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Solutions for the assignment for risk and return 1. The following historical returns data for the last 10 years are gathered for stock XYTEL. Year Annual return(%) 1995 42.1 1994 -10.9 1993 20.4 1992 12.5 1991 10.3 1990 45.8 1989 -30.5 1988 11.4 1987 10.2 1986 -2.2 The stock price was $25.6 at the end of 1985, what would be the stock price at the end of 1989? A. $22.50 B. $21.36 C. $23.55 D. $24.15 E. $26.78 Answer: B Solution Closing price of 1989=(Closing price of 1985)(1+ return in 1986)(1+ return in 1987) (1+ return in 1988) )(1+ return in 1989) = 25.6(1-0.022)(1+0.102)(1+0.114)(1-0.305)=$21.36 2. Rank the historical volatility of the following portfolios in descending order: small stocks, Treasury bills, long-term government bonds, and common stocks. A. Common stocks, long-term government bonds, small stocks, and Treasury bills B. Treasury bills, small stocks, long-term government bonds, and common stocks C. Small stocks, common stocks, long-term government bonds, and Treasury bills D. Long-term government bonds, small stocks, common stocks, and Treasury bills E. Small stocks, long-term government bonds, common stocks, and Treasury bills Answer: C 3. The standard deviation of the security A and B is 10% and 30%, respectively. The correlation coefficient of A and B is precisely –1. What should be the portfolio weight of the security A so that the portfolio of A and B has a zero variance? A. 25% B. 50% C. 75% D. 10% E. 90% Answer: C Solution Since the correlation coefficient between A and B is -1, P wA A wB B wA (10) wB (30) 0% wA (10) (1 wA )(30) 0% Solving the above equation, the percentage weight of A is 75%. 4. Answer the following two questions concerning portfolio risk/return measures versus the risk/return measures of the individual securities that make up the portfolio. Assume all weights are positive. 1) Can the return on the portfolio ever be less than the lowest return on an individual security in the portfolio? 2) Can the variance of the portfolio ever be less than the lowest variance of an individual security in the portfolio? A. 1) yes, 2) yes B. 1) no , 2) yes C. 1) yes, 2) no D. 1) no , 2) no Answer: B 5. You have a portfolio consisting of equal amounts of GM stock and Treasury bills. If you replace one-third of the GM stock with more Treasury bills, the variance of the expected portfolio returns will A. increase B. decrease C. remain unchanged Answer: B 6. Which of the following statements is/are true about the variance of the possible future returns on a financial asset? I. The variance is a weighted average of the squared deviations of the actual returns from the expected returns. II. The greater the dispersion in the possible returns on the firm's stock, the greater the variance of the possible returns, all else equal. III. The variance of the possible returns on a risk-free asset is zero. A. I only B. II only C. III only D. II and III only E. I, II, and III Answer: E 7. The following table shows the forecasted distribution of returns on the market portfolio. What is the market risk premium if the risk-free rate is 8%? State Prob. Of State Return for State Boom 0.35 0.4 Good 0.40 0.2 Recession 0.10 0.1 Depression 0.15 -0.3 A. .070 B. .105 C. .165 D. .235 E. .305 Answer: B The expected return on the market portfolio is 18.5%. The market risk premium = The expected return on the market portfolio – the risk-free rate = 18.5% - 8% = 10.5% 8. What is the expected return of the asset B given that the portfolio return is 21% and given the following information? Asset Port. Weight Expected Return A 0.3 15% B 0.3 C 0.3 25% D 0.1 30% A. 13% B. 14% C. 14.5% D. 20% E. 17% Answer: D wP wA k A wB k B wC kC wD k D 21% (0.30)(15%) (0.30)(k B ) (0.30)(25%) (0.10)(30%) k B 20% 9. Given the following information on the portfolio and that the beta of the portfolio is 0.881, what is the beta of E? Stock Investment ($) Beta A 15,000 0.65 B 10,000 0.70 C 5,000 1.10 D 12,500 0.89 E 7,500 A. 1.22 B. 1.32 C. 1.42 D. 1.52 E. 1.62 Answer C Solution Question 9 portfolio beta problem portfolio beta= 0.881 security amount invested($) security beta portfolio weight weighted beta A 15000 0.65 0.3 0.195 B 10000 0.7 0.2 0.14 C 5000 1.1 0.1 0.11 D 12500 0.89 0.25 0.2225 E 7500 0.15 50000 1 weighted beta of E= 0.2135 beta of E= 1.42 10. Under the CAPM, the ratio of