In the following, assume that the CAPM is true. Denote by rM the return of the m

Question

In the following, assume that the CAPM is true. Denote by rM the return of the market portfolio, i the beta of security i with the market portfolio, and i,M the correlation between security i and the market portfolio M. You have the following information about the economy:

• Security A: E(rA) = 0.095, A = 0.30, A = 0.75

• Security B: E(rB) = 0.125, B = 0.25, B,M = 1.0

• Security C: E(rC) = 0.050, C = 0.40, C,M = 0.0

a) Find the risk-free rate rf of this economy.

b) Find the expected return E(rM) of the market portfolio.

c) Find the standard deviation M of the market portfolio.

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Explanation / Answer

A risk free asset is a zero beta asset. Since correlation between security C and market is 0, the beta of security C will also be zero. Therefore security C is a risk free asset and hence, risk free rate would be 0.05 or 5%. Market portfolio and Security B has correlation coefficient of 1. That means security B is the mirror image of the market. Therefore they both will have the same returns. Hence Expected return of the market would be 0.125 or 12.50%. Standard deviation of the market portfolio will be equal to standard deviation of Security B. Therefore it will be 0.25 or 25%.

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