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The supervisor's portfolio: the market price risk of German banks from 2001 to 2003 - Analysis and models for risk aggregation

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  • Memmel, Christoph
  • Wehn, Carsten

Abstract

The Value at Risk of a portfolio differs from the sum of the Values at Risk of the portfolio's components. In this paper, we analyze the problem of how a single economic risk figure for the Value at Risk of a hypothetical portfolio composed of different commercial banks might be obtained for a supervisor. Using the daily profits and losses and the daily Value at Risk figures of twelve German banks for the period from 2001 to 2003, we estimate the Value at Risk of the entire portfolio. We assume a reduced-form model and neglect the effects of a potential bankruptcy of one of the banks. We analyze different models for the cross-correlation of the banks? profits and losses. In an empirical study, we apply backtesting methods to determine which aggregation model leads to the best out-of-sample estimates for the portfolio's economic risk figure. Our main findings can be summarized in three statements. (i) The portfolio's Value at Risk can be estimated from time series data very well. (ii) During "normal" times, the portfolio's Value at Risk is much lower than the sum of the single Values at Risk. (iii) The relative marginal risk contribution depends on the bank in question and is between 0.05 and 0.62. --

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Bibliographic Info

Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 2: Banking and Financial Studies with number 2005,02.

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Date of creation: 2005
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Handle: RePEc:zbw:bubdp2:4257

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Keywords: Value at Risk; portfolio; cross-correlation; market risk regulation; risk forecast; model validation;

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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  2. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  3. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  4. Kerkhof, F.L.J. & Melenberg, B., 2002. "Backtesting for Risk-Based Regulatory Capital," Discussion Paper 2002-110, Tilburg University, Center for Economic Research.
  5. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value-at-Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, 06.
  6. Jaschke, Stefan & Stahl, Gerhard & Stehle, Richard, 2003. "Evaluating VaR Forecasts under Stress – The German Experience," CFS Working Paper Series 2003/32, Center for Financial Studies (CFS).
  7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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Cited by:
  1. Dirk Tasche, 2005. "Measuring sectoral diversification in an asymptotic multi-factor framework," Papers physics/0505142, arXiv.org, revised Jul 2006.

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