Petros has $20 million invested in the long-term corporate bonds and the bond portfolios expected annual rate of return is 7%, and the annual standard deviation is 12%. Petros's friend, Arman, who is a fund manager, advices him to invest in an index fund that closely tracks the Standard & Poors 500 Index. The index fund has an expected return of 15%, and its standard deviation is 17%.

a. Consider that Petros decides to put all his money in a combination of the index fund and Treasury bills. Taking above mentioned into account can he improve his expected rate of return without changing the risk of his portfolio? The Treasury bill yield is 5%.

b. Could Petros do even better by investing 40% in the corporate bond portfolio and 60% in the index fund? The correlation between the bond portfolio and the index fund is +.1(calculate portfolio expected return and standard deviation for comparison)