Suppose the market portfolio has an expected return of 12% and a standard deviation of 15%, and a mutual fund named Stellar Fund has an expected return of 18% and a standard deviation of 34%. The risk-free rate is 2%.
a. Suppose a client of yours has invested 70% of his investment budget in Stellar Fund, and the remaining 30% in the risk-free asset. What is the expected rate of return and standard deviation faced by your client?
b. You would like to demonstrate that the client should instead use the market portfolio along with the risk-free asset. To achieve the same level of expected return as before, what percentage of the client’s investment budget should be invested in the market portfolio, and what percentage should be invested in the risk-free asset?
c. If the client follows your recommendation and uses the market portfolio and risk-free asset to maintain the same expected return, what will be the standard deviation your client faces? Please comment on how this, along with the standard deviation calculated in part a, demonstrates why using the market portfolio is superior to using Stellar Fund.
This question involves both concepts and some simple calculations. The CAPM implies that the market portfolio is the optimal risky portfolio, and thus is the best portfolio to use along with either borrowing or lending at the risk-free rate of interest. Consider the following assets or portfolios:
Asset Expected return Standard Deviation Covariance with the market
A 10.0% 17.0% not given
B 14.0% 28.0% not given
C 8.0% 12.0% not given
D 3.0% 15.0% 0.000%