fuels  Marine Lubes  Special Products
  • 3. Bond Mathematics 3  Superior Kerosene Oil-Non PDS LPG (HP Gas) LPG Offered:  Domestic LPG  Commercial LPG  Industrial & Bulk LPG  Auto LPG  Piped LPG  Rasoi Ghar Lubes (HP Lubes) HP Lubricants are borne out of an intense and unrelenting R & D effort, which aims at producing quality products that enhance automotive performance standards. The range of HP Lubes is comprehensive and catering to the minutest needs; from new generation cars to ploughing tractors and industrial machinery. The range conforms strictly to OEM specifications, often taking the initiative in customization of products. Retail Retail Offered:  Auto LPG  CNG  Power  Turbo Jet Trade The activities of IT&S relate to  Crude oil imports,  Petroleum Product Imports / Exports,  Shipping,  Production planning for Refineries,  Supplies for domestic Markets,  Product exchange with other Indian Oil Companies and Oil price risk management. E & P HPCL, in consortium with E&P partners companies currently has 19 nos. blocks in India, and 4 nos. overseas blocks in Oman, Australia and Egypt. HPCL intends to leverage and consolidate its current position and formulate & implement a strategy for E&P business based on opportunities both within and outside India. Currently HP E&P has presence in 4 countries including India and plans to expand its portfolio in other countries which is a main area of focus of its Strategic Investment plan mainly in Middle East, South East Asia & Africa. Ventures Till Date JV‘s:  HPCL-Mittal Energy Ltd. (HMEL)  Hindustan Colas (HINCOL)  Prize Petroleum Company Limited  South Asia LPG Co Pvt. Ltd. ( SALPG)  Bhagyanagar Gas Limited (BGL)  Aavantika Gas Limited  Petronet India Limited (PIL)  Petronet MHB Limited (PMHBL)  Mangalore Refineries and Petrochemicals Limited (MRPL)  CREDA-HPCL Biofuel Limited (CHBL)  Sushrut Hospital and Research Centre
  • 4. Bond Mathematics 4 HPCL financial analysis: Figure1.1 Ratios- 2009: Asset Ratios Total assets/equity 4,39 Total liabilities/equity 3.39 Total liabilities/total assets 0.77 Sales/total assets 3.04 Liquidity Ratios Quick ratio 2.03 Current ratio 2.87 Interest cover 1.47 65,218.8 3 76,920.2 6 96,918.1 5 112,098. 27 131,803 2005 2006 2007 2008 2009 sales (in crores) sales (in crores) 2,347.52 1113.36 3000.43 2557.35 4158.17 2005 2006 2007 2008 2009 PBDIT (in crores) adjusted PBDIT 1277.33 405.63 1571.17 1134.88 574.98 2005 2006 2007 2008 2009 PAT (in crores) reported net profit 0 50 100 150 200 250 300 350 DIVIDEND EPS BOOK VALUE
  • 5. Bond Mathematics 5 Turnover ratios Sales/inventory 12.96 Sales/receivables 20.26 Sales/working cap 7.91 Profitability ratios Operating margin 2.27 Pretax income margin 0.63 Return on equity 3.08 Return on fixed assets 2.05 Return on total assets 0.75 As per the sales seen, there is a constant increase in sales and volumes. The profit should also increase but there is a decline over last 2 years. This decrease is due to the negative results of stock adjustments in the P&L account, which says that HPCL‘s shares have been undervalued and the company was getting devalued. This can be clearly seen in the trend of EPS and the same is reflected in the net profits. Asset ratios show that total assets have 22.7% equity and 77.3% debt. The liabilities have been raised high against Rs.1 of equity i.e Rs.3.39, which is not a good sign. Sales/total assets is a good ratio of 3.04. HPCL is earning good sales out of this assets. Liquidity ratios of HPCL are good. The company has the ability to meet its short term debt obligations. It has very high short term solvency. There is a lot of liquidity in the company leading to opportunity costs. They can use this money in more investments. Interest cover ratio is quite fine and company earnings seem to be consistent. Turnover ratios show that sales inventory ratio is above 6.94 indicating excessive efficiency in sales performance. Similarly, sales receivable ratio of 20.26 signifies efficient debt management. However, considering the liquid nature of industry it operates, the ratio needs to be bought down below 15. Profitability ratios show that they are just touching margins.ROE should be around 12%. To improve their profits HPCL has to reduce its costs or has increase its volumes and sales or can increase its prices. But being a public company, it is not that easy to increases prices as they have to abide by the government policies and subsidiaries. Despite of these subsidy mechanisms, one can say that HPCL is gaining good profits. Growth ratios (2009) Net sales growth (%) 18.83 Core EBITDA growth (%) 37.22 EBIT growth (%) 47.02 PAT growth (%) -49.34 EPS growth (%) -49.34
  • 6. Bond Mathematics 6 Competitive analysis (2009): The competitor‘s in the public sector: IOCL, BPCL and MRPL. The competitor‘s in the private sector: RIL, CPCL The competitor‘s in the MNC are: Essar, BP The major competitors amongst these would be IOCL, BPCL and RIL Figure1.2 0 50000 100000 150000 200000 250000 300000 350000 HPCL IOCL RIL BPCL sales (in crores) sales (in crores) 0 5000 10000 15000 20000 25000 30000 HPCL IOCL RIL BPCL Adjusted PBDIT (in crores) Adjusted PBDIT (in crores) 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 HPCL IOCL RIL BPCL PAT (in crores) PAT (in crores) 0 200 400 600 800 1000 1200 HPCL IOCL RIL BPCL Stock price STOCK PRICE (June 2,2010)
  • 7. Bond Mathematics 7 Table1.2 Valuation Parameters HPCL IOCL RIL BPCL P/E 9.5 8.36 20.3 13.63 EV/NET SALES 0.25 0.29 2.08 0.25 EV/EBITDA 8.28 8.36 12.12 8.09 The above results clearly show that RIL is a big player and a tough competitor to HPCL. RIL market cap is high and all their valuation parameters are high, which indicates that to compete with RIL, HPCL‘s best adoption should be to expand its business and sales. IOCL is the next competitor to HPCL and BPCL is on same margins as HPCL, but all three companies are better in profits than HPCL. HPCL should adopt to better business plans and strategies to set a race with these companies. Threat of Intense segment rivalry: • Is witnessed in the holistic service offered by the retail outlet majors (IOCL,HPCL ,BPCL) If IOCL has Swagat outlets HPCL and BPCL has Club HP and Pure for Sure outlets. It is noted that most of these outlets have same facilities like Quality verification checks, Truck driver amenities etc, leading to intense segment rivalry. • However IOCL has the edge in terms of vast refining and distribution network, hence is the market leader. Threat of new entrants: • In the current INDIAN scenario, entry and exit barriers are high and profit potential is high. • But firms face more risk because poorer-performing firms stay in and fight it out. Like, IBP was facing bleak prospects till the time INDIAN OIL purchased it with a premium of over 60%. • Till the recent crude OIL spike, Reliance Retail petroleum, ESSAR OIL and SHELL gave a head-on clash (frontal attack in select locations) with OIL PSU‘s. • Adding to it newer plants come with better crude handling and therefore refinery margins are good, thus reflected in the net margins. Threat of Supplier’s growing bargaining power: • Petroleum is synonymous with OPEC cartel. • Big-wigs like Exxon-Mobil, Total, Occidental Petroleum, IOCL, and BPCL are not shielded from the vagaries of OPEC. • Though OPEC claims that it‘s the tax structure in the respective countries which makes petroleum products expensive, crude OIL price varies in in accordance with production levels of OPEC. • Today due to Global meltdown, Crude OIL prices are declining.
  • 8. Bond Mathematics 8 • But OPEC has already initiated significant production cuts whose effect might be felt in the forthcoming months. Threat of Substitute Products: • Is from cleaner and efficient fuels like Compressed Natural Gas (CNG), where it was implemented on a war-footing in Delhi to control emissions. • Central Government‘s encouragement in the form of Bio-fuel purchase policy for 5% bio- fuel blended Diesel fuel. • Electric car – Reva also poses a challenge to the existing players. Threat of buyer’s growing bargaining power: • ‗Consumer is always the king ‗– is apt in the case of petroleum products in India. • Consumer‘s interests‘ are protected by the Government by not raising the fuel prices beyond a limit and indirectly consumer is exercising his bargaining power. • Also all the OIL PSU‘s offer varied services to the consumer including intangible ones like frequent quality checks and tangible ones like amenities ATM , Car care etc which was not even a moot concept in the past
  • 9. Bond Mathematics 9 Oil industry Table1.3 Oil and Gas Exploration & Production The economic crisis left an impact on the oil and gas industry globally. The economic downturn that followed resulted in unprecedented demand destruction. The industry is on a path of recovery due to fiscal measures announced by various governments. The major deepwater basins of the world namely the East coast of India, Gulf of Mexico, Africa and Brazil continue to witness huge levels of activity and investment. The structural theme for investment in the sector remains valid. The world‘s insatiable need for reliable and affordable energy continues to grow unabated. This calls for substantial investments, access to resources and newer technologies to unlock resources from challenging locations. The International Energy Agency (IEA), in its World Energy Outlook 2009, estimates that by the year 2030, global energy demand is expected to increase by 49% from its current level. Oil and natural gas are expected to remain primary energy sources and are expected to meet 51% of the global demand. Increasing concern for climate change augurs well for natural gas as it is an environmentally benign fuel with carbon emissions far lower than other fossil fuels.
  • 10. Bond Mathematics 10 IEA estimates that the world requires investments to the tune of $ 11 trillion in the oil and gas sector over the next 20 years implying an annual investment of over $ 500 billion. FY 2009-10 was a year of steady growth. Oil prices rose from an average of $ 46/barrel (bbl) in January 2009 to touch $ 75/bbl in December 2009. Average WTI prices remained at $ 70/bbl vis-à-vis $86/bbl for the previous year. Henry Hub natural gas price averaged at $ 4/Million Metric British Thermal Unit (MMBTU) for FY 2009-10 as against an average of $ 7.87/MMBTU in FY 2008-09. The year 2009 also saw the global oil demand slip to 84.93 MBPD, a decrease of 1.5% over 2008. IEA forecasts that the global oil demand is set to increase by 1.67 MBPD or 2.0% to 86.60 MBPD in 2010. Figure1.3 Kirirt parekh recommendations on future oil prices An experts group, headed by former Planning Commission member Kirit Parikh, submitted its much awaited report on pricing policy for four major oil products, namely, petrol, diesel, kerosene and LPG. The committee has recommended that prices of petrol and diesel to be market-determined, both at the refinery gate and retail levels, whereas the prices of kerosene and domestic LPG can be partially raised by Rs 6 per litre and Rs 100 per cylinder respectively. For kerosene and LPG, the committee has recommended linking fuel prices with per capita income and selective allocations to poorer families through smart cards linked with unique identities (UID) project. 29.6% 7.9% 10.9% 5.3% 8.0% 1.8% 1.6% 0.1% 9.2% 25.5% Refinery crude throughput, 2006 IOCL BPCL HPCL KRL CPCL BRPL NRL ONGC MRPL RIL
  • 11. Bond Mathematics 11 The committee has accepted the subsidy formula proposed by Oil and Natural Gas Corporation (ONGC) aimed at reducing burden of oil companies. The formula suggests an incremental rate of taxes on higher crude oil price realization from the nomination blocks of ONGC and Oil India Ltd (OIL). The proposed subsidy sharing formula shall keep the government‘s subsidy contribution from budget in the range of Rs 19,780-23,340 crore at various crude price levels. A summary of recommendations and their impact has been provided in Annexure. According to D.R.Dogra, Managing Director & CEO , CARE Ltd. ― The impact on the oil and gas industry, if any of the recommendations by the committee is implemented, will be extremely positive‖. The complete deregulation of auto-fuels and sharp hikes in the prices of cooking fuels would help the government in reducing fiscal deficit and thus curtail its borrowings. The three public sector oil marketing companies, namely, Indian Oil Corporation, Bharat Petroleum Corporation Ltd and Hindustan Petroleum Corporation Ltd, would be able to reduce their under-recoveries considerably. However, the complete deregulation may prompt private players such as Reliance, Essar and Shell to re-open their retail fuel outlets, putting pressure on market share of public sector oil marketing companies (OMCs). In the past, the entry of private players in retail fuel market had resulted in an erosion of about 10 per cent in the market share of public sector OMCs. The proposed hike in prices of cooking fuels coupled with reduction in allocation of kerosene under the public distribution scheme (PDS) by 20 per cent would reduce under-recoveries by about Rs 16,454 crore, whereas, the auto-fuel deregulation would avert Rs 13,997 crore of under-recoveries. In the opinion of CARE Research, this is a landmark report, but implementation is the key. Although the report is in line with the wish-list of most of the market participants, implementation of the recommendations needs to be keenly watched for. ―The situation is tricky for the Government, as it needs to strike a balance between reducing the subsidy burden on the public sector oil and gas undertakings, reducing the fiscal deficit and managing the current inflationary scenario, given the economy being in the process of revival and attempting to restore its buoyancy‖ added Mr Dogra. It may be noted that similar kind of recommendations made by the Chaturvedi committee in 2008 were rejected by the government. Also, practicability of the selective allocations to poorer families through smart cards linked with UID project also needs to be evaluated by the government keeping in view the infrastructure requirement for the same. Although diesel is a major contributor to the total underrecoveries, its deregulation needs to be carefully evaluated as the agriculture sector (consuming 12 percent of diesel) and transport industry (consuming 40 per cent of diesel), the backbone of the Indian economy, are the major consumer of the fuel.
