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?

Explanation / Answer

Conclusion:

Though the expected return on gold is higher it has higher deviation (risk) which is indicated by its higher coefficient of variation,

As I am a risk taker I would invest in gold. It promises higher return with higher risk.

Investment in stock market: Deviation State of the economy Probability (p) Return ('r) r * p from mean (d) d^2 p*D^2 Boom 0.15 25 3.75 16.5 272.25 40.8375 Moderate growth 0.35 20 7.00 11.5 132.25 46.2875 Weak growth 0.25 5 1.25 -3.5 12.25 3.0625 No growth 0.25 -14 -3.50 -22.5 506.25 126.5625 8.50 216.75 Expected return 8.50 % Standard deviation = 216.75 14.72 % Coefficient of variation = Std. deviation/Mean = 14.72/8.5 = 1.73 Investment in Gold: Deviation State of the economy Probability (p) Return ('r) r * p from mean (d) d^2 p*D^2 Boom 0.15 -30 -4.50 -38.5 1482.25 222.3375 Moderate growth 0.35 -9 -3.15 -17.5 306.25 107.1875 Weak growth 0.25 35 8.75 26.5 702.25 175.5625 No growth 0.25 50 12.50 41.5 1722.25 430.5625 13.60 935.65 Expected return 13.60 % Standard deviation = 935.65 30.59 % Coefficient of variation = Std. deviation/Mean = 30.59/13.6 = 2.25

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