![Measuring Expected Return And Risk
• EXPECTED RATE OF RETURN
n
E (R) = pi Ri
i=1
STANDARD DEVIATION OF RETURN ( Expected Risk of the return)
= [ pi (Ri - E(R) )2
] 1/2
Example 3:
Mr. Red invested in equity shares of White Ltd., its anticipated returns and associated
probabilities are given below:
Return (%) -15 -10 5 10 15 20 30
Probability 0.05 0.10 0.15 0.25 0.30 0.10 0.05
You are required to calculate the expected rate of return and risk in terms of standard
deviation.](https://image.slidesharecdn.com/unittworiskandreturn-240922154400-942f8608/85/Unit-Two-Risk-and-Return-Accounting-Finance-ppt-14-320.jpg)
Unit Two Risk and Return Accounting Finance.ppt
- 1. Chapter 2 Risk and Return of Investment Meaning of Return the primary motivating force that drives investment. It is a gain or loss from an investment made. And it does have two components an income component and a capital gain or loss component. The income component is cash you receive while owning the asset while the capital gain or loss component is when the value of asset owned is appreciating in price or depreciating.
- 2. o The return may be defined in terms of (i)Realized return, i.e., the return which has been earned, 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. 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.
- 3. Meaning of Risk • It is the possibility that actual future returns will deviate from expected returns • From the perspective of financial analysis then, it is the possibility that the actual cash flow will be different from forecasted cash flows (returns). Therefore if an investment’s returns are known for certainty the security is called a risk free security. An example on this regard is Government treasury securities.
- 4. Types of Risks (I)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. 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. Such interest rate risk usually appears through the change in market price of fixed income securities. 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. It shows the impact of inflation or deflation on the investment. The inflation risk is related to interest rate risk because as inflation increases, the interest rates also tend to increase.
- 6. (I)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. • Types of Unsystematic Risk: (a)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. (b)Financial Risk: Refers to how a firm finances its activities. It refers to the degree of leverage or degree of debt financing used by a firm in the capital structure. Higher the degree of debt financing, the greater is the degree of financial risk. The presence of interest payment brings more variability in the earning available for equity shares. This is also known as financial leverage. (c) 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. • The operational risk is further classified into following types. Model risk: Model risk is the risk involved in using various models to value financial securities. It is due to probability of loss resulting from the weaknesses in the financial model used in assessing and managing a risk. People risk: arises when people do not follow the organization’s procedures, practices and/or rules. Legal risk: arises when parties are not lawfully competent to enter an agreement among them. Furthermore, this relates to regulatory risk, where a transaction could conflict with a government policy or particular legislation (law) might be amended in the future with retrospective effect.
- 9. Measures of Historical Rates of Return
- 11. Example :1 • 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.
- 12. Measuring of historical risk Example:2 •The rate of return of equity shares of Wipro Ltd., for past six years are given below: Year 01 02 03 04 05 06 Rate of return (%) 12 18 -6 20 22 24 Solution: Calculation of Average Rate of Return ( R ) Calculate variance and standard deviation
- 13. Example3:Suppose have collected returns for New Honda Dealership Inc. and for Harry’s Automotive Repair Inc. for past 4 years. Based on the return on Dealership and Repair : 1. Calculate average return 2. calculate variance and standard deviation Return Year Dealership Repair 2001 19 14 2002 39 8 2003 15 11 2004 0 19
- 14. Measuring Expected Return And Risk • EXPECTED RATE OF RETURN n E (R) = pi Ri i=1 STANDARD DEVIATION OF RETURN ( Expected Risk of the return) = [ pi (Ri - E(R) )2 ] 1/2 Example 3: Mr. Red invested in equity shares of White Ltd., its anticipated returns and associated probabilities are given below: Return (%) -15 -10 5 10 15 20 30 Probability 0.05 0.10 0.15 0.25 0.30 0.10 0.05 You are required to calculate the expected rate of return and risk in terms of standard deviation.
- 15. Calculation of expected return and risk in terms of standard deviation Return(R) Probability (P) (P ×R) (𝐑− 𝐑 ഥ ) (𝐑−𝐑 ഥ )𝟐 (𝐑−𝐑 ഥ )𝟐 x P -15 0.05 - 0.75 -24.5 600.25 30.0125 -10 0.10 -1.0 -19.5 380.25 38.0250 5 0.15 0.75 -4.5 20.25 3.0375 10 0.25 2.50 0.5 0.25 0.625 15 0.30 4.50 5.5 30.25 9.0750 20 0.10 2.00 10.5 110.25 11.0250 30 0.05 1.50 20.5 420.25 21.0125 1.00 𝑹 ഥ= 9.5% ∑ (𝐑−𝐑 ഥ )𝟐 x P =112.8125 Expected Return 𝑹 ഥ=9.5% Standard Deviation ∑ (𝐑−𝐑 ഥ )𝟐 x P =ξ𝟏𝟏𝟐.𝟖𝟏𝟐𝟓= 𝟏𝟎.𝟔𝟐𝟏
- 16. 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% You are required to calculate the expected rate of return and risk in terms of standard deviation. Solution: E(r) Dealership = 0.25(40) + 0.55(15) + 0.2(-1) = 18.05% E (r) Repair = 13.15% 198.1475 2 18.05 1 0.2 2 18.05 15 0.55 2 18.05 40 0.25 2 Dealership σ Dealership = 14.08% Repair = 4.20% Return is more uncertain for the dealership
- 17. 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. In such cases, a relative measure of dispersion should be employed for comparison. 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.
- 18. The formula for the calculation of coefficient of variation is: 𝐂 𝐨𝐞𝐟𝐟𝐢𝐜 𝐢𝐞𝐧 𝐭𝐨𝐟𝐕 𝐚𝐫𝐢𝐚𝐭𝐢𝐨𝐧= 𝐒 𝐭 𝐚𝐧𝐝𝐚𝐫𝐝𝐝𝐞𝐯 𝐢𝐚𝐭 𝐢𝐨𝐧 𝐌 𝐞𝐚𝐧 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. Example: 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: 𝐂 𝐨𝐞𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐭𝐨𝐟𝐕 𝐚𝐫𝐢𝐚𝐭 𝐢𝐨𝐧(𝐂 𝐨𝐦 𝐩𝐚𝐧𝐲𝐀 ) = 𝐁 𝐫𝟏𝟕,𝟎𝟕𝟖 𝟑𝟎,𝟎𝟎𝟎 𝒙𝟏𝟎𝟎= 𝟓𝟔.𝟗𝟑% 𝐂 𝐨𝐞𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐭𝐨𝐟𝐕 𝐚𝐫𝐢𝐚𝐭 𝐢𝐨𝐧ሺ 𝐂 𝐨𝐦 𝐩𝐚𝐧𝐲𝐁 ሻ= 𝐁 𝐫𝟐𝟓,𝟎𝟎𝟎 𝟑𝟓,𝟎𝟎𝟎 𝒙𝟏𝟎𝟎= 𝟕𝟏.𝟒𝟐%