![The rate of return from an investment consists of the yield and capital
appreciation:
𝐑𝐚𝐭𝐞 𝐨𝐟 𝐫𝐞𝐭𝐮𝐫𝐧 (𝐑 ) =
𝐈𝐭 + [𝐏𝐭 − 𝐏𝐭−𝟏]
𝐏𝐭−𝟏
Where Rt = Rate of return per time period 't'
It = Income for the period ’t’
Pt = Price at the end of time period ’t’
Pt-1 = Initial price, i.e., price at the beginning of the period ’t’
𝐑𝐚𝐭𝐞 𝐨𝐟 𝐫𝐞𝐭𝐮𝐫𝐧 𝐑 =
𝐈𝐭
𝐏𝐭−𝟏
+
𝐏𝐭 − 𝐏𝐭−𝟏
𝐏𝐭−𝟏
Current yield + Capital gain yield
13](https://image.slidesharecdn.com/invtchapter2ppt-240404191021-a0bd2805/85/Invt-Chapter-2-ppt-pptx-best-presentation-13-320.jpg)
Invt Chapter 2 ppt.pptx best presentation
- 1. CHAPTER TWO RISK AND RETURN 1
- 2. Concept of Return and Risk • Investment return and risk are fundamental to understanding market behavior. The entire scenario of security analysis is built on two concepts; Risk & return. • The risk and return constitute the framework for taking investment decision. • There are different motives for investment. – The most prominent among all is to earn a return on investment. 2
- 3. 1. Return • The return is the basic motivating force and the principal reward in the investment process. • The return may be defined in terms of –(i) Realized return, i.e., the return which has been earned, The realized returns in the past allow an investor to estimate cash inflows in terms of dividends, interest, bonus, capital gains, etc, available to the holder of the investment. and –(ii) Expected return, i.e., the return which the investor anticipates to earn over some future investment period. The expected return is a predicted or estimated return and may or may not occur. 3
- 4. 2. Risk: • Risk in investment analysis means that future returns from an investment are unpredictable. The concept of risk may be defined as the possibility that the actual return may not be same as expected. In other words, risk refers to the chance that the actual outcome (return) from an investment will differ from an expected outcome. • Investments having greater chances of variations are considered more risky than those with lesser chances of variations. 4
- 5. Types of Risk: 1. Systematic Risk/ Non-diversifiable risk –It refers to that portion of variability in return which is caused by the factors affecting all the firms. –It refers to fluctuation in return due to general factors in the market such as money supply, inflation, economic recessions, interest rate policy of the government, political factors, credit policy, tax reforms, etc. these are the factors which affect almost all firms. –The systematic risk is also called the general risk. 5
- 6. Types of Systematic Risk: a) Market risk: The market risk refers to variability in return due to change in market price of investment. There are different social, economic, political and firm specific events which affect the market price of equity shares. b) Interest Rate Risk: The interest rate risk refers to the variability in return caused by the change in level of interest rates. c) Purchasing-Power Risk/ Inflation Risk: The inflation risk refers to the uncertainty of purchasing power of cash flows to be received out of investment. 6
- 7. 2. Unsystematic Risk/ diversifiable risk • The unsystematic risk represents the fluctuation in return from an investment due to factors which are specific to the particular firm and not the market as a whole. • These factors are largely independent of the factors affecting market in general. • Since these factors are unique to a particular firm, these must be examined separately for each firm and for each industry. • These factors may also be called firm-specific as these affect one firm without affecting the other firms. 7
- 8. Types of Unsystematic Risk: 1) Business Risk: Business risk refers to the variability in incomes of the firms and expected dividend there from, resulting from the operating condition in which the firms have to operate. 2) Financial Risk: Refers to how a firm finances its activities. Investors will look at the firm’s capital structure. It refers to the degree of leverage or degree of debt financing used by a firm in the capital structure. 3) Operational risk: Operational risks are the business process risks failing due to human errors. This risk will change from industry to industry. It occurs due to breakdowns in the internal procedures, people, policies and systems. 8
