Question

Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 9.5% and 12.5%, respectively. The beta of A is .8, 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 15% annually, while that of B is 36%, and that of the index is 25%. 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.) Alpha 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

a). Using CAPM, required return for A = risk-free rate + beta*(market return - risk-free rate)

= 5% + 0.8*(10%-5%) = 9.00%

Alpha for A = Expected return - required return = 9.5% - 9% = 0.5%

required return for B = risk-free rate + beta*(market return - risk-free rate)

= 5% + 1.7*(10%-5%) = 13.50%

Alpha for B = Expected return - required return = 12.5% - 13.5% = -1.0%

b-1). Sharpe measure for A = (Expected return - risk-free return)/volatility = (9.5%-5%)/15% = 0.30 (or 30.00%)

Sharpe measure for B = (Expected return - risk-free return)/volatility = (12.5%-5%)/36% = 0.21 (or 20.83%)

Sharpe measure for S&P500 = (Expected return - risk-free return)/volatility = (10%-5%)/25% = 0.20 (or 20.00%)

b-2). Portfolio A should be chosen since it is giving more extra return per unit of volatility.