Question 12.2: Calculating the Variance and Standard Deviation Suppose the ...
Calculating the Variance and Standard Deviation
Suppose the Supertech Company and the Hyperdrive Company have experienced the following returns in the last four years:
| Year | Supertech Return | Hyperdrive Return |
| 2008 | -.20 | .05 |
| 2009 | .50 | .09 |
| 2010 | .30 | -.12 |
| 2011 | .10 | .20 |
What are the average returns? The variances? The standard deviations? Which investment was more volatile?
To calculate the average returns, we add up the returns and divide by 4. The results are:
Supertech average return =\overline{R}={.70}/{4}=.175
Hyperdrive average return =\overline{R}={.22}/ {4}= .055
To calculate the variance for Supertech, we can summarize the relevant calculations as follows:
| (1) | (2) | (3) | (4) | |
| Year | Actual Return | Average Return | Deviation (1) – (2) | Squared Deviation |
| 2008 | -.20 | .175 | -.375 | .140625 |
| 2009 | .50 | .175 | .325 | .105625 |
| 2010 | .30 | .175 | .125 | .015625 |
| 2011 | .10 | .175 | -.075 | .005625 |
| Totals | \underline{\underline{.70} } | \underline{\underline{.000} } | \underline{\underline{.267500} } |
Because there are four years of returns, we calculate the variance by dividing .2675 by (4 – 1) = 3:
| Supertech | Hyperdrive | |
| Variance (σ²) | .2675/3 = .0892 | .0529/3 = .0176 |
| Standard deviation (σ) | \sqrt{.0892}=.2987 | \sqrt{.0176}=.1327 |
For practice, verify that you get the same answer as we do for Hyperdrive. Notice that the standard deviation for Supertech, 29.87 percent, is a little more than twice Hyperdrive’s 13.27 percent; Supertech is thus the more volatile investment.