2.1. Chapter 8 Risk and Returns Answer [PDF]

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NAME: DEBUYAN, JOEBET L. COURSE, YEAR & SECTION: BSMA II-B CHAPTER 8 Risk and Returns 8-5



BETA AND REQUIRED RATE OF RETURN The stock of Orange Inc., has a required rate return of 14%, the required rate of return on the market 11% and the risk-free rate is 5%



Given: r=14% rRF=5% rM=11% a. What is the market risk premium? FORMULA: rM-rRF SOLUTION: 11%-5%=6% ANSWER: 6% b. What is the stock’s beta? FORMULA: r=rRF+(rM-rRF)b SOLUTION: 14%=5%+(11%-5%)b 14%=5%+6%b 9%=6%b b=1.5 ANSWER: 1.5 c. If the required return on the market increased to 12%, what would happen to the stock’s required rate of return? Assume that the risk-free rate and the beta remain unchanged. FORMULA: r=rRF+(rM-rRF)b SOLUTION: 5%+(12%-5%)×1.5 5%+10.5% r= 15.5% ANSWER: 15.5% 8-6



EXPECTED RETURNS expected future returns: Probability 0.1 0.2 0.4 0.2 0.1



Stocks X and Y have the following probability distributions of X (10%) 2 12 20 38



Y (35%) 0 20 25 45



a. Calculate the expected rate of return for Stock Y (rx= 12%). rY= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%) = 14% versus 12% for X.



ANSWER: ry= 14% rx=12%



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b. Calculate the standard deviation of expected returns, x, for Stock X (y = 20.35%). Now calculate the coefficient of variation for Stock Y. Is it possible that most investors will regard Stock Y as being less risky than Stock X? Explain. SOLUTION: = (-10% – 12%)2(0.1) + (2% – 12%)2(0.2) + (12% – 12%)2(0.4) + (20% – 12%)2(0.2) + (38% – 12%)2(0.1) = 148.8%. ANSWER: X = 12.20% versus 20.35% for Y. CVX = X/ rX = 12.20%/12% = 1.02 ANSWER: CVY = 20.35%/14% = 1.45.



YES, as we computed that stock Y has a larger percentage of returns expectations than Stock X. 8-7



PORTFOLIO REQUIRED RETURN Jack is the manager of a $10 million mutual fund and he decides to invest in the three stocks with the following amounts and betas Stock A B C



Investment $3M 2M 5M



Beta 1.60 0.90 (0.70)



If the required market return is 12% and the risk-free rate is 4%, what is the fund’s required rate of return? Portfolio beta = (0.3)(1.6) + (0.2)(0.9) + (0.5)(-0.7) = 0.48 + 0.18 – 0.35 = 0.31. rp



= rRF + (rM – rRF)(bp) = 4% + (12% – 4%)(0.31) = 6.48%.



ANSWER: 6.48% 8-10



CAPM AND REQUIRED RETURN Bradford Manufacturing Company has a beta of 1.45, while Farly Industries has a beta of 0.85. The required return on an index fund that holds the entire stock market is 12.0%. The risk-free rate of interest is 5%. By how much does Bradford’s required return exceed Farley’s required return?



FORMULA: r=rM+(rM-rRF)b SOLUTION: BRADFORD COMPANY r=12%+(12%-5%)1.45 r=12%+(7%)1.45 r=22.15% FARLEY COMPANY r=12%+(12%-5%)0.85 r=12%+(7%)0.85 r=17.95%



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Exceed of returns= Br-Fr = 22.15%-17.95% =4.2% ANSWER: 4.2% 8-13



CAPM, PORTFOLIO RISK, AND RETURN Consider the following information for three stocks, Stocks X, Y, and Z. The returns on the three stocks are positively correlated but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.) Stock X Y Z



Expected Return 9.00% 10.75 12.50



Standard Deviation 15% 15 15



Beta 0.8 1.2 1.6



Fund Q has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.) a. What is the market risk premium rM - rRF? Using Stock X: SOLUTION:



9% = rRF + (rM – rRF)bX 9% = 5.5% + (rM – rRF)0.8 (rM – rRF) = 4.375%. ANSWER: 4.375% b. What is the beta of Fund Q? SOLUTION:



bQ = 1/3(0.8) + 1/3(1.2) + 1/3(1.6) bQ = 0.2667 + 0.4000 + 0.5333 bQ = 1.2. ANSWER: 1.2 c. What is the required return of Fund Q? SOLUTION:



rQ = 5.5% + 4.375%(1.2) rQ = 10.75%. ANSWER: 10.75% d. Would you expect the standard deviation of Fund Q to be less than 15%, equal to 15%, or greater than 15%? Explain. ANSWER: Due the returns on the 3 stocks included in Portfolio Q are not perfectly positively correlated therefore one would expect the standard deviation of the portfolio to be less than 15%. 8-14



PORTFOLIO BETA Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio’s beta is 1.12. Now suppose



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you decided to sell one of the stocks in your portfolio with a beta of 1.0 for $7,500 and use the proceeds to buy another stock with a beta of 1.75. What would your portfolio’s new beta be? SOLUTION:



Old portfolio beta 1.12= 0.95b + 0.05 1.07 = 0.95b 1.1263 = b.



$142,500 $7,500 = $150,000 (b) + $150,000 (1.00)



New portfolio beta = 0.95(1.1263) + 0.05(1.75) = 1.1575  1.16. ANSWER: 1.16 8-15



CAPM AND REQUIRED RETURN AM Inc. has a beta of 1.4 and PM Inc. has a beta is 0.7. The required market return is 16% and the risk-free rate is 7%. After the financial crisis, the expected rate of inflation built into risk-free rate falls by 2 percentage points and the required market return falls to 12%. Other conditions do not change. What will be the respective differences in the required returns for AM Inc. and PM Inc.?



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Required Returns of PM Inc. decrease 3.4%



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PORTFOLIO BETA Suppose you are the manager of a mutual fund and hold a $10million stock portfolio with a beta of 1.30. The required market risk premium 7% and the risk-free rate is 4%. You expect to invest an additional fund of $5 million in a number of stocks and the final required return of the aggregated fund is expected to be 16%. What should be the average beta of the new stocks added to the portfolio.



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1.7143= (10,000,000/15,000,000)+(5,000,000x/15,000,000) 1.7143= 0.867 + 0.333X 0.8473= 0.333X X= 2.544. ANSWER: 2.544