Sapm

SECURITY ANALYSIS AND PORTFOLIO
MANAGEMENT

Take calculated risks. That is quite different from
being rash.

1 BY: PROF. N.N.PANDEY 10/22/12

SECURITY
 Investments in capital markets are in various financial instruments.

 These instruments may be of various category with different characteristics.

 These are called securities in the market parlance.

 It includes shares,bonds,debentures or any marketable securities of a like nature of any
company,Govt.securities or semi-Govt.bodies.


SECURITY ANALYSIS
 Security analysis in both traditional sense and modern sense involves the projection of
future dividend, or earnings flows, forecast of the share price in the future and
estimating the intrinsic value of a security based on the forecast of earnings or dividends.

 In addition to above, the modern approach includes risk and return analysis for the
securities.

 Basically securities analysis contains the analysis of:

 The trend and scenario of the economy.
 The trend and scenario of the industry to which company belongs.
 The strength and weakness of company itself viz. promoters and management track
record, financial results, projections of expansion, diversification, tax planning etc.


PORTFOLIO
 A combination of such securities with different risk-return characteristics will
constitute the portfolio of the investors.

 Thus ,a portfolio is a combination of various assets and/or instruments of
investments.


PORTFOLIO MANAGEMENT
 Portfolio analysis includes portfolio construction, selection of securities, revision of
portfolio, evaluation and monitoring of the performance of the portfolio.

 All these are part of the subject of portfolio management which is a dynamic concept
,subject to daily and hourly changes based on the information flows and a host of
economic and non-economic forces operating in the country on the markets and
securities.


INVESTMENT
 Investment is parting with one’s fund, to be used by another party, user of fund, for
productive activity.

 It can mean giving an advance or loan or contributing to the equity(ownership capital)
or debt capital of a corporate or non-corporate business entity.

 In other words, investing means building up to meet future consumption demand with
the intention of making surpluses or profits, as they are popularly known.


INVESTMENT ACTIVITY
(ACQUISITION OF ASSETS)
1. FINANCIAL ASSETS 2. PHYSICAL ASSETS
CASH HOUSE
SAVER LAND
BUILDINGS
FLATS
BANK DEPOSITS
INVESTOR GOLD
P.F./LIC SILVER
OTHER METALS
PENSION 3. MARKETABLE
ASSETS
POST OFFICE
CERTIFICATES SHARES, BONDS, CONSUMER
& GOVT. SECURITIES, DURABLES
DEPOSITS M.F. SCHEMES, UTI

NEW STOCK
MARKET
ISSUE


RISK-RETURN RELATIONSHIP
 RISK : Risk is inherent in any investment. This risk may relate to loss or delay in

repayment of the principal capital or loss or non-payment of interest or variability of
returns. While some investments are almost risk less like Govt.securities or bank
deposits, others are more risky.

 RETURN: Return differs amongst different instruments. The most important factor

influencing return is risk. Normally, the higher the risk ,the higher is the return. See
the figure in the next slide……..


RISK RETURN RELATIONSHIP

Venture fund(highest risk)

Equity shares

convertible debentures / MFs

Non-convertible debentures
RETURN

PSU BONDS

Lowest Risk (Bank
deposits)

RISK


INVESTMENT VS SPECULATION
 It is for a longer time horizon.  It is for a short period of time.
 It requires higher risk.
 It requires moderate risk.
 It’s objective is to get high returns
 It’s objective is to get a moderate along with higher risk.
return with a limited risk.
 It considers fundamental factors and  It considers inside information,
evaluate the performance of the hearsays and market behavior.
company regularly.
 Investor uses his own funds and avoid  Speculator uses borrowed funds to
borrowed funds. supplement his personal resources.


THE INVESTMENT PROCESS
 Determine the investment objectives and policies
 Undertake security analysis
 Construct a portfolio
 Review the portfolio
 Evaluate the performance of the portfolios


TYPES OF INVESTORS
 The contrarians

 Trend followers and

 Hedgers and holders


THE INVESTMENT ENVIRONMENT
 FINANCIAL INSTRUMENTS

 FINANCIAL INTERMEDIARIES

 FINANCIAL MARKETS


ASSIGNMENT FOR DISCUSSIONS- 1
DIFFERENT KIND OF SECURITIES:
FOR EXAMPLE:

 EQUITY SHARES
 SWEAT EQUITY
 NON-VOTING SHARES
 RIGHT SHARES
 BONUS SHARES
 CUMULATIVE PREFERENCE SHARES
 DEBENTURES
 BONDS
 ZERO COUPON BONDS
 DEEP DISCOUNT BONDS…….ETC….


CASELETS-1: Small Cement Company (SCC) , Efficient
Cement Company (ECC) and Big Cement Company (BCC)
EVENT PROBABILITY RETURNS
(effect on price) SCC ECC BCC

5% decline 20% -5% 0% 5%

Flat 30% 10% 10% 10%

5% increase 40% 25% 20% 15%

10% increase 10% 35% 30% 25%

MAKE AN INVESTMENT CHOICE WITH JUST THESE DETAILS.


EXPECTED RETURNS
SCC : 20%* -5% + 30%* 10% + 40%* 25% +
10%* 35% = 15.5%

ECC : 14%

BCC : 12.5%


CASELETS – 2 & 3
(2) You have invested Rs. 50,000/- , 30% of which is invested in
Company– A, which has an expected rate of return of 15%, and
70% of which is invested in Company- B, with an expected return
of 12%. What is the return on your portfolio? What is the
expected percentage rate of return?
(3) The current market price of a share is Rs.300/- An investor buys
100 shares. After one year he sells these shares at a price of
Rs.360/- and also receives the dividend of Rs.15/- per share.
Find out his total return, % return, dividend yield and capital
gains and capital gains yield.


SOLUTION - 2
Return on portfolio:
Company A : .30 x Rs.50,000 x .15 = Rs.2,250
Company B : .70 x Rs.50,000 x .12 = Rs.4,200

TOTAL RETURN : 2,250 + 4,200 = Rs.6,450

Expected percentage rate of return:
6,450/ 50,000 x 100 = 12.9%


SOLUTION-3
Initial Investment = 300 x 100 = Rs.30,000
Dividend earned = 15 x 100 = Rs. 1,500
Capital gains = ( 360 – 300 ) x 100 = Rs.6,000
Total Return = 1,500+ 6,000 = 7,500
Total percent Return = 7,500/30,000 x 100
= 25%
Dividend Yield = 15/300 x 100 = 5%
Capital Gains yield = 6,000/30,000 x 100
= 20%


CASELETS - 4
Shares A and B have the following probability
Distribution of possible future returns:
Probability(pi) A (%) B (%)
0.1 -15 -20
0.2 0 10
0.4 5 20
0.2 10 30
0.1 25 50
(a) Calculate the expected rate of return for each share and standard deviation of
return for each share
(b) Calculate the coefficient of variation
(c) Which share is less risky. Explain.


