The stock of Foundations of Finance Inc. trades at $40 a share. Its end-of-year price and dividend will depend on the state of the economy by the end of the year as follows: Stock price $50 Dividend $2 Boom Normal economy Recession $43 $1 $34 $0.5 a. Calculate the expected holding-period return and standard deviation of the holding period return of Foundations of Finance Inc. Assume all three scenarios are equally likely. [1 point] b. Calculate the expected return and standard deviation of a portfolio invested half in Foundations of Finance Inc. and half in Treasury bills. Assume the return on Treasury bills is 4%. (1 point] Assume an investor has mean-variance utility preferences U = E(R) - 0.5A02 with coefficient of risk aversion A = 5. The market expected return is E(RM) = 5% and the standard deviation of the market is OM = 10%. The risk-free rate is Rs = 2%. Under CAPM, what's the weight of the risk-free assets (We) on your optimal portfolio? You run a regression of the excess returns of stock A on the excess returns of the market portfolio M and obtain the following output: RA - Rx = -.04 + 1.0x(RM - R ) + error The expected return of the market portfolio is 10% and the risk-free rate is 5%. a. What is the alpha of stock A? [1 point] b. What is the expected return of stock A? [1 point] C. Challenging: Suppose you are a fund manager and you want to build your portfolio such that it has an alpha of 2% and a beta of zero. What must be your portfolio's weights on stock A, the market, and risk-free asset? [2 points) To estimate the annual) expected return of a security we use the average of the historical (annual) returns of the security. a. What kind of average would you use? [1 point] I. Arithmetic average II. Geometric average Please circle ONE (if you circle both, it counts as no answer) b. Justify your answer: Why do you think we should use Arithmetic instead of Geometric average, or vice versa? [1 point] The following table reports the expected return and standard deviation of different portfolios. Investment Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4 Expected Return (E(R)) 0.12 0.15 0.21 0.24 Standard deviation (0) 0.30 0.50 0.16 0.21 Assume investors have mean-variance utility preferences U = E(R) - 0.5A02 a. What does A represent? [1 point I. Investors required return II. Investors risk aversion Investors demanded compensation for risk It is a quantity positively correlated with the certainty equivalent V. Preferences for one unit of return per 0.5 units of risk III. IV. Circle all the correct answers. There could be more than one. b. Which portfolio would an investor with A = 4 select? (2 points c. Which portfolio would a risk-neutral investor select? 2 points) Under CAPM, more risk-averse individuals hold a portfolio of risky assets that is tilted toward stocks with low covariance risk relative to the portfolio of risky assets held by less risk-averse individuals. II. III. True False Uncertain Why? 7 Investing all your wealth in the portfolio with the highest Sharpe Ratio is the strategy that will give you the best chance of meeting your goals. I. II. Yes No Why? Question 4 [3 points) Suppose that the Capital Asset Pricing Model (CAPM) holds. The market portfolio has an expected return of 9% and a standard deviation of 16%. Stock AAA has an expected return of 12%, a beta of 1.4, and a standard deviation of 28%. a. What is the risk-free rate? [1 point] b. What is the alpha of stock AAA? [1 point) c. What proportion of the total risk of stock AAA is idiosyncratic? [1 point] Suppose the interest rate is 5%. You inherit a trust (a perpetuity) that will eventually pay you $10,000 a year forever. You will receive the first $10,000 payment exactly three years from today. a. What is the trust worth at the moment you start collecting payments (i.e. in three years from today) [1 point] b. What is the trust worth today? [1.5 points] c. A bank offers to exchange your trust for another stream of yearly payments that also lasts forever but whose first payment will be made exactly one year from today instead of three. What is the highest yearly payment that the bank is willing to offer you in exchange for your trust? [1.5 points] Is it possible that a given investment option (e.g. a portfolio or an individual stock) has a low Sharpe ratio but still be part of a portfolio on the efficient frontier? I. II. Yes No