Diversification and Value-at-Risk

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

See all articles by Christophe Perignon

Christophe Perignon

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

Abstract

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

Perignon, 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 Perignon

HEC Paris - Finance Department ( email )

1 rue de la Liberation
Jouy-en-Josas Cedex, 78351
France

Daniel Robert Smith (Contact Author)

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

GPO Box 2434
2 George Street
Brisbane, Queensland 4001
Australia
+61 7 3138 2947 (Phone)
+61 7 3138 2947 (Fax)

Simon Fraser University ( email )

8888 University Drive
Burnaby, British Colombia V5A 1S6
Canada
778-782-4675 (Phone)
778-782-4920 (Fax)

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

Financial Research Network (FIRN)

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

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

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