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chapter11 - Chapter 11 Optimal Portfolio Choice 11-1 a Let...

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Chapter 11 Optimal Portfolio Choice 11-1. a. Let i n be the number of share in stock I, then G 200,000 0.5 n 4,000 25 × = = M 200,000 0.25 n 625 80 × = = V 200,000 0.25 n 25,000 2 × = = The new value of the portfolio is v G M p 30n 60n 3n = + + $232,500 = b. Return 232,500 1 16.25% 200,000 = = c. The portfolio weight are the fraction of value invested in each stock G M V n 30 GoldFinger: 51.61% 232,500 n 60 Moosehead: 16.13% 232,500 n 3 Venture: 32.26% 232,500 × = × = × = 11-2. Both calculations of expected return of a portfolio give the same answer. 11-3. If the price of one stock goes up, the other stock price always goes up as well.
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100 Berk/DeMarzo • Corporate Finance: The Core 11-4. a. A B 10 20 5 5 2 9 R 3.5% 6 21 30 7 3 8 25 R 6 12% + + + + = = + + + = = ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 A 0.1 0.035 0.2 0.08 0.05 0.035 1 Variance of A 5 0.05 0.035 0.02 0.035 0.09 0.035 0.01123 Volatility of A = SD(R ) Variance of A .01123 10.60% 0 1 Variance of B 5 + + + = + + = = = = = ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 B .21 0.12 0.3 0.12 0.07 0.12 0.03 0.12 0.08 0.12 0.25 0.12 0.02448 Volatility of B = SD(R ) Variance of B .02448 15.65% + + + + + = = = = b. ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) 0.1 0.035 0.21 0.4 0.2 0.035 0.3 0.12 0.05 0.035 0.07 0.12 1 Covariance 0.05 0.035 0.03 0.12 5 0.02 0.035 0.08 0.12 0.09 0.035 0.25 0.12 0.00794 + + + = + +
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