Portfolio Management: Practice Problems

1301 WordsJan 31, 20126 Pages
UNIVERSITY OF ILLINOIS AT CHICAGO Liautaud Graduate School of Business Department of Finance Professor Hsiu-lang Chen 1 Practice Problem I In choices under uncertainty, individuals maximize his or her expected utility U! Part I. Expected Utility (Lecture 1) A casino company offers a simple game which is described as follows: The prize of the game depends on two unbiased coins you toss. If both heads appear, you get $200. If both tails appear, you get $100. Otherwise, you get $150. 1. The company offers you a promotion as follows: A cash of $145 or a chance to win the prize of the coin game. Your utility function is U(W)= -1/W. What is your choice? What is the lowest cash offer that you are willing to quit from playing the game? 2. After…show more content…
d. What would be the investor 's certainty equivalent return for the optimally chosen combination? 2. Consider an investor who has an asset allocation of 50% in equities and the rest in T-Bills. Suppose the expected rate of return on equities is 10%/year and the standard deviation of the return on equities is 15%/year. T-Bills earn 6%/year. a. What is the implied risk aversion coefficient of the investor? b. Plot the CAL along with a couple of indifference curves for the investor type identified above. c. Use Excel’s solver to maximize the investor’s utility and confirm that you get a 50% allocation in stocks. 3. You can invest in a risky asset with an expected rate of return of 20% per year and a standard deviation of 40% per year or a risk free asset earning 4% per year or a combination of the two. The borrowing rate is 9% per year. a. What is the range of risk aversion for which a client will neither borrow nor lend, that is, for which the allocation to this risky investment is 100%? b. Draw the Capital Allocation Line. Indicate the points corresponding to (i) 50% in the risk-less asset and 50% in the risky asset; and (ii) -50% in the riskless asset and 150% in the risky asset. c. Compute the expected rate of return and standard deviation for (i) and (ii). d. Suppose you have a target risk level of 50% per year. How would you construct a portfolio of the risky and the riskless asset to attain this target level of risk? What is the
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