Standard Deviation of Returns

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.
Security returns are known to be approximately normally distributed, which makes it easy to make some inferences from the value of the standard deviation. This is because the normal distribution is the familiar symmetric bell shaped curve and the mean splits the distribution right down the middle.

The following rules of thumb apply to the normal distribution.

Span
 Probabilty
+/- 1 SD
 68%
+/- 2 SD
 96%
+/- 3 SD
 100%

+/-2 standard deviations is actually 95.44% but, as this is only a rule of thumb, we'll use 96%, which is easier to divide by two.

Normal Probabilty Brackets


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!.

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