Fat Tailed and Normal VaR & ETL Estimates
A real world risk modeling framework must assume the existence of fat-tailed markets – those exhibiting extreme losses, coupled with market asymmetry, tail dependence and the evaporation of diversification during market stresses. However, typical VaR measures are based only on the thin-tailed, symmetric normal distribution curve, resulting in overly optimistic VaR estimates that inadequately account for the extreme events.
As demonstrated by these Daily Risk Statistics, Cognity’s patented real-world risk modeling approach empowers risk managers with fat-tailed VaR estimates that do not suffer from the over-optimism of typical VaR measures.
Select an index below to see today’s estimates of fat-tailed VaR and fat-tailed ETL (Expected Tail Loss), along with the widely used “normal” VaR for major global indices.
Simulations for the fat-tailed model were produced using a skewed stable distributional assumption capturing all higher moments of the distribution fitted over a sample of 450 daily observations prior to the evaluation date. These more accurate distributions are used to simulate 50,000 scenarios and calculate risk estimates. Simulations for the normal model were produced by Gaussian distribution fitted over a sample of 450 daily observations prior to the evaluation date. The number of simulations was the same as in the stable case – 50,000.
The parameters of the normal model were computed using exponentially weighted moving average estimation with a decay factor of 0.94 (to make the model more reactive to volatility clustering) whereas the stable model takes into account the clustering of the volatility effect and autocorrelation through the ARMA-GARCH framework assuming skewed fat-tailed residuals. For the backtesting we used rolling window with 450 observations. All results are out-of-sample risk estimates for the subsequent day.
Please contact your BISAM representative for a more detailed description of the methodology employed.
Index returns data is provided with permission from Dow Jones, Standard and Poor’s, NASDAQ, Russell Investments and MSCI Barra. Data is sourced through Rimes Technologies and directly from exchanges. Cognity risk analytics and risk management software customers integrate these fat-tailed prcoess into their every day risk reporting processes.