- 9. The operational risk is further classified into following types. a) Model risk: Model risk is the risk involved in using various models to value financial securities. b) People risk: arises when people do not follow the organization’s procedures, practices and/or rules. c) Legal risk: arises when parties are not lawfully competent to enter an agreement among them. d) Political risk: is the risk that occurs due to changes in government policies. Such changes may have an unfavorable impact on an investor. 9
- 10. Causes of Risk: A number of factors which can cause risk in an investment arena include the following: –Wrong method of investment –Wrong timing of investment –Wrong quantity of investment –Interest rate risk –Nature of investment instrument –Nature of industry in which the company is operating –Maturity period (length of investment) –Terms of lending –National and international factors 10
- 11. Risk and Expected Return Risk and expected return are the two key determinants of an investment decision. Risk, in simple terms, is associated with the variability of the rates of return from an investment; how much do individual outcomes deviate from the expected value? Another major factor determining the investment decision is the rate of return expected by the investor. The rate of return expected by the investor consists of the yield and capital appreciation. 11
- 12. Determinants of the Rate of Return The three major determinants of the rate of return expected by the investor are: 1. The time preference risk-free real rate 2. The expected rate of inflation 3. The risk associated with the investment, which is unique to the investment. Hence, Required return = Risk-free real rate + Inflation premium + Risk premium 12
- 13. The rate of return from an investment consists of the yield and capital appreciation: 𝐑𝐚𝐭𝐞 𝐨𝐟 𝐫𝐞𝐭𝐮𝐫𝐧 (𝐑 ) = 𝐈𝐭 + [𝐏𝐭 − 𝐏𝐭−𝟏] 𝐏𝐭−𝟏 Where Rt = Rate of return per time period 't' It = Income for the period ’t’ Pt = Price at the end of time period ’t’ Pt-1 = Initial price, i.e., price at the beginning of the period ’t’ 𝐑𝐚𝐭𝐞 𝐨𝐟 𝐫𝐞𝐭𝐮𝐫𝐧 𝐑 = 𝐈𝐭 𝐏𝐭−𝟏 + 𝐏𝐭 − 𝐏𝐭−𝟏 𝐏𝐭−𝟏 Current yield + Capital gain yield 13
- 14. Example: The following information is given for a corporate bond. Price of the bond at the beginning of the year: Br. 90, Price of the bond at the end of the year: Br. 95.40, Interest received for the year: Br. 13.50. Compute the rate of return. Solution: The rate of return can be computed as follows: Rate of return R = 𝟏𝟑. 𝟓 + 𝟗𝟓. 𝟒𝟎 − 𝟗𝟎 𝟗𝟎 = 𝟎. 𝟐𝟏𝐨𝐫 𝟐𝟏 % 𝐩𝐞𝐫 𝐚𝐧𝐧𝐮𝐦 The return of 21% consists of: 15% current yield and 6% capital gain yield. 14
- 15. Example 2: The average market prices and dividend per share of Blue Ltd. for the past 6 years are given below: Required: Calculate the average rate of return for past 6 years. 15 Year Average market price (Br.) Dividend per share (Br.) 2002 38 1.8 2003 45 2.0 2004 53 2.5 2005 50 2.0 2006 61 2.6 2007 68 3.0
- 16. Year Average market price (Br.) Capital gain (%) Dividend/s hare (Br.) Div yield (%) ROR (%) A B = 𝐏𝐭−𝐏𝐭−𝟏 𝐏𝐭−𝟏 C D = C/(A-1) E = B + D 2002 38 - 1.8 - - 2003 45 18.42 2.0 5.26 23.68 2004 53 17.78 2.5 5.55 23.33 2005 50 -5.66 2.0 3.77 -1.89 2006 61 22.00 2.6 5.20 27.2 2007 68 11.48 3.0 4.92 16.4 16 Solution: R = 1/5 (23.68+23.33-1.89+27.2+16.40) = 1/5(88.72) = 17.75 %
- 17. Risk measurement • A useful measure of risk should somehow take into account both the probability of various possible "bad" outcomes and their associated magnitudes. • Instead of measuring the probability of a number of different possible outcomes, the measure of risk should somehow estimate the extent to which the actual outcome is likely to diverge from the expected. • For this purpose, range, variance, standard deviation and coefficient of Variation can be used to measure the risk. 17
- 18. Example: • The rate of return of equity shares of Wipro Ltd., for past six years are given below: Required: Calculate the average rate of return, variance and standard deviation. 18 Year 1 2 3 4 5 6 Rate of return (%) 12 18 -6 20 22 24
