Solutions_Homework2

Solutions_Homework2 - Ch. 6 17. a. E(rC) = rf + y[E(rP) rf]...

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Ch. 6 17. a. E(r C ) = r f + y[E(r P ) – r f ] = 8 + y(18 - 8) If the expected return for the portfolio is 16%, then: 16 = 8 + 10 y Therefore, in order to have a portfolio with expected rate of return equal to 16%, the client must invest 80% of total funds in the risky portfolio and 20% in T-bills. b. Client’s investment proportions: 20.0% in T-bills 0.8 × 25% = 20.0% in Stock A 0.8 × 32% = 25.6% in Stock B 0.8 × 43% = 34.4% in Stock C c. σ C = 0.8 × σ P = 0.8 × 28% = 22.4% 18. a. σ C = y × 28% If your client prefers a standard deviation of at most 18%, then: y = 18/28 = 0.6429 = 64.29% invested in the risky portfolio b. E(r C ) = 8 + 10y = 8 + (0.6429 × 10) = 8 + 6.429 = 14.429% 20. a. If the period 1926 - 2005 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(r M ) - r f = 8.39%, σ M = 20.54% (we use the standard deviation of the risk premium from Table 6.8). Then y * is given by: That is, 49.72% of the portfolio should be allocated to equity and 50.28% should be allocated to T-bills. b. If the period 1986 - 2005 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(r M ) - r f = 8.60%, σ M = 16.24% and y* is given by:
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Therefore, 81.52% of the complete portfolio should be allocated to equity and 18.48% should be allocated to T-bills. c.In part (b), the market risk premium is expected to be higher than in part (a) and market risk is lower. Therefore, the reward-to-volatility ratio is expected to be higher in part (b), which explains the greater proportion invested in equity. 21. a. E(r C ) = 8% = 5% + y(11% – 5%) b. σ C = y σ P = 0.50 × 15% = 7.5% c.The first client is more risk averse, allowing a smaller standard deviation. CFA PROBLEMS 6. (0.6 × $50,000) + [0.4 × ( - $30,000)] - $5,000 = $13,000 7. (b) 8. Expected return for equity fund = T-bill rate + risk premium = 6% + 10% = 16% Expected return of client’s overall portfolio = (0.6 × 16%) + (0.4 × 6%) = 12% Standard deviation of client’s overall portfolio = 0.6 × 14% = 8.4% 9. Reward-to-volatility ratio = Ch. 7 15. The probability distribution is: Probability Rate of Return 0.7 100% 0.3 −50% Mean = [0.7 × 100] + [0.3 × ( - 50)] = 55% Variance = [0.7 × (100 - 55) 2 ] + [0.3 × ( - 50 - 55) 2 ] = 4725 Standard deviation = 4725 1/2 = 68.74%
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16. σ P = 30 = y σ = 4 0 y y = 0.75 E(r P ) = 12 + 0.75(30 - 12) = 25.5% 17. The correct choice is c. Intuitively, we note that since all stocks have the same expected rate of return and standard deviation, we choose the stock that will result in lowest risk. This is the stock that has the lowest correlation with Stock A. More formally, we note that when all stocks have the same expected rate of return,
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Solutions_Homework2 - Ch. 6 17. a. E(rC) = rf + y[E(rP) rf]...

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