Standard Deviation is a measure of how closely a series of numbers tracks its expected value. The formula is:
 |
Standard Deviation is often written as a lower case Greek sigma.
- N is the number of observations
- xi is the actual value of the ith observation
- x bar is the expected value of xi
Calculating this number is more complex than it seems. If you are intending to measure it yourself, please read the White Paper found in the Information Center "Understanding and Measuring Risk - A Statistical Approach".
Many people think the lower the standard deviation the better, but that's not necessarily true. Take two portfolios: one with a standard deviation of annual returns of 15 percentage points, the other with a standard deviation of 18 percentage points. Which portfolio has more risk? You really can't tell until you know their average return. Therefore, statisticians have come up with a better measure for variability, which is particularly useful when you are trying to compare portfolios with significantly different means: the Coefficient of Variance (CV), which is defined as:
 |
Where σ (sigma) is the standard deviation and μ (mu) is the mean.
| PORTFOLIO: | A | B |
| Standard Deviation | 15 percentage points | 18 percentage points |
| Mean Return | 12% | 30% |
| In 68% of all years, the actual return will vary between | -3% to 27% | 12% to 48% |
| Coefficient of Variation | 125% | 60% |
Most people would say portfolio B has less risk. This is the reason why many sophisticated investors use CV to evaluate the volatility of a portfolio, particularly when comparing portfolios that have different means, such as an index versus a high performance fund.
For a detailed explanation of this topic, take a look at "Understanding and Measuring Risk - A Statistical Approach" in the Information Center.
