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Unformatted text preview: CHAPTER 6: RISK AND RISK AVERSION 1. a.The expected cash flow is: (0.5 $70,000) + (0.5 200,000) = $135,000 With a risk premium of 8% over the riskfree rate of 6%, the required rate of return is 14%. Therefore, the present value of the portfolio is: $135,000/1.14 = $118,421 b. If the portfolio is purchased for $118,421, and provides an expected cash inflow of $135,000, then the expected rate of return [E(r)] is derived as follows: $118,421 [1 + E(r)] = $135,000 Therefore, E(r) = 14%. The portfolio price is set to equate the expected rate or return with the required rate of return. c.If the risk premium over Tbills is now 12%, then the required return is: 6% + 12% = 18% The present value of the portfolio is now: $135,000/1.18 = $114,407 d. For a given expected cash flow, portfolios that command greater risk premia must sell at lower prices. The extra discount from expected value is a penalty for risk. 2. When we specify utility by U = E(r) 0.005A 2 , the utility level for Tbills is 7%. The utility level for the risky portfolio is: U = 12 0.005A 18 2 = 12 1.62A In order for the risky portfolio to be preferred to bills, the following inequality must hold: 12 1.62A > 7 A < 5/1.62 = 3.09 A must be less than 3.09 for the risky portfolio to be preferred to bills. 61 3. Points on the curve are derived by solving for E(r) in the following equation: U = 5 = E(r) 0.005A 2 = E(r) 0.015 2 The values of E(r), given the values of 2 , are therefore: 2 E(r) 0% 5.000% 5% 25 5.375% 10% 100 6.500% 15% 225 8.375% 20% 400 11.000% 25% 625 14.375% The bold line in the following graph (labeled Q3, for Question 3) depicts the indifference curve. E(r) 5 4 U (Q 3,A = 3) U (Q 4,A = 4) U (Q 5,A = 0) U (Q 6,A < 0) 4. Repeating the analysis in Problem 3, utility is now: U = E(r) 0.005A 2 = E(r) 0.020 2 = 4 The equalutility combinations of expected return and standard deviation are presented in the table below. The indifference curve is the upward sloping line in the graph above, labeled Q4 (for Question 4). 62 2 E(r) 0% 4.000% 5% 25 4.500% 10% 100 6.000% 15% 225 8.500% 20% 400 12.000% 25% 625 16.500% The indifference curve in Problem 4 differs from that in Problem 3 in both slope and intercept. When A increases from 3 to 4, the increased risk aversion results in a greater slope for the indifference curve since more expected return is needed in order to compensate for additional . The lower level of utility assumed for Problem 4 (4%...
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This note was uploaded on 03/10/2011 for the course FMIS 3601 taught by Professor Vizanko during the Spring '08 term at University of Minnesota Duluth.
 Spring '08
 Vizanko

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