Michael, Inc. is an investment advisory firm that uses an asset allocation model that recommends the portion of each client's portfolio to be invested in a growth fund (G), an income fund (I), and a money market fund (M). To maintain diversity in each client's portfolio, the firm places limits on the percentage of each portfolio that may be invested in each of the three funds. General guidelines indicate that the amount invested in the growth fund must be between 20% and 40% of the total portfolio value. Similar percentages for the other two funds stipulate that between 20% and 50% of the total portfolio value must be in the income fund and at least 30% of the total portfolio value must be in the money market fund. In addition, the company attempts to assess the risk tolerance of each client and adjust the portfolio to meet the needs of the individual investor. A new client has $1,000,000 to invest, and Michael has assigned the following risk constraint for this client: 0.05G + 0.02I <= 0.04M. The company is currently forecasting annual yields of 18% for the growth fund, 12.5% for the income fund, and 7.5% for the money market fund. Based on the information provided, how should the new client be advised to allocate all or part of the one million dollars among the growth, income, and money market funds? b. Solve this LP problem and recommend how much of the $1,000,000 should be invested in each of the three funds. What is the annual return (in dollars) and the annual percent yield?

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 34P

Related questions

Question

Michael, Inc. is an investment advisory firm that uses an asset allocation model that
recommends the portion of each client's portfolio to be invested in a growth fund (G),
an income fund (I), and a money market fund (M). To maintain diversity in each client's portfolio,
the firm places limits on the percentage of each portfolio that may be invested in each of the three
funds. General guidelines indicate that the amount invested in the growth fund must be between 20%
and 40% of the total portfolio value. Similar percentages for the other two funds stipulate that
between 20% and 50% of the total portfolio value must be in the income fund and at least 30% of the
total portfolio value must be in the money market fund.

In addition, the company attempts to assess the risk tolerance of each client and adjust the portfolio to
meet the needs of the individual investor. A new client has $1,000,000 to invest, and Michael has
assigned the following risk constraint for this client: 0.05G + 0.02I <= 0.04M.

The company is currently forecasting annual yields of 18% for the growth fund, 12.5% for the income
fund, and 7.5% for the money market fund. Based on the information provided, how should the new
client be advised to allocate all or part of the one million dollars among the growth, income, and
money market funds?

b. Solve this LP problem and recommend how much of the $1,000,000 should be invested in each
of the three funds. What is the annual return (in dollars) and the annual percent yield?

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