1.6.5 Index VaR

Definition

Value at Risk (VaR) is a statistical technique used to measure and quantify the level of financial risk within the firm, portfolio, or index over a specific time frame. VaR is calculated by assessing the amount of potential loss, the probability of occurrence for the amount of loss, and the time frame. For example, a 20% one-year VaR at the 99.5% confidence level, indicates that there is a 0.5% chance of losing at least 20% i.e. the maximum possible loss is 20% except in the 0.5% worst scenarios.

1-year VaR is calculated at a 99.5% and a 95% confidence interval at each point in time from the mean of 1.5.2 Total Investment Return and 1.6.1 Historical Volatility. Rolling 5-year and 10-year windows are used to compute the mean return and volatility, and the following two parametric approaches of computation are applied:

Gaussian VaR

Assumes a normal distribution of returns and computes Value-at-risk as follows:

where:

 is the 1.5.2 Total Investment Return of the index at time t.
 is inverse of the normal distribution for c (which is 1-, where  is the level of significance, here 0.5%)
 is the volatility of the index at time t
 is the value of the index at time 

Cornish-Fisher VaR

It is a modification of the Gaussian VaR and accounts for the skewness and excess kurtosis in the returns distribution

where:

 is the total return of the index at time t.
 is the inverse of the normal distribution for c (which is 1-, where  is the level of significance, here 0.5%)
 is the modified z-score accounting for the non-normality in the returns distribution
 is the skewness of the return distribution

 is the excess kurtosis of the return distribution 
 is the volatility of the index at time t
 is the value of the index at time