(From 'Introduction to Mathematical Programming' by W. Winston and M. Venkataramanan) A portfolio manager has been asked to invest $1,000,000. The...
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9. (From “Introduction to Mathematical Programming” by W. Winston and M.
Venkataramanan) A portfolio manager has been asked to invest $1,000,000. The
investment research deve10pment department has identified six mutual funds
with varying investment strategies, resulting in different potential returns and
associated risks, summarized as follows fund 1 2 3 4 5 6
price per share ($) 455 76 110 17 23 22
expected return ('Z.) 30 20 15 12 10 7
risk category high high high med med low One way to control the risk is to limit the amont of money invested in the various
funds. To that end, the management has specified the following guidelines. The
total dollar amount invested in high risk funds must be between 50% and 75%
of the total investment. The total dollar amount invested in medium risk funds
must be between 20% and 30% of the total investment. The total dollar amount
invested in low risk funds must be at least 5% of the total investment. A second
way to control risk is to diversify. The management has specified that the shares
in each of funds 1 and 2 should not be less than 10% of the shares in the total
portfolio. With these guidelines, write and solve and optimizatin problem that
maximizes the expected investment return. Be careful! “total dollar amount
invested” is not necessarily the entire $1,000, 000 dollars.

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