Therefore, the standard deviation is
We summarize the data on percentage returns on these two types of investment over this 7-year period in the following table, where all figures have been rounded to one decimal place.
COMMON STOCKS U.S. TREASURY BILLS
Standard deviation 20.6% 1.4%
It can be seen that while investment in common stocks yielded the higher average rate of return, the returns on Treasury bills were considerably less variable. In the context of this example, the standard deviation can be viewed as providing a measure of the uncertainty, or risk, associated with investment returns. We see that while average returns were higher for common stocks than for Treasury bills, the associated risk, as measured by the standard deviation of returns, was also higher. (Similar results, which are predicted by finance theory, emerge from the analysis of larger sets of returns data.)
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