投資學(xué)第10版習(xí)題答案(已改無錯(cuò)字)
2022-08-23 04:09:05 本頁面
【正文】 folio, first pute the beta, the mean excess return, and the variance of the optimal risky portfolio:βP = wM + (wA βA ) = + [(–) 180。 ] = E(RP) = αP + βPE(RM) = [(–) 180。 (–%)] + ( 8%) = %Since A = , the optimal position in this portfolio is:In contrast, with a passive strategy:224。A difference of: The final positions are (M may include some of stocks A through D):Bills1 – =%M 180。 =A 180。 (–) 180。 (–) =B 180。 (–) 180。 =– C 180。 (–) 180。 (–) =D 180。 (–) 180。 =– (subject to rounding error)%18. a. If a manager is not allowed to sell short, he will not include stocks with negative alphas in his portfolio, so he will consider only A and C:Αs2(e) A3,364C3,600The forecast for the active portfolio is:α = ( ) + ( ) = %β = ( ) + ( ) = s2(e) = ( 3,364) + ( 3,600) = 1,σ(e) = %The weight in the active portfolio is:Adjusting for beta:The information ratio of the active portfolio is:Hence, the square of the Sharpe ratio is:Therefore: S = The market’s Sharpe ratio is: SM = When short sales are allowed (Problem 17), the manager’s Sharpe ratio is higher (). The reduction in the Sharpe ratio is the cost of the short sale restriction.The characteristics of the optimal risky portfolio are: With A = , the optimal position in this portfolio is:The final positions in each asset are: Bills1 – =%M 180。 (1 ) =A 180。 180。 =C 180。 180。 =b. The mean and variance of the optimized plete portfolios in the unconstrained and shortsales constrained cases, and for the passive strategy are:E(RC )Unconstrained % = = Constrained % = = Passive % = = The utility levels below are puted using the formula: Unconstrained 8% + % – ( ) = %Constrained 8% + % – ( ) = %Passive 8% + % – ( ) = % 19. All alphas are reduced to times their values in the original case. Therefore, the relative weights of each security in the active portfolio are unchanged, but the alpha of the active portfolio is only times its previous value: % = %The investor will take a smaller position in the active portfolio. The optimal risky portfolio has a proportion w* in the active portfolio as follows:The negative position is justified for the reason given earlier.The adjustment for beta is:Since w* is negative, the result is a positive position in stocks with positive alphas and a negative position in stocks with negative alphas. The position in the index portfolio is: 1 – (–) = To calculate the Sharpe ratio for the optimal risky portfolio we pute the information ratio for the active portfolio and the Sharpe ratio for the market portfolio. The information ratio of the active portfolio is times its previous value:A = = – and A2 =Hence, the square of the Sharpe ratio of the optimized risky portfolio is:S2 = S2M + A2 = (8%/23%)2 + = S = Compare this to the market’s Sharpe ratio: SM = = The difference is: Note that the reduction of the forecast alphas by a factor of reduced the squared information ratio and the improvement in the squared Sharpe ratio by a factor of: = 20. If each of the alpha forecasts is d
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