In: Finance
A stock had returns of 18.66 percent, 22.09 percent, −15.35 percent, 9.17 percent, and 28.24 percent for the past five years. What is the standard deviation of the returns?
Standard deviation is 17.06%
Step-1:Calculation of average return | ||||||
Year | Return | |||||
1 | 18.66% | |||||
2 | 22.09% | |||||
3 | -15.35% | |||||
4 | 9.17% | |||||
5 | 28.24% | |||||
Total | 62.81% | |||||
Average return | 62.81% | / | 5 | = | 0.12562 | |
Step-2:Calculation of variance | ||||||
Year | Return | Average return | ||||
a | b | c=(a-b)^2 | ||||
1 | 18.66% | 12.56% | 0.003719 | |||
2 | 22.09% | 12.56% | 0.009078 | |||
3 | -15.35% | 12.56% | 0.077908 | |||
4 | 9.17% | 12.56% | 0.001151 | |||
5 | 28.24% | 12.56% | 0.02458 | |||
Total | 0.116435 | |||||
Variance | = | 0.116435 | / | 4 | = | 0.02911 |
Step-3:Calculation of standard deviation | ||||||
Standard deviation | = | Variance | ^ (1/2) | |||
= | 0.02911 | ^ (1/2) | ||||
= | 17.06% |