Consider a risky asset X with an expected rate of return of 12% and a standard deviation of 7%. The Treasury Bill rate of return is 3%. You hold a portfolio of total market value $4,000,entirely invested in the risky asset.

a.Consider leveraging your portfolio. You borrow an additional $2000 to invest in the riskyasset. Suppose that the borrowing rate is equal to the Treasury Bill rate. Calculate the Sharperatio of your leveraged portfolio and compare it to the Sharpe ratio of your initial portfolio.

b.Suppose that the borrowing rate now is higher than the Treasury Bill rate and equal to 6%.Calculate the Sharpe ratio of the leveraged portfolio as constructed in part a. Comment on theresult.

c.Using a borrowing rate of 6%, calculate the realized return of your leveraged portfolio if theasset X falls by 30%. If the maintenance margin is set at 55%, will you receive a margin call? Explain your answer.

d. Instead of taking leverage buying on margin asset X, your broker suggests you add another riskyasset Y to your initial portfolio. The asset Y has an expected return of 8%, a standard deviationof 9% and a correlation of 0.1 with asset X. Will adding asset Y improve your portfolio?