Question

Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 9.1% and 12.1%, respectively. The beta of A is .7, while that of B is 1.7. The T-bill rate is currently 5%, while the expected rate of return of the S&P 500 index is 10%. The standard deviation of portfolio A is 27% annually, while that of B is 48%, and that of the index is 37%. a. If you currently hold a market index portfolio, what would be the alpha for Portfolios A and B? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 1 decimal place.) Portfolio A % Portfolio B % b-1. If instead you could invest only in bills and one of these portfolios, calculate the sharpe measure for Portfolios A and B. (Round your answers to 2 decimal places.) Sharpe Measure Portfolio A Portfolio B b-2. Which portfolio would you choose? Portfolio A Portfolio B

Answer 1

Answer:

A.) ALPHA

Portfolio A = 8.5%

Portflio B = 13.5%

B.) Sharpe measure

Portfolio A = 0.1519

Portflio B = 0.1479

Explanation:

T- bill rate (Rf) =5%

S&P 500 index ( Rm) = 10%

Portfolio A;

Expected rate of return = 9.1%

Beta (B) = 0.7

Standard deviation (s) = 27%

Portfolio B;

Expected rate of return = 12.1%

Beta (B) = 1.7

Standard deviation = 48%

Required rate of return for both portfolios;

Rf + B × (Rm - Rf)

Portfolio A :

5% + 0.7 ×(10% - 5%) = 5% + 0.7 × (5%)

5% + 3.5% = 8.5%

Portfolio B :

5% + 1.7 ×(10% - 5%) = 5% + 1.7 × (5%)

5% + 8.5% = 13.5%

A) Alpha(A) of Portfolio A and B ;

A = Expected return - Required return

Alpha of portfolio A :

9.1% - 8.5% = 0.6%

Alpha of Portfolio B:

12.1% - 13.5% = - 1.4%

B.) Sharpe measure for portfolio A and B;

Sharpe ratio = (Expected rate of return - Rf) / s

Portfolio A = (9.1% - 5%)/27% = 0.1519

Portfolio B = (12.1% - 5%)/48% = 0.1479

I will choose Portfolio A