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 7.2 percent and a standard deviation of 10.2 percent. The risk-free rate is 4.2 percent, and the expected return on the market portfolio is 12.2 percent. Assume the capital asset pricing model holds.

What expected rate of return would a security earn if it had a .47 correlation with the market portfolio and a standard deviation of 55.2 percent? (Do not round intermediate calculations and enter your answer as a percent rounded 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 7.2 percent and a standard deviation of 10.2 percent. The risk-free rate is 4.2 percent, and the expected return on the market portfolio is 12.2 percent. Assume the capital asset pricing model holds.

Explanation / Answer

Correlation (Security, Market Portfolio)

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

Cov (Security, Market Portfolio) = .47 X .552 X .102 = .026

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

Beta = .026/(.102^2) = 2.50

So as per CAPM

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

Expected Return = 4.2+2.50(12.2-4.2) = 24.20%

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