Question

A portfolio that combines the risk-free asset and the market
portfolio has an expected return of 7.4 percent and a standard
deviation of 10.4 percent. The risk-free rate is 4.4 percent, and
the expected return on the market portfolio is 12.4 percent. Assume
the capital asset pricing model holds.

What expected rate of return would a security earn if it had a .49
correlation with the market portfolio and a standard deviation of
55.4 percent? **Enter your answer as a percent
rounded to 2 decimal places.**

Expected rate of return ________%

Answer #1

Let the weight of risk free in the portfolio be 1-w and weight
of market portfolio be w

Hence, Expected return of the portfolio=w*12.4%+(1-w)*4.4%

=>w*12.4%+(1-w)*4.4%=7.4%

=>w=(7.4%-4.4%)/(12.4%-4.4%)

=>w=0.375

Weight of market portfolio=0.375

Weight of risk free=0.625

Standard Deviation of portfolio=w*Standard Deviation of martket
portfolio

=>10.4%=0.375*Standard Deviation of market portfolio

=>Standard Deviation of market portfolio=10.4%/0.375=27.733%

Beta of security=correlation*standard devaition of security/standard deviation of market=0.49*55.4%/27.733%=0.97883388

Expected return=risk free+beta*(market-risk
free)=4.4%+0.97883388*(12.4%-4.4%)=12.231%

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