- 19. Calculation of Average Rate of Return ( R ) 𝑅 = ∑𝑅 𝑁 = 12 + 18 − 6 + 20 + 22 + 24 6 = 15 % σ2 = ∑(R − R)2 N 19 Year Rate of Return (%) Mean (𝐑) (𝐑 − 𝐑) (𝐑 − 𝐑)𝟐 2001 12 15 -3 9 2002 18 15 3 9 2003 -6 15 -21 441 2004 20 15 5 25 2005 22 15 7 43 2006 24 15 9 81 ∑(𝐑 − 𝐑)𝟐 =614
- 20. 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝜎2 = 614 6 = 𝟏𝟎𝟐. 𝟑𝟑 𝜎 = 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 102.33 = 𝟏𝟎. 𝟏𝟐 % Example 2: Suppose have collected returns for New Honda Dealership Inc. and for Harry’s Automotive Repair Inc. for past 4 years. 20 Return on Year Dealership Repair 2001 19 14 2002 39 8 2003 15 11 2004 0 19 ∑= 73 ∑=52 𝐑𝐞𝐭𝐮𝐫𝐧 𝐑 = ∑𝐑 𝐍 = 𝟕𝟑 𝟒 = 𝟏𝟖. 𝟐𝟓 = 𝟓𝟐 𝟒 = 𝟏𝟑
- 22. Example 3: Mr. Red invested in equity shares of White Ltd., its anticipated returns and associated probabilities are given below: Required: Calculate the expected rate of return and risk in terms of standard deviation. 22 Return (%) -15 -10 5 10 15 20 30 Probability 0.05 0.10 0.15 0.25 0.30 0.10 0.05
- 23. Return(R) Probability (P) (R × P) (𝐑 − 𝐑) (𝐑 − 𝐑)𝟐 (𝐑 − 𝐑)𝟐 x P -15 0.05 - 0.75 -24.5 600.25 30.0125 -10 0.10 -1.0 -19.5 380.25 38.025 5 0.15 0.75 -4.5 20.25 3.0375 10 0.25 2.50 0.5 0.25 0.0625 15 0.30 4.50 5.5 30.25 9.075 20 0.10 2.00 10.5 110.25 11.025 30 0.05 1.50 20.5 420.25 21.0125 1.00 𝑹 = 9.5% ∑(𝑹 − 𝑹)𝟐 x P = 112.25 23 Solution: Calculation of expected return and risk in terms of standard deviation Expected Return 𝑹 = 9.5% Standard Deviation ∑(𝐑 − 𝐑)𝟐 x P = 𝟏𝟏𝟐. 𝟐𝟓 = 10.60
- 24. Example 4: The probabilities and associated returns of Modern Foods Ltd. are given below: Calculation of expected return and risk in terms of standard deviation 24 Return (%) 12 15 18 20 24 26 30 Probability 0.05 0.10 0.24 0.26 0.18 0.12 0.05 Return(R) Probability (P) (P × R) (𝑹 − 𝑹) (𝐑 − 𝐑)𝟐 (𝐑 − 𝐑)𝟐 x P 12 0.05 0.60 - 8.56 73.2736 3.664 15 0.10 1.50 - 5.56 30.9136 3.091 18 0.24 4.32 - 2.56 6.5536 1.573 20 0.26 5.20 - 0.56 0.3136 0.082 24 0.18 4.32 3.44 11.8336 2.130 26 0.12 3.12 5.44 29.5936 3.551 30 0.05 1.50 9.44 89.1136 4.456 1.00 𝐑 = 20.56% ∑(𝐑 − 𝐑)𝟐 x P = 18.547
- 25. • Expected Return 𝑹 = 20.56% • Standard Deviation ∑(𝐑 − 𝐑)𝟐 x P = 𝟏𝟖. 𝟓𝟒𝟕 = 4.31 % Example: Suppose have estimated possible returns for New Honda Dealership Inc. and Harry’s Automotive Repair for the coming year based on how the economy does Return on: Economy Prob. Dealership Repair Boom 0.25 40% 6% Average 0.55 15% 15% Bust 0.20 -1% 17% Required: Calculate the expected rate of return and risk in terms of standard deviation. 25
- 26. Solution For Dealership 26 Return(R) Probability (P) (P × R) (𝑹 − 𝑹) (𝐑 − 𝐑)𝟐 (𝐑 − 𝐑)𝟐 x P 0.40 0.25 0.1 0.2195 0.0482 0.012 0.15 0.55 0.0825 -0.0305 0.0009 0.0005 -0.01 0.2 -0.002 -0.1905 0.0363 0.0073 1.00 𝐑 = 18.05% ∑(𝐑 − 𝐑)𝟐 x P = 0.0198 Dealership = 14.08% Repair = 4.20% Return is more uncertain for the dealership
- 27. Coefficient of Variation • Standard Deviation is an absolute measure. • It is not suitable for comparison, particularly when investment proposals involve different capital outlay or different monetary values of probable cash inflows. • For comparison in such cases, coefficient of variation approach is the best measure. • This realization is responsible for the emergence of coefficient of variation approach in capital risk analysis. 27 𝐂𝐨𝐞𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐭 𝐨𝐟 𝐕𝐚𝐫𝐢𝐚𝐭𝐢𝐨𝐧 = 𝐒𝐭𝐚𝐧𝐝𝐚𝐫𝐝 𝐝𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 𝐌𝐞𝐚𝐧
- 28. • Assume you reached at the result of mean of company A and B, were Br 30,000 and Br 35,000 respectively, and Standard deviation of 17,078 and 25,000 respectively, determine Coefficient of variation: Answer: 𝐂𝐨𝐞𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐭 𝐨𝐟 𝐕𝐚𝐫𝐢𝐚𝐭𝐢𝐨𝐧 (𝐂𝐨𝐦𝐩𝐚𝐧𝐲 𝐀) = 𝐁𝐫 𝟏𝟕, 𝟎𝟕𝟖 𝟑𝟎, 𝟎𝟎𝟎 𝒙 𝟏𝟎𝟎 = 𝟓𝟔. 𝟗𝟑 % 𝐂𝐨𝐞𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐭 𝐨𝐟 𝐕𝐚𝐫𝐢𝐚𝐭𝐢𝐨𝐧 𝐂𝐨𝐦𝐩𝐚𝐧𝐲 𝐁 = 𝐁𝐫 𝟐𝟓, 𝟎𝟎𝟎 𝟑𝟓, 𝟎𝟎𝟎 𝒙 𝟏𝟎𝟎 = 𝟕𝟏. 𝟒𝟐 % The coefficient of variation suggests that, the more is the coefficient of variation of a project, the greater is the risk associated with that project. 28