SOLUTION- 4
FOR SHARE A:
r% pi ripi% (r – r¯) (r-r¯)2 (r-r¯)2pi(%)
-15 0.1 -1.5 -20 400 40
0 0.2 0 -5 25 5
5 0.4 2 0 0 0
10 0.2 2 5 25 5
25 0.1 2.5 20 400 40
r¯ = 5 σ2 =90
Since σ2 = 90 , σ = √90 = 9.5%


SOLUTION – 4
Similarly for share – B:
Expected rate of return = 19% and S.D. = 17%

(b) Coefficient of variation = σ / r
For share A = 9.5% / 5% = 1.9
For share B = 17% / 19% = 0.89

( C) Share B is less risky than share A. Since coefficient of variation
( a measure of relative risk) is smaller for Share B.


RISK RETURN PROFILE OF TWO ASSET PORTFOLIO
Portfolio return, Rp = w1R1 + w2R2
Portfolio risk, σ2p = w21 σ21 + w22 σ22 +
2 w1w2 Cov(R1R2)
Here, Cov(R1R2) = ρ σ1 σ2
And, w1+ w2 = 1
Or, we can write ,
σ2p = w21 σ21 + w22 σ22 + 2 w1w2 ρ σ1 σ2
now, we will examine two special cases of perfect
positive correlation and perfect negative correlation
which is very significant in portfolio theory.


RISK RETURN PROFILE OF TWO ASSET PORTFOLIO
FIRM 1 FIRM 2
Return 15% 30%
S.D. 10% 20%
With perfect positive correlation ( ρ = +1)
Portfolio risk, σ2p = w21 σ21 + w22 σ22 + 2 w1w2 σ1 σ2
= (w1 σ1 + w2 σ2)2
or, σp = w1 σ1 + w2 σ2


PORTFOLIO RETURN AND RISK WITH C.C. = 1
ALL FIGURES IN %
W1 100 80 60 50 40 20 0

W2 0 20 40 50 60 80 100

Rp 15 18 21 22.5 24 27 30

σp 10 12 14 15 16 18 20


PORTFOLIO RETURN AND RISK WITH C.C. = - 1
Portfolio risk, σ2p = w21 σ21 + w22 σ22 - 2 w1w2 σ1 σ2
= (w1 σ1 - w2 σ2)2
or, σp = w1 σ1 - w2 σ2
ALL FIGURES IN %
W1 100 80 60 50 40 20 0
W2 0 20 40 50 60 80 100
Rp 15 18 21 22.5 24 27 30
σp 10 4 2 5 8 14 20


FUNDAMENTAL ANALYSIS
 Equity shares have an economic worth which is based on existing and expected
earnings capacity.
 Fundamental analysis attempts to find out the fair value or intrinsic value of
securities so that the investors can decide to buy or not to buy the securities at
the current market price.
 The basic premise is that in the long run, the market price tends to move
towards its fair or intrinsic value.
 Small investors sometimes take narrow approach to fundamental analysis which
is called bottom-up-approach.
 However, a broader framework for fundamental analysis is known as ‘top-
down-approach’ or Economic-Industry-Company (EIC) Approach.


FUNDAMENTAL ANALYSIS

ECONOMY

INDUSTRY

COMPANY

E-I-C ANALYSIS


VARIABLES AND TECHNIQUES FOR ECONOMIC
ANALYSIS
There are several indicators which can be used to identify the
state of economy like:
 Gross domestic product (GDP)
 Business cycles viz. depression, recovery, boom, recession
 Inflation
 Interest rates
 Monetary policy, money supply, and liquidity
 Industrial growth rate – sect oral and total
 Agricultural output and rainfall pattern
 Fiscal policy of the Government
 Foreign exchange reserves
 Growth of infrastructural facilities


VARIABLES AND TECHNIQUES FOR ECONOMIC
ANALYSIS
 Global Economic scenario and confidence
 General Economic sentiments and confidence in the economy
 Economic and political stability
SOURCES OF INFORMATION FOR ECONOMIC ANALYSIS
• Reserve bank of India, monthly bulletin.
• Reserve bank of India, Annual Reports.
• RBI, Reports on currency and finance, different issues.
• Statistics on Indian Economy, RBI.
• Centre for Monitoring of Indian Economy (CMIE), monthly reviews and annual reports
• Economic surveys, Government of India, different issues
• Public enterprise survey, GOI


IMPORTANCE OF INDUSTRY ANALYSIS
 Firms in each different industry typically experience similar levels
of risk and similar rates of returns. As such, industry analysis can
also be useful in knowing the investment worthiness of a firm.
 Mediocre stocks in a growth industry usually outperform the best
stocks in a stagnant industry. This points out the need for knowing
not only company prospects but also industry prospects.


CLASSIFICATION OF INDUSTRIES
 PRODUCT LINE WISE : Automobiles, steel, cement, textiles
etc.
 SECTOR WISE : Agriculture, mining, construction,
manufacturing, IT, services, transportation etc.
 BUSINESS CYCLE WISE: Growth , cyclical and defensive


KEY INDICATORS IN INDUSTRY ANALYSIS
The analysts is free to choose his or her own indicators for analyzing the
prospect of an Industry. However , many commonly adopt the following
indicators.
(A) Performance factors like:

 Past sales at least for three years
 Future sales for at least two years
 Past earnings at least for three years
 Future earnings for at least two years

(B) Environment factors like:
 Attitude of government
 Lab our conditions
 Competitive conditions
 Technological progress
(C) Industry life cycle (pioneering/growing/stagnation/decline)
(D ) SWOT analysis for the industry


SOME RELEVANT QUESTIONS FOR INDUSTRY ANALYSIS
 Are the sales of industry growing in relation to the growth in Gross National product
( GNP) ?
 What is overall return on investment (ROI) ?
 What is the cost structure of the industry ?
 Is the industry in a stable position ? Does the success or failure depend upon any single
critical factor ?
 What is the impact of taxation upon the industry ?
 Are there any statutory controls in matters of raw materials prices, distribution etc ?
 What is the industrial relations scenario of the industry ?
 Is the industry highly competitive ? Is it dominated by one or two major companies ?
Are they Indian or foreign ? Is there sufficient export potential ?Are international prices
comparable to domestic prices ?


