1.Optimal risky portfolios

Take the following information on the Kelly Fund:

The risk-free rate is 4%. A risky portfolio, the Kelly Fund, has an expected rate of return of 11% and a standard deviation of 21%.

A.What is the Sharpe ratio of the Kelly Fund? Sharpe Ratio = 0.3333

B.If a client invests 50% in the Kelly Fund and 50% in the risk-free rate, what will be the expected return and standard deviation of their complete portfolio?

Expected Return = 7.5%

Standard Deviation = 10.5%

C.What is the Sharpe ratio of their complete portfolio?= 0.3333

AND add the following: there is another risky portfolio, the Faust Fund, with an expected rate of return of 7% and standard deviation of 16%. The correlation coefficient between the returns of your risky portfolio and this new risky portfolio is 0.25.

A.What is the Sharpe ratio of the Faust Fund?

B.Despite the fact that one of the risky funds, either Kelly or Faust, has a superior Sharpe ratio, the relatively low correlation between the two funds may mean that combined investment in the two risky portfolios may provide a better Sharpe ratio. Find the equation in the text for the optimal portfolio and solve for the weights invested in Kelly and Faust that get you this portfolio.

C.What is the Sharpe ratio of the optimal portfolio?

D.If your client wants the same expected return as in question 2B above, what would be their weights in the optimal risky portfolio and the risk-free rate?

E.What would be the standard deviation of your client's complete portfolio now, using the optimal portfolio as the risky portfolio?