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 6.9 percent and a standard deviation of 9.9 percent. The risk-free rate is 3.9 percent, and the expected return on the market portfolio is 11.9 percent. Assume the capital asset pricing model holds.

What expected rate of return would a security earn if it had a .44 correlation with the market portfolio and a standard deviation of 54.9 percent? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 6.9 percent and a standard deviation of 9.9 percent. The risk-free rate is 3.9 percent, and the expected return on the market portfolio is 11.9 percent. Assume the capital asset pricing model holds.

Explanation / Answer

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A portfolio that combines the risk-free asset and the market portfolio has an expected return of 15% and a standard deviation of 18%. The risk free rate is 5%, an the expected return on the market portfolio is 14%. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a .5 correlation with the market portfolio and a standard deviation of 40%?

Correlation (Security, Market Portfolio)

= Cov (Security, Market Portfolio)/ (Standard Deviation Security X Standard Deviation Market)

Cov (Security, Market Portfolio) = .50 * .40 * .18 = .036

We know Beta for Security = Cov (Security, Market Portfolio)/Variance Market

Beta = .036/(.18^2) = 1.11

So as per CAPM

Expected Return on Security = Risk Free Rate + Beta*(Market Return

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