COMPANY ANALYSIS
The basic objective of company analysis is to identify better
performing companies in an industry. Various steps involved
are as follows:
1. Analysis of the management of the company to evaluate its trust-worthiness
and its capacity and efficiency to counter any untoward situation in the
industry.
2. Analysis of the financial performance of the company to forecast the future
expected earnings capacity.
3. Evaluation of long term vision and strategies of the company in terms of the
organizational strength and resources of the company, and
4. Analysis of key success factor for a particular industry and the strength of
the particular firm in respect of that factor.


COMPANY ANALYSIS
The ultimate objectives of company analysis are:
1. To analyze the past as well as present earnings to forecast the future earnings of the
company.
2. To find out the fair value (intrinsic value) of the share.
ANALYZING COMPANY’S EARNINGS WITH THE HELP OF
FOLLOWING RATIOS:
i. EBIT/PBT/PAT
ii. RETURN ON EQUITY(ROE)
iii. EARNINGS PER SHARE (EPS)
iv. DIVIDEND PER SHARE(DPS)
v. DIVIDEND PAYOUT RATIO( DP RATIO)
vi. PRICE EARNING RATIO ( PE RATIO)
vii. MARKET TO BOOK VALUE RATIO (PB RATIO)
viii. YIELD


SOME RELEVANT QUESTIONS IN COMPANY
SELECTION
 What is the size of the company and it’s relative position in the industry?
 What is the quality of the company’s management?
 What are the investment programmes and financing plan of the company?
 What is the track record of the company?
 What is the financial position of the company?
 What are the growth prospects of the company?
 What is the valuation of the company’s stock?


MODEL FRAMEWORK FOR INTEGRATED
FINANCIAL ANALYSIS ( FOR 5 YEARS)
 Analysis of profitability
 Overall ratio analysis to evaluate the performance and financial position
 Analysis of quality of current assets, loans and advances
 Analysis of crucial notes to the accounts and financial policies
 Analysis of Auditors’ reports
 Analysis of quality of earnings
 Analysis of dividend policies
 Analysis of cash flow statement
 Analysis of capital market valuation
 Analysis of corporate governance report / Director’s report
 Strategic issues emanating out of analysis.


DISCUSS BASED ON RISK

 Long SAIL
 Long SAIL & Long TISCO
 Long SAIL & Long HUL
 Long HUL, Long TISCO, Long ACC & Long INFOSYS.


EFFICIENT MARKET THEORY
 Stock prices are determined by a number of factors such as fundamental factors,
technical factors and psychological factors.
 The behavior of stock prices is studied with the help of different methods such as
fundamental analysis and technical analysis.
 Fundamental analysis seeks to evaluate the intrinsic value of securities by studying the
fundamental factors affecting the performance of the economy, industry and companies.
 The basic assumption of Technical analysis is that stock price movement is quite orderly
and not random. It tries to study the patterns in stock price behavior through charts and
predict the future movement in prices.
 There is a third theory on stock prices behavior which questions this assumptions.
 This theory came to be known as Random Walk Theory because of its principal
contention that share price movements represent a random walk rather than an orderly
movement.


RANDOM WALK THEORY
 A change occurs in the price of a stock only because of certain changes in the
economy, industry, or company.
 Information about these changes alters the stock prices immediately and the
stock moves to a new level, either upwards or downwards, depending on the
type of information.
 This rapid shift to a new equilibrium level whenever new information is
received, is a recognition of the fact that all information which is known is fully
reflected in the price of the stock.
 Further change in the price of the stock will occur only as a result of some
other new piece of information which was not available earlier.


RANDOM WALK THEORY
 Thus, according to this theory, changes in stock prices show independent
behaviour and are dependent on the new pieces of information that are received
but within themselves are independent of each other.
 Each price change is independent of other price changes because each change is
caused by a new piece of information.
 The basic premise in Random walk theory is that the information on changes in
the economy, industry and company performance is immediately and fully
spread so that all investors have full knowledge of the information. There is an
instant adjustment in stock prices either upwards or downwards.
 Thus, the current stock price fully reflects all available information on the
stock.


RANDOM WALK THEORY
 Therefore, the price of a security two days ago can in no way help in
speculating the price two days later.
 The price of each day is independent. It may be unchanged, higher or lower
from the previous price, but that depends on new pieces of information being
received each day.
 The Random walk theory presupposes that the stock markets are so efficient
and competitive that there is immediate price adjustment.
 This is the result of good communication system.
 Thus, the random walk theory is based on the hypothesis that the stock markets
are efficient.
 Hence, this theory later came to be known as the efficient market theory or
efficient market hypothesis ( EMH)


EFFICIENT CAPITAL MARKET
An efficient capital market is one in which security prices equal their intrinsic
values at all times, and where most securities are correctly priced. This happens
because of the followings:
 Large number of investors in the market
 Free flow of information to all the investors
 Every investor is capable to interpret the information
 Every kind of price-sensitive information is discounted in the prices
immediately
 No one is in a position to influence the market unduly.


INDIAN STOCK MARKET MOVING TOWRDS EFFICIENCY
In the last 15-20 years several procedural and regulatory changes have been
introduced to achieve market efficiency viz.
 Automated / Online Trading System
 Depository System
 Changes in Settlement System
 Ban on Badla
 Introduction of Derivatives
 Provision of full disclosure and transparency
 Provision to check insider trading
 Corporatization of Stock Exchanges


FORMS OF MARKET EFFICIENCY
 The capital market is considered to be efficient in three different forms: the
weak form, semi-strong form and the strong form.
 THE WEAK FORM OF THE EFFICIENT MARKET HYPOTHESIS
(EMH) says that the current prices of stocks already fully reflect all the
information that is contained in the historical sequence of prices. The new price
movements are completely random.
 They are produced by new pieces of information and are not related or
dependent on past price movements.
 Therefore, there is no benefit in studying the historical sequence of prices to
gain abnormal returns from trading in securities.
 The weak form of the efficient market hypothesis is thus a direct repudiation of
technical analysis.


