# ch7_answers - CHAPTER 7: CAPITAL ALLOCATION BETWEEN THE...

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7-1 CHAPTER 7: CAPITAL ALLOCATION BETWEEN THE RISKY ASSET AND THE RISK-FREE ASSET 1. Expected return = (0.7 ± 18%) + (0.3 ± 8%) = 15% Standard deviation = 0.7 ± 28% = 19.6% 2. Investment proportions: 30.0% in T-bills 0.7 ± 25% = 17.5% in Stock A 0.7 ± 32% = 22.4% in Stock B 0.7 ± 43% = 30.1% in Stock C 3. Your reward-to-variability ratio: 3571 . 0 28 8 18 S = ± = Client's reward-to-variability ratio: 3571 . 0 6 . 19 8 15 S = ± = 4. Client P 0 5 10 15 20 25 30 0 1 02 03 04 0 ± (%) E(r) % CAL (Slope = 0.3571)

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7-2 5. 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 ² 8 . 0 10 8 16 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 ³ 25% = 20.0% in Stock A 0.8 ³ 32% = 25.6% in Stock B 0.8 ³ 43% = 34.4% in Stock C c. ´ C = 0.8 ³ ´ P = 0.8 ³ 28% = 22.4% 6. a. ´ C = y ³ 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 ³ 10) = 8 + 6.429 = 14.429% 7. a. 3644 . 0 44 . 27 10 28 5 . 3 01 . 0 8 18 A 01 . 0 r ) r ( E y 2 2 P f P * = = ± ± ² = ³ ² = Therefore, the client’s optimal proportions are: 36.44% invested in the risky portfolio and 63.56% invested in T-bills. b. E(r C ) = 8 + 10y* = 8 + (0.3644 ³ 10) = 11.644% ´ C = 0.3644 ³ 28 = 10.203% 8. a. Slope of the CML 20 . 0 25 8 13 = ± = The diagram follows. b. My fund allows an investor to achieve a higher mean for any given standard deviation than would a passive strategy, i.e., a higher expected return for any given level of risk.
7-3 CML and CAL 0 2 4 6 8 10 12 14 16 18 01 0 2 0 3 0 Standard Deviation Expected Retrun CAL: Slope = 0.3571 CML: Slope = 0.20 9. a. With 70% of his money invested in my fund’s portfolio, the client’s expected return is 15% per year and standard deviation is 19.6% per year. If he shifts that money to the passive portfolio (which has an expected return of 13% and standard deviation of 25%), his overall expected return becomes: E(r C ) = r f + 0.7[E(r M ) ± r f ] = 8 + [0.7 ² (13 – 8)] = 11.5%

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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.

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ch7_answers - CHAPTER 7: CAPITAL ALLOCATION BETWEEN THE...

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