Do Banks Overstate their Value-at-Risk?

The answer seems to be yes, at least when we are talking about Canadian Banks according to this manuscript. And the reason that the researchers give is that the banks are extra cautious in reporting their VaR's. That is totally understandable as nobody wants to play around with extreme events.

But more importantly, what they are reporting is that the banks are not fully measuring their diversification benefits from various products, regions, functions and risk categories. This is not surprising. Aggregating and collecting data across large banks is a gigantic task and for this to happen on a daily basis is incredibly difficult if not time consuming.

Despite increases in IT technology, hard disk and performance, grid computing, usage of bootstrapping, time series and other statistical techniques, we are still not at the age that every transaction can be captured, matrixed (algebra that is), correlations determined, risk factors updated and then overall VaR calculated is way away still. This is why the authors might have gotten better results if they had measured the monthly var rather than a daily var, but there you go!

Christophe Perignon, Zi Yin Deng and Zhi Jun Wang,
Do Banks Overstate their Value-at-Risk?,
Journal of Banking & Finance,
In Press, Accepted Manuscript, Available online 4 September 2007
Abstract:
This paper is the first empirical study of banks’ risk management systems based on nonanonymous daily
Value-at-Risk (VaR) and profit-and-loss data. Using actual data from the six largest Canadian commercial
banks, we uncover evidence that banks exhibit a systematic excess of conservatism in their VaR estimates.
The data used in this paper have been extracted from the banks’ annual reports using an innovative
Matlab-based data extraction method. Out of the 7,354 trading days analyzed in this study, there are only
two exceptions, i.e., days when the actual loss exceeds the disclosed VaR, whereas the expected number
of exceptions with a 99% VaR is 74. For each sample bank, we extract from historical VaRs a risk-overstatement
coefficient, ranging between 19% and 79%. We attribute VaR overstatement to several factors, including extreme
 cautiousness and underestimation of diversification effects when aggregating VaRs across business lines
and/or risk categories. We also discuss the economic and social cost of reporting inflated VaRs.

All this to be taken with a grain of piquant salt!!!