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%