Diversification and Value-at-Risk

29 Pages Posted: 20 Sep 2007 Last revised: 14 Mar 2013

See all articles by Christophe Pérignon

Christophe Pérignon

HEC Paris - Finance Department

Daniel R. Smith

Queensland University of Technology - School of Economics and Finance; Simon Fraser University; Financial Research Network (FIRN)

Date Written: September 22, 2008


A pervasive and puzzling feature of banks' Value at Risk (VaR) is its abnormally high level, which leads to excessive regulatory capital. A possible explanation for the tendency of commercial banks to overstate their VaR is that they incompletely account for the diversification effect among broad risk categories (e.g. equity, interest rate, commodity, credit spread, and foreign exchange). By underestimating the diversification effect, bank's proprietary VaR models produce overly prudent market risk assessments. In this paper, we examine empirically the validity of this hypothesis using actual VaR data from major US commercial banks. In contrast to the VaR diversification hypothesis, we find that US banks show no sign of systematic underestimation of the diversification effect. In particular, diversification effect used by banks is very close to (and quite often larger than) our empirical diversification estimates. A direct implication of this finding is that individual VaRs for each broad risk category, just like aggregate VaRs, are biased risk assessments.

Keywords: Value-at-Risk, Diversification, Correlation, Sources of Risk

JEL Classification: G21, G28, G32

Suggested Citation

Pérignon, Christophe and Smith, Daniel Robert, Diversification and Value-at-Risk (September 22, 2008). Available at SSRN: https://ssrn.com/abstract=1015590 or http://dx.doi.org/10.2139/ssrn.1015590

Christophe Pérignon

HEC Paris - Finance Department ( email )

1 rue de la Liberation
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Daniel Robert Smith (Contact Author)

Queensland University of Technology - School of Economics and Finance ( email )

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Brisbane, Queensland 4001
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+61 7 3138 2947 (Fax)

Simon Fraser University ( email )

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HOME PAGE: http://www.sfu.ca/~drsmith

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane

HOME PAGE: http://www.firn.org.au

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