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Value at risk and efficiency under dependence and heavy-tailedness: models with common shocks

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Abstract

This paper presents an analysis of diversification and portfolio value at risk for heavy-tailed dependent risks in models with multiple common shocks. We show that, in the framework of value at risk comparisons, diversification is optimal for moderately heavy-tailed dependent risks with common shocks and finite first moments, provided that the model is balanced, i.e., that all the risks are available for portfolio formation. However, diversification is inferior in balanced extremely heavy-tailed risk models with common factors. Finally, in several unbalanced dependent models, diversification is optimal, even though there is extreme heavy-tailedness in common shocks or in idiosyncratic parts of the risks. Analogues of the obtained results further hold for efficiency comparisons of linear estimators in random effects models with dependent and heavy-tailed observations.

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Authors and Affiliations

  1. Department of Economics, Harvard University, Littauer Center, 1805 Cambridge St., Cambridge, MA, 02138, USA

    Rustam Ibragimov

  2. Haas School of Business, University of California at Berkeley, 545 Student Services Building, #1900, Berkeley, CA, 94720-1900, USA

    Johan Walden

Authors
  1. Rustam Ibragimov
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  2. Johan Walden
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Correspondence to Rustam Ibragimov.

Additional information

We thank the NUS Risk Management Institute for support, and Daniel Ahn, Shashibhushan Borade, John Campbell and Tian Tian Qiu for valuable discussions. Ibragimov gratefully acknowledges research support provided by the National Science Foundation grant SES-0820124. We also thank an anonymous referee for many helpful comments and suggestions.

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Ibragimov, R., Walden, J. Value at risk and efficiency under dependence and heavy-tailedness: models with common shocks. Ann Finance 7, 285–318 (2011). https://doi.org/10.1007/s10436-010-0166-2

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