The Level and Quality of Value-at-Risk Disclosure by Commercial Banks

1. The Level and Quality of Value-at-Risk Disclosure by Commercial Banks Christophe Pérignon, HEC Paris Daniel R. Smith, Simon Fraser University Risk Management in Financial Institutions 23-25 April 2009

2. Introduction “Disclosure of quantitative measures of market risk, such as value-at-risk is enlightening only when accompanied by a thorough discussion of how the risk measures were calculated and how they related to actual performance” Alan Greenspan

3. 1% 0 VaR is a quantile of the trading revenue (P&L) distribution e.g. Bank of America VaR(99%, 1 day) on December 31, 2008 was $140 mio 1-day ahead P/L distribution Losses Gains VaR(99%, 1 day)

4. 0 VaR is a quantile of the trading revenue (P&L) distribution Increase in Volatility Losses Gains VaR VaR

5. Our Objective • Joint Assessment of: LevelQuality of VaR disclosure by commercial banks • When quantity and quality are both at acceptable levels  Reduction in information asymmetry

6. Our Contributions • Survey of actual VaR disclosures in the world • Formal test of whether daily VaRs are • Accurate: Lead to the correct number of exceptions • Informative: Forecast next-day volatility of trading revenues

7. Part 1: Level of VaR Disclosure • VaR Disclosure Index (VaRDI) • Sample: 10 largest US commercial banks, 6 largest Canadian commercial banks, and top-50 international commercial banks • Sample Period: Entire post-1996 Market Risk Amendment period for US and Canadian banks, and year 2005 for top-50 international banks • Data Source: Annual reports

8. VaR Disclosure Index (VaRDI) 1. VaR Characteristics a. Score of 1 if Holding Period (e.g. 1 day, 1 month) b. Score of 1 if Confidence Level (e.g. 99%, 95%) 2. Summary VaR Statistics a. Score of 1 if High, Low, or Average VaR b. Score of 1 if Year-End VaR c. Score of 1 if VaR by Risk Category (e.g. Currency, Fixed Income, Equity) d. Score of 1 if Diversification Effect is accounted for 3. Intertemporal Comparison a. Score of 1 if Summary Information about the Previous Year VaR 4. Daily VaR Figures a. Score of 1 if Histogram of Daily VaRs, or score of 2 if Plot of Daily VaRs 5. Trading Revenues a. Score of 1 if Hypothetical Revenues b. Score of 1 if Revenues without Trading Fees c. Score of 1 if Histogram of Daily Revenues, or score of 2 if Plot of Daily Revenues 6. Backtesting a. Score of 1 if Number of Exceptions, or score of 2 if Zero Exceptions b. Score of 1 if Explanation of Exceptions

9. VaRDI for 10 Largest US Banks (1/2)

10. VaRDI for 10 Largest US Banks (2/2)

11. VaRDI in the U.S. and in Canada (1996-2005)

12. VaRDI in the World (2005)

13. VaRDI by Country (2005)

14. VaR Methods Currently Used by Banks (2005)

15. Historical Simulation (HS) • HS method based on the one-year unconditional distribution of the risk factors • HS-based VaRs are under-responsive to changes in conditional risk • Mechanical disconnection between 1-day VaR and actual volatility on the next day • True in practice?

16. Part 2: Quality of VaR Disclosure • Backtesting • Forecast Trading Revenue Volatility

17. Part 2a: Backtesting

18. Part 2b: Forecasting Trading Revenue Volatility • For each country included in our survey, we look for a bank disclosing a graph of daily VaR and trading revenues over a long enough sample period • Bank of America (US) • Credit Suisse First Boston (Switzerland) • Deutsche Bank (Germany) • Royal Bank of Canada (Canada) • Société Générale (France) • All banks have VaRDIs of at least 13 points • They all use Historical Simulation, except Deutsche Bank

19. Data Extraction • Actual VaRs and trading revenues are not available in a machine-readable format • We extract the data from the graphs included in annual reports using a Matlab-based technique • Convert PDF file into JPG • Import JPG file into Matlab • Add vertical lines on the image • Zoom in and click on each data point • Convert Matlab coordinates into graph coordinates • Many experiments and simulations are presented in the appendix

20. Bank of America Credit Suisse First Boston Deutsche Bank Royal Bank of Canada Societé Générale The Bank of America

21. Measuring VaR Accuracy • We look for a statistical link between VaRt+1|t and the volatility of the trading revenue Rt+1 • We use a simple GARCH model as a benchmark • “Unfair horse race”: risk manager knows the bank’s positions, unlike the econometrician

22. Methodology • In-Sample Augmented GARCH • Out-of-Sample Regression

24. Conclusion (Part I) • We use public information about VaR disclosed by banks in their annual reports • Large differences in the level of disclosure among US commercial banks • Upward trend in the amount of information disclosed to the public • US VaR disclosures are below average • Large differences in the level of disclosure across countries • Historical Simulation is the most popular VaR method

25. Conclusion (Part II) • Unlike the level of disclosure, the quality of VaR shows no sign of improvement over time • Disconnection between 1-day VaR and actual volatility on the next day • HS-based VaR helps little in forecasting the volatility of future trading revenues • Its incremental forecasting ability over a simple GARCH model is very limited • Only exception: Deutsche Bank

26. The Level and Quality of Value-at-Risk Disclosure by Commercial Banks Christophe Pérignon, HEC Paris Daniel R. Smith, Simon Fraser University Risk Management in Financial Institutions 23-25 April 2009