27. Portfolio risk and return (S7.4) Percival Hygiene has $10 million invested in long-term corporate bonds. This bond portfolio’s expected annual rate of return is 9%, and the annual standard deviation is 10%. 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 14%, and its standard deviation is 16%.

a. 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 6%.