Ms. Wallstreet has decided that she will invest all her money by forming a portfolio using just a single fund and the risk-free asset. Therefore, her portfolio will consist of only the risk-free asset and a fund, and nothing else. Short selling is allowed.

Two different fund managers (A and B) are trying to convince Ms. Wallstreet that they should be the single fund that she invests in. Ms. Wallstreet knows that you are taking Investment course, and she wants to get your advice before committing to one of the two funds. You obtain the following information about the two funds, the market, and the risk-free asset:

Fund A: rA =12%, sdA =14%

FundB: rB =25%, sdB =40%

Market: rM = 14%, sdM = 18%

Risk Free Rate: rf = 7%

1. Calculate the Sharpe Ratio of Fund A and Fund B.
2. Which fund do you recommend and why?
3. You also mention to Ms. Wallstreet the possibility of just investing in the market portfolio through an index fund, instead of Fund A or B. Is this recommended over investing in either Fund A or Fund B? Why or why not?
4. Ms. Wallstreet then decides that she would like to earn a mean return of 40% per year. Tell her exactly how to invest to do so in the best way (what would her portfolio be?). What standard deviation will her portfolio have?