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

1. The payoff matrix give is as follows         

10

now, let us consider that the Carrigtons decide to invest X dollars into the stock market and 100000-X dollars into the commodity market.

So, in case of expanding economy the returns will be 15X +5(100000-X)

and in case of economic recession the returns will be -5X + 10(100000-X)

Now, for an optimal investment strategy the returns that the Carringtons expect when there is expanding economy and economic recession should be the same. so, we equate the above two expressions i.e

15X +5(100000-X) = -5X + 10(100000-X)

solving the above expression we get 25X = 500000

I.E X=20000 and 100000-X = 80000

so, the Carriingtons should invest 20000 dollars in stock market and 80000 in the commodity market.

2. The expected profit can be obtained by putting thee values of the investment in any of the above equation

if we put it in the first then we have (0.15x20000)+(0.05x80000)= 3000+4000=7000 dollars

if we put it in the second then we have (-0.05x20000)+(0.1x80000)= -1000+8000=7000 dollars

thus, the expected return on the investment using the optimal strategy is 7000 dollars.

Expanding Economy Economic recession Stock market Investment 15 -5 X Commodity Investment 5

10

100000-X

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