C in part b the market risk premium is expected to be

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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-variability ratio is expected to be higher in part (b), which explains the greater proportion invested in equity. 24. Assuming no change in risk tolerance, that is, an unchanged risk aversion coefficient (A), then higher perceived volatility increases the denominator of the equation for the optimal investment in the risky portfolio (Equation 6.12). The proportion invested in the risky portfolio will therefore decrease. 6-8
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25. a. E(r C ) = 8% = 5% + y(11% – 5%) 5 . 0 5 11 5 8 y = = b. σ C = y σ P = 0.50 × 15% = 7.5% c. The first client is more risk averse, allowing a smaller standard deviation. 26. Data: r f = 5%, E(r M ) = 13%, σ M = 25%, and = 9% B f r The CML and indifference curves are as follows: P borrow lend CAL E(r) σ 5 9 13 25 CML 27. For y to be less than 1.0 (so that the investor is a lender), risk aversion (A) must be large enough such that: 1 A σ r ) E(r y 2 M f M < = 1.28 0.25 0.05 0.13 A 2 = > For y to be greater than 1.0 (so that the investor is a borrower), risk aversion must be small enough such that: 1 A σ r ) E(r y 2 M f M > = 0.64 0.25 0.09 0.13 A 2 = < For values of risk aversion within this range, the client will neither borrow nor lend, but instead will hold a complete portfolio comprised only of the optimal risky portfolio: y = 1 for 0.64 ≤ Α ≤ 1.28 6-9
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28. a. The graph for Problem 26 has to be redrawn here, with: E(r P ) = 11% and σ P = 15% b. For a lending position: 2.67 0.15 0.05 0.11 A 2 = > For a borrowing position: 0.89 0.15 0.09 0.11 A 2 = < Therefore, y = 1 for 0.89 A 2.67 M CML E(r) σ 5 9 13 25 11 15 CAL F 29. The maximum feasible fee, denoted f, depends on the reward-to-variability ratio. For y < 1, the lending rate, 5%, is viewed as the relevant risk-free rate, and we solve for f as follows: 25 5 13 15 f 5 11 = % 2 . 1 25 8 15 6 f = × = For y > 1, the borrowing rate, 9%, is the relevant risk-free rate. Then we notice that, even without a fee, the active fund is inferior to the passive fund because: 16 . 0 25 9 13 13 . 0 15 9 11 = < = 6-10
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More risk tolerant investors (who are more inclined to borrow) will not be clients of the fund even without a fee. (If you solved for the fee that would make investors who borrow indifferent between the active and passive portfolio, as we did above for lending investors, you would find that f is negative: that is, you would need to pay investors to choose your active fund.) These investors desire higher risk-higher return complete portfolios and thus are in the borrowing range of the relevant CAL. In this range, the reward-to-variability ratio of the index (the passive fund) is better than that of the managed fund. 30. Indifference curve 2 31. Point E 32. (0.6 × $50,000) + [0.4 × ( $30,000)] $5,000 = $13,000 33. b 34. 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% 35. Reward to variability ratio = 71 . 0 14 10 = 6-11
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6-12 CHAPTER 6: APPENDIX 1. By year end, the $50,000 investment will grow to: $50,000 × 1.06 = $53,000 Without insurance , the probability distribution of end-of-year wealth is: Probability Wealth No fire 0.999 $253,000 Fire 0.001 $ 53,000 For this distribution, expected utility is computed as follows: E[U(W)] = [0.999 × ln(253,000)] + [0.001 × ln(53,000)] = 12.439582 The certainty equivalent is: W CE = e 12.439582 = $252,604.85 With fire insurance
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c In part b the market risk premium is expected to be...

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