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Chapter 4 - Risk > RETURN DISTRIBUTIONS
RETURN DISTRIBUTIONS
Normal (or Gaussian) distribution
A distribution is said to be normal if there is a high probability that an observation will be close to the average and a low probability that an observation is far away from the average. A normal distribution curve peaks at the average value.
A normal distribution shown in Figure 4.10 has special properties that are useful if we can assume returns or excess returns are normally distributed. If returns are normally distributed we can use the average return and variability or standard deviation of returns to describe the distribution of returns, such that:
• Approximately 68% of returns will be within a range of 1 standard deviation above and below the average return.
• Approximately 95% of returns will be within a range of 2 standard deviations above and below the average return.
• Approximately 99.7% of returns will be within a range of 3 standard deviations above and below the average return.2
