An Introduction to Value-At-Risk, Fourth Edition

Chapter 2

VOLATILITY AND CORRELATION

Value-at-Risk (VaR) is essentially a measure of volatility, specifically how volatile a bank's assets are. Assets that exhibit high volatility present higher risk. VaR also takes into account the correlation between different sets of assets in the overall portfolio. If the market price performance of assets is closely positively correlated, this also presents higher risk. So, before we begin the discussion of VaR we need to be familiar with these two concepts. Readers who have an investor's understanding of elementary statistics may skip this chapter and move straight to Chapter 3.

STATISTICAL CONCEPTS

The statistics used in VaR calculations are based on well-established concepts. There are standard formulae for calculating the mean and standard deviation of a set of values. If we assume that X is a random variable with particular values x, we can apply the basic formula to calculate mean and standard deviation. Remember that the mean is the average of the set of values or observations, while the standard deviation is a measure of the dispersion away from the mean of the range of values. In fact, the standard deviation is the square root of the variance, but the variance, being the sum of squared deviations of each value from the mean divided by the number of observations, is of little value for us.

Arithmetic mean

We say that the random variable ...