Suppose you are a fund manager, managing an active fund with an expected return of 16% and a standard deviation of 25%. There is also an index fund tracking the FTSE 100, which has an expected return of 12% and a standard deviation of 20%. The risk-free rate is 4%. (a) Calculate the Sharpe ratio of your active fund and the index fund. Compare the ratios and provide an interpretation in no more than four sentences. [10 pts) Your client has 75% of their wealth invested in your fund and the remaining 25% in the risk-free asset. They consider switching their risky investment to the index fund. (b) Calculate the expected return and the risk (standard deviation of a portfolio with 75% invested in the index fund and 25% in the risk-free asset. (5 pts] (C) Suppose your client does not want to exceed the risk level found in part (b). Calculate the maximum expected return that they can achieve under this condition by combining your fund with the risk-free asset. What portfolio allocation (i.e., what combination of the risk-free asset and one of the risky funds) should your client choose? [10 pts) (a) What is the fee (as a percentage of the investment in your fund) you could charge your client to make them indifferent between investing in your fund or the index fund? [10 pts) a