Suppose that the percentage annual return you obtain when you invest a dollar in
ID: 3223062 • Letter: S
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.
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%
Question : Which of the 3 options would you prefer-(1) invest in gold alone, (2) invest in the market alone, or (3) invest 40% in the market and 60% in gold? Why?
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
Ans: Given the percentage annual return we obtain when we invest a dollar in gold or stock market which is dependent on the general state of national economy.
From the table given above, the preference to be given is the 3rd option ie. invest 40% in the stock market whereas 60% in gold. For the justification, first take look on probability of economy in all the 4 stages viz, Boom, Moderate Growth, Weak Growth & No Growth. From the probability point of view, the highest probability is for Moderate Growth Stage. Simultaneously look for the corresponding Market Return (20%) as well as Gold Return (-9%) and we find that at this stage the investor would have 20% of market return with least loss in gold return ie. 9% loss only. Keeping this in mind let's go for the probability again. The next high probability of return in economy is shared by the stages of Weak Growth & No Growth which is 0.25. Check for the corresponding values of Market Return & Gold Return and we find that during these stages it's more inclined to Gold Return rather than on the stock market.Whereas whenever the national economy is in the boom stage,which have 15% occuring percentage, invest money in stock market is prefered than in gold. In contrary stage Gold investment is prefered.
Having a look at the gain percentage and the loss percentage, the investor would prefer the 3rd option which more than obvious. So, your answer is 3. Hope you decipher my expanation. Thank you.
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