"A fund manager at Pacific Investment Management Corporation (PIMCO) manages a large investment fund for a number of client organizations within Los Angeles and other Southern California counties. The fund currently has $5,000,000 in uninvested cash and the manager is interested in selecting an optimal investment instrument for the next six months. Three promising investment alternatives have been identified: a selected stock portfolio, a portfolio of government securities, and a portfolio of financial derivatives. The manager knows that the rates of return for these investments are influenced by such external factors as interest rates. For example, investing in a stock portfolio or a portfolio of financial derivatives when interest rates are increasing could lead to a low if not negative rate of return. These investments must be converted to cash at the end of the six month period. The portfolio of government securities has a six month maturity. PIMCO charges a 1% annual administrative fee for managing the investment fund.
The manager has characterized the external environment under the conditions that the interest rates will either increase, remain the same, or decrease over the investment period. Based on this simplification, the manager estimates the gross annual returns to be 1%, 8%, and 11% respectively for the stock portfolio, -6%, 5%, and 19% for the financial derivatives under each of the same scenarios noted. The gross return on the government securities portfolio is estimated to be 7%. From historical experience, the manager estimates that there is a 20% likelihood that interest rates will increase over the investment period and a 30% chance that rates will decrease.
In addition, a financial research firm will provide the fund manager with a prediction on the future direction of interest rates for a fee of $20,000. Reviewing a summary of the research firm's past performance over a similar time frame, the manager notes that the firm predicted that interest rates would increase 8 out of 10 times when they actually increased and 2 times out of 10 when they decreased. Seven times out of 10 the firm correctly predicted that rates would remain unchanged although they were incorrect on 2 occasions out of 10 when rates actually increased. Similarly, the firm correctly predicted a decrease in rates 6 times out of 10 and incorrectly predicted a decrease on 1 of 10 occasions when rates remained unchanged.
a. Develop a decision tree and/or complete payoff tables to represent the alternatives and outcomes for consideration by PIMCO.
b. Use the expected value approach to recommend which alternative PIMCO should follow in order to maximize expected contribution or return. Provide also, if the financial research firm is recommended, the investment strategy to follow when the results are given. Provide a complete narrative of all steps taken in the decision process and the justification for the indicated recommendation. "
In this solution we develop a decision tree to represent the alternatives and outcomes for consideration by PIMCO.