Statistical Skeletons

In order to fully understand VaR modeling it is necessary to get to grips with some fundamental statistical theory. These bare bones are fleshed out in the statistics primer which provides a more formal treatment. The way in which the data is distributed has an important bearing on the effectiveness of statistical methods to measure risks. Most VaR methods assume:

Normal distribution. That the data in the form of price changes of instruments has a normal distribution. A normal distribution is one that has a mean equal to its mode and median and is symmetric about the mean. The price changes may be expressed in absolute or percentage terms. Stable standard deviation of returns. That the variation of returns about the mean is stable and does not vary over time. The variation of returns is measured by the distribution’s standard deviation.
No serial correlation. That there is no serial correlation between returns. This is particularly important when extrapolating results for a single holding period to multiple holding periods.