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Homework answers / question archive / An investment has the following return distribution
An investment has the following return distribution. How much is its expected return and standard deviation?
| State of Economy | Probability | Return |
| Peak | 0.1 | 10% |
| Contraction | 0.5 | 0% |
| trough | 0.2 | 2% |
| Expansion | 0.2 | 15% |
4.4% and 6.04%
5.4% and 7.85%
4.4% and 3.64%
6.75% and 6.71%
Expected return = 0.1*0.1 + 0.5*0 + 0.2*0.02 + 0.2*0.15
Expected return = 0.01 + 0 + 0.004 + 0.03
Expected return = 0.044 or 4.4%
Standard deviation = [0.1(0.1 - 0.044)^2 + 0.5(0 - 0.044)^2 + 0.2(0.02 - 0.044)^2 + 0.2(0.15 - 0.044)^2]^1/2
Standard deviation = [0.00031 + 0.00097 + 0.00012 + 0.00225]^1/2
Standard deviation = 0.0604 or 6.04%
