CFA Level 1 – Quantitative Methods, Normal Distribution
Statistical analysis of data sets usually involves modelling the data as a distribution of its values. There are several common types of distributions to which data series usually fall under. The most common distribution is the Normal Distribution.
The Normal Distribution is very common in nature and for randomly occurring series. For example, the heights of people in a population and normally distributed. The Normal Distribution is commonly used in finance, although it should be noted that extreme movements in asset prices are much more likely than the normal distribution implies.
It is important to remember the percentage of observations which lie within standard deviations away from the mean in the normal distribution.
- 65% of observations are within 1 standard deviation movement.
- 90% of observations are within 1.65 standard deviations movement.
- 95% of observations are within 1.96 standard deviation movement.
- 99% of observations are within 2.58 standard deviation movement.
Thus if an asset’s price is $120 and its standard deviation is 30 (calculated from annual data) there is only a 5% chance of the asset price falling more than $58.8 (1.96 standard deviations) in a year.