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

Answer 1

Following are the details:

Micro Forecasts

	Exp Ret (%)	Beta	Std Dev (%)
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

	Exp Ret (%)	Std Dev (%)
T Bills	8	0
Passive Equity Portfolio	18	26

Questions:

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.)

Considering that the Passive Equity Portfolio as a benchmark index, the difference between the expected returns of a stock and the expected return of the portfolio is a measure of excess return.

Expected Excess Return

Expected excess Return of Stock A = Expected Return of Stock A - Expected Return of Passive Equity Portfolio

= 25% - 18% = 7%

Expected excess Return of Stock B = Expected Return of Stock B - Expected Return of Passive Equity Portfolio

= 19% - 18% = 1%

Expected excess Return of Stock C = Expected Return of Stock C - Expected Return of Passive Equity Portfolio

= 16% - 18% = - 2%

Expected excess Return of Stock D = Expected Return of Stock D - Expected Return of Passive Equity Portfolio

= 12% - 18% = - 6%

Alphas

An individual stock's alpha is given by the following equation:

where

= Return of individual stock,S

= Risk-free Rate, 8%

= Return on benchmark index, 18%

= beta of individual stock

= (25 - 8) - [0.8 * (18 - 8)] = 17 - [0.8 * 10] = 17 - 8 = 9.0

= (19 - 8) - [1.2 * (18 - 8)] = 11 - [1.2 * 10] = 11 - 12 = -1.0

= (16 - 8) - [0.6 * (18 - 8)] = 8 - [0.6 * 10] = 8 - 6 = 2.0

= (12 - 8) - [0.7 * (18 - 8)] = 4 - [0.7 * 10] = 4 - 7 = - 3.0

Plugging in the numbers, we get the following table:

Stock A	25	8	0.8	18	9.0
Stock B	19	8	1.2	18	-1.0
Stock C	16	8	0.6	18	2.0
Stock D	12	8	0.7	18	-3.0

Residual Variances:

The residual variance of a stock is expressed as

For Stock A,

For Stock B,

For Stock C,

For Stock D,

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

Need the Covariance matrix or Coefficient of Covariance to solve this part

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

Need the Covariance matrix or Coefficient of Covariance to solve this part

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.)

Need the Covariance matrix or Coefficient of Covariance to solve this part

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.)

Need the Covariance matrix or Coefficient of Covariance to solve this part