Nicole Nelson has come into an inheritance from her grandparents. She is attempt

Question

Nicole Nelson has come into an inheritance from her grandparents. She is attempting to decide among several investment alternatives. The return after one year is dependent primarily on the interest rate during the next year. The rate is currently 7%, and she anticipates it will stay the same or go up or down by at most 2 points. The various investment alternatives plus their returns ($10,000s) given the interest rate changes are shown in the following table. Interest Rates Investments 5% 6% 7% 8% 9% Money market fund 1.7 2.8 3.0 3.6 4.5 Stock growth fund 5 3 3.5 5 7.5 Bond fund 5 4 3.5 3 2 Government fund 4 3.6 3.2 2.8 2.1 Risk fund 12 7 4.2 9.3 16.7 Savings bonds 3 3 3.2 3.4 3.5 Determine the best investment using the following decision criteria. a. Maximax b. Maximin c. Equal likelihood d. Assume that Nicole, with the help of a financial newsletter and some library research, has been able to assign probabilities to each of the possible interest rates during the next year as follows: Interest Rate 5% 6% 7% 8% 9% Probability 0.1 0.2 0.4 0.2 0.1 Supplement 1 • Operational Decision-Making Tools: Decision Analysis 43 Using expected value, determine her best investment decision.

Explanation / Answer

a. Maximax: Under this approach, first the maximum returns for each invsetment type will be selected. The next step will be to select the investment that offers the maximum of the above maximum returns. ("max" function can be used in excel).

The maximum rates for each investment types are - 4.5, 7.5, 5, 4, 16.7, 3.5. The maximum of these returns is 16.7% being offered by the risk fund.

Thus, "risk fund" is the best investment under the maximax criteria.

b. maximin: Under this approach, first the minimum returns for each invsetment type will be selected. The next step will be to select the investment that offers the maximum of the above minimum returns.

Maximizing the above minimum returns, we get the return of 4.2% being offered by the risk fund.

Thus, "risk fund" is the best investment under the maximin criteria.

c. equal likelihood: Under the equal likelihood criteria it is assumed that all the rates are equally likely to occur. In this case the average return for each investment will be calculated and then the highest return will be selected. Average return = sum of all returns/5

The highest average return = 9.84% and is being offered by risk fund. Hence "risk fund" will be the best investment using the equal likelihood method.

d. This method will use weighted average approach. Weighted average for an investment= sum of (probability*return)

For example, for money market fund, weighted average = 0.1*1.7 + 0.2*2.8 + 0.4*3 + 0.2*3.6 + 0.1*4.5 = 3.10

"Risk fund" is the best investment as it has the highest expected value of 7.81%.

expected value = weighted average, using the probabilities as weights.

5% 6% 7% 8% 9% Investments Maximum Money market fund 1.7 2.8 3.0 3.6 4.5 4.5 Stock growth fund 5.0 3.0 3.5 5.0 7.5 7.5 Bond fund 5.0 4.0 3.5 3.0 2.0 5.0 Government fund 4.0 3.6 3.2 2.8 2.1 4.0 Risk fund 12.0 7.0 4.2 9.3 16.7 16.7 Savings bonds 3.0 3.0 3.2 3.4 3.5 3.5

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