SEMI STRONG FORM OF THE EFFICIENT MARKET
HYPOTHESIS
 It says that current prices of stocks not only reflect all informational content of historical
prices, but also reflect all publicly available information about the company being
studied.
 Examples of publicly available information are – corporate annual reports, company
announcements, press releases, announcements of forthcoming dividends, stock splits
etc.
 The semi-strong hypothesis maintains that as soon as the information becomes public the
stock prices change and absorb the full information.
 The implication of semi-strong hypothesis is that fundamental analysts cannot make
superior gains by undertaking fundamental analysis because stock prices adjust to new
pieces of information as soon as they are received.
 There is no time gap in which a fundamental analysts can trade for superior gains. Thus,
the semi-strong hypothesis repudiates fundamental analysis.


STRONG FORM OF THE EFFICIENT MARKET HYPOTHESIS

 The strong form of the efficient market hypothesis maintains that the current
security prices reflect all information both publicly available information as well
as private or inside information.
 This implies that no information, whether public or inside, can be used to earn
superior returns consistently.
 The directors of companies and other person occupying senior management
positions within companies have access to much information that is not
available to the general public. This is known as inside information.
 Mutual funds and other professional analysts who have large research facilities
may gather much private information regarding different stocks on their own.
 These are private information not available to the investing public at large.


STRONG FORM OF THE EFFICIENT MARKET HYPOTHESIS

 The strong form efficiency tests involve two type of tests.
 The first type of tests attempt to find whether those who have access to
inside information have been able to utilize profitably such inside
information to earn excess return.
 The second type of tests examine the performance of mutual funds and the
recommendations of investment analysts to see if these have succeeded in
achieving superior returns with the use of private information generated by
them.
 The results of research on strong form EMH may be summarized as follows:
(a) Inside information can be used to earn above average returns.
(b) Mutual Funds and investment analysts have not been able to earn superior
returns by using their private information.
In conclusion, it may be stated that the strong form hypothesis is Invalid as regards
inside information, but valid as regards private Information other than inside
information.


SHARE VALUATION MODEL
 The valuation model used to estimate the intrinsic value of a share is the present value
model.
 The intrinsic value of a share is the present value of all future amounts to be received in
respect of the ownership of that share, computed at an appropriate discount rate.
 In other words, the intrinsic value of a share is the present value of all the future benefits
expected to be received from that share.
 ONE YEAR HOLDING PERIOD:
S0 = D1/ (1 + K )1 + S1/ (1 + K )1
Here, D1 = Amount of dividend expected to be received at
the end of one year.
S1= selling price expected to be realized on sale of
the share at the end of one year.
K = Rate of return required by the investor.


EXAMPLE
Suppose, an investor expects to get Rs. 3.50 as dividend from
a share next year and hopes to sell off the share at Rs. 45
After holding it for one year, and if his required rate of return
Is 25%, the present value of this share to the investor can be
Calculated as follows:
S0 = 3.5 / 1.25 + 45 / 1.25 = 2.8 + 36 = Rs. 38.8

This is the intrinsic value of the share. The investor would buy
This share only if its market price is lower than this value.


MULTIPLE YEAR HOLDING PERIOD
S0 = D1 / (1+K)1 + D2 / (1+K)2 + D3 / (1+K)3+ ……………
+ ( Dn + Sn ) / (1+K)n
Here, D1, D2, D3 , Dn = Annual dividends to be received each
year
Sn = sale price at the end of the holding period
k = investor’s required rate of return
n = holding period in years
EXAMPLE: suppose an investor expects to get Rs. 3.5, 4, and
4.5 as dividend from a share during the next three years and
Hopes to sell it off at Rs. 75 at the end of the third year and if
his required rate of return is 25%, the present value of this
Share to the investor can be calculated as follows:
S0 = 3.5 / (1.25)1 + 4 / (1.25)2 + 4.5 / (1.25)3 + 75 / (1.25)3
= 2.8 + 2.56 + 2.3 + 38.4 = 46.06


CONSTANT GROWTH MODEL OR GORDON’S
SHARE VALUATION MODEL
S0 = D1 / K – g or D0 (1 + g) / k – g
Here , g = expected dividend growth rate
According to this model, the intrinsic value of a share is equal
To next year’s expected dividend divided by the difference
Between the appropriate discount rate for the stock and its
Expected dividend growth rate.
Suppose, a company has declared a dividend of Rs. 2.5 per
Share for the current year. The company has been following
A policy of enhancing its dividends by 10% every year and is
Expected to continue this policy in future also. An investor
who is considering the purchase of the share of this company
Has a required rate of return of 15%.
The intrinsic value of share will be 2.5 (1.10) / 0.15 – 0.10
= 2.75/.05 = Rs. 55
The investor would be advised to purchase the share if the current
Market price is lower than Rs.55.


MULTIPLE GROWTH MODEL
 The constant growth assumption may not be realistic in many situations.
 A typical situation for many companies may be that a period of extraordinary growth
(either good or bad) will prevail for a certain number of years, after which growth will
change to a level at which it is expected to continue indefinitely. This situation can be
represented by a two-stage growth model.
 In this model, the future time period is viewed as divisible into two different growth
segments, the initial extraordinary growth period and the subsequent constant growth
period.
 During initial period growth rates will be variable from year to year, while during the
subsequent period the growth rate will remain constant from year to year.
 The investor has to forecast the time N up to which growth rates would be variable and
after which the growth rate would be constant.


MULTIPLE GROWTH MODEL
 This would mean that the present value calculations will have to be spread over
two phases, where one phases would last until time N and the other would
begin after time N to infinity.
 The intrinsic value of the share is then the sum of the present values of two
dividends flows : (a) the flow from period 1 to N which we will call V 1 and (b)
the flow from period N+1 to infinity, referred to as V2. This means:
S 0 = V 1+ V 2
and, V1 = D1 / ( 1+ K )1 + D2 / (1+ K)2 + …….+ DN / (1+K)N
V2 = DN ( 1+ g ) / (k – g ) (1+K)N


EXAMPLE
A company paid a dividend of RS. 1.75 per share during the
Current year. It is expected to pay a dividend of Rs. 2 per
Share during the next year. Investors forecast a dividend of
RS.3 and Rs. 3.50 per share respectively during the two
Subsequent years. After that it is expected that annual
Dividends will grow at 10% per year into an indefinite future.
If the investor’s required rate of return is 20%, the intrinsic
Value of the share can be calculated as follows:
V1 = 2 / (1.2)1 + 3/ (1.2)2 + 3.5 / (1.2)3
= Rs. 5.78
V2 = 3.5(1.1) / (0.20- 0.10)(1.2)3 = 3.85/ (.10)(1.2)3
= Rs. 22.28
We know, S0 = V1+ V2
= 5.78 + 22.28 = 28.06


