Percival Hygiene has $10 million invested in long-term corporate bonds. This bond portfolio’s expected annual rate of return is 12%, and the annual standard deviation is 12%. Amanda Reckonwith,...

Percival Hygiene has $10 million invested in long-term corporate bonds. This bond portfolio’s expected annual rate of return is 12%, and the annual standard deviation is 12%. Amanda Reckonwith, Percival’s financial adviser, recommends that Percival consider investing in an index fund that closely tracks the Standard & Poor’s 500 index. The index has an expected return of 13%, and its standard deviation is 16%.

Suppose Percival puts all his money in a combination of the index fund and Treasury bills. Can he thereby improve his expected rate of return without changing the risk of his portfolio? The Treasury bill yield is 4%.