6 Risk measures and extreme value theory

• The most widely used risk measure in practice is Value–at-Risk (VAR)

• To forecast the VaR of a single asset or an entire portfolio of assets for one period ahead, it is necessary to know the distribution of returns, the conditional mean at time T+1, and the conditional variance at time T+1, and therefore this parametric approach is the most sensitive, as it is not assumption–free

• There is also non–parametric approach, which takes the certain quantile of historical returns (usually the 95-th quantile is considered), but this approach has no predictive ability

• The major problem with parametric VaR is distribution assumption. Although normal distribution is usually assumed (which is unrealistic due to asymmetry and heavy tails) does not account for skewness and kurtosis. Therefore, the normal quantile can be adjusted for skewness and kurtosis using Cornish–Fisher expansion