  • 13. Bond Mathematics 13 Conclusive report 2010 Looking at the financial results of the company for this year 2009-2010, company has recommended Rs 12 of dividend/share as against Rs 5.25 last year. The dividend/share has been increasing gradually which is a good significance for the shareholders. The sales/income from operations have been decreased from 136885.22 Cr in year 2008-2009 to 119453.33 Cr in year 2009-2010. The company‘s gross profits earned are 2564.29 Cr as against 2620.66 Cr. But the PAT has doubled from 757.39 Cr in 2008-2009 to 1475.15 Cr in year 2009-2010. The physical performance of market sales has increased from 25.39 million metric tonnes in 2008-2009 to 26.27 MMT in 2009-2010. The company‘s turnover has decreased from last year highest achieved turnover of 121510.39 Cr to 113163.38 Cr in this year. It is a matter of pride for the company to be ranked 311 amongst Global Fortune 500 Companies, 1002 amongst Forbes Global 2000 Companies and 111 in the list of World‘s Most Reputed Companies brought out by the Global Reputation Institute. HPCL aims to conduct our business with highest standards of corporate governance. HPCL has implemented the ―Right to Information Act (RTI)‖ in letter as well as spirit. HPCL has also implemented the Integrity Pact in liaison with ―Transparency International‖. The Integrity Pact forbids vendors from using any type of unwarranted influence for furthering their interests while in turn ensuring them fairness, transparency and equal opportunity in their association with the Corporation. 1. The Company is engaged in the following business segments: a) Downstream i.e. Refining and Marketing of Petroleum Products b) Exploration and Production of Hydrocarbons Segments have been identified taking into account the nature of activities and the nature of risks and returns. 2. Segment Revenue comprises of the following: a) Turnover (Net of Excise Duties) b) Subsidy from Government of India c) Other income (excluding interest income, dividend income and investment income) 3. There are no geographical segments.  Average Gross Refining Margins during the year ended March 2010, were US $ 2.68 per BBL as against US $ 3.97 per BBL during the corresponding previous year.  The prices of LPG (Domestic) and SKO (LPG) are subsidised as per the scheme approved by the Government of India. Subsidy amounting to Rs. 609.43 crores (2008-09 : Rs. 574.23 crores) for the year has been accounted at 1/3rd of the subsidy rates for 2002-03.  In principle approval of Government of India for Budgetary Support amounting to Rs. 5563.13 crores (2008-09 : Oil Bonds for Rs. 14,692.77 crores), has been received and the same have been accounted under ‗Recovery under Subsidy Schemes‘.  During the year, ONGC and GAIL offered discount amounting to Rs. 3247.14 crores (2008-09 : Rs. 7176.95 crores) on Crude Oil, SKO and LPG purchased from them.
  • 14. Bond Mathematics 14  During the current year, investments in ―6.35% Oil Marketing Companies' GOI Special Bonds 2024‖ amounting to Rs. 4603.73 crores have been reclassified from ‗Long Term Investments‘ to ‗Current Investments‘. Consequently, an amount of Rs. 756.88 crores has been provided in the books of accounts towards diminution in the value for this investment.  The employee cost for the year 2009-10 is higher due to provision made for Rs. 318.25 crores towards revision in the salary for non-management staff, and perquisites & retiral benefits for management employees. Overall the emerging global scenario and economic slowdown has influenced HPCL to greater extent. However consistent performance of the corporation and efficient management has managed to maintain the profitability of the corporation at sustained levels. HPCL still expects a wide road to be travelled towards achievement of its goal and target.
  • 15. Bond Mathematics 15 BOND MARKET IN INDIA The Bond Market in India with the liberalization has been transformed completely. The opening up of the financial market at present has influenced several foreign investors holding upto 30% of the financial in form of fixed income to invest in the bond market in India. The bond market in India has diversified to a large extent and that is a huge contributor to the stable growth of the economy. The bond market has immense potential in raising funds to support the infrastructural development undertaken by the government and expansion plans of the companies. Sometimes the unavailability of funds become one of the major problems for the large organization. The bond market in India plays an important role in fund raising for developmental ventures. Bonds are issued and sold to the public for funds. Bonds are interest bearing debt certificates. Bonds under the bond market in India may be issued by the large private organizations and government company. The bond market in India has huge opportunities for the market is still quite shallow. The equity market is more popular than the bond market in India. At present the bond market has emerged into an important financial sector. The government securities market has witnessed significant transformation in the 1990s in terms of market design. The most significant developments include introduction of auction- based price determination for government securities, development of new instruments and mechanisms for government borrowing as well as participation by new market participants, increase in information dissemination on market borrowings and secondary market transactions, screen based negotiations for trading, and the development of the yield curve for government securities for marking-to-market portfolios of banks. During the last one decade, RBI introduced the system of primary dealers (PDs) and satellite dealers (since discontinued from December 2002), introduced delivery versus payment (DvP) in securities settlement, expanded the number of players in the market with facility for non-competitive bidding in auctions, and allowed wider participation in constituent Subsidiary General Ledger (SGL) accounts. The government securities market also benefited from emergence of liquidity arrangement through the Liquidity Adjustment Facility (LAF), expansion of the repo markets, complete stoppage of automatic monetisation of deficits, and emergence of self regulatory bodies, such as, the Primary Dealers Association of India (PDAI) and the Fixed Income Money Markets and Derivatives Association (FIMMDA).Continuous reforms in the G- Sec market are being undertaken for improving market design and liquidity.
  • 16. Bond Mathematics 16 To enhance liquidity and efficiency, some important initiatives have been taken in the Indian debt market such as:  introduction of repo/reverse repo operations in government securities to facilitate  participants of manage short term liquidity mismatches  operationalisation of Negotiated Dealing system (NDS), an automated electronic trading platform  establishment of Clearing Corporation of India Ltd. (CCIL) for providing an efficient and guaranteed settlement platform  introduction of G-secs in stock exchanges  introduction of Real time Gross Settlement System (RTGS) which addresses settlement risk and facilitates liquidity management,  adoption of a modified Delivery-versus-Payment mode of settlement which provides for net settlement of both funds and securities legs and  Announcement of an indicative auction calendar for Treasury Bills and Dated Securities. Central government securities: bonds and t-bills The different types of bond market in India Primary market: •Issuance of securities through autions •Issuance of securities with pre-announced coupon bonds •Issuance of securities through tap sale •Issuance of securities in conversion of maturing treasury bills/dated securities Secondary markets: •Trading on stock exchanges: NSE, BSE, OTCEI •Most of the secondary market trades in government securities are negotiated between participants (Banks, FIs, PDs, MFs) having SGL accounts with RBI. These may be negotiated directly between counter parties or negotiated through brokers. NDS of RBI provides an electronic platform for negotiating trades in government securities. If a broker is involved, the trade is reported to the concerned exchange. Trades are also executed on electronic platform of the WDM segment of NSE. WDM segment of NSE provides trading and reporting facilities for government securities •Repo and reverse repo •Wholesale debt market •Retail debt market Corporate bond market Municipal bond market Governmen t & agency bond market Funding bond market Mortgage backed & collateral debt obligation bond market
  • 17. Bond Mathematics 17 Table 2.1 Market Segment Issuer Instruments Government securities Central Government Zero Coupon Bonds, Coupon Bearing Bonds, Treasury Bills, STRIPS State Governments Coupon Bearing Bonds Public sector bonds Government Agencies / Statutory Bodies Govt. Guaranteed Bonds, Debentures Public Sector Units PSU Bonds, Debentures, Commercial Paper Private sector bonds Corporates Debentures, Bonds, Commercial Paper, Floating Rate Bonds, Zero Coupon Bonds, Inter-Corporate Deposits Banks Certificates of Deposits, Debentures, Bonds Financial Institutions Certificates of Deposits, Bonds The major reforms in the bond market in India  The system of auction introduced to sell the government securities  The introduction of delivery versus payment (DvP) system by the Reserve Bank of India to nullify the risk of settlement in securities and assure the smooth functioning of the securities delivery and payment  The computerization of the SGL  The launch of innovative products such as capital indexed bonds and zero coupon bonds to attract more and more investors from the wider spectrum of the populace  Sophistication of the markets for bonds such as inflation indexed bonds  The development of the more and more primary dealers as creators of the Government of India bonds market  The establishment of the a powerful regulatory system called the trade for trade system by the Reserve Bank of India which stated that all deals are to be settled with bonds and funds  A new segment called the Wholesale Debt Market (WDM) was established at the NSE to report the trading volume of the Government of India bonds market  Issue of ad hoc treasury bills by the Government of India as a funding instrument was abolished with the introduction of the Ways And Means agreement
  • 18. Bond Mathematics 18 Participants and products in debt markets: Table 2.2 Issuer Instrument Maturity Investors Central government Dated securities 2-30 years RBI, Banks, Insurance companies, Provident Funds, Mutual Funds, Individuals, PDs Central government T-Bills 91/182/364 days RBI, Banks, Insurance companies, Provident Funds, Mutual Funds, Individuals, PDs State government Dated securities 5-13 years RBI, Banks, Insurance companies, Provident Funds, Mutual Funds, Individuals, PDs PSUs Bonds, Structured Obligations 5-10 years Banks, Insurance companies, Provident Funds, Mutual Funds, Individuals, Corporate Corporate Debentures 1-12 years Banks, Corporate, Mutual Funds Corporate, PDs Commercial paper 7 days to 1 year Banks, Corporate Financial institutions, Mutual funds, Individuals, FIIs Scheduled commercial banks Certificates of deposit (CDs) 7 days to 1 year Banks, Corporations, Individuals, companies, Trusts, Funds, Associations, FIs, NRIs Financial Institutions 1 year to 3 years Scheduled commercial banks Bank Bonds 1-10 years Corporations, Individual companies, Trusts, Funds, Associations, FIs, NRIs Municipal Corporation Municipal Bonds 0-7 years Banks, Corporations, Individuals, Companies, Trusts, Funds, Associations, FIs, NRIs Securities market and financial system The securities market has two interdependent and inseparable segments, the new issues (primary market) and the stock (secondary) market. Primary market The primary market provides the channel for sale of new securities from the actual issuers to the primary investors based on their perception of the bond instrument. Primary market provides opportunity to issuers of securities; government as well as corporates, to raise resources to meet their requirements of investment and/or discharge some obligation.
