EC3114 - Financial Economics Vinay P NUNDLALL Problem Set 3 Solutions Question 1 Data: If = 3%, E(rm) = 15%, OM = 36%, and 'f = 12% B The Capital Market Line and indifference curves are as follows: Borrower P 15 S (y > 1) 12 Lender E[rp] - rf S (y < 1) 3 F 36 Std Deviation For y to be less than 1.0 (that the investor is a lender), risk aversion (A) must be large enough such that: y= A? M ~2 A> 0.15-0.03 > =0.93 0.362
For y to be greater than 1 (the investor is a borrower), A must be small enough: y= E(rm) -rf> 1 A< 2 AOM =0.23 0.362 0.15-0.12 For values of risk aversion within this range, the client will neither borrow nor lend but will hold a portfolio composed only of the optimal risky portfolio: y = 1 for 0.23 ? A ? 0.93 Question 2 1. Which of the following statements is(are) true? I) Risk-averse investors reject investments that are fair games. II) Risk-neutral investors judge risky investments only by the expected returns. III) Risk-averse investors judge investments only by their riskiness. IV) Risk-loving investors will not engage in fair games. A. I only B. II only C. I and II only D. II and III only E. II, III, and IV only C. Risk-averse investors consider a risky investment only if the investment offers a risk premium. Risk-neutral investors look only at expected returns when making an investment decision. 2. A portfolio has an expected rate of return of 0.15 and a standard deviation of 0.15. The risk-free rate is 6%. An investor has the following utility function: U = E(r) - 0.5 As2 Which value of A makes this investor indifferent between the risky portfolio and the risk-free asset? A. 5 B. 6 C. 7 D. 8 E. 9 D. U = 0.06 = 0.15 - Aff2(0.15)2; 0.06 - 0.15 = - Aff2(0.0225); -0.09 = - 0.01125A; A = 8; U = 0.15 - 8ff2(0.15)2 = 6%; U(Rf) = 6%.
3. The exact indifference curves of different investors A. cannot be known with perfect certainty. B. can be calculated precisely with the use of advanced calculus. C. although not known with perfect certainty, do allow the advisor to create more suitable portfolios for the client. D. cannot be known with perfect certainty and although not known with perfect certainty, do allow the advisor to create more suitable portfolios for the client. D. Indifference curves cannot be calculated precisely, but the theory does allow for the creation of more suitable portfolios for investors of differing levels of risk tolerance. 4. Steve is more risk-averse than Edie. On a graph that shows Steve and Edie's indifference curves, which of the following is true? Assume that the graph shows expected return on the vertical axis and standard deviation on the horizontal axis. I) Steve and Edie's indifference curves might intersect. II) Steve's indifference curves will have flatter slopes than Edie's. III)