MULTIPLIER APPROACH TO SHARE VALUATION
 Many investor and analysts value shares by estimating an appropriate multiplier
for the share. The price-earnings ratio (P/E ratio) is the most popular
multiplier used for the purpose.
 P/E ratio = share price / EPS
 The intrinsic value of a share is taken as the current earnings per share or the
forecasted future earnings per share times the appropriate P/E ratio for the
share.
 For example, if the current EPS of a share is Rs. 8 and if the investor feels that
appropriate P/E ratio for the share is 12, then the intrinsic value of the share
would be taken as Rs. 96.
 Investment decision to buy or sell the share would be taken after comparing
this intrinsic value with the current market price of the share.


ASSIGNMENT FOR DISCUSSION- 2
NEW ISSUE MARKET OR PRIMARY MARKET AND ITS
FUNCTIONS
PARTIES INVOLVED:
 Manager to the issue
 Registrar to the issue
 Underwriters
 Bankers to the issue
 Government and statutory agencies etc….
PLACEMENT TO THE ISSUE
 Offer through prospectus
 Bought out deals
 Private placement
 Right issue
 Book building etc


ASSIGNMENT FOR DISCUSSION- 2
 GREEN SHOE OPTION
 RED HERRING PROSPECTUS
 E-IPO
 QUALIFIED INSTITUTIONAL BUYERS (QIBs)
 STOCKINVEST
 FUNCTIONS AND POWER OF SEBI
 SECONDARY MARKET
 PRIMARY VS. SECONDARY MARKET
 FUNCTIONS OF SECONDARY MARKET
 PRINCIPAL WEAKNESSES OF INDIAN STOCK MARKET


PORTFOLIO SELECTION THROUGH MARKOWITZ MODEL
 The objective of every rational investor is to maximize his returns and minimize the
risk .
 Diversification is the method adopted for reducing risk.
 It essentially results in the construction of portfolios.
 The proper goal of portfolio construction would be to generate a portfolio that provides
the highest return and the lowest risk.
 Such a portfolio would be known as the optimal portfolio or efficient portfolio.
 The process of finding the optimal portfolio is described as portfolio selection
 The conceptual framework and analytical tools for determining the optimal portfolio in
disciplined and objective manner have been provided by Harry Markowitz.
 His method of portfolio selection has come to known as the MAROWITZ MODEL.
 In fact MM is the base of modern portfolio theory.


FEASIBLE SET OF PORTFOLIOS
 With a limited number of securities an investor can create a very large number of
portfolios by combining these securities in different proportions.
 This is also known as the portfolio opportunity set .
 Each portfolio in the opportunity set is characterized by an expected return and a
measure of risk ,viz.,variance or standard deviation of returns.
 Not every portfolio in the opportunity set is of interest to an investor.
 In the opportunity set some portfolios will obviously be dominated by others.
 A portfolio will dominate another if it has either a lower standard deviation and the
same expected return as the other, or a higher expected return and the same standard
deviation as the other.
 Portfolios that are dominated by other portfolios are known as inefficient portfolios.


EFFICIENT SET OF PORTFOLIOS
PORTFOLIO NO. EXPECTED RETURN(%) STANDARD DEVIATION

1 5.6 4.5
2 7.8 5.8
3 9.2 7.6
4 10.5 8.1
5 11.7 8.1
6 12.4 9.3
7 13.5 9.5
8 13.5 11.3
9 15.7 12.7
10 16.8 12.9


EXERCISE-1
A share is currently selling for Rs.65/-. The company is expected to
Pay a dividend of Rs. 2.50 on the share at the end of the year. It is reliably
Estimated that the share will sell for Rs.78/- at the end of the year.

A. Assuming that the dividend and prices forecasts are accurate, would you
buy the share to hold it for one year, if your required rate of return were
12% ?

B. Given the current price of Rs.65/- and the expected dividend of Rs.2.50,
what would the price have to be at the end of one year to justify
purchase of the share today, if your required rate of return were 15% ?


SOLUTION
A. The share valuation model for one year holding period is:
S0 = D1/ (1 + K )1 + S1/ (1 + K )1
= 2.5/1.12 + 78 / 1.12
= 2.23 + 69.64 = 71.87
Since, the current price i.e Rs. 65 is lower than the intrinsic
Value of the share i.e. 71.87, the share is under priced and
can be bought.
B. 65 = 2.5 / 1.15 + X / 1.15
Or, X = 72.25
A selling price of Rs. 72.25 at the end of the year would justify
The purchase of the share at current price of Rs.65.


EXERCISE-2
 A company paid dividends amounting to Rs. 0.75 per share during
the last year. The company is expected to pay Rs. 2 per share
during the next year. Investors forecast a dividend of Rs.3 per
share in the year after that. Thereafter, it is expected that
dividends will grow at 10% per year into an indefinite future.
Would you buy/sell the share if the current price of the share is
Rs. 54? Investor’s required rate of return is 15%.


ANSWER
S0 = V1 + V2

V1 = 2 / (1+0.15)1 + 3 / ( 1+ 0.15)2 = 1.74 + 2.27 = 4.01
V2 = 3( 1+ 0.10) / ( 0.15 – 0.10 ) ( 1+0.15)2
= 3.3 / ( 0.05) ( 1.15)2 = 49.91

S0 = 4.01 + 49.91 = 53.92
The current market price of the share ( Rs. 54 ) is equal to
The intrinsic value ( Rs. 53.92). As the share is fairly priced
No trading is recommended.


CAPITAL ASSET PRICING MODEL ( CAPM )
 The model was developed in mid- 1960s by three researchers William Sharpe,
John Lintner and Jan Mossin.
 The CAPM is really an extension of the portfolio theory of Markowitz.
 The portfolio theory is a description of how rational investors should build
efficient portfolios and select the optimal portfolios.
 The CAPM derives the relationship between the expected return and risk of
individual securities and portfolios in the capital markets if everyone behaved in
the way the portfolio theory suggested.


