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Backtesting Value-at-Risk Models: A Multivariate Approach

Center for Applied Economics & Policy Research Working Paper No. 004-2010

44 Pages Posted: 16 Apr 2010  

Cristina Danciulescu

Tulane University - Finance & Economics

Date Written: April 3, 2010


The purpose of this paper is to develop a new and simple backtesting procedure that extends the previous work into the multivariate framework. We propose to use the multivariate Portmanteau statistic of Ljung-Box type to jointly test for the absence of autocorrelations and cross-correlations in the vector of hits sequences for di fferent positions, business lines or financial institutions. Simulation exercises illustrate that this shift to a multivariate hits dimension delivers a test that increases significantly the power of the traditional backtesting methods in capturing systemic risk: the building up of positive and significant hits cross-correlations which translates into simultaneous realization of large losses at several business lines or banks. Our multivariate procedure is addressing also an operational risk issue. The proposed technique provides a simple solution to the Value-at-Risk(VaR) estimates aggregation problem: the institution's global VaR measure being either smaller or larger than the sum of individual trading lines' VaRs leading to the institution either under- or over- risk exposure by maintaining excessively high or low capital levels. An application using Pro t and Loss and VaR data collected from two international major banks illustrates how our proposed testing approach performs in a realistic environment. Results from experiments we conducted using banks' data suggest that the proposed multivariate testing procedure is a more powerful tool in detecting systemic risk if it is combined with multivariate risk modeling i.e. if covariances are modeled in the VaR forecasts.

Keywords: Risk Management, Value-at-Risk, Backtesting, Multivariate Testing, Systemic Risk, Operational Risk

JEL Classification: C12, C32, C52, G28, G32

Suggested Citation

Danciulescu, Cristina, Backtesting Value-at-Risk Models: A Multivariate Approach (April 3, 2010). Center for Applied Economics & Policy Research Working Paper No. 004-2010. Available at SSRN: or

Cristina Danciulescu (Contact Author)

Tulane University - Finance & Economics ( email )

A.B. Freeman School of Business
7 McAlister Drive
New Orleans, LA 70118
United States

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