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The hidden dangers of historical simulation

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  • Matthew Pritsker

Abstract

Many large financial institutions compute the Value-at-Risk (VaR) of their trading portfolios using historical simulation based methods, but the methods' properties are not well understood. This paper theoretically and empirically examines the historical simulation method, a variant of historical simulation introduced by Boudoukh, Richardson and Whitelaw (1998) (BRW), and the Filtered Historical Simulation method (FHS) of Barone-Adesi, Giannopoulos, and Vosper (1999). The Historical Simulation and BRW methods are both under-responsive to changes in conditional risk; and respond to changes in risk in an asymmetric fashion: measured risk increases when the portfolio experiences large losses, but not when it earns large gains. The FHS method appears promising, but requires additional refinement to account for time-varying correlations; and to choose the appropriate length of historical sample period. Preliminary analysis suggests that 2 years of daily data may not contain enough extreme outliers to accurately compute 1% VaR at a 10-day horizon using the FHS method.

Suggested Citation

  • Matthew Pritsker, 2001. "The hidden dangers of historical simulation," Finance and Economics Discussion Series 2001-27, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:2001-27
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    References listed on IDEAS

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    Cited by:

    1. Scheicher, Martin & Raunig, Burkhard, 2008. "A value at risk analysis of credit default swaps," Discussion Paper Series 2: Banking and Financial Studies 2008,12, Deutsche Bundesbank.
    2. Michael S. Gibson, 2001. "Incorporating event risk into value-at-risk," Finance and Economics Discussion Series 2001-17, Board of Governors of the Federal Reserve System (U.S.).
    3. Kubitza, Christian & Gründl, Helmut, 2016. "Systemic risk: Time-lags and persistence," ICIR Working Paper Series 20/16, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    4. Pritsker, Matthew, 2006. "The hidden dangers of historical simulation," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 561-582, February.
    5. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters,in: The Risks of Financial Institutions, pages 513-548 National Bureau of Economic Research, Inc.
    6. Rossignolo, Adrián F. & Fethi, Meryem Duygun & Shaban, Mohamed, 2013. "Market crises and Basel capital requirements: Could Basel III have been different? Evidence from Portugal, Ireland, Greece and Spain (PIGS)," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1323-1339.
    7. Zhou, Jian, 2014. "Modeling conditional covariance for mixed-asset portfolios," Economic Modelling, Elsevier, vol. 40(C), pages 242-249.
    8. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 84-108.
    9. Wagner Piazza Gaglianone & Luiz Renato Lima & Oliver Linton & Daniel R. Smith, 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 150-160, January.
    10. Scheicher, Martin & Raunig, Burkhard, 2008. "A value at risk analysis of cedit default swaps," Working Paper Series 968, European Central Bank.
    11. Audrino, Francesco & Barone-Adesi, Giovanni, 2005. "Functional gradient descent for financial time series with an application to the measurement of market risk," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 959-977, April.
    12. Rossignolo, Adrian F. & Fethi, Meryem Duygun & Shaban, Mohamed, 2012. "Value-at-Risk models and Basel capital charges," Journal of Financial Stability, Elsevier, vol. 8(4), pages 303-319.
    13. Ryohei Kawata & Masaaki Kijima, 2007. "Value-at-risk in a market subject to regime switching," Quantitative Finance, Taylor & Francis Journals, vol. 7(6), pages 609-619.
    14. Christophe Hurlin & Sessi Tokpavi, 2007. "Une Evaluation des Procédures de Backtesting," Working Papers halshs-00159846, HAL.
    15. Sean D. Campbell, 2005. "A review of backtesting and backtesting procedures," Finance and Economics Discussion Series 2005-21, Board of Governors of the Federal Reserve System (U.S.).
    16. Zikovic, Sasa & Aktan, Bora, 2011. "Decay factor optimisation in time weighted simulation -- Evaluating VaR performance," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1147-1159, October.
    17. Quaranta, Anna Grazia & Zaffaroni, Alberto, 2008. "Robust optimization of conditional value at risk and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2046-2056, October.
    18. Dionne, Georges & Duchesne, Pierre & Pacurar, Maria, 2009. "Intraday Value at Risk (IVaR) using tick-by-tick data with application to the Toronto Stock Exchange," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 777-792, December.
    19. Jian Zhou, 2012. "Extreme risk measures for REITs: a comparison among alternative methods," Applied Financial Economics, Taylor & Francis Journals, vol. 22(2), pages 113-126, January.
    20. Peter Christoffersen & Sílvia Gonçalves, 2004. "Estimation Risk in Financial Risk Management," CIRANO Working Papers 2004s-15, CIRANO.

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    Risk ; Econometric models;

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