  • 19. Bond Mathematics 19 They may issue the securities at face value, or at a discount/premium and these securities may take a variety of forms such as equity, debt etc. They may issue the securities in domestic market and/or international market. The primary market issuance is done either through public issues or private placement. A public issue does not limit any entity in investing while in private placement, the issuance is done to select people. In terms of the Companies Act, 1956, an issue becomes public if it results in allotment to more than 50 persons. This means an issue resulting in allotment to less than 50 persons is private placement. There are two major types of issuers who issue securities. The corporate entities issue mainly debt and equity instruments (shares, debentures, etc.), while the governments (central and state governments) issue debt securities (dated securities, treasury bills). The price signals, which subsume all information about the issuer and his business including associated risk, generated in the secondary market, help the primary market in allocation of funds. Secondary market Secondary market refers to a market where securities are traded after being initially offered to the public in the primary market and/or listed on the Stock. The secondary market enables participants who hold securities to adjust their holdings in response to changes in their assessment of risk and return. They also sell securities for cash to meet their liquidity needs. The secondary market has further two components, namely the over-the-counter (OTC) market and the exchange-traded market. OTC is different from the market place provided by the Over The Counter Exchange of India Limited. OTC markets are essentially informal markets where trades are negotiated. Most of the trades in government securities are in the OTC market. All the spot trades where securities are traded for immediate delivery and payment take place in the OTC market. The exchanges do not provide facility for spot trades in a strict sense. Closest to spot market is the cash market where settlement takes place after some time. Trades taking place over a trading cycle, i.e. a day under rolling settlement, are settled together after a certain time (currently 2 working days). Trades executed on the leading exchange (National Stock Exchange of India Limited (NSE) are cleared and settled by a clearing corporation which provides novation and settlement guarantee. Nearly 100% of the trades settled by delivery are settled in demat form. NSE also provides a formal trading platform for trading of a wide range of debt securities including government securities. A variant of secondary market is the forward market, where securities are traded for future delivery and payment. Pure forward is outside the formal market. The versions of forward in formal market are futures and options. In futures market, standardised securities are traded for future delivery and settlement. These futures can be on a basket of securities like an index or an individual security. In case of options, securities are traded for conditional future delivery. There are two types of options–a put option permits the owner to sell a security to the writer of options at a predetermined price while a call option permits the owner to purchase a security from the writer of the option at a predetermined price. These options can also be on individual stocks or basket of stocks like index. Two exchanges, namely NSE and the Bombay Stock Exchange, (BSE) provide trading of derivatives of securities. The past few years in many ways have been remarkable for securities market in India. It has grown exponentially as measured in terms of amount raised from the market, number of stock exchanges and other intermediaries, the number of listed stocks, market capitalisation, trading volumes and turnover on stock exchanges, and investor population. Along with this growth, the profiles of the investors, issuers and intermediaries
  • 20. Bond Mathematics 20 have change significantly. The market has witnessed fundamental institutional changes resulting in drastic reduction in transaction costs and significant improvements in efficiency, transparency and safety. Reforms in the securities market, particularly the establishment and empowerment of SEBI, market determined allocation of resources, screen based nation-wide trading, dematerialisation and electronic transfer of securities, rolling settlement and ban on deferral products, sophisticated risk management and derivatives trading, have greatly improved the regulatory framework and efficiency of trading and settlement. Indian market is now comparable to many developed markets in terms of a number of qualitative parameters. Securities market & economic development Three main sets of entities depend on securities market. While the corporate and governments raise resources from the securities market to meet their obligations, the households invest their savings in the securities. Corporate Sector: The 1990s witnessed emergence of the securities market as a major source of finance for trade and industry. A growing number of companies are accessing the securities market rather than depending on loans from FIs/banks. The corporate sector is increasingly depending on external sources for meeting its funding requirements. There appears to be growing preference for direct financing (equity and debt) to indirect financing (bank loan) within the external sources. The listing agreements have been amended recently requiring the companies to disclose shareholding pattern on a quarterly basis. As per the shareholding pattern of companies listed on NSE at end of March 2008, it is observed that on an average the promoters hold about 56.12% of total shares. Though the non-promoter holding is about 41.91%, Individuals held only 13.07% and the institutional holding (FIIs, MFs, VCFs-Indian and Foreign) accounted for 19.37%. Governments: Along with increase in fiscal deficits of the governments, the dependence on market borrowings to finance fiscal deficits has increased over the years. During the year 1990-91, the state governments and the central government financed nearly 14% and 18% respectively of their fiscal deficit by market borrowing. In percentage terms, depend ence of the state governments on market borrowing did not increase much during the decade 1991-2001. However, their dependence on market borrowing has been increasing since then to reach 38% during 2003-04. In case of central government, it increased to 73% by 2007-08, The central government and the state governments now-a-days finance about three fourth and one fourth of their fiscal deficits respectively through borrowings from the securities market. Households: According to RBI data, household sector accounted for 84.8% of gross domestic savings in Fixed Income Investment instruments during 2006-07. They invested 55.7% of financial savings in deposits, 24.2 % in insurance/provident funds, and 6.5% in securities market including government securities, units of mutual funds and other securities (out of which investment in Gilts has been 0.2%). Thus, the fixed income bearing instruments are the most preferred assets of the household sector.
  • 21. Bond Mathematics 21 Trading platforms for bonds NSE National Stock Exchange of India Limited (NSE) was given recognition as a stock exchange in April 1993. Objectives:  establishing a nationwide trading facility for all types of securities,  ensuring equal access to all investors all over the country through an appropriate communication network,  providing a fair, efficient and transparent securities market using electronic trading system,  enabling shorter settlement cycles and book entry settlements, and  Meeting the international benchmarks and standards. Within a short span of life, above objectives have been realized and the Exchange has played a leading role as a change agent in transforming the Indian Capital Markets to its present form. NSE has set up infrastructure that serves as a role model for the securities industry in terms of trading systems, clearing and settlement practices and procedures. The standards set by NSE in terms of market practices, products, technology and service standards have become industry benchmarks and are being replicated by other market participants. It provides screen-based automated trading system with a high degree of transparency and equal access to investors irrespective of l;geographical location. The high level of information dissemination through on-line system has helped in integrating retail investors on a nation- wide basis. The Exchange currently operates three market segments, namely Capital Market Segment, Wholesale Debt Market Segment and Futures and Options segment. NSE has been playing the role of a catalytic agent in reforming the market in terms of microstructure and market practices. Right from its inception, the exchange has adopted the purest form of demutualised set up whereby the ownership, management and trading rights are in the hands of three different sets of people. This has completely eliminated any conflict of interest and helped NSE to aggressively pursue policies and practices within a public interest framework. It has helped in shifting the trading platform from the trading hall in the premises of the exchange to the computer terminals at the premises of the trading members located country- wide and subsequently to the personal computers in the homes of investors and even to hand held portable devices for the mobile investors. Settlement risks have been eliminated with NSE‘s innovative endeavors in the area of clearing and settlement viz., reduction of settlement cycle, professionalisation of the trading members, fine-tuned risk management system, dematerialisation and electronic transfer of securities and establishment of clearing corporation. As a consequence, the market today uses the state-of-art information technology to provide an efficient and transparent trading, clearing and settlement mechanism. NSE provides a trading platform for of all types of securities-equity and debt, corporate and government and derivatives. On its recognition as a stock exchange under the Securities Contracts (Regulation) Act, 1956 in April 1993, it commenced operations in the Wholesale Debt Market (WDM) segment in June 1994, in the Capital Market (CM) segment
  • 22. Bond Mathematics 22 in November 1994, and in Futures & Options (F&O) segment in June 2000. The Exchange started providing trading in retail debt of Government Securities in January 2003. NDS The first step towards electronic bond trading in India was the introduction of the RBIs Negotiated Dealing System in February 2002. NDS, facilitates screen based negotiated dealing for secondary market transactions in government securities and money market instruments, online reporting of transactions in the instruments available on the NDS and dissemination of trade information to the market. Government Securities (including T-bills), call money, notice/term money, repos in eligible securities are available for negotiated dealing through NDS among the members. NDS members concluding deals, in the telephone market in instruments available on NDS, are required to report the deal on NDS system within 15 minutes of concluding the deal. NDS interfaces with CCIL for settlement of government securities transactions for both outright and repo trades done/reported by NDS members. Other instruments viz, call money, notice/term money, commercial paper and certificate of deposits settle as per existing settlement procedure. Table 2.3
  • 23. Bond Mathematics 23 With the objective of creating a broad-based and transparent market in government securities and thereby enhancing liquidity in the system, the NDS was designed to provide:  Electronic bidding in primary market auctions (T-Bills, dated securities, state government securities) by members,  Electronic bidding for OMO of RBI including repo auctions under LAF,  Screen based negotiated dealing system for secondary market operations,  Reporting of deals in government securities done among NDS members outside the system (over telephone or using brokers of exchanges) for settlement,  Dissemination of trade information to NDS members,  Countrywide access of NDS through INFINET,  Electronic connectivity for settlement of trades in secondary market both for outright and repos either through CCIL or directly through RBI, and Creation and maintenance of basic data of instruments and members. The functional scope of the NDS relating to trading includes:  giving/receiving a Quote,  placing a call and negotiation (with or without a reference to the quote),  entering the deals successfully negotiated, setting up preferred counterparty list and exposure limits to the counterparties,  dissemination of on-line market information such as the last traded prices of securities, volume of transactions, yield curve and information on live quotes,  interface with Securities Settlement System for facilitating settlement of deals done in government securities and treasury bills  Facility for reporting on trades executed through the exchanges for information dissemination and settlement in addition to deals done through NDS. Figure 2.1 0 20 40 60 80 100 Aug/06 Nov/06 Feb/07 May/07 Aug/07 Nov/07 Feb/08 May/08 Aug/08 Nov/08 Feb/09 share of NDS call in total call volumes (%) share of NDS call in total call volumes (%)
  • 24. Bond Mathematics 24 Repo and reverse repo Repo or Repurchase Agreements are short-term money market instruments. Repo is nothing but collateralized borrowing and lending through sale/purchase operations in debt instruments. Under a repo transaction, a holder of securities sells them to an investor with an agreement to repurchase at a predetermined date and rate. In a typical repo transaction, the counterparties agree to exchange securities and cash, with a simultaneous agreement to reverse the transactions after a given period. To the lender of cash, the securities lent by the borrower serves as the collateral; to the lender of securities, the cash borrowed by the lender serves as the collateral. Repo thus represents a collateralized short term lending. A reverse repo is the mirror image of a repo. Banks and dealers use repos to finance inventories, to cover short positions, to create leverage and to hedge or to speculate on interest rate movements. Investors such as mutual funds, pension funds, insurance companies and corporate treasurers use repo markets to invest surplus cash, to earn incremental returns on their portfolios or to raise cash for investments. There are three types of repo, each with different costs and benefits that are reflected in the repo rate and the haircut: Figure 2.2 •the collateral is held on the balance sheet of the cash provider, granting immediate access in the event of default on the loan. Bilateral repo: •an agent stands between the security lender and cash provider and physically controls the securities offered as collateral. Triparty repo: •the security lender continues to hold the bond on their own balance sheet in a segregated account, raising the risk to the cash provider. Hold-in-custody repo: share in money market trading volumes, 2009 repo volume call volume CBLO volume Call: Market in which brokers and dealers borrow money to satisfy their credit needs, either to finance their own inventory of securities or to cover their customers' margin accounts. CBLO: A money market instrument that represents an obligation between a borrower and a lender as to the terms and conditions of the loan. Collateralized borrowing and lending obligations (CBLOs) are used by those who have been phased out of or heavily restricted in the interbank call money market. Repo: For the party selling the security (and agreeing to repurchase it in the future) it is a repo; for the party on the other end of the transaction, (buying the security and agreeing to sell in the future) it is a reverse repurchase agreement.
  • 25. Bond Mathematics 25 Wholesale Debt Market NSE accounts for nearly 70 % of the market share in capital market and 98 % market share in the derivatives market. The Wholesale Debt Market segment provides the trading platform for trading of a wide range of debt securities. Its product, which is now disseminated jointly with FIMMDA, the FIMMDA NSE MIBID/MIBOR is used as a benchmark rate for majority of deals struck for Interest Rate Swaps, Forwards Rate Agreements, Floating Rate Debentures and Term Deposits in the country. Its ‗Zero Coupon Yield Curve‘ as well as NSE-VaR for Fixed Income Securities have also become very popular for valuation of sovereign securities across all maturities irrespective of its liquidity and facilitated the pricing of corporate papers and GOI Bond Index. Figure 2.3 NSEs Capital Market segment offers a fully automated screen based trading system, known as the National Exchange for Automated Trading (NEAT) system, which operates on a strict price/time priority. It enables members from across the country to trade simultaneously with enormous ease and efficiency. Its Futures & Options segment provides trading of a wide range of derivatives like Index Futures, Index Options, Stock Options and Stock Futures. The Wholesale Debt Market segment deals in fixed income securities and is fast gaining ground in an environment that has largely focussed on equities. The Wholesale Debt Market (WDM) segment of the Exchange commenced operations on June 30, 1994. This provided the first formal screen-based trading facility for the debt market in the country. This segment provides trading facilities for a variety of debt instruments including Government Securities, Treasury Bills and Bonds issued by Public Sector Undertakings/ Corporates/ Banks like Floating Rate Bonds, Zero Coupon Bonds, Commercial Papers, Certificate of Deposits, Corporate Debentures, State Government loans, SLR and Non-SLR Bonds issued by Financial Institutions, Units of Mutual Funds and Securitized debt by banks, financial institutions, corporate bodies, trusts and others. Large investors and a high average trade value characterize this segment. Till recently, the market was purely an informal market with most of the trades directly negotiated and struck between various participants. The commencement of this segment by NSE has brought about transparency and efficiency to the debt market, along with effective monitoring and surveillance to the market.
