Chapter 9.5, Problem 18E

INVESTMENT STRATEGIES As part of their investment strategy, the Carrington’s have decided to put $\$100,000$ into stock market investments and also into purchasing precious metals. The performance of the investments depends on the state of the economy in the next year. In an expanding economy, it is expected that their stock market investment will outperform their investment in precious metals, whereas an economic recession will have precisely the opposite effect. Suppose the following payoff matrix gives the expected percentage increase or decrease in the value of each investment for each state of the economy:

$\begin{array}{l}\begin{array}{cc}\begin{array}{l}Expanding\\ economy\end{array}& \begin{array}{l}Economic\\ recession\end{array}\end{array}\\ \begin{array}{c}Stockmarketinvestment\\ Commodityinvestment\end{array}\left[\begin{array}{cc}20& -5\\ 10& 15\end{array}\right]\end{array}$

a. Determine the optimal investment strategy for the Carrington’s' investment of $100,000.

b. What profit can the Carrington’s expect to make on their investments over the year if they use their optimal investment strategy?