Backtesting VaR Accuracy: A New Simple 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.Value-at-Risk; Risk Management; Model Selection

Backtesting Value-at-Risk: A GMM Duration-based Test

This paper proposes a new duration-based backtesting procedure for VaR forecasts. The GMM test framework proposed by Bontemps (2006) to test for the distributional assumption (i.e., the geometric distribution) is applied to the case of VaR forecast validity. Using simple J-statistics based on the moments defined by the orthonormal polynomials associated with the geometric distribution, this new approach tackles most of the drawbacks usually associated with duration based backtesting procedures. In particular, it is among the first to take into account problems induced by the estimation risk in duration-based backtesting tests and to other a sub-sampling approach for robust inference derived from Escanciano and Olmo (2009). An empirical application of the method to Nasdaq returns confirms that using the GMM test has major consequences for the ex-post evaluation of risk by regulation regulatory authorities.Economics ;

Backtesting Value-at-Risk: A GMM Duration-Based Test

This paper proposes a new duration-based backtesting procedure for VaR forecasts. The GMM test framework proposed by Bontemps (2006) to test for the distributional assumption (i.e. the geometric distribution) is applied to the case of the VaR forecasts validity. Using simple J-statistic based on the moments defined by the orthonormal polynomials associated with the geometric distribution, this new approach tackles most of the drawbacks usually associated to duration based backtesting procedures. First, its implementation is extremely easy. Second, it allows for a separate test for unconditional coverage, independence and conditional coverage hypothesis (Christoffersen, 1998). Third, feasibility of the tests is improved. Fourth, Monte-Carlo simulations show that for realistic sample sizes, our GMM test outperforms traditional duration based test. An empirical application for Nasdaq returns confirms that using GMM test leads to major consequences for the ex-post evaluation of the risk by regulation authorities. Without any doubt, this paper provides a strong support for the empirical application of duration-based tests for VaR forecasts.Value-at-Risk; backtesting; GMM; duration-based test

A Non-parametric Test for Granger-Causality in Distribution with Application to Financial Contagion A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion A Nonparametric Test for Granger Causality in Distributi

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

Un test de validité de la Value at Risk

This paper proposes a new simple test of market risk models validation or Value at Risk (VaR) accuracy. The test exploits the idea that the sequence of VaR violations verifies the properties of a white noise. More precisely, we use the Multivariate Portmanteau statistic of Hosking [1980] to jointly test the absence of autocorrelation in the vector of violation sequences for various coverage rates considered as relevant for the management of risks. We show that this multivariate dimension appreciably improves the power properties of the VaR validation test for reasonable sample sizes. Classification JEL : C23, C11

Stocks and Bonds: Flight-to-Safety for Ever?

This paper gives new insights about flight-to-safety from stocks to bonds, asking whether the strength of this phenomenon remains the same in the current environment of low yields. The motivations lie in the conjecture that when yields are low, the traditional motives of flight-to-safety (wealth protection, liquidity) could not be sufficient, inducing weaker flight-to-safety events. Empirical applications using data for U.S. government bonds and the S&P 500 index, show indeed that when yields are low, the strength of flight-to-safety from stocks to bonds weakens. This result holds, even when controlling for the effects of traditional flight-to-safety factors including the VIX, the TED spreads and the overall level of illiquidity in the stock market. Moreover, we develop a bivariate model of flight-to-safety transfers that measures to what extent the strength of flight-to-safety from stocks to bonds is related to the strength of flight-to-safety from stocks to other safe haven assets (gold and currencies). Results show that when the strength of flight-to-safety from stocks to bonds decreases the strength of flight-to-safety from stocks to these safe haven assets increases. This result holds only in the low-yield environment, suggesting a kind of substitution effect of save haven assets, similar to the reaching for yield behavior

Stocks and Bonds: Flight-to-Safety for Ever?

This paper gives new insights about flight-to-safety from stocks to bonds, asking whether the strength of this phenomenon remains the same in the current environment of low yields. The motivations lie in the conjecture that when yields are low, the traditional motives of flight-to-safety (wealth protection, liquidity) could not be sufficient, inducing weaker flight-to-safety events. Empirical applications using data for U.S. government bonds and the S&P 500 index, show indeed that when yields are low, the strength of flight-to-safety from stocks to bonds weakens. This result holds, even when controlling for the effects of traditional flight-to-safety factors including the VIX, the TED spreads and the overall level of illiquidity in the stock market. Moreover, we develop a bivariate model of flight-to-safety transfers that measures to what extent the strength of flight-to-safety from stocks to bonds is related to the strength of flight-to-safety from stocks to other safe haven assets (gold and currencies). Results show that when the strength of flight-to-safety from stocks to bonds decreases the strength of flight-to-safety from stocks to these safe haven assets increases. This result holds only in the low-yield environment, suggesting a kind of substitution effect of save haven assets, similar to the reaching for yield behavior

Backtesting Value at Risk Accuracy : A New Simple Test

Université Paris

Comovement and Contagion in Financial Markets

Forthcomin