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 Total Investment Return 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:

VaR_{t} = (TR_{t} - Z_{c} \times \sigma_{t}) \times V_{t} |

where:

TR_{t} is the Total Investment Return of the index at time *t*.

Z_{c} is inverse of the normal distribution for c (which is 1-
\alpha, where
\alpha is the level of significance, here 0.5%)

\sigma_{t} is the volatility of the index at time t

V_{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

Z_{cf} = Z_{c} + \frac {(Z_{c}^2-1)S} {6} + \frac {(Z_{c}^3 - 3Z_{c})K} {24} - \frac {(2Z_{c}^3 - 5Z_{c})S^2} {36} |

VaR_{t} = (TR_{t} - Z_{cf} \times \sigma_{t}) \times V_{t} |

where:

TR_{t} is the total return of the index at time *t*.

Z_{c} is the inverse of the normal distribution for c (which is 1-
\alpha, where
\alpha is the level of significance, here 0.5%)

Z_{cf} is the modified z-score accounting for the non-normality in the returns distribution

S is the skewness of the return distribution

K is the excess kurtosis of the return distribution

\sigma_{t} is the volatility of the index at time t

V_{t} is the value of the index at time