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

### Resolved Question:

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.
Submitted: 7 years ago.
Category: Homework
Expert:  SteveS replied 7 years ago.

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Customer: replied 7 years ago.

How did you find

 a. Portfolio of index and treasury % index 62.5% % treasury 37.5%

and for b

 % bond 48.1% % index 51.9%
Expert:  SteveS replied 7 years ago.

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%.