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Percival Hygiene has $10 million invested in long-term corporate

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Percival Hygiene has $10 million invested in long-term corporate bonds. This bond portfolio’s expected annual rate of return is 9 percent, and the annual standard deviation is 10 percent. Amanda Reckonwith, Percival’s financial adviser, recommends that Percival consider investing in an index fund which closely tracks the Standard and Poor’s 500 index. The index has an expected return of 14 percent, and its standard deviation is 16 percent. 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 percent. b. Could Percival do even better by investing equal amounts in the corporate bond portfolio and the index fund? The correlation between the bond portfolio and the index fund is .1.

It's an iterative process, meaning you manually need to put in different mixes until you get what you want. This optimization process can be facilitated by using the "Solver" function in Excel, where you setup the problem in Excel and ask Excel to manually put in numbers until the goal is met. The goal in this case is to have the portfolio standard deviation = 10%.