Chapter 7 - Chapter 7 Answer Key: Problem Sets: 4-10 &...

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Chapter 7 – Answer Key: Problem Sets: 4-10 & 17-19 CFA Problems: 4, 5, & 7-11 Problem Sets: 4. The parameters of the opportunity set are: E(r S ) = 20%, E(r B ) = 12%, S = 30%, B = 15%,    From the standard deviations and the correlation coefficient we generate the covariance matrix [note that Cov(r S , r B ) =  S B ]: Bonds Stocks Bonds 225 45 Stocks 45 900 The minimum-variance portfolio is computed as follows: w Min (S) = 1739 . 0 ) 45 2 ( 225 900 45 225 ) r , r ( Cov 2 ) r , r ( Cov B S 2 B 2 S B S 2 B w Min (B) = 1 0.1739 = 0.8261 The minimum variance portfolio mean and standard deviation are: E(r Min ) = (0.1739 20) + (0.8261 12) 13.39% Min = 2 / 1 B S B S 2 B 2 B 2 S 2 S )] r , r ( Cov w w 2 w w [ = [(0.1739 2 900) + (0.8261 2 225) + (2 0.1739 0.8261 45)] 1/2 = 13.92%
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5. Proportion in stock fund Proportion in bond fund Expected return Standard Deviation 0.00% 100.00% 12.00% 15.00% 17.39% 82.61% 13.39% 13.92% minimum variance 20.00% 80.00% 13.60% 13.94% 40.00% 60.00% 15.20% 15.70% 45.16% 54.84% 15.61% 16.54% tangency portfolio 60.00% 40.00% 16.80% 19.53% 80.00% 20.00% 18.40% 24.48% 100.00% 0.00% 20.00% 30.00% Graph shown below. 6. 0.00 5.00 10.00 15.00 20.00 25.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 Tangency Portfolio Minimum Variance Portfolio Efficient frontier of risky assets CML INVESTMENT OPPORTUNITY SET The graph indicates that the optimal portfolio is the tangency portfolio with expected return approximately 15.6% and standard deviation approximately 16.5%.
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7. The proportion of the optimal risky portfolio invested in the stock fund is given by: ) r , r ( Cov ] r ) r ( E r ) r ( E [ ] r ) r ( E [ ] r ) r ( E [ ) r , r ( Cov ] r ) r ( E [ ] r ) r ( E [ w B S f B f S 2 S f B 2 B f S B S f B 2 B f S S 4516 . 0 ] 45
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This note was uploaded on 03/25/2011 for the course FIN 4514 taught by Professor Chen during the Spring '11 term at University of South Florida.

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Chapter 7 - Chapter 7 Answer Key: Problem Sets: 4-10 &...

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