Normal vs. Fat-Tailed VaR
How risky are today’s financial markets? What is a good risk measure and how is it estimated?
As an industry standard, Value at Risk (VaR) measures the worst expected loss of a portfolio over a specific time interval at a given confidence level. Most commercial risk analytics products today measure VaR based on the thin-tailed and symmetric normal, “bell-shaped” distribution curve. As demonstrated by the current crisis, these normal distribution assumptions result in overly optimistic VaR estimates and they inadequately account for extreme events.
While conventional risk management software platforms expose the failure of their normal VaR-based models by requiring "proprietary" fudge factors to model market shocks, FinAnalytica’s Cognity risk management software platform uses fat-tailed, asymmetrical distributions throughout, and incorporates the most advanced statistical methods to model extreme events, volatility clustering, regime switching and correlation shifts in times of market crisis.
Cognity risk analytics provide more accurate fat-tailed VaR estimates that do not suffer from the over-optimism of normal distributions. But Cognity goes beyond VaR and also provides the downside Expected Tail Loss (ETL) measure - the average or expected loss beyond VaR. As compared with volatility and VaR, ETL, also known as Conditional Value at Risk (CVaR) and Expected Shortfall (ES), is a highly informative and intuitive measure of extreme downside losses. By combining ETL with fat-tailed distributions, risk managers have access to the most accurate estimate of downside risk available today.
In response to the current market crisis, FinAnalytica is now providing daily estimates of fat-tailed VaR and fat-tailed ETL, along with the widely used "normal" VaR, for major global indices.
No secret methods. No gimmicks. Just the most accurate, transparent VaR and ETL estimates based on sound, published risk analytics research and risk management software methodologies.
Daily Indices Track Records
Using Cognity’s fat-tailed VaR methodology, large differences are observed between the conventional normal VaR and the fat-tailed VaR in times of crisis. The normal model fails to predict extreme events. In less turbulent times, the fat-tailed VaR estimates closely track those of the normal VaR.
Fewer Exceedances with Fat-Tailed VaR
In the chart at the top of the page, out-of-sample backtests show the predictive accuracy of the fat-tailed VaR and normal VaR models. The exceedances reflect the number of times the actual returns are greater than the predicted VaR.
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 FinAnalytica 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.