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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.

Suggested Citation

  • Memmel, Christoph & Wehn, Carsten, 2005. "The supervisor's portfolio: the market price risk of German banks from 2001 to 2003 - Analysis and models for risk aggregation," Discussion Paper Series 2: Banking and Financial Studies 2005,02, Deutsche Bundesbank.
    • Handle: RePEc:zbw:bubdp2:4257
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    References listed on IDEAS

    as
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    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    6. Kerkhof, Jeroen & Melenberg, Bertrand, 2004. "Backtesting for risk-based regulatory capital," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1845-1865, August.
    7. 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).
    8. 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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    More about this item

    Keywords

    Value at Risk; portfolio; cross-correlation; market risk regulation; risk forecast; model validation;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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