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How Informative Are Value-at-Risk Disclosures? Authors: Philippe Jorion Source: Accounting Review Date: October 2002 |
Since 1993, Value-at-Risk (VaR) has become an easy-to-understand standard benchmark for quantifying market risk. This paper aims to investigate the relationship (both cross sectional and over time) between publicly disclosed VaR measures and the volatility of trading revenues for 8 major US commercial banks (the first to publish VaR figures, before the Basel Committee strongly recommended that banks disclose their VaR).
Jorion's main objective is to check whether VaR disclosures can be used to predict the variability of banks' trading revenues. Thus, he extends the former work done by Benkowitz and O'Brien (2001) on private disclosure of VaR to regulators. As bank trading data is proprietary it is impossible to set up a traditional backtesting approach. That's why he uses an original approach that transforms the VaR number into a measure of dispersion, which leads to more powerful tests. The author uses 6 years of quarterly and annual historical data taken from the financial reports that those 8 banks published between 1994 and 2000.
To conduct his study, Jorion needed to know the forecasted volatility of quarterly trading revenues inferred from the bank's report of its trading VaR as of the end of the quarter. This series is created by making the assumption that the distribution of trading revenues is Gaussian (his methodology remains operational for all fixed and symmetrical conditional distributions, i.e. with a skewness coefficient equal to zero). Even though this approach is less appropriate for non linear instruments with an asymmetrical profile (like short term options), he only studies an aggregate portfolio of all the products a commercial bank can trade, reducing the impact of this assumption.
He tests the predictive power of the bank's quarterly VaR disclosures by conducting several regressions. The first one deals with the relationship between the absolute value of the unexpected trading revenue (difference between the trading revenue for quarter t+1 and the moving average of the quarterly trading revenue over the previous four quarters) and the forecasted volatility of the trading revenue. This parameter is inferred from the VaR measure disclosed by the bank in its annual report. The second regression conducted involves analyzing the relationship between the same explained variables used in the previous regression to which Jorion incorporates the outstanding notional value of the bank's derivatives contracts at the end of the previous quarter. The last regression introduces scale effects by dividing the regressand and the regressors by the previous quarter's assets.
Jorion finds significant positive slope coefficients and obtains a joint test of significance which strongly rejects the null hypothesis of zero slope.
A cross-sectional analysis done with a 2-step GLS approach (i.e. to consider heteroscedasticity effects), allows him to obtain the same conclusion as the previous one. Surprisingly he finds that, by incorporating the notional value of bank's derivatives contract, the goodness-of-fit does not increase significantly, showing the important role played by the VaR in explicating trading revenue.
In each case, the VaR-based volatility remains positively associated with the variation in expected future trading revenues. Those results allow him to conclude that the VaR measures published in the bank's financial reports offer a useful predictor of the market risk of the bank's trading activities. Shareholders have to assess whether average trading revenues compensate for the risk taken by the bank.
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