Artashes has $50 million invested in a portfolio of stocks and portfolio's expected annual rate of return is 10%, and the annual standard deviation is 15%. Artashes's friend, Lilit, who is a fund manager, advices him to invest in an index fund that closely tracks the Standard & Poor's 500 Index. The index fund has an expected return of 18%, and its standard deviation is 20%. a. Consider that Artashes 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 6%. b. Could Petros do even better by investing 60% in the stock portfolio and 40% in the index fund? The correlation between the stock portfolio and the index fund is +.6(calculate portfolio expected return, standard deviation and sharp ratio for comparison)