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 A and B are 9.8% and 14.6%, respectively. The beta of A is .6, while that of 8 is 1.7. 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 16% annually, while that of 8 is 37%, and that of the index is 26%. If you currently hold a market index portfolio, what would be the alpha for Portfolios A and B? If instead you could invest only in bills and one of these portfolios, calculate the sharpe measure for Portfolios A and B.

Explanation / Answer

The data can be summarised as below:

Expected return

Beta

Deviation

Portfolio A

9.8%

0.6

16%

Portfolio B

14.6%

1.7

37%

S & P 500

12%

1

26%

T-bills

6%

0

0

a.

Using the SML, the expected rate of return for any portfolio P is:

Alpha = Annual return – {Risk free return + Beta*(Market return – Risk free return)}

Alpha of portfolio A = 9.8% - {6% + 0.6(12%-6%)} = 9.8% - 9.6% = 0.2%

Alpha of portfolio B = 14.6% - {6% + 1.7(12% - 6%)} = 14.6% - 16.2% = -1.6%

b.

Sharpe measure = (Portfolio return – Risk free return) / Standard deviation

Sharpe measure for Portfolio A = (9.8% - 6%)/ 16% = 3.8 / 16 = 0.2375

Sharpe measure for Portfolio B = (14.6% - 6%) / 37% = 8.6 / 37 = 0.232

Expected return

Beta

Deviation

Portfolio A

9.8%

0.6

16%

Portfolio B

14.6%

1.7

37%

S & P 500

12%

1

26%

T-bills

6%

0

0

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.