Decision Alternatives

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.

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%)

Based on the expected return, would you rather invest your money in the stock market or in gold? Why

If I follow the formula of Expected Value then I will calculate the stock market as follows:

.15*25+ .35*20+.25*5+.25+ (-14)= 8.5%

Calculations for the Gold Market:

.15*(-30)+.35*(-9)+.25*35+.25*50= 13.6%

Therefore, it would be smarter to invest in the Gold market because the return rate is higher.

(Question)

Based solely on these values it does look like gold would be the better investment. However, when investing we often consider the risk of each investment. We can estimate the risk of each by finding the standard deviation for both gold and stocks:

https://www.mathsisfun.com/data/random-variables-mean-variance.html

A higher standard deviation would mean the investment is more risky. Would you consider adding these calculations to your post and commenting on which investment is more risky?