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 the Economy |
Probability |
Market Return |
Gold Return |
|
Boom |
0.15 |
25% |
-30% |
|
Moderate Growth |
0.35 |
20% |
-9% |
|
Weak Growth |
0.25 |
5% |
35% |
|
No Growth |
0.25 |
-14% |
50% |
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Question #1: Expected Return and Standard Deviation
Expected Return
Market Return
Gold Return
Based on expected returns, I would invest my money in the gold market because it has a higher expected return than the stock market. The gold market has an expected return of 13.6%, while the stock market has an expected return of 8.5%.
Standard Deviation
State of the Economy |
Probability |
Market Return |
Gold Return |
|
Boom |
0.15 |
25% |
-30% |
|
Moderate Growth |
0.35 |
20% |
-9% |
|
Weak Growth |
0.25 |
5% |
35% |
|
No Growth |
0.25 |
-14% |
50% |
| Expected Return |
8.5% |
13.6% |
|
| Variance |
0.0217 |
0.0910 |
|
| Standard Deviation |
0.1472 |
0.3016 |
Market Return
Gold Return
The standard deviation of gold (30.16%) than the standard deviation stock market (14.72%). This indicates that the investment made in gold has higher chances of swinging in both extremes than the investment made in the stock market. Thus, I would invest in the stock market as it is less risky than the investment made in gold.
Question #2: Gold or Stock Market?
Based on the expected return and standard deviations of both markets, I would invest in the stock market. While both markets have positive expected returns, the stock market is less risky than gold investment. Thus, I would invest in the stock market as it has positive expected returns and is less risky.
Question #3: Portfolio of Stock and Gold
State of the Economy |
Probability |
Market Return |
Gold Return |
|
Boom |
0.15 |
10% |
-12% |
|
Moderate Growth |
0.35 |
8% |
-4% |
|
Weak Growth |
0.25 |
2% |
14% |
|
No Growth |
0.25 |
-6% |
20% |
| Expected Return |
3.40% |
5.44% |
|
| Variance |
-0.02106 |
0.01455 |
|
| Standard Deviation |
-1.05% |
0.73% |
Expected Return
Stock Market Return
Gold Return
Standard Deviation
Stock Market Return
Gold Return
Based on the three options, I would invest in the stock market alone. This is because it has positive returns and is less risky than the other options.
