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		28		1.5		40
Stock B		22		2.0		62
Stock C		21		0.9		51
Stock D		16		1.0		46

Macro Forecasts
Asset	Expected Return (%)			Standard Deviation (%)
T-bills		8			0
Passive equity portfolio		20			25

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 active portfolio and the passive index. (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as decimals rounded to 4 places.)

Proportion in Active Portolio
Proportion in Passive Index

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

Improvement in Sharpe ratio

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