Suppose that the percentage annual return you obtain when you invest a dollar in

Question

Suppose that the percentage annual return you obtain when you invest a dollar in gold or the stock market is dependent on the general state of the national economy as indicated below. For example, the probability that the economy will be in "boom" state is 0.15. In this case, if you invest in the stock market your return is assumed to be 25%; on the other hand if you invest in gold when the economy is in a "boom" state your return will be minus 30%. Likewise for the other possible states of the economy. Note that the sum of the probabilities has to be 1--and is.

Based on the expected return, would you rather invest your money in the stock market or in gold? Why? Calculate with the standard deviation formula or consider the standard deviation in your response.

State of economy Probability Market Return Gold Return Boom 0.15 25% (-30%) Moderate Growth 0.35 20% (-9%) Week Growth 0.25 5% 35% No Growth 0.25 (-14%) 50%

Explanation / Answer

Let market return be X:

E(X) = xP(x) = 8.5

Var(X) = x² P(x) - [xP(x)]² = 289.00 - [8.5]² = 216.75

SD(X) = (216.75) = 14.72

Let gold return be Y:

E(Y) = yP(y) = 13.6

Var(Y) = y² P(y) - [yP(y)]² = 1094.60 - [13.6]² = 909.64

SD(Y) = (909.64) = 30.16

Based on the expected return, one should return in Gold because its expected value is greater than the expected value of stock market. But standard deviation of gold is higher that makes it more variable. Therefore, one should invest in stock market.

x P(x) x P(x) x²P(x) 25 0.15 3.75 93.75 20 0.35 7.00 140.00 5 0.25 1.25 6.25 -14 0.25 -3.50 49.00 Sum 1.00 8.5 289.000

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