Percival Hygiene has $10 million invested in long-term corporate bonds. This bond portfolios expected annual rate of return is 24%, and the annual standard deviation is 13%. Amanda Reckonwith, Percivals financial adviser, recommends that Percival consider investing in an index fund that closely tracks the Standard & Poors 500 Index. The index has an expected return of 20%, and its standard deviation is 18%. Suppose Percival puts all his money in a combination of the index fund and Treasury bills. The Treasury bill yield is 6%.

Can he thereby improve his expected rate of return without changing the risk of his portfolio?