Question

Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 7.1% and 8.3%, respectively. The beta of A is .6, while that of B is 1.5. The T-bill rate is currently 4%, while the expected rate of return of the S&P 500 index is 8%. The standard deviation of portfolio A is 21% annually, while that of B is 42%, and that of the index is 31% Think about what are the appropriate performance measures to use in question a and b and why. 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. Enter your answer as a percentage rounded 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. (Enter your answer as a decimal rounded to 2 decimal places.) Sharpe Measure Portfolio A Portfolio B

Answer 1

a). Alpha = E(r) - [rF + {Beta * (Market Return - rF)}]

Portfolio A's Alpha = 7.1% - [4% + {0.6 * (8% - 4%)}]

= 7.1% - [4% + 2.4%] = 7.1% - 6.4% = 0.7%

Portfolio B's Alpha = 8.3% - [4% + {1.5 * (8% - 4%)}]

= 8.3% - [4% + 6%] = 8.3% - 10% = -1.7%

b-1). Sharpe Ratio = [E(r) - rF] / S.D.(r)

Portfolio A's Sharpe Ratio = [7.1% - 4%] / 21% = 3.1% / 21% = 0.15

Portfolio B's Sharpe Ratio = [8.3% - 4%] / 42% = 4.3% / 42% = 0.10