Question

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		22		1.5		60
Stock B		19		1.8		72
Stock C		18		1.0		61
Stock D		13		1.0		56

Macro Forecasts
Asset	Expected Return (%)			Standard Deviation (%)
T-bills		9			0
Passive equity portfolio		17			23

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.)

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

Answer 1

a). Rf (risk-free rate) = 9%; Rm (Market return) = 17%

Note: The question does not mention whether residual variance is to be entered in %age or not. The above values are in percentage. If number format is required, please enter accordingly.

b).

Weight of risky portfolio (w0) = (Alpha/Residual variance)/((Rm-Rf)/Market variance)

= -5.95%/((17%-9%)/23%^2) = -0.1043

Beta-adjusted weight of risky portfolio (w*) = w0/(1+(1-Beta)*w0) = -1.043/(1+(1-1.3423)*-0.1043) = -0.1007 (Answer)

Weight of index portfolio = 1-w* = 1-(-0.1007) = 1.1007 (Answer)

Note: Question does not mention whether both weights have to be entered. Please enter accordingly.