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 60% of his investment budget in Stellar Fund, and the remaining 40% 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 (when the client had 60% in Stellar and 40% in the risk-free), 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.