Based on current dividend yields and expected capital gains, the expected rates
ID: 2711129 • Letter: B
Question
Based on current dividend yields and expected capital gains, the expected rates of return on portfolios Aand B are 10.1% and 15.6%, respectively. The beta of A is .6, while that of B is 1.8. The T-bill rate is currently 6%, while the expected rate of return of the S&P 500 index is 12%. The standard deviation of portfolio A is 26% annually, while that of B is 47%, and that of the index is 36%.
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 10.1% and 15.6%, respectively. The beta of A is .6, while that of B is 1.8. The T-bill rate is currently 6%, while the expected rate of return of the S&P 500 index is 12%. The standard deviation of portfolio A is 26% annually, while that of B is 47%, and that of the index is 36%.
Think about what are the appropriate performance measures to use in question a and b, and why.
Explanation / Answer
Answer (a)
Alpha
Portfolio A
0.50%
Portfolio B
-1.2%
Answer (b)
Sharpe Measure
Portfolio A
0.16
Portfolio B
0.20
Answer (c)
Based on Alpha and Sharpe measure taken together, we choose portfolio A
working
Expected return
Beta
Standard Deviation
Portfolio A
10.1%
0.60
26%
Porfolio B
15.6%
1.8
47%
S&P 500 Index
12%
36%
T-Bill rate
6%
Expected return of Portfolio A based on CAPM = rf+Beta (rm-rf)
= 6% + 0.60 *(12-6%)
= 6% + 0.6 * 6% = 6% +3.6%
= 9.6%
Excess return of portfolio A vis-à-vis expected return based on CAPM = 10.1% - 9.6%
= 0.50%
Alpha of Portfolio A = 0.50%
Expected return of Portfolio B based on CAPM = 6% + 1.8 * (12% - 6%)
= 6% + 1.8 * 6% = 6% + 10.8%
= 16.8%
Excess return of Portfolio B = 15.6% - 16.8% = -1.2%
Alpha of Portfolio B = -1.2%
Sharpe measure of Portfolio = (Portfolio Return – Risk-free rate) / standard deviation
Sharpe measure of Portfolio A = (10.1% - 6%)/26% = 4.1%/26% = 0.1576923 or 0.16 (rounded off)
Sharpe measure of Portfolio B = (15.6% - 6%)/47% = 9.6%/47% =0.2042 or 0.20 (rounded off)
Alpha
Portfolio A
0.50%
Portfolio B
-1.2%
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