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

ID: 2712879 • Letter: B

Question

Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 11% and 14%, respectively. The beta of A is .8, while that of B is 1.5. 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 10% annually, while that of B is 31%, and that of the index is 20%.

If you currently hold a market index portfolio, what would be the alpha for Portfolios A and B? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers 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. (Round your answers to 2 decimal places.)

Explanation / Answer

Alpha is the rate of return that exceeds what was expected or predicted by models like the capital asset pricing model (CAPM).

CAPM formula: = Rf + beta * (Rm - Rf )

where:

Rf = the risk-free rate of return =T Bill Rate = 6%
beta = the security's or portfolio's price volatility relative to the overall market, A= 0.8 & B = 1.5

Rm = the market return = rate of return of the S&P 500 index is 12%

CAPM A = 6% + 0.8 (12% - 6%) = 10.8%

CAPM B = 6% + 1.5 (12% - 6%) = 15%

Alpha = Actual Retrun -Expected Retrun

Portfolio A= 10.8 % -12 %= (1.2)

Portfolio B= 15% -12 %= 3%

2) Share measure = S(X) =(r A - R f ) / Std Dev A

Portfolio A = (10.8% -6% ) / 10% = 48%

Portfolio B= (15%-6%)/ 31% =29%

3Based on above calculation i would choose Portfolio A

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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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