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.

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