Question
Topic: Decision Alternatives Suppose that the percentage annual return you obtain when you invest a dollar in gold or the stock market is dependent on
Topic: 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? [*****THIS WAS MY ANSWER*****]
To answer this week's question, we have to look at Chapter 5 to do so.The question is: "Based on the expected return, would you rather invest your money in the stock market or in gold? Why?"Using the information provided (Table), if I was going to invest in either the market (Em) or gold (Eg), I would first need to figure out what the expected value was for each.
With this, Chapter 5 "Discrete Probability Distributions," under "Expectation" of our text book says: "The expected value of a discrete random variable of a probability distribution is the theoretical average of the variable. The formula is = E(X) = X P(X) The symbol E(X) is used for the expected value." (Bluman, p.277)
So, to find the expected value for the stock market and gold we follow this formula to get the expected value of x, Ex:
Market = Em = 0.15 25 + 0.35 20 + 0.25 5 + 0.25 (-14) = 8.5 or (8.5%)
Gold = Eg = 0.15 (-30) + 0.35 (-9) + 0.25 35 + 0.25 50 = 13.6 or (13.6%)
In conclusion, since the expected return for gold (13.6%) is higher than the expected return for the market ( 8.5%), I would likely invest in gold given the information provided in this scenario.
[*********MY PROFESSOR RESPONDED--Need help here!*********]
great job and well done on your calculations! 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?
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