 We have discussed earlier that the total risk of a security as measured by
standard deviation is composed of two components : systematic risk and
unsystematic risk or diversifiable risk.
 As investment is diversified and more and more securities are added to a
portfolio, the unsystematic risk is reduced.
 For a very well diversified portfolio, unsystematic risk tends to become zero
and the only relevant risk is systematic risk measured by beta (β) . Hence, it is
argued that the correct measure of a security’s risk is beta.
 It follows that the expected return of a security or a portfolio should be related
to the risk of that security or portfolio as measured by β.


 Beta is a measure of the security’s sensitivity to changes in market return.
 Beta values greater than one indicates higher sensitivity to market changes,
whereas beta value less than one indicates lower sensitivity to market changes.
A β value of one indicates that the security moves at the same rate and in the
same direction as the market. Thus, the beta of the market may be taken as
one.
 The relationship between expected return and beta of a security can be
determined graphically.
 Let us consider an XY graph where expected returns are plotted on the Y axis
and beta coefficients are plotted on the X axis. A risk free asset has an expected
return equivalent to Rf and beta coefficient of zero. The market portfolio M has
a beta coefficient of one and expected return equivalent to Rm. A straight line
joining these two points is known as the security market line ( SML ). This is
illustrated in next figure.



E®
M

E(Rm)

Rf

1 BETA


 The security market line provides the relationship between the
expected return and beta of a security or portfolio.
 This relationship can be expressed in the form of the following
equation : Ri = Rf + βi ( Rm - Rf )
 A part of the return on any security or portfolio is a reward for
bearing risk and the rest is the reward for waiting , representing
the time value of money.
 The risk free rate, Rf ( which is earned by a security which has no
risk ) is the reward for waiting. The reward for bearing risk is the
risk premium.


 The risk premium of a security is calculated as the product of beta
and the risk premium of the market which is the excess of
expected market return over the risk free return, that is
( Rm - Rf ), thus expected return on a security = risk free return
+ ( beta X risk premium of market )
 To illustrate the application of CAPM, let us consider a simple
example. There are two securities P and Q having values of beta
as 0.7 and 1.6 respectively. The risk free rate and expected
market return are assumed to be 6% and 15%.
 The expected return on security P may be worked out as shown
below: 6 + 0.7 ( 15 – 6 ) = 12.3%
 The expected return on Q = 6 + 1.6 ( 15 – 6 ) = 20.4%

 Security P with a beta of 0.7 has an expected return of 12.3%
whereas security Q with a higher beta of 1.6 has a higher expected
return of 20.4%.
 CAPM represents one of the most important discoveries in the
field of finance .
 The model postulates that systematic risk is the only important
ingredient in determining expected return.
 As investors can eliminate all unsystematic risk through
diversification, they can be expected to be rewarded only for
bearing systematic risk and not total risk.


PRICING OF SECURITIES WITH CAPM
 The CAPM can also be used for evaluating the pricing of
securities. It provides a framework for assessing whether a
security is underpriced, overpriced or correctly priced.
 According to CAPM, each security is expected to provide a return
commensurate with it’s level of systematic risk.
 A security may be offering more returns than the expected
returns, making it more attractive. On the contrary, another
security may be offering less return than the expected return,
making it less attractive.
 The expected return on a security can be calculated using the
CAPM formula. Let us designate it as the theoretical return.


PRICING OF SECURITIES WITH CAPM
 The real rate of return or estimated return to be realized from
investing in a security can be calculated as follows :
 Ri = ( P1 – P0 ) + D1 / P0
Here, Ri = The estimated return
P0 = Current market price
P1 = Estimated market price after one year
D1 = Anticipated dividend for the year
If the expected return on a security calculated according to CAPM is
lower than the actual or estimated return offered by that security,
the
Security will be considered to be underpriced otherwise overpriced.

EXAMPLE
Security Estimated Return (%) Beta
A 30 1.6
B 24 1.4
C 18 1.2
D 15 0.9
E 15 1.1
F 12 0.7
The risk free rate of return is 10%, while the market return is
Expected to be 18%.


EXAMPLE
 We can use CAPM to determine which of these securities are correctly priced.
 For this we have to calculate the expected return on each security using the
CAPM equation :
Ri = R f + β i ( R m - Rf )
Given that Rf = 10 and Rm = 18
A = 10 + 1.6 ( 18 – 10)
= 10 + 12.8
= 22.8%
Similarly, the expected return on each security can be
Calculated by substituting the beta value of each security
In the equation.


EXAMPLE
 The expected return according to CAPM and the estimated return of each
security are tabulated below:
SECURITY EXPECTED RETURN ESTIMATED RETURN
( CAPM)
A 22.8 30
B 21.2 24
C 19.6 18
D 17.2 15
E 18.8 15
F 15.6 12
Securities A and B provide more return than the expected return and hence may
be assumed to be underpriced. C,D,E,and F are overpriced.


EXERCISE – 1
 A security pays a dividend of Rs 3.85 and sells currently at Rs. 83.
The security is expected to sell at Rs. 90 at the end of the year.
The security has a beta of 1.15. The risk free rate is 5% and the
expected return on market index is 12%. Assess whether the
security is correctly priced.


SOLUTION -1
 To assess whether a security is correctly price, we need to calculate (a) the
expected return as per CAPM formula, and (b) the estimated return :
EXPECTED RETURN :
Ri = R f + β i ( R m - Rf )
= 5 + 1.15 ( 12 – 5 )
= 13.05%
ESTIMATED RETURN :
Ri = ( P 1 – P 0 ) + D 1 / P 0
= ( 90 – 83 ) + 3.85 / 83
= 13.07%
As the estimated return on the security is more or less equal to the expected
Return, the security is fairly priced.


EXERCISE – 2
 The following data are available to you as portfolio manager :
security estimated return ( %) beta standard deviation(%)
A 30 2.0 50
B 25 1.5 40
C 20 1.0 30
D 11.5 0.8 25
E 10.0 0.5 20
Market index 15 1.0 18
Govt. security 7 0 0
(a)In terms of the security market line, which of the securities listed above are
underpriced? (b) Assuming that a portfolio is considered using equal proportions
of the five securities listed above, calculate the expected return and risk of
Such a portfolio

SOLUTION - 2
 Expected return using CAPM model: A = 23% , B = 19% , C =
15% ,D = 13.4% , E = 11%
 Securities A, B and C are underpriced.
 Systematic risk of the portfolio( Βp ) = 1.16
 Expected return of portfolio using CAPM = 16.28%


MEASUREMENT OF SYSTEMATIC RISK ( β )
 Systematic risk is the variability in security returns caused by
changes in the economy or the market.
 All securities are affected by such changes to some extent, but
some securities exhibit greater variability in response to market
changes. Such securities are said to have higher systematic risk.
 The average effect of a change in the economy can be represented
by the change in the stock market index.
 The systematic risk of a security can be measured by relating that
security’s variability with the variability in the stock market Index.
 A higher variability would indicate higher systematic risk and vice
versa.


