Diversification and Value-at-Risk
HEC Paris - Finance Department
Daniel R. Smith
Queensland University of Technology - School of Economics and Finance; Simon Fraser University; Financial Research Network (FIRN)
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.
Number of Pages in PDF File: 29
Keywords: Value-at-Risk, Diversification, Correlation, Sources of Risk
JEL Classification: G21, G28, G32working papers series
Date posted: September 20, 2007 ; Last revised: March 14, 2013
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