Integrative—Expected return, standard deviation, and coefficient of variation An asset is currently being considered by Perth Industries. The probability distribution of expected returns for this asset is shown in the following table,
j |
Pr |
Return, r |
||
1 |
0.05 |
15.00% |
||
2 |
0.15 |
5.00% |
||
3 |
0.70 |
0.00% |
||
4 |
0.05 |
−5.00% |
||
5 |
0.05 |
−10.00% |
.
a.Calculate the expected value of return, r,
for the asset.
b. Calculate the standard deviation, for the asset's returns.
c. Calculate the coefficient of variation,
CV, for the asset's returns.
S. no. | Probability (P) | Return = R | P * R | P * (R - R')^{2} |
1 | 0.05 | 15.00% | 0.01 | 0.00102 |
2 | 0.15 | 5.00% | 0.01 | 0.00027 |
3 | 0.70 | 0.00% | 0.00 | 0.00004 |
4 | 0.05 | -5.00% | 0.00 | 0.00017 |
5 | 0.05 | -10.00% | -0.01 | 0.00058 |
Expected return (R') = | 0.0075 | 0.00207 | ||
Expected return | 0.75% | |||
Standard Deviation | =SQRT(0.02624) | |||
Standard Deviation | 0.045 | 4.5% | ||
CV | =Standard Deviation / R' | |||
CV | =0.045 / 0.00207 | 6.064468466 |
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