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

ID: 2710365 • Letter: B

Question

Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 13.0% and 15.0%, respectively. The beta of A is .8, while that of B is 1.3. The T-bill rate is currently 7%, while the expected rate of return of the S&P 500 index is 14%. The standard deviation of portfolio A is 20% annually, while that of B is 41%, and that of the index is 30%.

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.)

b) 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.)

Explanation / Answer

a) The excess returns of a fund relative to the return of a benchmark index is the fund's alpha

So portfolio A's alpha = Its return - market return = 13% - 14% = -1.0%
So portfolio B's alpha = Its return - market return = 15% - 14% = 1.0%

b) Sharp ratio can be calculated using the formula as below

Sharpe ratio = (Mean portfolio return Risk-free rate)/Standard deviation of portfolio return

So Sharp Ratio of A = (13% - 7%) / 20% = 30.0%

and Sharp Ratio of B = (15% - 7%) / 41% = 19.5%

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

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

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