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CASE STUDY ANNABELLE INVESTMENT IN THE MARKET
Annabelle Sizemore has cashed in some treasury bonds and a life insurance policy that her parents had accumulated over the years for her. She has also saved some money in certificates of deposit and savings bonds during the 10 years since she graduated from college. As a result, she has $120,000 available to invest. Given the recent rise in the stock market, she feels that she should invest all of this amount there. She has researched the market and has decided that she wants to invest in an index fund tied to S&P stocks and in an Internet stock fund. However, she is very concerned about the volatile of Internet stocks. Therefore, she wants to balance her risk to some degree.
She has decided to select an index fund from Shield Securities and an
Internet stock fund from Madison Funds, Inc. She has also decided that the proportion of the dollar amount she invests in the index fund relative to the
Internet fund should be at least one-third but that she should not invest more than twice the amount in the Internet fund that she invests in the index fund. The price per share of the index fund is $175, whereas the price per share of the
Internet fund is $208. The average annual return during the last 3 years for the index fund has been 17%, and for the Internet stock fund it has been 28%. She anticipates that both mutual funds will realize the same average returns for the coming year that they have in the recent past; however, at the end of the year she is likely to re-evaluate her investment strategy anyway. Thus, she wants to develop an investment strategy that will maximize her return for the coming year.
(a) Formulate a linear programming model for Annabelle that will indicate how much money she should invest in each fund and solve this model (by Simplex
Method).
(b) Suppose Annabelle decides to change her risk-balancing formula by eliminating the restriction that the proportion of the amount
Annabelle Sizemore has cashed in some treasury bonds and a life insurance policy that her parents had accumulated over the years for her. She has also saved some money in certificates of deposit and savings bonds during the 10 years since she graduated from college. As a result, she has $120,000 available to invest. Given the recent rise in the stock market, she feels that she should invest all of this amount there. She has researched the market and has decided that she wants to invest in an index fund tied to S&P stocks and in an Internet stock fund. However, she is very concerned about the volatile of Internet stocks. Therefore, she wants to balance her risk to some degree.
She has decided to select an index fund from Shield Securities and an
Internet stock fund from Madison Funds, Inc. She has also decided that the proportion of the dollar amount she invests in the index fund relative to the
Internet fund should be at least one-third but that she should not invest more than twice the amount in the Internet fund that she invests in the index fund. The price per share of the index fund is $175, whereas the price per share of the
Internet fund is $208. The average annual return during the last 3 years for the index fund has been 17%, and for the Internet stock fund it has been 28%. She anticipates that both mutual funds will realize the same average returns for the coming year that they have in the recent past; however, at the end of the year she is likely to re-evaluate her investment strategy anyway. Thus, she wants to develop an investment strategy that will maximize her return for the coming year.
(a) Formulate a linear programming model for Annabelle that will indicate how much money she should invest in each fund and solve this model (by Simplex
Method).
(b) Suppose Annabelle decides to change her risk-balancing formula by eliminating the restriction that the proportion of the amount