4. (10 pts) Portfolios A and B lie on the capital allocation line shown below. What is the risk-free rate X?

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1 First Midterm Exam Fall 017 Econ Closed Book. Formula Sheet Provided. Calculators OK. Time Allowed: 1 Hour 15 minutes All Questions Carry Equal Marks 1. (15 pts). Investors can choose to purchase either a risky portfolio or a risk-free asset. The riskfree rate is 3 percent per annum. The risky portfolio costs $480 today. In one year s time, it will be worth $300 with probability 0.5, and $750 with probability What is the Sharpe ratio of the risky portfolio?. (0 pts). There are two possible outcomes for stocks A and B; each will either earn a return of +0% or -10%. Here are the probabilities of the four possible joint outcomes: B return is -10% B return is +0% A return is -10% 10% 0% A return is +0% 0% 50% Find the covariance between the percentage returns of stocks A and B. 1/ 3. (10 pts) Sue s utility function is w where w is wealth in dollars. Sue is offered an asset which has a 30% chance of being worth $100 and a 70% chance of being worthless. What is the certainty equivalent of this gamble for Sue? 4. (10 pts) Portfolios A and B lie on the capital allocation line shown below. What is the risk-free rate X? 5. (15 pts) Suppose that there are two possible assets: debt and equity. Debt has an expected return of 6% and a standard deviation of 5%. Equity has an expected return of 10% and a standard deviation of 10%. Debt and equity are mutually uncorrelated. The risk-free rate is %. If an investor is selecting a portfolio of debt and equity to maximize the Sharpe ratio, what share will (s)he invest in equity? 1

2 6. (30 points) Multiple choice questions. Only one option is correct. Please indicate which one it is. (i) Which of the following best describes the reforms to money market mutual funds that took place in the fall of 016? A. Introduction of floating net asset value for all money market mutual funds. B. Introduction of floating net asset value for retail funds investing in Treasury securities. C. Introduction of floating net asset value for retail funds investing in commercial paper. D. Introduction of floating net asset value for institutional funds investing in Treasury securities. E. Introduction of floating net asset value for institutional funds investing in commercial paper. (ii) Which of the following is the CPI total inflation rate over the 1 months ending in July 017 (the data released as of our class discussion of inflation)? A. 0%. B. 1.7%. C. 3.% D. 6.1%. E. 10.4% (iii) Which of the following describes the tri-party repo market? A. A trading venue for executing repo market transactions. B. A market for repo contracts denominated in a foreign currency. C. A repo market in which each lender has three different borrowers. D. A repo market that does not use collateral. E. A market for repo in which the collateral management is handled by a third party. (iv) If a Treasury Bill maturing 90 days after settlement has a face value of $10,000 and a quoted yield of 1 percent per annum, how much will you pay for it? A. $10,000 B. $9,975 C. $9,970 D. $9,960 E. $10,100 (v) The effective annual rate on an investment is 6.8 percent. What is the annual percentage return with continuous compounding? A..86 percent B percent C 6.58 percent D. 6.9 percent E percent

3 (vi) Which of the following is true of the historical distribution of annual returns on the S&P500 index? A. They have a standard deviation of 8 percent per annum and are normal B. They have a standard deviation of 8 percent per annum and are skewed to the left C. They have a standard deviation of 8 percent per annum and are skewed to the right D. They have a standard deviation of 17 percent per annum and are skewed to the left E. They have a standard deviation of 17 percent per annum and are skewed to the right (vii) Suppose that there are two risky assets: stock X and stock Y, and a riskfree asset. John and Sue are both maximize mean-variance utility. John invests 50% of his wealth in the riskfree asset, 0% in stock X and 30% in stock Y. Sue invests none of her wealth in the riskfree asset. How much of her wealth does she invest in stock Y? A. 30%. B. 40% C. 60% D. 80% E. It cannot be determined from the information provided. (viii) Suppose that there are 5 stocks, each of which has returns with standard deviation 5 percent. The stocks are all mutually uncorrelated. You form an equal weighted portfolio of these stocks. What is the standard deviation of this portfolio? A. 1 percent. B. 5 percent. C. 6.5 percent. D. 10 percent. E. 5 percent. (ix) Mary has a wealth of $100 and a utility function uw ( ) = ln( W) where W is wealth. What is her coefficient of relative risk aversion? A. 0. B. 0.5 C. 1 D. E. 10 A (x) Mark has a utility function Er () σ where Er () is the expected return, σ is variance, and A is the coefficient of absolute risk aversion, which is equal to. Mark is splitting his wealth between one risky asset with an expected return 10% and a standard deviation 0% and a risk-free asset with a return of 5%. If he is maximizing utility, what fraction will he invest in the risky asset? A. 1.5% B. 50% C. 6.5% D. 75% E. 100% 3

4 Solutions and Grading Rubic. Er () r 1. The Sharpe ratio is f σ () r r f = The return is = with probability 0.5 and 70 = 9 with probability So Er () = * + * = = The variance of returns is , *( ) + *( ) = *( ) + *( ) = = , The Sharpe ratio is points were awarded for computing the expected return correctly, 5 points were awarded for computing the variance of returns correctly, and 5 points were awarded for getting the Sharpe ratio. Students who wrote down the formula for the Sharpe ratio correctly, but got the expectation and variance wrong still got 5 points. (However, it had to be clear that the Sharpe Er ( p) rf ratio was, not just ratios of arbitrary variables). points were deducted for purely σ p algebraic mistakes.. For both stocks A and B, the probability of returns being -10% is 30% and the probability of returns being +0% is 70%. So the expected return on stocks A and B are both which is 11 percent. So the covariance is 0.1*( 10 11)*( 10 11) + 0.*( 10 11)*(0 11) + 0.*(0 11)*( 10 11) + 0.5*(0 11)*(0 11) = 9% 8 points for knowing that the expected return on both stocks was 11 percent. 17 points for getting everything right, including the precise form of the covariance, but making an algebra mistake. 3. The certainty equivalent solves 1/ 1/ 1/ C = 0.3* *0 = 3 Hence the certainty equivalent is $9. No partial credit was given on this question. 4. The weight on equity is ( )* = ( )* ( )* points off for algebra mistake if everything was set up correctly. 5 points off if failed to subtract the risk free rate from returns to get excess returns. (5 points off even if subtracted the 4

5 risk free rate of one of the two risky returns but not the other). No credit if the formula was otherwise mis-applied. 5. %. No partial credit was given on this question. 6. (i) E (ii) B (iii) E (iv) B (v) C (vi) D (vii) C (viii) B (ix) C (x) C 3 points for each part. 5