standard deviation

standard deviation

1. calculation:

   • * obtain the arithmetic mean * obtain the set of deviations from the mean * square each deviation * divide the sum of the squared deviations by the number of observations to obtain the population variance * take the square root of the variance to obtain the standard deviation

2. represents the average amount by which the values in the distribution deviate from the arithmetic mean

3. normal distributions

   • 68.26% - two thirds within one standard deviation
   • 95.5% of all observations within two standard deviations
   • 99.75% of all observations within three standard deviations of the mean

4. limitation

   • actual returns are not neatly/symmetrically dispersed
     • most long-run distributions of equity returns are positively skewed

5. The most commonly used method to quantify risk

6. Measures how widely dispersed are the possible outcomes around the mean expected outcome

7. measures non-systemic risk

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