You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The t-bill rate is 7%.

a) One of your clients chooses to invest 70% of a portfolio in your risky fund and 30% in t-bills. What is the expected return and standard deviation of your clients portfolio?

b) What is the Sharpe Ratio of the risky portfolio you offer? What is the Sharpe Ratio of your clients portfolio?

c) If another client wants a 15% expected return on a portfolio that invests in t-bills and the risky portfolio, what percentage of her assets will she have to put in the risky portfolio? What will be the standard deviation of the rate of return of this complete portfolio?

d) A third client wants the highest expected return on a complete portfolio that does not have a standard deviation of returns greater than 20%. What would be this expected return?

e) A fourth client is thinking about investing in a passive risky portfolio, the S&P 500 stock index, instead of your risky portfolio. Assume that the S&P 500 stock index has an expected return of 13% and a standard deviation of 25%. If the client is thinking about investing 70% of his portfolio in the passive index, then what is his expected return and standard deviation? Can you show that this client can do better using your risky portfolio instead of the passive index?

f) What fee (as a percentage of assets invested) could you charge clients to invest in your risky portfolio so that they would be indifferent between using your portfolio or the S&P 500 stock index described above? (Hint: Think about how the fee would change the Sharpe Ratio of your risky portfolio.)