FIN 320 SPRING 2024 Problem Set 6

1. Award: 10.00 points 2. Award: 10.00 points To convince investors to accept greater volatility, you must: decrease the risk premium. increase the risk premium. decrease the real return. decrease the risk-free rate. increase the risk-free rate. References Multiple Choice Learning Objective: 12-03 Discuss the historical risks on various important types of investments. Difficulty: 1 Basic Section: 12.3 Average Returns: The First Lesson Standard deviation is a measure of which one of the following? Average rate of return Volatility Probability Risk premium Real returns References Multiple Choice Learning Objective: 12-03 Discuss the historical risks on various important types of investments. Difficulty: 1 Basic Section: 12.4 The Variability of Returns: The Second Lesson            

3. Award: 10.00 points 4. Award: 10.00 points Inside information has the least value when financial markets are: weak form efficient. semiweak form efficient. semistrong form efficient. strong form efficient. inefficient. References Multiple Choice Learning Objective: 12-04 Explain the implications of market efficiency. Difficulty: 1 Basic Section: 12.6 Capital Market Efficiency Which one of the following statements related to market efficiency tends to be supported by current evidence? It is easy for investors to earn abnormal returns. Short-run price movements are easy to predict. Markets are most likely only weak form efficient. Mispriced stocks are easy to identify. Markets tend to respond quickly to new information. References Multiple Choice Learning Objective: 12-04 Explain the implications of market efficiency. Difficulty: 1 Basic Section: 12.6 Capital Market Efficiency            

7. Award: 10.00 points 8. Award: 10.00 points A stock had annual returns of 7 percent, − 28 percent, 13 percent, and 23 percent for the past four years. The arithmetic average of these returns is _____ percent while the geometric average return for the period is _____ percent. 3.75; 17.46 3.75; 1.72 17.75; 4.27 17.75; 17.46 3.75; 4.27 Arithmetic average = (.07 − .28 + .13 + .23)/4 Arithmetic average = .0375, or 3.75% Geometric return = [1.07(.72)(1.13)(1.23)] .25 − 1 Geometric return = .0172, or 1.72% References Multiple Choice Learning Objective: 12-01 Calculate the return on an investment. Difficulty: 2 Intermediate Section: 12.5 More about Average Returns The most important reason to diversify a portfolio is to: increase both returns and risks. eliminate all risks. eliminate asset-specific risk. eliminate systematic risk. lower both returns and risks. References Multiple Choice Learning Objective: 13-02 Discuss the impact of diversification. Difficulty: 1 Basic Section: 13.5 Diversification and Portfolio Risk            

9. Award: 10.00 points Consider the following information on three stocks: State of Economy Probability of State of Economy Rate of Return if State Occurs Stock A Stock B Stock C Boom .15 .27 .15 .11 Normal .65 .14 .11 .09 Bust .20 − .19 − .06 .05 A portfolio is invested 45 percent each in Stock A and Stock B, and 10 percent in Stock C. The expected T-bill rate is 3.2 percent. What is the expected risk premium on the portfolio? 5.55% 12.38% 1.67% 4.29% 8.75% E(R P ) Boom = .45(.27) + .45(.15) + .10(.11) = .2000 E(R P ) Normal = .45(.14) + .45(.11) + .10(.09) = .1215 E(R P ) Bust = .45(–.19) + .45(–.06) + .10(.05) = −.1075 E(R P ) = .15(.2000) + .65(.1215) + .20(−.1075) E(R P ) = .0875, or 8.75% RP P = .0875 − .032 RP P = .0555, or 5.55% References Multiple Choice Learning Objective: 13-01 Show how to calculate expected returns, variance, and standard deviation. Difficulty: 2 Intermediate Section: 13.1 Expected Returns and Variances      

11. Award: 10.00 points You have $21,600 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14.3 percent and Stock Y with an expected return of 8.1 percent. Your goal is to create a portfolio with an expected return of 12.5 percent. All money must be invested. How much will you invest in Stock X? $15,800 $18,273 $14,600 $15,329 $19,208 E( R p ) = .125 = .143 x + .081(1 − x ) x = .70968, or 70.968% Investment in Stock X = .70968($21,600) Investment in Stock X = $15,329 References Multiple Choice Learning Objective: 13-01 Show how to calculate expected returns, variance, and standard deviation. Difficulty: 2 Intermediate Section: 13.2 Portfolios      

