Based on current dividend yields and expected capital gains, the expected rates or return on portfolios A and B are 12% and 18%, respectively.  The beta of A is 0.7 while that of B is 1.6.  The T-bill rate is currently 4% while the expected rate of return of the S&P500 Index is 13%.  The standard deviation of portfolio A is 14% annually, while that of B is 26%, and that of the index is 15%.If you currently hold a market-index portfolio, would you chose to add either of these portfolios to your holdings?

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Asked Oct 22, 2019
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Based on current dividend yields and expected capital gains, the expected rates or return on portfolios A and B are 12% and 18%, respectively.  The beta of A is 0.7 while that of B is 1.6.  The T-bill rate is currently 4% while the expected rate of return of the S&P500 Index is 13%.  The standard deviation of portfolio A is 14% annually, while that of B is 26%, and that of the index is 15%.

If you currently hold a market-index portfolio, would you chose to add either of these portfolios to your holdings?

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Expert Answer

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Step 1

Capital asset pricing model can be used to study the how systematic risk on a particular asset is linked to expected return on the same asset.

The formula to calculate expected return using CAPM model is given below:

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ER = R,+ P,(ER-R,) Here ER, is expected return on investment i. R, is risk free returm P, is beta of investment i. (ER-R) is market risk premium.

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Step 2

To calculate expected return on portfolio A,

Substitute 4% for Rf, 0.7 for βi, 13% for ERm in the above formula,

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4%+0.7x (13% - 4%) ER = 4% + 0.7 x 9% = 4%+6.3% 10.3 %

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Step 3

To calculate expected return on portfolio B,

Substitute 4% for Rf, 1.6 for βi , 13...

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ER 4%+1.6x (13% -4%) =4% +1.6x 9% =4% + 14.4% 18.4%

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