Sessi Tokpavi

Backtesting value-at-risk accuracy: a simple new test

This paper proposes a new test of value-at-risk (VAR) validation. Our test exploits the idea that the sequence of VAR violations (hit function) ‐ taking value 1 ‐ α, if there is a violation, and ‐α otherwise ‐ for a nominal coverage rate α verifies the properties of a martingale difference if the model used to quantify risk is adequate (Berkowitz et al., 2005). More precisely, we use the multivariate portmanteau statistic of Li and McLeod (1981) ‐ extension to the multivariate framework of the test of Box and Pierce (1970) ‐ to jointly test the absence of autocorrelation in the vector of hit sequences for various coverage rates considered as relevant for the management of extreme risks. We show that this shift to a multivariate dimension appreciably improves the power properties of the VAR validation test for reasonable sample sizes.

A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion

This article introduces a kernel-based nonparametric inferential procedure to test for Granger causality in distribution. This test is a multivariate extension of the kernel-based Granger causality test in tail event. The main advantage of this test is its ability to examine a large number of lags, with higher-order lags discounted. In addition, our test is highly flexible because it can be used to identify Granger causality in specific regions on the distribution supports, such as the center or tails. We prove that the test converges asymptotically to a standard Gaussian distribution under the null hypothesis and thus is free of parameter estimation uncertainty. Monte Carlo simulations illustrate the excellent small sample size and power properties of the test. This new test is applied to a set of European stock markets to analyze spillovers during the recent European crisis and to distinguish contagion from interdependence effects.

Conditional Value-at-Risk: An Alternative Measure for Low-Risk Strategies?

In contrast with existing literature that focuses on conditional Value-At-Risk (CVaR) as a portfolio risk measure, we examine here the properties of portfolios built to minimize CVaR. We look into the stability and performance potential of CVaR-optimal portfolios and compare our results with Minimum Variance portfolios. Finally, we run realistic simulations of risk-minimizing strategies using CVaR as risk measure and compare their performances to otherwise identical variance minimizing strategies.