  • 26. Bond Mathematics 26 Retail Debt Market Netting factor (%) Figure 2.4 With a view to encouraging wider participation of all classes of investors across the country (including retail investors) in government securities, the Government, RBI and SEBI have introduced trading in government securities for retail investors. Trading in this retail debt market segment (RDM) on NSE has been introduced w.e.f. January 16, 2003. Main participants in the retail debt market include mutual funds, provident funds, pension funds, private trusts, state-level and district-level co-operative banks, housing finance companies, NBFCs and RNBCs, corporate treasuries, Hindu Undivided Families (HUFs), and individual investors. The reasons why the retail debt market boomed were: 1995-96 saw the worst ever liquidity crunch. The stock market plunged to its nadir, financial institutions were unable to disburse sanctioned amounts, and the GDR route failed to bring in enough funds. To raise money, industry needed a new instrument. It found one in retail debt. The old retail finance culture tilted towards equity is poised to give way to a more equitable debt-equity ratio dictated by financial prudence and market forces. Conclusion: The securities markets in India have witnessed several policy initiatives, which have refined the market micro-structure, modernised operations and broadened investment choices for the investors. The irregularities in the securities transactions in the last quarter of 2000-01, hastened the introduction and implementation of several reforms. While a Joint Parliamentary Committee was constituted to go into the irregularities and manipulations in all their ramifications in all transactions relating to securities, decisions were taken to complete the process of demutualisation and corporatisation of stock exchanges to separate ownership, funds (%) 0 20 40 60 80 100 funds (%) securities (%)
  • 27. Bond Mathematics 27 management and trading rights on stock exchanges and to effect legislative changes for investor protection, and to enhance the effectiveness of SEBI as the capital market regulator. T+5 basis: introduced from July 2, 2001 T+3 basis: introduced from April 1, 2002 T+2 basis: introduced from April 1, 2003 All deferral products: banned from july2, 2002 1381 companies listed at NSE: March 2008 Derivative trading at NSE: June 12, 2000 Trading in index options: June 4, 2001 Trading in individual securities: July 2, 2001 Short term S&P CNX Nifty were introduced: January, 2008 long term S&P CNX Nifty were introduced: March 3, 2008 Due to rapid changes in volatility in the securities market from time to time, there was a need felt for a measure of market volatility in the form of an index that would help the market participants. NSE launched the India VIX, a volatility index based on the S&P CNX Nifty Index Option prices. Volatility Index is a measure of market‘s expectation of volatility over the near term. SEBI allowed the direct market access (DMA): April 3, 2008. Short sell and the facility for securities lending and borrowing scheme: April 21, 2008. The Debt markets in India have also witnessed a series of reforms, beginning in the year 2001-02 which was quite eventful for debt markets in India, with implementation of several important decisions like setting up of a clearing corporation for government securities, a negotiated dealing system to facilitate transparent electronic bidding in auctions and secondary market transactions on a real time basis and dematerialisation of debt instruments. Further, Adoption of modified Delivery-versus-Payment mode of settlement: March 2004 Securities was standardized to T+1 cycle: May 11, 2005 Order matching trading platform (NDS-OM) was introduced: August 2005 Short sale was permitted in G-secs: 2006 ‗When issued‘ (WI) trading in Central Government Securities was introduced: 2006 Ensures safe settlement with Straight through Processing (STP)
  • 28. Bond Mathematics 28 Bond basic concepts Features:  Nominal, principal or face amount — the amount on which the issuer pays interest, and which, most commonly, has to be repaid at the end. Some structured bonds can have a redemption amount which is different to the face amount and can be linked to performance of particular assets such as a stock or commodity index, foreign exchange rate or a fund. This can result in an investor receiving less or more than his original investment at maturity.  Issue price — the price at which investors buy the bonds when they are first issued, which will typically be approximately equal to the nominal amount. The net proceeds that the issuer receives are thus the issue price, less issuance fees.  Maturity date — the date on which the issuer has to repay the nominal amount. As long as all payments have been made, the issuer has no more obligation to the bond holders after the maturity date. The length of time until the maturity date is often referred to as the term or tenor or maturity of a bond. The maturity can be any length of time, although debt securities with a term of less than one year are generally designated money market instruments rather than bonds. Most bonds have a term of up to thirty years. Some bonds have been issued with maturities of up to one hundred years, and some even do not mature at all. In early 2005, a market developed in euros for bonds with a maturity of fifty years. In the market for U.S. Treasury securities, there are three groups of bond maturities: o short term (bills): maturities up to one year; o medium term (notes): maturities between one and ten years; o long term (bonds): maturities greater than ten years.  Coupon — the interest rate that the issuer pays to the bond holders. Usually this rate is fixed throughout the life of the bond. It can also vary with a money market index, such as LIBOR, or it can be even more exotic. The name coupon originates from the fact that in the past, physical bonds were issued which had coupons attached to them. On coupon dates the bond holder would give the coupon to a bank in exchange for the interest payment. • Tax free bonds – public sector companies in India are sometimes permitted to issue bonds with tax- free interest. In this case bond- holder pays no tax on the interest • Trustee – when a debenture issue is made, a trustee is appointed (usually an FI / bank). The trustee is responsible to ensure that the company fulfils its contractual obligations • Trust (bond) indenture or Debenture trust deed – a complex and lengthy legal agreement between the company and the debenture trustee, stating the conditions under which a bond has been issued, rights of debenture holders, rights of the issuing company, and responsibilities of the trustee.
  • 29. Bond Mathematics 29 • Debenture Redemption Reserve (DRR) – has to be created for the redemption of all debentures with a maturity period exceeding 18 months. The DRR must be equal to atleast 50% of the amount of redemption Table 3.1 Kinds of bonds: The following descriptions are not mutually exclusive, and more than one of them may apply to a particular bond.  Zero-coupon bonds pay no regular interest. They are issued at a substantial discount to par value, so that the interest is effectively rolled up to maturity (and usually taxed as such). The bondholder receives the full principal amount on the redemption date. An example of zero coupon bonds is Series E savings bonds issued by the U.S. government. Zero-coupon bonds may be created from fixed rate bonds by a financial institution separating "stripping off" the coupons from the principal. In other words, MODIFIABLE INTOPARAMETERSCLASSIFICATION BONDS coupon zero coupon treasury strips floating rate bonds other variations maturity callable bonds puttable bonds convertible bonds principal amortising sinking fund asset based securities
  • 30. Bond Mathematics 30 the separated coupons and the final principal payment of the bond may be traded separately. See IO (Interest Only) and PO (Principal Only).  Strip bonds - Zero coupon bonds have a duration equal to the bond's time to maturity, which makes them sensitive to any changes in the interest rates. Investment banks or dealers may separate coupons from the principal of coupon bonds, which is known as the residue, so that different investors may receive the principal and each of the coupon payments. This creates a supply of new zero coupon bonds. The coupons and residue are sold separately to investors. Each of these investments then pays a single lump sum. This method of creating zero coupon bonds is known as stripping and the contracts are known as strip bonds. "STRIPS" stands for Separate Trading of Registered Interest and Principal Securities.  Fixed rate bonds have a coupon that remains constant throughout the life of the bond.  Floating rate notes (FRNs) have a variable coupon that is linked to a reference rate of interest, such as LIBOR or Euribor. For example the coupon may be defined as three month USD LIBOR + 0.20%. The coupon rate is recalculated periodically, typically every one or three months.  Inflation linked bonds in which the principal amount and the interest payments are indexed to inflation. The interest rate is normally lower than for fixed rate bonds with a comparable maturity. However, as the principal amount grows, the payments increase with inflation. The United Kingdom was the first sovereign issuer to issue inflation linked Gilts in the 1980s. Treasury Inflation-Protected Securities (TIPS) and I-bonds are examples of inflation linked bonds issued by the U.S. government.  Other indexed bonds, for example equity-linked notes and bonds indexed on a business indicator (income, added value) or on a country's GDP.  Callable bonds: A bond which the issuer has the right to redeem prior to its maturity date, under certain conditions. When issued, the bond will explain when it can be redeemed and what the price will be. In most cases, the price will be slightly above the par value for the bond and will increase the earlier the bond is called. A company will often call a bond if it is paying a higher coupon than the current market interest rates. Basically, the company can reissue the same bonds at a lower interest rate, saving them some amount on all the coupon payments; this process is called "refunding." Unfortunately, these are also the same circumstances in which the bonds have the highest price; interest rates have decreased since the bonds were issued, increasing the price. In many cases, the company will have the right to call the bonds at a lower price than the market price. If a bond is called, the bondholder will be notified by mail and have no choice in the matter. The bond will stop paying interest shortly after the bond is called, so there is no reason to hold on to it. Companies also typically advertise in major financial publications to notify bondholders. Generally, callable bonds will carry something called call protection. This means that there is some period of time during which the bond cannot be called. It is also called redeemable bond, opposite of irredeemable bond or non-callable bond.
  • 31. Bond Mathematics 31  Puttable bond or put bond is a combination of straight bond and embedded put option. The holder of the puttable bond has the right, but not the obligation, to demand early repayment of the principal. The put option is usually exercisable on specified dates. This type of bond protects investors: if interest rates rise after bond purchase, the future value of coupon payments will become less valuable. Therefore, investors sell bonds back to the issuer and may lend proceeds elsewhere at a higher rate. Bondholders are ready to pay for such protection by accepting a lower yield relative to that of a straight bond. Of course, if an issuer has a severe liquidity crisis, it may be incapable of paying for the bonds when the investors wish. The investors also cannot sell back the bond at any time, rather specified dates. However, they would still be ahead of holders of non- puttable bonds, who may have no more right than 'timely payment of interest and principal' (which could perhaps be many years to get all their money back). The price behaviour of puttable bonds is the opposite of that of a callable bond. Since call option and put option are not mutually exclusive, a bond may have both options embedded.  A debenture in corporate finance is a medium- to long-term debt instrument used by large companies to borrow money. In some countries the term is used interchangeably with bond, loan stock or note. Debentures are generally freely transferable by the debenture holder. Debenture holders have no voting rights and the interest paid to them is a charge against profit in the company's financial statements. In the United States, debenture refers specifically to an unsecured corporate bond. However, in the United Kingdom a debenture is usually secured. In Asia, if repayment is secured by a charge over land, the loan document is called a mortgage; where repayment is secured by a charge against other assets of the company, the document is called a debenture; and where no security is involved, the document is called a note or 'unsecured deposit note'. Types: 1. Convertible debentures, which are convertible bonds or bonds that can be converted into equity shares of the issuing company after a predetermined period of time. "Convertibility" is a feature that corporations may add to the bonds they issue to make them more attractive to buyers. In other words, it is a special feature that a corporate bond may carry. As a result of the advantage a buyer gets from the ability to convert; convertible bonds typically have lower interest rates than non-convertible corporate bonds. 2. Non-convertible debentures, which are simply regular debentures, cannot be converted into equity shares of the liable company. They are debentures without the convertibility feature attached to them. As a result, they usually carry higher interest rates than their convertible counterparts. Call and Put Provision – provides an option to the issuing company to redeem the debentures at a specified price before maturity. Call price may be more than the par / face value, and this difference is called the Call Premium (In India, generally 5%). Put
  • 32. Bond Mathematics 32 option is an option to the debenture holder to seek redemption at a specified time at a specified price  Sinking fund provision is just a pool of money set aside by a corporation to help repay a bond issue. Typically, bond agreements (called indentures) require a company to make periodic interest payments to bondholders throughout the life of the bond, and then repay the principal amount of the bond at the end of the bond's lifespan.  Amortising: Charges made against the interest received on a debt in order to offset a premium paid for the debt. Thus, with each periodic payment, a debtor is not only paying back interest, but also part of his or her premium. This leads to higher periodic payments than in the case when only interest is paid out. However, a payment schedule which includes premium amortization makes debt management easier, especially if the principal is large. While paying just the interest each period will lead to a low outflow of cash each month, the debtor might not save enough to pay the principal. Thus, amortizing the premium each period also reduces the credit risk of the debt, since the creditor gets some part of the principal each time period, as opposed to allowing a debtor to forfeit on all of it at the maturity of the loan. Amortization of premium is a common feature in cases when a person or company takes on a large amount of debt at one time, such as a mortgage.  Asset-backed securities are bonds whose interest and principal payments are backed by underlying cash flows from other assets. Examples of asset-backed securities are mortgage-backed securities (MBS's), collateralized mortgage obligations (CMOs) and collateralized debt obligations (CDOs).  Subordinated bonds are those that have a lower priority than other bonds of the issuer in case of liquidation. In case of bankruptcy, there is a hierarchy of creditors. First the liquidator is paid, then government taxes, etc. The first bond holders in line to be paid are those holding what is called senior bonds. After they have been paid, the subordinated bond holders are paid. As a result, the risk is higher. Therefore, subordinated bonds usually have a lower credit rating than senior bonds. The main examples of subordinated bonds can be found in bonds issued by banks, and asset- backed securities. The latter are often issued in tranches. The senior tranches get paid back first, the subordinated tranches later.  Perpetual bonds are also often called perpetuities or 'Perps'. They have no maturity date. The most famous of these are the UK Consols, which are also known as Treasury Annuities or Undated Treasuries. Some of these were issued back in 1888 and still trade today, although the amounts are now insignificant. Some ultra-long- term bonds (sometimes a bond can last centuries: West Shore Railroad issued a bond which matures in 2361 (i.e. 24th century)) are virtually perpetuities from a financial point of view, with the current value of principal near zero.  Successive bonds are those where sureties are discharged and new sureties are taken, the two sets of sureties become jointly liable for a breach of the bond which accrued before discharge, and the right of contribution exists as between co-sureties. The new bond relates back, and the two sets of sureties are jointly liable for a breach committed prior to the second execution.
