Back-testing CVaR estimates

Conduct back-testing of Conditional Value-at-Risk (CVaR) estimates produced by the generic nonparametric high-dimensional value-at-risk algorithm.

Background

The paper develops and empirically evaluates a nonparametric algorithm for estimating portfolio Value-at-Risk (VaR) and CVaR from historical, volatility-normalized returns across many underlying financial instruments. The reported empirical evaluation focuses exclusively on 99% daily VaR estimates for an ensemble of 500 portfolios spanning 49 futures instruments.

Although the algorithm computes the full portfolio-return probability density function and therefore can in principle produce CVaR estimates at arbitrary confidence levels, the paper does not evaluate the accuracy of those CVaR estimates against realized future losses. The authors explicitly leave this empirical validation for subsequent work.

References

We leave back-testing of CVaR estimates as a future exercise.

— A generic nonparametric value-at-risk estimator for high dimensions  (2608.17481 - Sun, 18 Aug 2026) in Introduction

In the future, we recommend repeating our experiments for higher maximum sample sizes than those considered here, especially if one is interested in detecting underestimations of smaller magnitude, since we were only able to make meaningful statements for considerably large underestimations.

— On E-Backtesting: Generalizations and Sample Size Determination  (2609.05089 - Oestmann et al., 4 Sep 2026) in Section 6.2, Extreme value distributions; Section 6.4, Analytic derivation of sample size bounds