12. Award: 10.00 points Your portfolio is invested 25 percent each in Stocks A and C, and 50 percent in Stock B. What is the standard deviation of your portfolio given the following information? State of Economy Probability of State of Economy Rate of Return if State Occurs Stock A Stock B Stock C Boom .07 .28 .14 .11 Good .55 .19 .12 .09 Poor .36 − .21 .07 .06 Bust .02 − .65 .03 − .03 6.52% 9.64% 12.72% 10.89% 7.39% E( R p ) Boom = .25(.28) + .5(.14) + .25(.11) = .1675 E( R p ) Good = .25(.19) + .5(.12) + .25(.09) = .1300 E( R p ) Poor = .25(−.21) + .5(.07) + .25(.06) = −.0025 E( R p ) Bust = .25(−.65) + .5(.03) +.25(−.03) = −.155 E( R p ) = .07(.1675) + .55(.13) + .36(−.0025) + .02(−.155) E( R p ) = .0792 σ p = [.07(.1675 − .0792) 2 + .55(.13 − .0792) 2 + .36(−.0025 − .0792) 2 + .02(−.155 − .0792) 2 ] .5 σ p = .0739, or 7.39% References Multiple Choice Learning Objective: 13-01 Show how to calculate expected returns, variance, and standard deviation. Difficulty: 2 Intermediate Section: 13.2 Portfolios      

14. Award: 10.00 points What is the expected return on this portfolio? Stock Expected Return Number of Shares Price per Share A − .02 1,400 $15.57 B .11 2,800 $57.08 C .05 3,600 $27.75 7.86% 9.43% 8.17% 4.67% 5.90% Portfolio value = 1,400($15.57) + 2,800($57.08) + 3,600($27.75) Portfolio value = $21,798 + 159,824 + 99,900 Portfolio value = $281,522 E( r ) = ($21,798/$281,522)( − .02) + ($159,824/$281,522)(.11) + ($99,900/$281,522)(.05) E( r )= .0786, or 7.86% References Multiple Choice Learning Objective: 13-01 Show how to calculate expected returns, variance, and standard deviation. Difficulty: 2 Intermediate Section: 13.2 Portfolios      

15. Award: 10.00 points 16. Award: 10.00 points Your portfolio has a beta of 1.24. The portfolio consists of 6 percent U.S. Treasury bills, 40 percent Stock A, and 54 percent Stock B. Stock A has a risk level equivalent to that of the overall market. What is the beta of Stock B? 1.44 1.52 1.56 1.84 1.96 β Portfolio = 1.24 = (.06)(0) + (.40)(1) + (.54β B ) β B = 1.56 The beta of a risk-free asset is zero. The beta of the market is 1. References Multiple Choice Learning Objective: 13-03 Summarize the systematic risk principle. Difficulty: 2 Intermediate Section: 13.6 Systematic Risk and Beta You own a portfolio equally invested in a risk-free asset and two different stocks. One of the stocks has a beta of 1.32. The total portfolio is equally as risky as the market. What is the beta of the second stock? 1.46 .88 1.94 1.68 1.54 β p = 1.0 = (1/3)(0) + (1/3)(β 2 ) + (1/3)(1.32) β 2 = 1.68 References Multiple Choice Learning Objective: 13-04 Describe the security market line and the risk-return trade-off. Difficulty: 2 Intermediate Section: 13.6 Systematic Risk and Beta            

19. Award: 10.00 points The common stock of Alpha Manufacturers has a beta of 1.24 and an actual expected return of 13.25 percent. The risk-free rate of return is 3.7 percent and the market rate of return is 11.78 percent. Which one of the following statements is true given this information? The actual expected stock return will graph above the security market line. The stock is currently underpriced. To be correctly priced according to CAPM, the stock should have an expected return of 13.56 percent. The stock has less systematic risk than the overall market. The actual expected stock return indicates the stock is currently overpriced. E( r ) = .037 + 1.24(.1178 − .037) E( r ) = .1372, or 13.72% The stock is overpriced because its actual expected return is less than the CAPM return. References Multiple Choice Learning Objective: 13-04 Describe the security market line and the risk-return trade-off. Difficulty: 2 Intermediate Section: 13.7 The Security Market Line      

20. Award: 10.00 points Suppose you observe the following situation: Security Beta Expected Return A 1.16 .1137 B .92 .0984 Assume these securities are correctly priced. Based on the CAPM, what is the return on the market? 9.99% 11.42% 10.35% 9.78% 11.01% (.1137 − R f )/1.16 = (.0984 − R f )/.92 R f = .0398, or 3.98% .1137 = .0398 + 1.16(R M − .0398) R M = .1035, or 10.35% References Multiple Choice Learning Objective: 13-04 Describe the security market line and the risk-return trade-off. Difficulty: 2 Intermediate Section: 13.7 The Security Market Line      