the risk premiums of two assets is the same as the ratio of their betas. A. True B. False Answer A Since kA = kf + (A)(RPM) kA - kf = (A)(RPM) kB = kf + (B)(RPM) kB - kf = (B)(RPM) kA k f RP A M A kB k f RP B M B 11. You hold three stocks in your portfolio - stock A, stock B, and stock C. The portfolio beta is 1.50. Stock A constitutes 20 percent of the dollar value of your holdings and has a beta of 1.00. If you sell all of your holdings in stock A, and replace them with an equal investment in stock D (which has a beta of 1.25), your new portfolio beta will be ________ . A. .850 B. 1.250 C. 1.450 D. 1.550 E. 1.625 Answer: D Solution Let R stand for the remainder of the portfolio. Then, Before rebalancing the portfolio, we have wA A wR R P (0.2)(1.00) (0.8) R 1.50 0.8 R 1.50 0.20 1.30 1.30 R 1.625 0.8 After rebalancing the portfolio, we have wD D wR R P (0.2)(1.25) (0.8)(1.625) p 1.55 p 12. You hold five stocks in your portfolio - stock A, stock B, stock C, stock D, and stock E. The portfolio beta is 1.00. Stock E constitutes 20 percent of the dollar value of your holdings and has a beta of 1.50. If you sell all of your holdings in stock E, and use half the funds to invest in stock F (which has a beta of .60), and the remainder to invest in the risk-free asset, your new portfolio beta will be ________. A. .76 B. .89 C. .97 D. 1.18 E. 1.24 Answer: A Solution Let R stand for the remainder of the portfolio. Then, Before rebalancing the portfolio, we have wE E wR R P (0.2)(1.5) (0.8) R 1 0.8 R 1 0.3 0.7 0.7 R 0.875 0.8 After rebalancing the portfolio, we have wF F w f f wR R P (0.1)( 0.6) (0.1)( 0.0) (0.8)( 0.875 ) p 0.06 0.7 0.76 p 13. The standard deviation of returns on Japanese stocks is 16.81 percent. The average return is 12.73 percent. Assume that the frequency distribution of returns is essentially normal. Then the lower limit of 95% confidence interval of returns on Japanese stocks is A. 0% B. –4.08% C. -20.89% D. –37.70% E. -6.05% Answer C Solution The lower limit of the 95 percent confidence interval = average return – (2)(standard deviation) = 12.73 – (2)(16.81) = -20.89% Use the following information to answer questions 14-16. Returns in the next period for two stocks, A and B, and the market, M, are given by the following probability distribution: Associated Rate of Return State of the Probability of A B M Economy the State Boom 0.25 40% 50% 40% Normal 0.5 0 5 15 Recession 0.25 -10 -5 -15 14. What is the expected rate of return for the portfolio AB, which consists of 50% invested in A and 50% invested in B? A. 6.625% B. 7.625% C. 8.625% D. 9.625% E. 10.625% Answer: E E[kAB]= wA E[kA]+ wB E[kB] =(0.5)(7.5%) + (0.5)(13.75) =10.625% 15. What is the standard deviation of the portfolio AB, which consists of 50% invested in A and 50% invested in B? The correlation coefficient between A and B is 1. A. 17.26 B. 18.26 C. 19.26 D. 20.26 E. 21.26 Answer: D Solution Since the correlation coefficient between A and B is 1, P wA A wB B (0.5)(19 .20 ) (0.5)( 21 .32 ) 20 .26 % 16. What is the beta of A? A. 0.88 B. 0.98 C. 0.58 D. 0.68 E. 0.78 Answer: A Solution ~ ~ cov(k A , k M ) 334 0.88 P 2 M 380 17. To estimate the beta of Ford’s common stock, you regressed the monthly returns of Ford on the monthly returns of the S&P 500. The intercept of the regression line was 3% and the estimated slope was 0.6. If the S&P 500 is expected to earn 15% return this year and the yield on the T bill is 5%, what is the expected annual return on the Ford common stock this year according to the CAPM? A. 11% B. 7% C. 8% D. 9% E. 10% Answer: A Solution The estimated beta of the Ford stock is 0.6 Using the equation of the SML, k k RF (k M k RF ) k 5 0.6(15 5) 11% 18. Investing only in a S&P 500 Index mutual fund that should have a beta of 1.0 and the riskless security such as T-bills is probably the simplest asset allocation strategy. Assume that the expected return of the S&P 500 Index is 12% and the expected return on the treasury bills is 5%. If you want to get an expected return of 10% per year, what should be the weight on the S&P 500 Index mutual fund? A. 67.52% B. 70.23% C. 73.56% D. 72.56% E. 71.43% Answer: E E[kM,f]= wM E[kM]+ wf kf =wM (12%)+ wf (5%) =wM (12%)+ (1-wM)(5%) 7wM = 5 wM = 71.43%

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posted: | 9/15/2011 |

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