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Modelling dynamic portfolio risk using risk drivers of elliptical processes

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  • Schmidt, Rafael
  • Schmieder, Christian

Abstract

The situation of a limited availability of historical data is frequently encountered in portfolio risk estimation, especially in credit risk estimation. This makes it, for example, difficult to find temporal structures with statistical significance in the data on the single asset level. By contrast, there is often a broader availability of cross-sectional data, i.e., a large number of assets in the portfolio. This paper proposes a stochastic dynamic model which takes this situation into account. The modelling framework is based on multivariate elliptical processes which model portfolio risk via sub-portfolio specific volatility indices called portfolio risk drivers. The dynamics of the risk drivers are modelled by multiplicative error models (MEM) - as introduced by Engle (2002) - or by traditional ARMA models. The model is calibrated to Moody's KMV Credit Monitor asset returns (also known as firm-value returns) given on a monthly basis for 756 listed European companies at 115 time points from 1996 to 2005. This database is used by financial institutions to assess the credit quality of firms. The proposed risk drivers capture the volatility structure of asset returns in different industry sectors. A characteristic temporal structure of the risk drivers, cyclical as well as a seasonal, is found across all industry sectors. In addition, each risk driver exhibits idiosyncratic developments. We also identify correlations between the risk drivers and selected macroeconomic variables. These findings may improve the estimation of risk measures such as the (portfolio) Value at Risk. The proposed methods are general and can be applied to any series of multivariate asset or equity returns in finance and insurance.

Suggested Citation

  • Schmidt, Rafael & Schmieder, Christian, 2007. "Modelling dynamic portfolio risk using risk drivers of elliptical processes," Discussion Paper Series 2: Banking and Financial Studies 2007,07, Deutsche Bundesbank.
    • Handle: RePEc:zbw:bubdp2:5608
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    References listed on IDEAS

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    Cited by:

    1. Hashorva, Enkelejd, 2009. "Asymptotics for Kotz Type III elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 927-935, April.
    2. N.H. Bingham & John M. Fry & Rüdiger Kiesel, 2010. "Multivariate elliptic processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 352-366.
    3. Hashorva, Enkelejd, 2008. "Tail asymptotic results for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 158-164, August.
    4. Emiliano Valdez, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 257-262, August.

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    More about this item

    Keywords

    Portfolio risk modelling; Elliptical processes; Credit risk; multiplicative error model; volatility clustering;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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