As part of their investment strategy, the Carringtons have decided to put $100,0

Question

As part of their investment strategy, the Carringtons 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. (a) Determine the optimal investment strategy for the Carringtons' investment of $100,000. (Round your answers to the nearest dollar.) stocks $ commodities $ (b) What profit can the Carringtons expect to make on their investments over the year if they use their optimal investment strategy? (Round your answer to the nearest dollar.) $

Explanation / Answer

(a) We treat the problem as a matrix game in which the carringtons are the row palyer.

Letting p =[p1,p2] denote their optimal strategy, we find that

p1 = (d-c) /(a+d-b-c) = (15-10) /{20+15-(-15)-10} = 5/40 = 1/8

p2 = 1-p1 = 1-1/8 = 7/8

Thus, the carrington should put (1/8)(100000) = 12500 into stock market.

and (7/8)(100000) = 87500 into commodity investment.

(b) The expected payoff is equal to

E = (ad - bc)/(a+d-b-c)

E = {20x15 - (-15)x10}/{20+15-(-15)-10}

= (300+150)/(40) =450/40

= 45/4

= 11.25

Thus the carrington can expect to make a profit of 11.25% on their total investment of $100,000

that is a profit of (0.1125)x(100000) = $112500

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