  • 33. Bond Mathematics 33 Pricing factors Interest rates change over time, based on a variety of factors, particularly base rates set by central bank. If the coupon on the bond is lower than the prevailing interest rate, then this pushes the price down, and conversely, high interest rates reduce the attractiveness of a given coupon, and so reduce the price. In buying a bond, one is in effect buying a set of cash flows, which are discounted according to the buyers perception of how interest and exchange rates will move over its life. Price determination in the debt markets The price of a bond in the markets is determined by the forces of demand and supply, as is the case in any market. The price of a bond also depends on the changes in:  Economic conditions  General money market conditions, including the state of money supply in the economy  Interest rates prevalent in the market and the rates of new issues  Future Interest Rate Expectations  Credit quality of the issuer Note: There is, however, a theoretical underpinning to the determination of the price of the bond based on the measure of the yield of the security. Supply and demand affect prices, especially in the case of market participants which are constrained in the set of investments they make. Insurance companies often have long term liabilities that they wish to hedge, which requires low risk, predictable cash flows, such as long dated government bonds. Bond pricing The cash flow of a fixed income product generally consists of several coupon payments over the period of the bond's life, and repayment of the principal at the time of maturity. Since these cash flows occur at several times in the future, the "Time Value of Money" approach is used to find the "Present Value" of each cash flow. The sum of all the present values of the bonds cash inflows of the bond is its theoretical value. Price–Discounted present value of debt service on an individual maturity. Debt service is calculated using the coupon and discounted at the yield. As a result, price and yield move in opposite directions.
  • 34. Bond Mathematics 34 • Yield – two types: – Current yield: ratio of the annual interest payment to the CMP eg. If the market price of a 12% Rs 1000 FV debenture is Rs 750, then current yield is 120/750 ie. 16% – Yield to Maturity: takes into account the payments of interest and principal over the life of the debenture. So it is the internal rate of return of the debenture Par bonds:  Coupon equals yield  Purchase price equals principal amount Discount bonds:  Coupon less than yield  Purchase price less than principal amount Premium bonds:  Coupon greater than yield  Purchase price greater than principal amount
  • 35. Bond Mathematics 35 Pricing a bond The price of a bond is the present value of its expected cash flow(s). The present value will be lower than the future value, as holding Rs100 next week is worth less than holding Rs100 now. There are a number of possible reasons for this: If inflation is high, the value will have eroded by the following week; if it remains in another person‘s possession for a further week, there is a potential credit risk; and there is no opportunity to invest the money until the following week, and therefore any potential return is delayed. The arithmetic assumes no credit risk or other (e.g. liquidity, tax) effects. It calculates the price of a risk-free bond, and therefore would need to be adjusted for other factors. Single Cash Flow Calculating the future value of an investment: - Starting from the simplest example, investing Rs100 for one period at 8% would give the following return: Return = 100 (1 + 8/100) = Rs108 In other words:- FV = PV (1 + r) where FV is the future value (i.e. cash flow expected in the future) PV is the present value r is the rate of return Assuming the same rate of return, if the investment is made for two periods, then:- FV = 100 (1 + 8/100)(1 + 8/100) In other words:- FV = PV (1 + r)2 And in general: FV = PV (1 + r)n where n is the number of periods invested, at a rate of return, r.If we want to calculate the price (i.e present value) of a bond as a function of its future value, we can rearrange this equation:- P = F/ (1+ r)n where P is the price of the bond and is the same as the ‗present value‘. The future value is the expected cash flow i.e. the payment at redemption n periods ahead. Discount Rate r is also referred to as the discount rate, i.e the rate of discount applied to the future payment in order to ascertain the current price. 1/ (1+ r)n is the value of the discount function at period n. Multiplying the discount function at period n by the cash flow expected at period n gives the value of the cash flow today. Relationship between discount rate and coupon rate: Discount rate less than the coupon rate implies that the security is traded at a premium. Discount rate greater than the coupon
  • 36. Bond Mathematics 36 rate implies that the security is traded at a discount. Discount rate equal to the coupon rate implies that the security is traded at a par. Multiple Cash Flow In practice, most bonds have more than one cash flow and therefore each cash flow needs to be discounted in order to find the present value (current price). This can be seen with another simple example - a conventional bond, paying an annual coupon and the face value at maturity. The price at issue is given as follows: Where P = ‗dirty price‘ c = annual coupon r i = % rate of return which is used in the ith period to discount the cash flow (in this example, each period is one year) R = redemption payment at time n The above example shows that a different discount rate is used for each period (r r etc 1, 2, ). Whilst this seems sensible, the more common practice in bond markets is to discount using a redemption yield and discount all cash flows using this rate. In theory, each investor will have a slightly different view of the rate of return required, as the opportunity cost of not holding money now will be different, as will their views on, for example, future inflation, appetite for risk, nature of liabilities, investment time horizon etc. The required yield should, therefore, reflect these considerations. In practice, investors will determine what they consider to be a fair yield for their own circumstances. They can then compute the corresponding price and compare this to the market price before deciding whether – and how much – to buy or sell. Pricing a bond with a semi annual coupon follows the same principles as that of an annual coupon. A ten year bond with semi annual coupons will have 20 periods (each of six months maturity); and the price equation will be: where c = coupon y = Redemption Yield (in % on an annualised basis) In general, the bond maths notation for expressing the price of a bond is given by:- Where PV ( cf t) is the present value of the cash flow at time t
  • 37. Bond Mathematics 37 Dirty prices and clean prices When a bond is bought or sold midway through a coupon period, a certain amount of coupon interest will have accrued. The coupon payment is always received by the person holding the bond at the time of the coupon payment (as the bond will then be registered in his name). Because he may not have held the bond throughout the coupon period, he will need to pay the previous holder some ‗compensation‘ for the amount of interest which accrued during his ownership. In order to calculate the accrued interest, we need to know the number of days in the accrued interest period, the number of days in the coupon period, and the money amount of the coupon payment. In most bond markets, accrued interest is calculated on the following basis:- Coupon interest x no. of days that have passed in coupon period total no of days in the coupon period Prices in the market are usually quoted on a clean basis (i.e. without accrued) but settled on a dirty basis (i.e. with accrued). Relationship between price and yield There is a direct relationship between the price of a bond and its yield. The price is the amount the investor will pay for the future cash flows; the yield is a measure of return o n those future cash flows. Hence price will change in the opposite direction to the change in the required yield. There are a number of different formulae for the relationship between price and yield. Looking at the price-yield relationship of a standard i.e. non-callable bond, the shape such as below is seen: Figure 3.1 As the required yield increases, the factor by which future cash flows are discounted also increases and therefore the present value of the cash flow decreases. Hence the price decreases as yield increases.
  • 38. Bond Mathematics 38 Money market yields Money market yields are quoted on a different basis and therefore in order to compare short- term bonds and money market instruments it is necessary to look at them on a comparable basis. Uses of Yield Curves and Yield Curve Theories A yield curve is a graphical representation of the term structure of yields for a given market. It attempts to show, for a set of bonds that have differing maturities but otherwise similar characteristics, how the yield on a bond varies with its maturity. Yield curves are therefore constructed from (as far as possible) a homogeneous group of bonds: we would not construct a yield curve using both government and corporate securities, given the different categories of risk. Yield curves are used for a number of different purposes. For example, government securities‘ yield curves demonstrate the tightness (and expected tightness) of monetary policy; allow cross-country comparisons; assist pricing of new issues; assess relative value between bonds; allow one to derive implied forward rates; and help traders/investors understand risk. As there are a number of different types of yield curve that can be constructed, different ones are used for different purposes. There are various theories of the yield curve, which attempt to explain the shape of the curve, depending on, inter alia, investors‘ preferences/views: Preferred Habitat (again investors have a maturity preference, but will shift from their preferred maturity if the increase in yield is deemed sufficient compensation to do so). These are all demand-based; supply-based factors include government policy (fiscal position, views on risk, views on optimal portfolio etc). • risk premia increase with time so, other things being equal, one would expect to see a rising yield curve Liquidity Preference Theory • forward rates govern the curve - these are simply expectations of future spot rates and do not take into account risk premia Pure Expectations Hypothesis • the yield curve depends on supply and demand in different sectors and each sector of the yield curve is only loosely connected to others Segmented Markets Hypothesis
  • 39. Bond Mathematics 39 Flat Yield This is the simplest measure of yield (also known as current yield, interest yield, income yield or running yield). It is given by:- Flat yield = Coupon rate (%) x 100 Clean price This is a very crude measure. It does not take into account accrued interest; nor does it take into account capital gain/loss (i.e. it assumes prices will not change over the holding period); nor does it recognise the time value of money. It can only sensibly be used as a measure of value when the term to maturity is very long (as coupon income will be more dominant in the total return than capital gain/loss). Simple Yield This is a slightly more sophisticated measure of return than flat yield, which takes into account capital gain, although it assumes that it accrues in a linear fashion over the life of the bond. However, it does not allow for compounding of interest; nor does it take into account accrued interest as it uses the clean price in the calculation. Simple Yield = [Coupon Rate + (100 - clean price) x 100] x clean price Years to maturity Obviously a bond in its final coupon period is, in terms of its cash flows, directly comparable with a money market instrument. In this case simple interest yield calculations are used (ie no need to discount at a compounded rate). Redemption Yield (Yield to Maturity) A redemption yield is that rate of interest at which the total discounted values of future payments of income and capital equate to its price in the market. Where P = dirty price (ie including accrued interest) c = coupon R = redemption payment n = no of periods y = redemption yield It is also referred to as the Internal Rate of Return or the Yield to Maturity. When quoting a yield for a bond, it is the redemption yield that is normally used, as all the factors contributing to the return can be captured in a single number. The redemption yield takes into account the time value of money by using the discount function: each cash flow is discounted to give its net present value. Obviously a near coupon is worth more than a far coupon because it can be reinvested but also, in nearly all cases (except for negative interest rates), the real coupon amount will be greater the sooner it is received.
  • 40. Bond Mathematics 40 However, this measure gives only the potential return. The limitations of using the redemption yield to discount future cash flows are:  The redemption yield assumes that a bond is held to maturity. (i.e. the redemption yield is only achieved if a bond is held to maturity);  It discounts each cash flow at the same rate;  It assumes a bondholder can reinvest all coupons received at the same rate i.e. the redemption yield rate (i.e. assumes a flat yield curve), whereas in reality coupons will be reinvested at the market rate prevailing at the time they are received;  The discount rate used for a cash flow in, say, three years‘ time from a 5 year bond will be different from the rate used to discount the three year payment on a 10 year bond. The redemption yield curve suffers from these limitations. The curve is used for simple analysis, and can also be used when there are insufficient bonds available to construct a more sophisticated yield curve. Net redemption yields The above equation has looked at gross returns, but bond investors are likely to be subject to tax: possibly both on income and capital gain. The net redemption yield, if taxed on both coupon and redemption payments, is given by:- P = Dirty price c = Coupon R = Redemption payment r net = net redemption yield This is a simple example. In practice, if withholding tax is imposed the equation is not so simple as a percentage of tax will be imposed at source with the remainder being accounted for after the payment has been received. As tax rules can materially affect the price of bonds, their effects need to be taken into account in any yield curve modelling process in order to avoid distortions in the estimated yield curve. Spot rate: Each spot rate is the specific zero coupon yield related to that maturity and therefore gives a more accurate rate of discount at that maturity than the redemption yield. It also means that assumptions on reinvestment rates are not necessary. Spot rates take into account current spot rates, expectations of future spot rates, expected inflation, liquidity premia and risk premia.
  • 41. Bond Mathematics 41 Various curves Zero coupon curve Forward zero coupon yield Par yield P = Price (dirty) c = Coupons n = Number of periods f i = ith period forward rate for one further period (i.e. the one-year rate in i years‘ time) y is the par yield z i is the rate of return at maturity i (i.e. the spot rates at maturity i) R is the redemption payment zero coupon curve •The curve resulting from the zero coupon (spot) rates is often referred to as the ‘Term Structure of Interest Rates’; the plot of spot rates of varying maturities against those maturities. This curve gives an unambiguous relationship between yield and maturity. •advantages: 1.finding relatively misvalued bonds, valuing swap portfolios and valuing new bonds at auction. 2. it discounts all payments at the appropriate rate, provides accurate present values and does not need to make reinvestment rate assumptions. forward zero coupon yield •the forward rate is such that an investor will be indifferent to investing for two years or investing for one year and then rolling over the proceeds for a further year. •(1+r1)(1+f1,2)=(1+r2)2 •advantages: 1. the implied forward rate equals the spot rate that prevails in the future. 2. the liquidity premium hypothesis suggests that the implied forward rate equals the expected future spot rate plus a risk premium. •real implied forward rates: (1+ nominal forward) = (1+ real forward)[(1+ inflation forward)] •Nominal forward = real forward + inflation forward par yield •The par yield is a hypothetical yield. It is the coupon that a bond would have in order to be priced at par, using the zero coupon rates in the discount function. This can be seen from the following equation.
