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Problem 8-17

A portfolio manager summarizes the input from the macro and micro forecasters in the following table:

Micro Forecasts

Asset Expected Return (%) Beta Residual Standard

Deviation (%)

Stock A 25 0.8 52

Stock B 19 1.2 61

Stock C 16 0.6 55

Stock D 12 0.7 47

Macro Forecasts

Asset Expected Return (%) Standard Deviation (%)

T-bills 8 0

Passive equity portfolio 18 26

a. Calculate expected excess returns, alpha values, and residual variances for these stocks. (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round "Alpha values" to 1 decimal place.)

Stock A Stock B Stock C Stock D

Excess returns % % % %

Alpha values % % % %

Residual variances

b. Compute the proportion in the optimal risky portfolio. (Do not round intermediate calculations. Enter your answer as decimals rounded to 4 places.)

Proportion:

c. What is the Sharpe ratio for the optimal portfolio? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places

Sharpe Ratio:

d. By how much did the position in the active portfolio improve the Sharpe ratio compared to a purely passive index strategy? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Active portfolio:

e. What should be the exact makeup of the complete portfolio (including the risk-free asset) for an investor with a coefficient of risk aversion of 3.0? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Final Positions

Bills %

M %

A %

B %

C %

D %

Total %

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