Why? . The stock of Foundations of Finance Inc. trades at $40 a share. Its end-of-year price and dividend will depend on the state of the economy by the end of the year as follows: Stock price $50 Dividend $2 Boom Normal economy Recession $43 $1 $34 $0.5 a. Calculate the expected holding-period return and standard deviation of the holding period return of Foundations of Finance Inc. Assume all three scenarios are equally likely. [1 point] b. Calculate the expected return and standard deviation of a portfolio invested half in Foundations of Finance Inc. and half in Treasury bills. Assume the return on Treasury bills is 4%. (1 point] Assume an investor has mean-variance utility preferences U = E(R) - 0.5A02 with coefficient of risk aversion A = 5. The market expected return is E(RM) = 5% and the standard deviation of the market is OM = 10%. The risk-free rate is Rs = 2%. Under CAPM, what's the weight of the risk-free assets (We) on your optimal portfolio? You run a regression of the excess returns of stock A on the excess returns of the market portfolio M and obtain the following output: RA - Rx = -.04 + 1.0x(RM - R ) + error The expected return of the market portfolio is 10% and the risk-free rate is 5%. a. What is the alpha of stock A? [1 point] b. What is the expected return of stock A? [1 point] C. Challenging: Suppose you are a fund manager and you want to build your portfolio such that it has an alpha of 2% and a beta of zero. What must be your portfolio's weights on stock A, the market, and risk-free asset? [2 points) To estimate the annual) expected return of a security we use the average of the historical (annual) returns of the security. a. What kind of average would you use? [1 point] I. Arithmetic average II. Geometric average Please circle ONE (if you circle both, it counts as no answer) b. Justify your answer: Why do you think we should use Arithmetic instead of Geometric average, or vice versa? [1 point] The following table reports the expected return and standard deviation of different portfolios. Investment Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4 Expected Return (E(R)) 0.12 0.15 0.21 0.24 Standard deviation (0) 0.30 0.50 0.16 0.21 Assume investors have mean-variance utility preferences U = E(R) - 0.5A02 a. What does A represent? [1 point I. Investors required return II. Investors risk aversion Investors demanded compensation for risk It is a quantity positively correlated with the certainty equivalent V. Preferences for one unit of return per 0.5 units of risk III. IV. Circle all the correct answers. There could be more than one. b. Which portfolio would an investor with A = 4 select? (2 points c. Which portfolio would a risk-neutral investor select? 2 points) Under CAPM, more risk-averse individuals hold a portfolio of risky assets that is tilted toward stocks with low covariance risk relative to the portfolio of risky assets held by less risk-averse individuals. II. III. True False Uncertain Why? 7 Investing all your wealth in the portfolio with the highest Sharpe Ratio is the strategy that will give you the best chance of meeting your goals. I. II. Yes No Why? Question 4 [3 points) Suppose that the Capital Asset Pricing Model (CAPM) holds. The market portfolio has an expected return of 9% and a standard deviation of 16%. Stock AAA has an expected return of 12%, a beta of 1.4, and a standard deviation of 28%. a. What is the risk-free rate? [1 point] b. What is the alpha of stock AAA? [1 point) c. What proportion of the total risk of stock AAA is idiosyncratic? [1 point] Suppose the interest rate is 5%. You inherit a trust (a perpetuity) that will eventually pay you $10,000 a year forever. You will receive the first $10,000 payment exactly three years from today. a. What is the trust worth at the moment you start collecting payments (i.e. in three years from today) [1 point] b. What is the trust worth today? [1.5 points] c. A bank offers to exchange your trust for another stream of yearly payments that also lasts forever but whose first payment will be made exactly one year from today instead of three. What is the highest yearly payment that the bank is willing to offer you in exchange for your trust? [1.5 points] Is it possible that a given investment option (e.g. a portfolio or an individual stock) has a low Sharpe ratio but still be part of a portfolio on the efficient frontier? I. II. Yes No Why