 The systematic risk of a security is measured by a statistical
measure called Beta.
 The input data required for the calculation of beta are the
historical data of returns of the individual security as well as the
returns of a representative stock market index.
 Two statistical methods may be used for the calculation of beta,
namely correlation method or the regression method.
 The regression model postulates a linear relationship between a
dependent variable and an independent variable. The model helps
to calculate the values of two constants, namely α and β


 Beta measures the change in the dependent variable in response to
unit change in the independent variable, while alpha measures the
value of the dependent variable even when the independent
variable has zero value. The regression equation is as follows:
Y=α + β x
where, Y = dependent variable
x = independent variable
α and β are constants.
The formula for α and β are :
α = Y¯ - β x¯and β = nΣXY –(ΣX)(ΣY)/ nΣX2 –
(ΣX)2


Where , n = number of items
Y¯ = Mean value of the dependent variable scores
X¯ = Mean value of independent variable scores
Y = dependent variable scores
X = independent variable scores
For the calculation of beta, the return of the individual security is
taken as the dependent variable, and the return of the market index
Is taken as the independent variable. The regression equation is :
Ri = α + β Rm
Here , Ri = Return of the individual security


 Rm = Return of the market index
 α = Estimated return of the security when the market is
stationary
 β = Change in the return of the individual security in
response to unit change in the market index. It is thus,
the measure of systematic risk of a security.
 A security can have betas that are positive, negative or
zero.
 As beta measures the volatility of a security’s return
relative to the market, the larger the beta, the more
volatile the security.
 A stock with beta greater than 1.0 has above average
risk, 1.0 means average risk and less than 1.0 means
lesser risk.

 For example, when market returns move up by 5%, a stock with
beta of 1.5 would find its returns moving up by 7.5 % ( 5x1.5).
Similarly, decline in market returns by 5% would produce a
decline of 7.5% in the return of the individual security.
 In using the beta factor for investment, the investor assume that
the relationship between the security variability and market
variability will continue to remain the same in future also.
 That’s why beta is calculated from historical data of returns.


EXAMPLE -1
 Monthly returns data (in %) are prescribed below for ITC stock and BSE index
for a 12 month period:
MONTH ITC BSE INDEX
1 9.43 7.41
2 0.00 - 5.33
3 - 4.31 -7.35
4 - 18.92 - 14.64
5 - 6.67 1.58
6 26.57 15.19
7 20.00 5.11
8 2.93 0.76
9 5.25 - 0.97


EXAMPLE-1

MONTH ITC BSE INDEX
10 21.45 10.44
11 23.13 17.47
12 32.83 20.15
CALCULATE BETA OF ITC STOCK.
ANS: 1.384


ARBITRAGE PRICING MODEL
 The Arbitrage Pricing Model ( APM) looks very similar to the
CAPM, but it’s features are significantly different.
 The CAPM is a single factor model whereas the APM is a multi
factor model.
 Arbitrage Pricing Theory , out of which the APM arises, states
that the expected return on investment is dependent upon how
that investment reacts to a set of individual macro – economic
factors (the degree of reaction being measured by the betas ) and
the risk premium associated with each of those macro-economic
factors.
 Basically, CAPM says that :
E ( R i ) = R f + βi ( Rm - R f )

ARBITRAGE PRICING MODEL
 Let ( Rm - Rf ) is expressed by λ
 APM holds that : E(Ri ) = Rf + λ1 βi1 + λ2 βi2 + λ3 βi3
 Where , λ1 , λ2 and λ3 are the average risk
premium for each of the three factors in the
model and βi1 , βi2 and βi3 are measures of the
sensitivity of the of the particular security ‘i’ to
each of the three factors.
 Several factors appear to have been identified
as being important viz. changes in the
industrial production in the economy, changes
in the inflation rate, real interest rate, level of
money supply in the economy etc.

PORTFOLIO REVISION
 In portfolio management, the maximum emphasis is placed on
portfolio analysis and selection which leads to the construction of
optimal portfolio. Very little discussion is seen on portfolio
revision which is as important as portfolio analysis and selection.
 The financial markets are continually changing. In this dynamic
environment, a portfolio that was optimal when constructed may
not continue to be optimal with the passage of time. It may have
to be revised periodically so as to ensure that it continues to be
optimal.


NEED FOR REVISION
 The primary factor necessitating portfolio revision is changes in
the financial markets since the creation of the portfolio. But,
sometimes it needs to be revised due to investors related factors
also like:
1. Availability of additional funds for investment
2. Change in risk tolerance
3. Change in the investment goal
4. Need of funds for alternative use.
Thus, the need for portfolio revision may arise from changes in the
Financial market or changes in the investor’s position, namely his
Financial status and preferences.

MEANING OF PORTFOLIO REVISION
 A portfolio is a mix of securities selected from a vast universe of
securities.
 Two variables determine the composition of a portfolio ; the first
is the securities included in the portfolio and the second is the
proportion of total funds invested in each security.
 Portfolio revision involves changing the existing mix of securities.
 This may be effected either by changing the securities currently
included in the portfolio or by altering the proportion of funds
invested in the securities.
 Portfolio revision thus leads to purchases and sales of securities.
 The ultimate aim of portfolio revision is maximization of returns
and minimization of risk.

CONSTRAINTS IN PORTFOLIO REVISION
 Transaction cost
 Taxes
 Statutory stipulations
 Intrinsic difficulty


PORTFOLIO REVISION STRATEGIES
ACTIVE REVISION STRATEGY
PASSIVE REVISION STRATEGY OR FORMULA PLANS:
1. CONSTANT RUPEE VALUE PLAN
2. CONSTANT RATIO PLAN
3. DOLLAR COST AVERAGING

The choice of the strategy would depend on the investor’s
Objectives, skills, resources and time.


