Multiple Choice Questions: (20 points) Choose the correct answer from the following choices. Make your selection clear and distinct, otherwise you will not get credit. 1.Asset A has an expected return of 15% and a reward-to-variability ratio of 0.4. Asset B has an expected return of 20% and a reward-to-variability ratio of 0.3. A risk-averse investor would prefer a portfolio using the risk-free asset and A) asset A B) asset B C) no risky asset D) cannot tell from data provided 2. The type of risk which is diversifiable is called A) systematic risk B) unsystematic risk C) systematic and unsystematic risk D) market-wide risk or market-risk 3.Diversification is most effective when security returns are A) high B) negatively correlated C) positively correlated D) uncorrelated 4.The Sharpe ratio also can be defined as A) the slope of the CAL B) the intercept of the CAL C) the risk to reward ratio D) the CAL to CML ratio 5. The optimal risky portfolio can be identified by finding A) the minimum-variance point on the efficient frontier B) the maximum-return point on the efficient frontier C) the tangency-point of the capital allocation line and the efficient frontier D) none of the above answers is correct Conceptual Questions-1 (10 points) Choose TRUE FALSE for the statements below from A to C. Make your selection clear and distinct, otherwise you will not get credit. Let an investor be considering two risky portfolios: X and Y to construct a complete portfolio C with a risk-free asset. The reward-to-variability ratio of portfolio X is 0.18 and reward to variability ratio of portfolio Y is 0.14. Choose TRUE/FALSE for the following statements. A. Lower reward-to-variability ratio of portfolio Y implies that its capital allocation line is steeper than that of X. (4 points) (TRUE FALSE) (4 points) B. CAL will plot above CAL, (TRUE FALSE) c. Combination of portfolio Y and risk-free asset will provide lower expected return for any level of risk than combination of portfolio X and risk-free asset. (2 points) (TRUE/FALSE) Conceptual Questions-2 (10 points) Aimee is considering investing in two risky portfolios ABC and XYZ. She wants to choose one risky portfolio (either ABC or XYZ) for investment purposes. A. If she decides to construct a complete portfolio by choosing one risky portfolio and a risk - free asset, what will determine the risky portfolio choice for Aimee's investment? (4 points) a. Reward-to-variability ratio (Sharpe Ratio) b. Correlation between ABC and XYZ. c. Risk tolerance level of investors B. Once she has selected the risky portfolio, what factor / characteristic will explain her allocation of wealth between the risky portfolio and risk-free asset in the complete portfolio? Why? [Hint: Use a graph to reflect on what you will explain in words] (6 points) Short Numerical Problems Problem 1 (10 points) A A mutual fund manager is offering a portfolio that will provide return of 6%, 8%, 12%, and 7% over the next four quarters respectively. What is the geometric average return per quarter? (4 points) B. Suppose you bought some stock at the beginning of the year for $35 per share. At the end of the year, the price is $40 per share. During the year, you got a $1.25 dividend per share. Compute the holding period return and dividend yield over a one-year period. (3 points) C The standard deviation of return on investment A is 0.15 while the standard deviation of return on investment B is 0.25. If the covariance of returns on A and B is 0.030, compute the correlation coefficient between the returns on A and B. (3 points) Problem 2 (20 points) An investor constructs an optimal-portfolio P with two risky stocks X and Y. The expected rate of return of stock X is 15% and standard deviation is 25% and expected return of stock Y is 12% and standard deviation is 20%. The risk-free rate is 5%. The correlation coefficient between the stocks is 0.15. The optimal-portfolio weights of X and Y are 67.04% and 32.96% respectively. A. Compute the expected return and standard deviation of the optimal portfolio. (5 points) B. If the investor wants an expected return of 18% from a complete-portfolio C formed by using the optimal-portfolio P and risk-free rate, what proportion of X, Y, and risk-free asset should the investor invest in the complete portfolio? (5 points) 5 Problem 2 (Continued) C. What is the standard deviation of the above complete-portfolio C that provides 18% return? (5 points) D. What are the reward-to-risk ratios of the optimal-portfolio P and the complete-portfolio C? Explain your results. Why they are same or different. Provide an argument by reflecting on the capital allocation lines on which the positions of C and can be plotted. (5 points) 6 Problem 3 (10 points) A. Use the following information to answer the questions below: Security Return(SI) Return(S2) 16% 20% B 12% 25% Risk-free asset return=4% SI is State-1 and S2 is State-2; Prob(S1) - 0.6; Prob(S2) -0.4 i). What is the expected return on Security A and the expected return on Security B? (2 points) ii). What is the portfolio expected return with 140% of wealth invested in A and the remainder in the risk-free asset via borrowing at the risk-free interest rate? (3 points) 7 Problem 3 (continued) A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Standard Deviation Expected Return 15% Stock fund (S) 32% 23 Bond fund (B) 9 The correlation between the fund returns is 0.15. What is the Sharpe ratio for the minimum variance portfolio (MVP)? (5 points) [Hint: The minimum-variance CAL is the line joining the risk-free asset to the minimum-variance portfolio (MVP). Now calculate slope of line after characterizing the minimum-variance portfolio.) 8 Problem 4 (20 points) Jack has a portfolio with two stocks ABC and XYZ with the following parameters: $ Invested Expected Standard Return Deviation of Return ABC $6000 8.23% 4.45% 7.96% XYZ $4000 9.76% The correlation coefficient between ABC and XYZ is 0.45 A. Compute expected return of the portfolio. (5 points) B. Calculate covariance of ABC and XYZ stock. (5 points) C. Compute the standard deviation of the portfolio. (10 points) 9