  • 42. Bond Mathematics 42 Relationship between curves The par, zero and forward curves are related. Figure 3.2 In an environment of upward sloping yield curves, the zero curve will sit above the par curve because the yield on a coupon bearing bond is affected by the fact that some income is received before the maturity date, and the rate used to discount these payments will be lower than the rate used to discount the payment at maturity. Also, as the forward curve gives marginal rates derived from the zero curve, it will be above the zero curve. The opposite is true in a downward sloping yield curve environment.
  • 43. Bond Mathematics 43 Debt management products (calculations) Treasury bill Treasury bills are short term discount instruments (usually of less than one year maturity) and therefore are useful funding instruments in the early stages of a debt market when investors do not want to lock in to long maturities. They are issued at a discount to their face value and have one payment on redemption. The advantages of Treasury bills are that they are simple, tradeable in the secondary market and are government credit risk. However, because of their short maturities they need to be rolled over frequently, meaning that the future cost of debt servicing is uncertain. Also, shorter maturities result in a very short government yield curve: a longer yield curve is obviously beneficial to developing financial markets as it provides information and allows pricing of new products. There are a number of issues to take into account before issuing Treasury bills. For example, how will they be issued and to whom? If the government wishes to reach a wide range of investors, including the retail sector, then this could mean that the government is a competitor to the banking system, which could actually stifle market development (although this will, of course, provide the private sector with a benchmark). Also, if issuing to the retail investor, an auction process may prove difficult to understand and to price correctly. The government may need to think of other distribution channels (e.g. banks themselves, although they may charge a fee for this, making issuance expensive). A further consideration is minimum denomination (smaller if the retail investor is to be attracted) and whether to set a minimum price. In more developed countries, Treasury bills are also used for monetary management purposes. The increase (decrease) of Treasury bill issuance will affect the liquidity position of banks by withdrawing (increasing) liquidity from the market. Calculation of Treasury bill yield/price The discount rate is described as the return on a discount instrument compared with its redemption value (also referred to as par or face value) in the future. It is given by the following formula: Treasury bills Conventi onal bonds Converti ble bonds Floating rate bonds Zero coupon bonds & strips
  • 44. Bond Mathematics 44 For the yield and price on a treasury bill, the following formulae are used: Or, simply, face value minus discount. It is important to note that the discount rate (often referred to as the rate of interest) and the yield on a Treasury bill are not the same. The discount rate is a market convention. Using the discount rate gave an easy calculation from rate to price and a fairly close approximation to true yield. Conventional bonds A 'conventional' bond is one that has a series of fixed coupons and a redemption payment at maturity. Coupons are usually paid annually or semi-annually. A conventional bond, e.g. ‗6% 2005‘, is a bond that has a 6% coupon and a repayment date in 2005. The prospectus will detail the terms and conditions applied to the bond, including the dates of the coupon payments and the final maturity of the bond. For example, if the above bond has semi-annual coupon payments, then for each Rs100 of the bond purchased, the holder will receive Rs3 coupon payment every six months up to the maturity of the bond. This is a ‗standard‘ bond issued by governments, although it does not necessarily suit all investors, not least because the receipt of regular coupon payments introduces reinvestment risk, as coupons need to be re-invested at rates of interest that are uncertain at the time of purchasing the bond. The conventional bond can be thought of as offering a nominal yield that takes into account the real yield and anticipated inflation. The real yield required can be thought of as the sum of two components: a real return and a risk premium reflecting the uncertainty of inflation12. This can be written as: where N is the nominal return R is the real yield Pe is the expected inflation rate over the period the bond is held RP is the risk premium The risk premium is the amount the market demands for unanticipated inflation. It is difficult to exactly price the risk premium, but if we know the market‘s view of inflation expectations then it is possible to have some idea of the size of the risk premium, by looking at the difference between nominal and real rates in the market. Obviously in countries with high inflation, the risk premium will be greater, given the uncertainty. But the very act of issuing index-linked debt (suggesting that the government is confident of reducing inflation) may help reduce the risk premium built into conventional debt. In countries where inflation has been low and stable, investors will feel more certain that the value of their investment will not be eroded and therefore will demand a lower risk premium.
  • 45. Bond Mathematics 45 Floating Rate Bonds A floating rate bond (―floater‖) has a coupon linked to some short-term reference rate e.g. an interbank rate. It is usually issued at a margin (or spread) above this reference rate. This ensures that the investor gets a current rate of return, whilst (usually) locking in his investment for a longer period than this. The price of a floater depends on the spread above or below the reference rate and any restrictions that may be imposed on the resetting of the coupon (e.g. if it has caps or floors) plus the usual credit and liquidity considerations. The rate is usually a market rate. An obvious measure of value to the issuer is the return given above or below the market index or benchmark rate (i.e. LIBID, in the UK‘s case). These margin values (if below market norm) indicate the better credit quality of government issuance. Corporates also issue floaters and may pay a small margin over a reference rate, depending on their credit quality. Because the value of the coupon in the future is not known, it is not possible to determine the future cash flows. This means that a redemption yield measure cannot be calculated for a floating-rate bond. simple margin The simple margin uses a comparison with the 'index' and calculates it throughout the life of the bond. However, it does not take into account the current yield effect on the price of the floater, since coupon payments received are given the same weight if the price is above or below par. Also, the discount/premium of the bond is amortised to par in a straight line over the life of the floater rather than discounted at a constantly compounded rate. To overcome these drawbacks, one can use a discounted margin. discount margin This measure attempts to discount all cash flows and to therefore give some idea of the Net Present Value of each cash flow. However, it makes an assumption that LIBOR will remain the same throughout the life of the bond. A more sophisticated technique would be to construct a projected LIBOR curve, and therefore discount at a more accurate rate. However, as the maturity of the floater is usually short term (and that this method also necessitates some form of assumption) it is not usually employed.
  • 46. Bond Mathematics 46 Convertible bonds Some governments have issued convertible bonds. These normally offer the investor the option of converting from one type of security to another, e.g. short to long-term or vice versa, fixed to floating or indexed. In issuing them the government hopes that the investor will pay a premium for the option, and that this premium will more than offset the cost to the government if the option is exercised. Equity-convertible bonds may be useful if the government is planning to privatise certain assets, such as state-owned enterprises, and wishes to obtain some of the value of the privatisation proceeds early. For instance, a security convertible into an equity could be sold for 100, redeemable in 2 years time or convertible at the investor‘s option into, say, 10 shares of a certain enterprise which is to be privatised. If the estimated market value of that enterprise rises during the period, the investor will exercise his option and convert; and if its value has risen much faster than expected, the opportunity cost to the government - through selling the option to buy at a fixed price - may outweigh the premium received for selling the option. If the enterprise‘s estimated value falls, the investor will buy the shares more cheaply in the market and not exercise the option. If it turns out, for whatever reason, that the enterprise is not privatised, some compensation may need to be paid to the investor. Zero coupon bonds and strips A zero coupon bond has only one (redemption) payment and is sold at a discount to its face value. In pricing the bond, it will be discounted at its spot rate i.e. the rate of discount specific to that maturity. The price of a zero coupon bond is therefore given by:- Where R is the redemption payment Zi is the spot rate relating to period i: (the maturity of the bond) The discount rate used (Zi ) can be thought as the redemption yield of a zero-coupon bond. The zero coupon bond has a number of advantages over its conventional counterpart. The zero coupon bond consists of a single point cash flow and therefore, by purchasing a selection of such bonds, the investor can build up the cash flows he wants, rather than receiving - and possibly needing to reinvest - frequent coupons. This allows far more efficient asset/liability management and eliminates reinvestment risk. Zero coupon bonds can therefore be used as building blocks from which to construct financial instruments such as annuities or deferred payment bonds. A zero coupon bond also has greater duration (for the same maturity) and greater convexity (for the same duration) than coupon bonds. This makes them potentially attractive to a large part of the market; for example, traders, who trade on risk and are looking for increased volatility; investors who want long duration assets; fund managers who are seeking to match the duration of their portfolios and have, for example, long duration pension liabilities.
  • 47. Bond Mathematics 47 Strips A strip is a zero coupon bond, derived from separating a standard coupon-bearing bond into its constituent interest and principal payments that can then be separately held or traded as zero-coupon bonds22. For example, a 5-year bond with an annual coupon could be separated into six zero-coupon bonds, five representing the cash flows arising from coupons and one relating to the principal repayment. For Rs100 nominal worth of this bond with, say, a 6% coupon paying on 1 June each year the following cash flow would result from stripping:- Figure 3.3 Thus, stripping would leave five zero coupon bonds of Rs6.00 (nominal), maturing on 1 June each year and one zero coupon bond of Rs100 (nominal) maturing on 1 June in five years time. As most strip markets trade on yield rather than price, it follows that a standard yield formula should be used to calculate settlement value, to avoid any disputes. where: P = Price per Rs100 nominal of the strip y = Gross redemption yield (decimal) ie if the yield is 8% then y = 0.08 r = Exact number of days from the settlement/issue date to the next quasi coupon date (the quasi coupon date is a date on which a coupon would be due were the bond coupon bearing than the shortest strip) s = Exact number of days in the quasi-coupon period in which the settlement date falls n = Number of remaining quasi-coupon period after the current period So far we have seen the relationship between various factors for determination of the bond price. These factors plat eminent role in decision making process of bond management. The Objective of the project ―Effective bond management‖ requires us to have basic concept of the above discussed aspects to understand its impact on the bond prices thereby the effective bond management.
  • 48. Bond Mathematics 48 Measures of risk and return Duration Duration is a measure of:  Duration is a measure of interest rate risk exposure of a financial asset and it measures the sensitivity of a security‘s price to interest rate.  It is the approximate percentage change in the value of a fixed income security that will result from a 1% change in interest rates.  There were various ways of measuring the ‗riskiness‘ of the bond, and perhaps the most common was the time to maturity. All other things being equal, the longer the bond the greater the volatility of its price (risk). However, this measure only takes into account the final payment (not any other cash flows), does not take into account the time value of money and therefore does not give an accurate comparison of relative ‗riskiness‘ across bonds.  Duration is a weighted average of the maturity of all the income streams from a bond or portfolio of bonds. It allows us to compare the riskiness of bonds with different maturities, coupons etc.  Investors use duration to measure the volatility of the bond. The higher the duration (the longer an investor needs to wait for the bulk of the payments), the more its price will drop as interest rates go up.  It can be said that duration is how long it would take for you to get your money back if a rise in interest rates causes your bond portfolio to drop in value.  A zero coupon bond duration equals maturity. When there are interim payments, duration will be less than maturity. For a deep discount bond, a point is reached at which duration actually decreases as maturity increases. a • the approximate sensitivity of a bond's value to interest rate changes b • a bond's lifetime that accounts for the entire pattern of cash flows over the life of the bond (i.e the weighted average time to recovery of all interest payemnts plus principal) c • the number of years needed to fully recover the purchase price of a bond given the present value of its cash flows d • the price volatility of a zero coupon bond with that number of years to maturity e • the number for each bond that summarizes 3 key factorsthat affect the sensitivity of a bond's price to a change in interest rates: maturity, coupon and YTM
  • 49. Bond Mathematics 49 In mathematical terms, this is expressed as:- Macauley Duration = Where D= duration of the bond CF= interest or principal payment at time t t= time period in which principal or coupon interest is paid n= number of periods to maturity i= the yield to maturity (market rate interest rate) Modified duration For a 5-year bond with a 10% annual coupon, imagine that the shaded area represents the net present value of each cash flow; and that the shaded areas are weights along a seesaw. The Macauley duration is the point at which the seesaw balances. The relation between Macauley duration, price and yield is given by: (1) Where, ΔP / Δy = Proportional change in price with respect to change in yield P = price y/fc = yield/frequency of coupon payments per annum D = Macauley duration From Macauley duration, we can express Modified Duration, which is a measure of the price sensitivity of a bond: Substituting Modified Duration into equation (1) above and slightly rearranging gives:- Figure 4.1
  • 50. Bond Mathematics 50 Modified Duration describes the sensitivity of a price of a bond to small changes in its yield – and is often referred to as the volatility of the bond. It captures, in a single number, how a bond‘s maturity and coupon affect its exposure to interest rate risk. It provides a measure of percentage price volatility, not absolute price volatility and is a measure of the percentage price volatility of the full (i.e. dirty) price. For any small change in yield, the resulting percentage change in price can be found by multiplying yield change by Modified Duration as shown below:- % change in price = - (Modified Duration) x yield change (in basis points) (3) The negative sign in the equation is, of course, necessary as price moves in the opposite direction to yield. Figure 4.2 However, there are limitations in using Modified Duration in predicting the price/yield relationship. It is only valid for small changes in yield; for parallel shifts in the yield curve; and for small time horizons. The reasons for these limitations can be more clearly seen from the graph below. The price/yield relationship estimated from the Modified Duration of a bond is linear (shown by the tangent to the curve at Po) whilst the actual price/yield relationship is a curve. There is therefore an error when using Modified Duration to estimate price movements Duration is used as a way to ensure that a goal to be met in the future will not be affected by interest rate changes. The ―duration gap‖ is a well respected subject among banks. DG = DA – (MVL/MVA)* DL DG = duration gap (which you want it to be zero if you are duration matching) DA = duration of the assets MVL = market value of the liabilities MVA = market value of the assets DL = duration of the liabilities
  • 51. Bond Mathematics 51 Table 4.1 Convexity duration α 1/coupon • higher coupon lead to quicker recovery of the bond's value, resulting inshorter duration duration α 1/YTM • higher yields produce lower present values of cash receipts received far out in time, thereby diminishing their relative value duration α maturity • duration expands with time to maturity but at a decreasing rate percentage price change • the percentage change in a bond's price is approximately equal to negative modified duration times the change in yield price change • the change in a bond's price is approximately equal to percentage change in prices times the original price estimated price • the estimated bond's price is approximately equal to percentage changes in prices times original price plus the original price a • Convexity is a measure of the sensitivity of a bond‘s price to changes in yield. b •It is also a measure of the degree to which a bond‘s price-yield curve departs from a straight line. This characteristic affects the estimates of a bond‘s price volatility. c •Modified Duration indicates how the price of a bond varies for small changes in yield. However, for large changes in yield, two bonds that have the same yield and the same Modified Duration can behave quite differently. This is due to the ‗error‘ in using modified duration. This error is explained by convexity d •It is the second derivative of a bond‘s price with respect to yield. The convexity of a bond is a measure of the curvature of its price/yield relationship.
