Stable ETL Optimal Portfolios and Extreme Risk Management

We introduce a practical alternative to Gaussian risk factor distributions based on Svetlozar Rachev's work on Stable Paretian Models in Finance (see [4]) and called the Stable Distribution Framework. In contrast to normal distributions, stable distributions capture the fat tails and the asymmetries of real-world risk factor distributions. In addition, we make use of copulas, a generalization of overly restrictive linear correlation models, to account for the dependencies between risk factors during extreme events, and multivariate ARCH-type processes with stable innovations to account for joint volatility clustering. We demonstrate that the application of these techniques results in more accurate modeling of extreme risk event probabilities, and consequently delivers more accurate risk measures for both trading and risk management. Using these superior models, VaR becomes a much more accurate measure of downside risk. More importantly Stable Expected Tail Loss (SETL) can be accurately calculated and used as a more informative risk measure for both market and credit portfolios. Along with being a superior risk measure, SETL enables an elegant approach to portfolio optimization via convex optimization that can be solved using standard scalable linear programming software. We show that SETL portfolio optimization yields superior risk adjusted returns relative to Markowitz portfolios. Finally we introduce an alternative investment performance measurement tools: the Stable Tail Adjusted Return Ratio (STARR), which is a generalization of the Sharpe ratio in the Stable Distribution Framework. “When anyone asks me how I can describe my experience of nearly 40 years at sea, I merely say uneventful. Of course there have been winter gales and storms and fog and the like, but in all my experience, I have never been in an accident of any sort worth speaking about. I have seen but one vessel in distress in all my years at sea (…) I never saw a wreck and have never been wrecked, nor was I ever in any predicament that threatened to end in disaster of any sort.”