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Does value-at-risk encourage diversification when losses follow tempered stable or more general Lévy processes?

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  • Michael Grabchak

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Abstract

In this paper, we address the question of when portfolio selection based on Value-at-risk encourages diversification [in the sense of Ibragimov (Quant Financ 9(5):565–580, 2009 )]. Specifically, we give sufficient conditions for the case when losses follow a Lévy process. When the process has finite variation, these conditions are also necessary. We then specialize our results to the case when losses have tempered stable distributions. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Michael Grabchak, 2014. "Does value-at-risk encourage diversification when losses follow tempered stable or more general Lévy processes?," Annals of Finance, Springer, vol. 10(4), pages 553-568, November.
  • Handle: RePEc:kap:annfin:v:10:y:2014:i:4:p:553-568
    DOI: 10.1007/s10436-014-0249-6
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    References listed on IDEAS

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    1. Rustam Ibragimov & Johan Walden, 2011. "Value at risk and efficiency under dependence and heavy-tailedness: models with common shocks," Annals of Finance, Springer, vol. 7(3), pages 285-318, August.
    2. Rustam Ibragimov, 2009. "Portfolio diversification and value at risk under thick-tailedness," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 565-580.
    3. Daníelsson, Jón & Jorgensen, Bjørn N. & Samorodnitsky, Gennady & Sarma, Mandira & de Vries, Casper G., 2013. "Fat tails, VaR and subadditivity," Journal of Econometrics, Elsevier, vol. 172(2), pages 283-291.
    4. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    5. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    6. Ibragimov, Rustam & Walden, Johan, 2008. "Portfolio diversification under local and moderate deviations from power laws," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 594-599, April.
    7. René Garcia & Éric Renault & Georges Tsafack, 2007. "Proper Conditioning for Coherent VaR in Portfolio Management," Management Science, INFORMS, vol. 53(3), pages 483-494, March.
    8. Michael Grabchak & Gennady Samorodnitsky, 2010. "Do financial returns have finite or infinite variance? A paradox and an explanation," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 883-893.
    9. Rustam Ibragimov & Johan Walden, 2010. "Optimal Bundling Strategies Under Heavy-Tailed Valuations," Management Science, INFORMS, vol. 56(11), pages 1963-1976, November.
    10. Walden, Johan & Ibragimov, Rustam, 2008. "Portfolio Diversification under Local and Moderate Deviations from Power Laws," Scholarly Articles 2640586, Harvard University Department of Economics.
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    Cited by:

    1. Michael Grabchak, 2016. "On the consistency of the MLE for Ornstein–Uhlenbeck and other selfdecomposable processes," Statistical Inference for Stochastic Processes, Springer, vol. 19(1), pages 29-50, April.

    More about this item

    Keywords

    Value-at-risk; Diversification; Lévy processes; Tempered stable distributions; Heavy tails; C16; G11; G18;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation

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