  • 52. Bond Mathematics 52 where, C= cash flow at time t t= period when the cash flow is expected to be received T= number of periods until maturity m= number of periods per year r= discount rate per period The approximate percentage price change due to convexity is:- % price change = ½ x convexity x (percentage yield change)2 Figure 4.3 The diagram shows the modified duration line relating to bonds AB and CD (i.e. a tangent to the price/yield curve at point P1). The price/yield curve for bond CD is clearly more convex than that for bond AB. This means that, at this point, for any given change of yield, bond CD will outperform AB. However, over time, the price yield curves will shift and therefore bond CD will not always outperform. Table 4.2 convexity α 1/coupon • the curvature relationship betwen yield and prices is greater for lower yields convexity α 1/YTM • the curavture is flatter for higher coupon bonds than lower coupon bonds convexity α duration • the curavture is greater for longer maturity bonds and therefore for long duration bonds
  • 53. Bond Mathematics 53 Comparison of two bonds Figure 4.4  Bond 1 is more convex than Bond 2  Price falls at a slower rate as yield increases  Bond Convexity is defined formally as the degree to which the duration changes when the yield to maturity changes. It can be used to account for the inaccuracies of the Modified Duration approximation. On top of that, if we assume two bonds will provide the same duration and yield then the bond with the greater convexity will be less affected by interest rate change. This can be easily visualized from the diagram above where the greater the "curvature", the lesser the price drop when interest rate increase.  But at the same time, if the interest rate increases, the expected yield increases and it can be observed in the above diagram that higher the convexity higher the price increases than the lesser convexity.  This shows that convexity has double advantage because when interest rates fall, bond prices rise very high comparatively when interest rates rise, the prices fall less. percentage price change •the percentage change in a bond's price associated with the convexity is approximately equal to the product of negative modified duration and change in yield plus the product of 1/2, convexity and change in yield price change • the change in a bond's price is approximately equal to percentage change in prices times price for both duration and convexity estimated price • the change in a bond's price is approximately equal to percentage change in prices times price for both duration and convexity plus original price Bond 1 _________ Bond 2 ------------
  • 54. Bond Mathematics 54 Immunization It is the strategy of protecting a portfolio against interest rate risk (i.e both price and reinvestment risk).  Zero coupon bond immunization: buy zero coupon bonds that match the desired future cash flows. (prefect immunization)  Coupon bond immunization: the process of balancing bond holdings such that price and reinvestment risks cancel out. (approximate immunization) Components of interest rate risk  Price risk: risk resulting from the inverse relationship between bond prices and required rates of return  Reinvestment rate risk: risk resulting from the uncertainty about the rate at which future coupon income can be reinvested. The two components of interest rate risk move in opposite directions. Hence, the strategy would be to purchase a bond with duration equal to the investment horizon.
  • 55. Bond Mathematics 55 Exposure of bonds to HPCL Background of bonds in HPCL HPCL issues NCD‘s (Debentures) and receives oil bonds. Bonds is a way to finance long term money requirements for the new projects. It is obligatory for HPCL to receive oil bonds from the government. As government subsidises oil prices, public sector companies have to face losses. Instead of paying back the losses to the company in cash, government issues oil bonds. Now, it is the company‘s task to manage these bonds for profits ( selling and issueing). Also called management of baond portfolio. This can be done in a very efficeint manner by implementing a tool called bond mathematics (which we have studied so far). Balance sheet 2008 – 2009 Table 5.1
  • 56. Bond Mathematics 56 As seen from the above investments, the modes of investments of HPCL are coupon bonds, convertible debentures, equity shares and NCDs. HPCL received 3 oil special bonds of 8108.35 Cr from the government of India which are mandatory. It bought convertible debenture from Prize Petroleum Co. Limited of 15 Cr. Also bought debentures from Shell MRPL Aviation Fuels and from Petronet India ltd of 18.54 Cr. As seen in the current investments, HPCL has been continuously been compensated by oil bonds in form of subsidy financing by GOI. In the year 2008-09 total outstanding oil bonds in hand of HPCL stood at 4594.64 Cr against 10 special oil bonds of 5682.39 Cr in year 2007- 08. This shows that the oil prices in 2009 have been sold by HPCL in the market to manage working capital requirement. All these bonds in this year have been discussed in detail below. But as an overall picture, HPCL has made huge investments of 12827.38 Cr in 2009 as against 5869.17 Cr in 2008. Most of their investments are bond based which are secured and gives fixed income. They are playing safe and hence their returns might be low due to low risk but their volumes are high this year comparitively.
  • 57. Bond Mathematics 57 Analysis MTM statement of oil bonds issued by govt. Of India as on 01-June -2009 7.47 % Oil Marketing Companies' GOI Special Bonds, 2012 Face value Issue date Maturity date coupon rate Yield Year to maturity 100 07-Mar- 2006 07-Mar-12 7.74% 7.5648% 6 All these calculations have been performed on HPCL. Yield, price, duration of the bonds can be calculated directly on excel. It has inbuilt formulae: PRICE(seetlement, maturity, rate, yld, redemption, frequency, [basis]); YIELD(settlement, maturity, rate, pr, redemption, frequency, [basis]); DURATION(settlement, maturity, coupon, yld,frequency, [basis]); But for calculation of convexity, there is no inbuilt formula, hence the following method as the formula for convexity is 1/(P(1+y)2 ) ∑ [CF/(1+y)2 (t2 +t)] A B Period CF Discounted flows t^2 + t a*b 1 7.74 3.72 2 7.45 2 7.74 3.86 6 23.18 3 7.74 3.86 12 46.43 4 7.74 3.86 20 77.39 5 7.74 3.86 30 116.09 6 107.74 53.86 42 2262.53 Sum 2533.12 1/(P((1+y)^2)) 0.0086 Convexity 21.89 Duration 4.91 % change in bond price 6.03 for 1% change in yield
  • 58. Bond Mathematics 58 The percentage change in bond price is calculated by (-D x Δy) + (o.5 x convexity x Δy2 ). The rupee change in bond price can be calculate by multiplying current bond price with the percentage change in bond price. As seen from the above bond, the yield is just above coupon rate, hence the bond price is trading at discount price of Rs99.75. The curve has less curvature which indicates less sensitivity in the bond prices due to the yield changes. Hence the observed convexity and the duration is also less. There is only 6.03% change in prices for 1% change in yield. This is obvious as the time to maturity is just 6 years which is the major factor for price volatility. 0 50 100 150 0 5 10 15 price yield curve price yield curve
  • 59. Bond Mathematics 59 7.61 % Oil Marketing Companies' GOI Special Bonds, 2015 Face value Issue date Maturity date coupon rate Yield time to maturity 100 07-Mar- 2006 07-Mar-15 7.61% 8.1467% 9 A B Period CF Discounted flows t^2 + t a*b 1 7.61 3.65 2 7.31 2 7.61 3.79 6 22.79 3 7.61 3.80 12 45.65 4 7.61 3.80 20 76.09 5 7.61 3.80 30 114.14 6 7.61 3.80 42 159.80 7 7.61 3.80 56 213.08 8 7.61 3.80 72 273.96 9 107.61 53.80 90 4842.45 sum 5755.31 % change in bond price 17.97 for 1% change in yield 1/(P((1+y)^2)) 0.0086 convexity 49.21 Duration 6.62 0 50 100 150 200 0 5 10 15 price yield curve price yield curve
  • 60. Bond Mathematics 60 The above bond is better than the previous bond in terms of yield or returns, hence the bond is traded at a discount price of Rs 97.55. The good curvature to the price yield curve, average duration and moderate convexity. For 1% change in yield, the price of this bond fluctuates to 17.97%.
  • 61. Bond Mathematics 61 6.35 % Oil Marketing Companies' GOI Special Bonds, 2024 Face value Issue date Maturity date coupon rate Yield time to maturity 100 23-Dec- 2008 07-Mar-15 6.35% 6.3495% 16 A B Period CF Discounted flows t^2 + t a*b 1 6.35 3.07 2 6.15 2 6.35 3.17 6 19.03 3 6.35 3.17 12 38.09 4 6.35 3.17 20 63.49 5 6.35 3.17 30 95.24 6 6.35 3.17 42 133.34 7 6.35 3.175 56 177.8 8 6.35 3.175 72 228.6 9 6.35 3.175 90 285.75 10 6.35 3.175 110 349.25 11 6.35 3.175 132 419.1 12 6.35 3.175 156 495.3 13 6.35 3.175 182 577.85 14 6.35 3.175 210 666.75 15 6.35 3.175 240 762 16 106.35 53.175 272 14463.6 Sum 18781.38
  • 62. Bond Mathematics 62 1/(P((1+y)^2)) 0.0088 convexity 166.06 duration 5.13 This bond has maturity of 16 years but its yield being almost equal to the coupon rate, the price in the market remains same. The curavture is less and but its duration convexity is high and hence for 1% change in yield there is 77.9% change in prices. 0 50 100 150 0 5 10 15 price yield curve price yield curve % change in bond price 77.90 for 1% change in yield
  • 63. Bond Mathematics 63 a b Period CF Discounted flows t^2 + t a*b 1 6.90 3.33 2 6.66 2 6.90 3.44 6 20.67 3 6.90 3.44 12 41.39 4 6.90 3.44 20 68.99 5 6.90 3.44 30 103.49 6 6.90 3.44 42 144.89 7 6.90 3.45 56 193.2 8 6.90 3.45 72 248.4 9 6.90 3.45 90 310.5 10 6.90 3.45 110 379.5 11 6.90 3.45 132 455.4 12 6.90 3.45 156 538.2 13 6.90 3.45 182 627.9 14 6.90 3.45 210 724.5 15 6.90 3.45 240 828 16 6.90 3.45 272 938.4 17 106.90 53.45 306 16355.7 sum 21985.84 6.90 % Oil Marketing Companies' GOI Special Bonds, 2026 Face value Issue date Maturity date coupon rate Yield time to maturity 100 04-Feb- 2009 04-Feb-26 6.90% 6.8986% 17
  • 64. Bond Mathematics 64 1/(P((1+y)^2)) 0.0088 convexity 192.40 duration 10.26 This bond has very good curvature and time to maturity and hence has high duration and convexity. Therefore, the change in yield by 1%, has 85.94% change in its prices. It is very sensitive. 0 50 100 150 200 250 0 5 10 15 price yield curve price yield curve % change in bond price 85.94 for 1% change in yield
  • 65. Bond Mathematics 65 8.00 % Oil Marketing Companies' GOI Special Bonds, 2026 Face value Issue date Maturity date coupon rate Yield time to maturity 100 23-Mar- 2009 23-Mar-26 8.00% 7.9980% 17 a b Period CF Discounted flows t^2 + t a*b 1 8.00 3.84 2 7.69 2 8.00 3.99 6 23.96 3 8.00 3.99 12 47.99 4 8.00 3.99 20 79.99 5 8.00 3.99 30 119.99 6 8.00 3.99 42 167.99 7 8.00 3.99 56 224 8 8.00 4 72 288 9 8.00 4 90 360 10 8.00 4 110 440 11 8.00 4 132 528 12 8.00 4 156 624 13 8.00 4 182 728 14 8.00 4 210 840 15 8.00 4 240 960 16 8.00 4 272 1088 17 108.00 54 306 16524 sum 23051.65
  • 66. Bond Mathematics 66 1/(P((1+y)^2)) 0.0086 Convexity 197.64 Duration 9.57 This bond too has high curvature and high time to maturity due to which its convexity and duration are high making it sensitive. Change in yield by 1% has impact on prices by 89.24%. As on June 1. 2009, the yield being equal to the coupon rate, the bond price remains same as the face value. 0 50 100 150 200 250 0 5 10 15 price yield curve price yield curve % change in bond price 89.24 for 1% change in yield
