Beyond VaR: entropic measures for extreme risk

Two new risk measures to quantify extreme events and how to use them when optimizing portfolios.

Interview summary

Dany Cajas, creator of the Riskfolio-Lib library for Python and author of a book on portfolio optimization, presents the two risk measures he showed at the IV JAR: entropic value at risk and relativistic value at risk. They aim to handle extreme risks, such as tail events or climate risk, which produce losses larger than those estimated by value at risk and conditional value at risk, and thus come closer to a better estimate of the most catastrophic scenarios.

As he explains, these measures are more robust, that is, less sensitive to changes in the input data, and they derive from statistical properties of the distributions, so they act as upper bounds on losses. They also allow risk to be diversified and can be applied to portfolio design, to the generation of stress scenarios and to the backtesting of losses in market risk. In his approach, based on disciplined convex programming, the models work like LEGO blocks: the risk measure is swapped and the problem is solved just the same, even using it as a constraint. Today he focuses on convex and integer optimization applied to investments, teaches courses and collaborates with open source projects such as CVXPY.

Topics covered

• Limitations of VaR and CVaR in the face of extreme risks
• Entropic value at risk and relativistic value at risk
• Robustness and statistical properties of the measures
• Applications: portfolios, stress scenarios and backtesting
• Disciplined convex programming: models as interchangeable blocks
• Riskfolio-Lib, courses and open source software