A portfolio that combines the risk-free asset and the market portfolio has an ex

Question

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 8 percent and a standard deviation of 11 percent. The risk-free rate is 5 percent, and the expected return on the market portfolio is 13 percent. Assume the capital asset pricing model holds.

What expected rate of return would a security earn if it had a .55 correlation with the market portfolio and a standard deviation of 56 percent?

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 8 percent and a standard deviation of 11 percent. The risk-free rate is 5 percent, and the expected return on the market portfolio is 13 percent. Assume the capital asset pricing model holds.

Explanation / Answer

Here, first we need to compute the beta of the news security.

Beta = Correlation coefficient x Standard Deviation of stock / Standard Deviation of market

           = 0.55 x 0.56 / 0.11

           = 2.80

We have following CAPM:

Expected return = Rf + (Rm- Rf) x beta

                                = 0.05 + (0.13-0.05) x 2.80

                                = 0.05 + 0.228

                                = 27.80%

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