  • 67. Bond Mathematics 67 8.20 % Oil Marketing Companies' GOI Special Bonds, 2024 Face value Issue date Maturity date coupon rate Yield time to maturity 100 15-Sep- 2009 15-Sep-24 8.20% 8.1977% 15 a b Period CF Discounted flows t^2 + t a*b 1 8.20 3.93 2 7.87 2 8.20 4.09 6 24.55 3 8.20 4.09 12 49.19 4 8.20 4.09 20 81.99 5 8.20 4.09 30 122.99 6 8.20 4.09 42 172.19 7 8.20 4.09 56 229.6 8 8.20 4.1 72 295.2 9 8.20 4.1 90 369 10 8.20 4.1 110 451 11 8.20 4.1 132 541.2 12 8.20 4.1 156 639.6 13 8.20 4.1 182 746.2 14 8.20 4.1 210 861 15 108.20 54.1 240 12984 sum 17575.63
  • 68. Bond Mathematics 68 This bond too has good curvature and time to maturity and hence good convexity and duration. It is sensitive for about 66.17% in prices for a change in 1% of yield. The yield on june 1, 2009 remains the same as coupon, hence the bond price is neither discounted nor premium. Convexity of all bonds Figure 5.1 Comparing convexity of all the bonds, it can be said that bonds with coupon rates 6.9%, 8% and 8.2% have high curavature indicating high sensitivity. In these bonds, if the yield decreases, the prices increase highly but at the same time if the yield increases, the prices decrease less comparitively. HPCL being the investor, this is an advantage to it. 0 50 100 150 200 250 0 5 10 15 price yield curve price yield curve 0 25 50 75 100 125 150 175 200 225 0 5 10 15 7.47%, 2012 7.61%, 2015 6.35%, 2024 6.9%, 2026 8%, 2026 8.2%, 2024 % change in bond price 66.17 for 1% change in yield 1/(P((1+y)^2)) 0.0085 Convexity 150.13 Duration 8.89
  • 69. Bond Mathematics 69 HPCL has lately started issuing NCDs in the market. The present bonds in the market are discussed below: HINDUSTAN PETROLEUM CORP LTD N/A S&P 12-Apr-2010 ISIN:INE094A07038, LOCAL CODE:PTHPCL137.70% Oil and Gas - Oil and Gas Fixed:Plain Vanilla Fixed Coupon Issuance Details Bond Issued Issue Date / Price / Yield 12-Apr-2010 Issue Spread: -- (--) Original Issue Amount: 10,00,00,00,000 INR Total Issue Amount: 10,00,00,00,000 INR Total Price to Public: INR Announcement Date: 12-Apr-2010 Auction Date: -- MTN: No Underwriters: Name Type Amount CITIBANK NA Joint Lead Manager AXIS BANK LTD Joint Lead Manager SBI CAPITAL MARKETS LTD Joint Lead Manager STANDARD CHARTERED BANK (INDIA BRANCH) Joint Lead Manager Principal / Coupon Information Maturity Date: 12-Apr-2013 100 Principal / Coupon Currency: INR / INR Amount Outstanding: 10,000,000,000 INR Coupon Type / Frequency: Fixed:Plain Vanilla Fixed Coupon / Annually Current Coupon / Next Pay Date: 7.7000 12-Apr-2011 Coupon Formula: -- Dated / First / Final Coupon: 12-Apr-2010 12-Apr-2011 12-Apr-2012 Irregular Coupon: None Cumulative Dividend: -- Ratings Rating Source Date Rating Watch Code Credit Information Svce of India 12-Apr-2010 AAA -- Moody's Long-term Issue Credit Rating 12-Apr-2010 N/A -- Standard & Poor's 12-Apr-2010 N/A -- 7.7 % fixed plain vanilla bond, HPCL 2013
  • 70. Bond Mathematics 70 Face value Issue date Maturity date coupon rate Yield Year to maturity 100 12-Apr-2010 12-Apr-13 7.70% 7.5333% 3 A B Period CF Discounted flows t^2 + t a*b 1 7.70 3.71 2 7.42 2 7.70 3.84 6 23.06 3 107.70 53.84 12 646.16 Sum 676.65 1/(P((1+y)^2)) 0.0086 Convexity 5.85 Duration 2.73 As seen the yield is 7.533, less than the coupon rate 7.7. It is an advantage to HPCL as it has to pay less interest rate to the receiver of the bond. The time to maturity is just 3 years and hence its duration and convexity are low. For a change in yield by 1%, there is only 0.19% change in price. Hence an advantage as an issuer. 0 20 40 60 80 100 120 140 0 5 10 15 price yield curve price yield curve % change in bond price 0.19 for 1% change in yield
  • 71. Bond Mathematics 71 7.35 % fixed plain vanilla bond, HPCL 2012 HINDUSTAN PETROLEUM CORP LTD N/A S&P 04-Dec-2009 ISIN:INE094A07020, LOCAL CODE:PTHPCL127.35 Oil and Gas - Oil and Gas Fixed:Plain Vanilla Fixed Coupon Issuance Details Asset Backed Security Issued Issue Date / Price / Yield 04-Dec-2009 Issue Spread: -- (--) Original Issue Amount: 5,00,00,00,000 INR Total Issue Amount: 5,00,00,00,000 INR Total Price to Public: INR Announcement Date: -- Auction Date: -- MTN: No Underwriters: Name Type Amount CITIBANK NA Lead Underwriter or Manager SBI CAPITAL MARKETS LTD Joint Lead Manager STANDARD CHARTERED BANK (INDIA BRANCH) Bookrunner Principal / Coupon Information Maturity Date: 04-Dec-2012 100 Principal / Coupon Currency: INR / INR Amount Outstanding: 5,000,000,000 INR Coupon Type / Frequency: Fixed:Plain Vanilla Fixed Coupon / Semiannually Current Coupon / Next Pay Date: 7.3500 Coupon Formula: -- Dated / First / Final Coupon: 04-Dec-2009 04-Jun-2010 04-Jun-2011 Irregular Coupon: Last Cumulative Dividend: -- Ratings Rating Source Date Rating Watch Code Credit Information Svce of India 04-Dec-2009 AAA -- Moody's Long-term Issue Credit Rating 04-Dec-2009 N/A -- Standard & Poor's 04-Dec-2009 N/A -- Face value Issue date Maturity date coupon rate Yield Year to maturity 100 04-Dec-2009 04-Dec-12 7.35% 7.2454% 3
  • 72. Bond Mathematics 72 A B Period CF Discounted flows t^2 + t a*b 1 7.35 3.54 2 7.09 2 7.35 3.67 6 22.02 3 107.35 53.67 12 644.06 Sum 673.18 1/(P((1+y)^2)) 0.0087 convexity 5.85 duration 2.74 Even this NCD has low yield of 7.2454 adding an advantage to the issuer. The curvature is less depicting less convexity. Duration is ought to be low as the time to maturity is just 3 years. 0 20 40 60 80 100 120 140 0 5 10 15 price yield curve price yield curve % change in bond price 0.18 for 1% change in yield
  • 73. Bond Mathematics 73 Study of yield: for NCD/ Oil bond We have seen oil bonds and NCDs have 3 basic elements, irrespective of the issuer and the investor. i.e 1. Coupon 2. Tenor 3. Face value To consider the appriopriate time of sale and issuance, the issuer has to understand the relation between above three components. The price of bond (oil bond) from the side of issuer depends on the yield expectation of the market. So, to ensure appriopriate time for sale of oil bond , the study of yield takes utmost importance. The yields are determined by similar government securities of same tenor and relevant spreads are added as per the market appetite and interest. For the study of appriopriate timing for sale of oil bond and its yield discovery, we have taken following bond: 8.00 % Oil Marketing Companies' GOI Special Bonds, 2026 Face value Issue date Maturity date coupon rate Yield time to maturity 100 23-Mar- 2009 23-Mar-26 8.00% 17 Indicative yields of G-secs 14 years G-sec with maturity of 22-jun-2024 with yield of 8.265 15 years G-sec with maturity of 02-aug-2027 with yield of 8.232 Interpolating the above G-sec: 8.265+ (8.232-8.265)/38* 22= 8.246 so we have derived equivalent yield from the relevant benchmark and considering the market expectations spreads are added to the benchmark yield to get the price. For similar bond, spread cn be presumed at 50 basis point. So effective yield becomes 8.746. To ensure accurate timing of the sale, we have to predict the movement of benchmarks. The recent movement of benchmarks is as shown below:
  • 74. Bond Mathematics 74 Figure5.2 Based on our above study the price of above bond comes to Rs96.39. Studying the graph and selling the same at appriopriate time at a yield of 7.4%, the price should come to Rs99.87. The technical analysis shows that it has an upward but has a tendency to fall due to following reasons. During this quarter, 7.4% seems to be dropped the least and this area has to be tapped for good profits. As seen, the maximum peaks touched are 8.2%, 8% and 7.8% in the recent quarter. So keeping this in mind, we can estimate that yields would not rise too high unless extreme market conditions. 7.4% is the best yield for the sale of bond only for this quarter. According to me, this is not the right time for sale, HPCL should wait for the next quarter as the yields might fall further to make the necessary decision.
  • 75. Bond Mathematics 75 Determination of Benchmark Table 5.2 Observing the indicative yields of the above G- sec, the following yields of the bonds can be predicted: Table 5.3 Description of Oil Bonds Issue Date Maturity Date Nearest G- sec considered Interpolation Benchm ark 7.47 % Oil Marketing Companies' GOI Special Bonds, 2012 07-Mar- 2006 07-Mar-12 2 jun, 11 : 5.699 3 sep, 12: 6.816 5.699 + (6.816- 5.699)/14*9 6.417 7.61 % Oil Marketing Companies' GOI Special Bonds, 2015 07-Mar- 2006 07-Mar-15 20 oct, 14: 7.166 14 jun, 15: 7.37 7.166 + (7.37- 7.166)/8*5 7.2935 6.35 % Oil Marketing Companies' GOI Special Bonds, 2024 23-Dec- 2008 23-Dec-24 22 jun, 24: 8.265 02 aug, 27: 8.232 8.265 + (8.232- 8.265)/38*22 8.246 6.90 % Oil Marketing Companies' GOI Special Bonds, 2026 04-Feb- 2009 04-Feb-26 22 jun, 24: 8.265 02 aug, 27: 8.232 8.265 + (8.232- 8.265)/38*22 8.246 8.00 % Oil Marketing Companies' GOI Special Bonds, 2026 23-Mar- 2009 23-Mar-26 22 jun, 24: 8.265 02 aug, 27: 8.232 8.265 + (8.232- 8.265)/38*22 8.246 8.20 % Oil Marketing Companies' GOI Special Bonds, 2024 15-Sep- 2009 15-Sep-24 22 jun, 24: 8.265 02 aug, 27: 8.232 8.265 + (8.232- 8.265)/38*22 8.246
  • 76. Bond Mathematics 76 We have seen all oil bonds are benchmarked to G- secs for determination of its yield. Since, the maturity of G- secs are not same as of oil bonds, we use mathematical tools to interpolate G- secs of nearer maturity to get benchmark for similar oil bonds. Specimen of the benchmark of government securities as on 19-07-10 is shown in table 5.2. Based on the same principle we have calculated the indicative yiled for al ol bonds. Spread factors are market determined and to be considered based on the market indications. Conclusion We have seen HPCL, a fortune 500 company has wide presence in bond market in form of Oil Bonds and Non Convertible debentures. The investments of HPCL have major impact on the financials of the corporation. Hence it is of top most priority to manage the fixed income securities effectively. As seen, bonds play a major role in funding projects and a good source of income. Hence, most of the companies opt for bond portfolios and its management. HPCL is no different and it has also entered into bond management. Managing, analysing and predicting bonds is not a difficult task. Bonds can be very well managed with the tool ‗bond mathematics‘. Mathematics is one of the keys to understanding the bond market. Grasping the concepts that underlie the bond market is the crucial task. Bond market maths can be reduced to a few key concepts: compounding and discounting; accrued interest; running yields; redemption yields; and spreads. Armed with knowledge of these concept and hefty amount of common sense, finding an undervalued bond in which to invest becomes less of a lottery. Studying bond yields, maturity, duration and convexity gives a clearer picture whether to buy that particular bond or not. At same time, what is the appropriate timing for the sale of bonds and the price at which it should be sold can also be determined. Such factors are crucial to make profits and to gain smart income. Research Methodology: An in-depth investigation of the industry conventions for calculating price and yield applied to plain vanilla bonds, including the exploration of implicit assumptions and interpretation of resulting numbers. We have further seen that bonds are sensitive to various market factors and its effective management can increase the profitability of the corporations. The advanced mathematical tools provide effective methods to systematically analyse the bonds and times its sale or issuance in the primary as well as secondary market.