# 1.6.5 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 indexâ€™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*.