Based on current dividend yields and expected capital gains, the expected rates

Question

Based on current dividend yields and expected capital gains, the expected rates of return on portfolios Aand B are 8.3% and 8.2%, respectively. The beta of A is .9, while that of B is 1.3. 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 29% annually, while that of B is 50%, and that of the index is 39%.

Think about what are the appropriate performance measures to use in question a and b, and why.

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.)

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.)

Based on current dividend yields and expected capital gains, the expected rates of return on portfolios Aand B are 8.3% and 8.2%, respectively. The beta of A is .9, while that of B is 1.3. 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 29% annually, while that of B is 50%, and that of the index is 39%.

Think about what are the appropriate performance measures to use in question a and b, and why.

Explanation / Answer

Alpha of Portfolio A:

Alpha of A = E(rA) – expected return predicted by CAPM

Alpha of A = 8.3% – (4% + 0.9 * (8% 4%))

Alpha of A = 0.7%

Alpha of Portfolio B:

Alpha of B = E(rB) – expected return predicted by CAPM

Alpha of B = 8.2% – (4% + 1.3 * (8% 4%))

Alpha of B = -1.0%

Part B

Sharpe Ratio of A = (Return on Portfolio A - Risk Free Rate)/ Standard Deviation of Portfolio A

Sharpe Ratio of A = (8.3% – 4%)/ 29%

Sharpe Ratio of A = 14.83%

Sharpe Ratio of Portfolio B:

Sharpe Ratio of B = (Return on Portfolio B - Risk Free Rate)/ Standard Deviation of Portfolio B

Sharpe Ratio of B = (8.2% - 4%)/ 50%

Sharpe Ratio of B = 8.40%

Using the Sharpe criterion, Portfolio A is the preferred portfolio

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