Solns Sets 2-3B - Chapter 5, CFA Study Problem Solutions 1....

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1. The expected dollar return on the investment in equities is $18,000 compared to the $5,000 expected return for T-bills. Therefore, the expected risk premium is $13,000. 5. E(r) = (0.9 × 20%) + (0.1 × 10%) =19% 6. The probability that the economy will be neutral is 0.50, or 50%. Given a neutral economy, the stock will experience poor performance 30% of the time. The probability of both poor stock performance and a neutral economy is therefore: 0.30 × 0.50 = 0.15 = 15% Chapter 6, Study Problem Solutions 4. a.The expected cash flow is: (0.5 × $70,000) + (0.5 × 200,000) = $135,000 With a risk premium of 8% over the risk-free 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 T-bills 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. 5. When we specify utility by U = E(r) – 0.5A σ 2 , the utility level for T-bills is: 0.07 The utility level for the risky portfolio is: U = 0.12 – 0.5A(0.18) 2 = 0.12 – 0.0162A In order for the risky portfolio to be preferred to bills, the following inequality must hold: 0.12 – 0.0162A > 0.07 A < 0.05/0.0162 = 3.09 A must be less than 3.09 for the risky portfolio to be preferred to bills. 1
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This note was uploaded on 09/27/2010 for the course BUSINESS 6F:111 taught by Professor Tongyao during the Spring '09 term at University of Iowa.

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Solns Sets 2-3B - Chapter 5, CFA Study Problem Solutions 1....

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