Conditional Value at Risk

We suggest a new methodology to overcome several well-known deeciencies of Value at Risk computations. Our approach mainly addresses two aspects of Value at Risk: rst, to avoid potentially disastrous clustering in predicted tail events we derive a new approach to accurately estimating the conditional distribution of asset returns using maximum entropy densities. Second, by the very nature of the maximum entropy model, we account for negative skewness and fat tails in asset returns. In particular, to obtain a robust and scalable estimate of the covariance matrix of the assets in the portfolio we extend an approach by Hull and White to the case of conditional distributions. In extensive experiments with historical stock index data we compare the proposed methodology to alternative estimation approaches using a new, simulation-based statistical testing procedure for serial dependence in the predicted tail events.