2.6.5 Index Value at Risk (VaR)

Value at Risk (VaR)

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 total investment returns and 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 index’s total investment return 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 volatility of the index at time t.
 is the value of the index at time t.

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 t.