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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 X .40 X .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 – Risk Free
Return)
Expected Return = 5+1.11(14-5) = 14.99%
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