ACTIVE REVISION STRATEGY
 Active revision strategy involves frequent and sometimes
substantial adjustments to the portfolio.
 Investors who undertake active revision strategy believe that
security markets are not continuously efficient. They believe that
securities can be mispriced at times giving an opportunity for
earning excess returns through trading in them.
 Thus, the objective of active revision strategy is to beat the
market.
 Active portfolio revision is essentially carrying out portfolio
analysis and portfolio selection all over again.
 Passive revision strategy, in contrast, involves only minor and
infrequent adjustment to the portfolio over time.

CONSTANT RUPEE VALUE PLAN
 This is one of the most popular or commonly used formula plans.
 In this plan, the investor constructs two portfolios, one
aggressive, consisting of equity shares and the other, defensive,
consisting of bonds and debentures.
 The purpose of this plan is to keep the value of the aggressive
portfolio constant, i.e. at the original amount invested in the
aggressive portfolio.
 As shares prices fluctuate, the value of the aggressive portfolio
keeps changing.
 When share prices are increasing, the total value of the aggressive
portfolio increases. The investor has to sell some of the shares


 When share prices are increasing, the total value of the aggressive
portfolio increases. The investor has to sell some of the shares
from his portfolio to bring down the total value of the aggressive
portfolio to the level of his original investment in it. The sale
proceeds will be invested in the defensive portfolio by buying
bonds and debentures. On the contrary, he will take opposite
action.
 Under this plan, the investor is effectively transferring funds from
the aggressive portfolio to the defensive portfolio and thereby
booking profit when share prices are increasing. Funds are
transferred from the defensive portfolio to the aggressive portfolio
when share prices are low. Thus the plan helps the investor to buy
shares when their prices are low and sell when prices are high.

 In order to implement this plan, the investor has to decide the
action points, i.e. when he should make the transfer of funds to
keep the rupee value of the aggressive portfolio constant. These
action points, or revision points, should be predetermined and
should be chosen carefully.
 For instance, the revision points may be predetermined as 10%,
15%, 20% etc. above or below the original investment in the
aggressive portfolio.
 If the revision points are too close, the number of transactions
would be more and the transaction costs would increase reducing
the benefits of revision.


 If the revision points are set too far apart, it may not be possible
to profit from the price fluctuations occurring between these
revision points.
 Let us consider an investor who has Rs.1,00,000 for investment.
He decides to invest Rs. 50,000 in an aggressive portfolio of
equity shares and the remaining Rs. 50,000 in a defensive
portfolio of bonds and debentures. He purchases 1250 shares
selling at Rs. 40 per share for his aggressive portfolio. The
revision points are fixed at 20% above or below the original
investment of Rs. 50,000.


PORTFOLIO EVALUATION
 Portfolio evaluation refers to the evaluation of the performance of
the portfolio.
 It is essentially the process of comparing the return earned on a
portfolio with the return earned on one or more other portfolios
or on a benchmark portfolio.
 Portfolio evaluation essentially comprises two functions,
performance measurement and performance evaluation.
 Performance measurement is an accounting function which
measures the return earned on a portfolio during the holding
period or investment period.


 Performance evaluation, on the other hand, addresses such issues
as whether the performance was superior or inferior, whether the
performance was due to skill or luck etc.
 While evaluating the performance of a portfolio, the return
earned on the portfolio has to be evaluated in the context of the
risk associated with that portfolio.
 The first step in portfolio evaluation is calculation of the rate of
return earned over the holding period.
 Return may be defined to include changes in the value of the
portfolio over the holding period plus any income earned over the
period.


 The rate of return earned by portfolio may be calculated and
compared with the rate of return earned by a representative stock
market index which can be used as a benchmark for comparative
evaluation.
 The portfolio may also be ranked in descending order of their
rates of return. But such straight forward rates of return
comparison may be incomplete and sometimes even misleading.
 The differential return earned by portfolio could be due entirely
to the differential risk exposure of the portfolio. Hence, the
returns have to be adjusted for risk before making any
comparision.


RISK ADJUSTED RETURNS
 One obvious method of adjusting for risk is to look at the reward
per unit of risk.
 Thus, the reward per unit of risk for different portfolios or mutual
funds may be calculated and the funds may be ranked in
descending order of the ratio. A higher ratio indicates better
performance.
 Two methods of measuring the reward per unit of risk have been
proposed by William Sharpe and Jack Trey nor respectively in
their pioneering work on evaluation of portfolio performance.


SHARPE RATIO
 The sharpe ratio is also known as the reward to variability ratio .
 It is the ratio of the reward or risk premium to the variability of
return or risk as measured by the standard deviation of return.
 The formula is: Sharpe ratio ( SR) = rp – rf / σp
Where,
rp = Realized return on the portfolio
rf = Risk free rate of return
σp = Standard deviation of portfolio return


TREYNOR RATIO
 The Trey nor ratio is also known as the reward to volatility ratio.
 It is the ratio of the reward or risk premium to the volatility of
return as measured by the portfolio beta.
 The formula is : Trey nor ratio ( TR) = rp – rf / βp
Where,
rp = Realized return on the portfolio
rf = Risk free rate of return
βp = portfolio beta
To understand the calculation of the two ratios
Let us consider an example:


EXAMPLE
 FUND RETURN(%) STANDARD DEVIATION (%) BETA
A 12 18 0.7
Z 19 25 1.3
M(market index) 15 20 1.0
The risk free rate of return is 7%.
The SR for the three funds are:
A = 12 – 7 / 18 = 0.277
Z = 19 – 7 / 25 = 0.48
M = 15 – 7 / 20 = 0.40
AS PER SHARPE’S PERFORMANCE MEASURE, FUND Z HAS PERFORMED
BETTER THAN BENCHMARK MARKET INDEX, WHILE FUND A HAS
PERFORM ED WORSE THAN THE MARKET INDEX.


EXAMPLE
The TR for the three funds are :
A = 12 – 7 / 0.7 = 7.14
Z = 19 – 7 / 1.3 = 9.23
M = 15 – 7 / 1.0 = 8
According to Trey nor performance measure also, fund Z has performed better
and
Fund A has performed worse than the benchmark.
 Both the ratios are relative measures of performance because they relate the
return to the risk involved.
 Sharpe uses the total risk as measured by standard deviation, while Trey nor
employs the systematic risk as measured by beta coefficient.
 For a fully diversified portfolio, Trey nor ratio would be the appropriate
measure of performance evaluation otherwise we should use Sharpe ratio.


Sapm

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