A portfolio manager summarizes the input from the macro and micro forecasters in the following table: Micro Forecasts Residual Expected Standard Asset Return (8) Beta Deviation (1) Stock A 21 1.4 51 Stock B 18 2.0 62 Stock C 17 1.2 54 Stock D 13 1.3 44 Macro Forecasts Asset Expected Return (2) Standard Deviation (X) T-bills Passive equity portfolio 15 24 Calculate the following for a portfolio manager who is not allowed to short sell securities. If allowed to short sell securities, the manager's Sharpe ratio is 0.2394. a. What is the cost of the restriction in terms of Sharpe's measure? (Do not round Intermediate calculations. Enter your answer as decimals rounded to 4 places.) Cost of restriction b. What is the utility loss to the investor (A = 3.6) given his new complete portfolio? (Do not round Intermediate calculations. Round your answers to 2 decimal places.) Cases Utility Levels Unconstrained 9% Constrained 96 Passive 96A portfolio manager summarizes the input from the macro and micro forecasters in the following table: Micro Forecasts Residual Expected Standard Asset Return (%) Beta Deviation (%) Stock A 22 0.9 52 Stock B 11 1.5 60 Stock C 10 0.6 54 Stock D 8 0.7 49 Macro Forecasts Asset Expected Return (%) Standard Deviation (%) T-bills 7 Passive equity portfolio 10 21 Calculate the following for a portfolio manager who is not allowed to short sell securities. If allowed to short sell securities, the manager's Sharpe ratio is 0.2782. a. What is the cost of the restriction in terms of Sharpe's measure? (Do not round intermediate calculations. Enter your answer as decimals rounded to 4 places.) Cost of restriction 0.0282 Xb. What is the utility loss to the investor (A = 2.6) given his new complete portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Cases Utility Levels Unconstrained 3.54 X % Constrained 3.67 X % Passive 4.00 X % Explanation Alpha (a) Expected Excess Return aj = ri - [rf+ Bix (rm - rf ) ] E ( ri ) - rf a4 = 22% - [7% + 0.9 x (10% - 7%) ] = 12.3% 22% - 7% = 15% ag = 11% - [7% + 1.5 x (10% - 7%) ] = - .5% 11% - 7% = 4% ac = 10% - [7% + 0.6 x (10% - 7%) ] = 1.2% 10% - 7% = 3% ap = 8% - [7% + 0.7 x (10% - 7%) ] = - 1.1% 8% - 7% = 1%Stocks A and C have positive alphas, whereas stocks B and D have negative alphas. The residual variances are: 62(eA) = 522 = 2,704 62 (eB ) = 602 = 3,600 62 (ec) = 542 = 2,916 02 (ep) = 492 = 2,401 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: a alot (e ) A 02 (e ) 02 (e ) sa/of (e ) A 12.3 2, 704.0 0. 0045 0.9170 C 1.2 2, 916.0 0. 0904 0. 0830 0. 0050 1.0000 The forecast for the active portfolio is: a = (0.9170 * 12.3) + (0.0830 x 1.2) = 11.38%B = (0.9170 = 0.9) + (0.0830 = 0.6) = 0.88 (8.91782 x 2,704) + (0.08302 x 2,916) = 2,294.03 47.90% o?(e) a(e) The weight in the active portfolio is: a/o?(e) 11.38/2,294.03 g = = = 0.7292 E(Rm) /o p 3/212 Adjusting for beta: . W B.7292 e - T - 9.6683 1+(1 - B) wp 1+[(1 - .88) x .7292] The information ratio of the active portfolio is: a 11.3791 A= = - 9.2376 o(e) 47 .8961 Hence, the square of the Sharpe ratio is