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 the promotion period ends, the company charges the entry fee $145 for the game. One day, a group of tourists, who all exhibit utility function U(W)= -1/W, visit the casino, but no one plays the coin game. To induce them to play, the company decides to raise the payoff, instead of lowering the entry fee. What will be the smallest compensatory risk premium the company has to offer? 3. Suppose now the utility function is U=E(r)-0.5A 2. (Inputs should be in a decimal format.) The company still charges the entry fee $145 for the game. For an investor with A=0.75, will the investor prefer this coin game to an instant risk-free rate of 1%?

Part II. Construction of Feasible Investment Opportunity Set and the Efficient Frontier (Lecture 3) 1. Consider two securities for the potential portfolio inclusion: E(r1)=25%,E(r2)=10%, 1=75%, 2=25%, 12 Draw all feasible investment combinations given these two risky assets in a plane of P, E(rp)} in Excel for four cases: (1) 12 =1, (2) 12 = 0.2, (3) 12 = - 0.2, (4) 12 = -1. What does the Efficient Frontier look like?


Part of this practice problem is constructed based on the homework assignment by Professor Schaumburg at Kellogg School of Management where I was visiting during my sabbatical...
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