#### Mutual Fund *Bullet Tour* Page 14

**Standard Deviation of Returns**

- A group of investing returns over some period of time is a set of data points.
- Standard deviation can best be described as the average difference between the values of the data points in a set and the mean of the data points in a set.
- The difference between the value of a data point and the mean is known as its deviation from the mean.
- Standard deviation is a measure of volatility. The greater the standard deviation the higher the volatility and the riskier the investment.
- Published standard deviations are usually annualized monthly standard deviations rather than the standard deviation of annual returns.
- Standard deviation is the standard measure of investment risk.
- Standard deviation measures the total risk of individual assets and portfolios of assets in terms of the volatility of returns.

**The following rules of thumb apply to the normal distribution.**

Span |
Probabilty |
---|---|

+/-
1 SD |
68% |

+/-
2 SD |
96% |

+/-
3 SD |
100% |

**Here's what you should note in the above:**

- Data points are much more likely to be near the mean than at the extremes.
- There's a 68% probability of a data point falling within one standard deviation of the mean.
- As the distribution is symmetric, there is a 34% probability (68% ÷ 2) that a data point will have a value between the mean and one standard deviation greater than the mean, and a 34% probability that a data point will have a value between the mean and one standard deviation less than the mean. And so on.
- Virtually all of the data points (99.7%) can be expected to be within three standard deviations of the mean.

For a little more detail and some examples, see Standard Deviation of Returns - Easy as 1-2-3!.

Relevant Content: