Portfolio Management: Practice Problems

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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
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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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