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Spectral risk measure of holding stocks in the long run

Author

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  • Zsolt Bihary

    (Corvinus University of Budapest, Corvinus Business School, Department of Finance)

  • Peter Csoka

    ("Momentum" Game Theory Research Group, Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Corvinus University of Budapest, Corvinus Business School, Department of Finance)

  • David Zoltan Szabo

    (School of Mathematics, University of Manchester)

Abstract

We investigate how the spectral risk measure associated with holding stocks rather than a risk-free deposit, depends on the holding period. Previous papers have shown that within a limited class of spectral risk measures, and when the stock price follows specific processes, spectral risk becomes negative at long periods. We generalize this result for arbitrary exponential Lévy processes. We also prove the same behavior for all spectral risk measures (including the important special case of Expected Shortfall) when the stock price grows realistically fast and when it follows a Geometric Brownian Motion or a Finite Moment Log Stable process. This result would suggest that holding stocks for long periods has a vanishing risk. However, using realistic models, we find numerically that the risk increases for a few decades and reaches zero at around 100 years. Therefore, we conclude that holding stocks is risky for all practically relevant periods.

Suggested Citation

  • Zsolt Bihary & Peter Csoka & David Zoltan Szabo, 2018. "Spectral risk measure of holding stocks in the long run," CERS-IE WORKING PAPERS 1812, Institute of Economics, Centre for Economic and Regional Studies.
  • Handle: RePEc:has:discpr:1812
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    References listed on IDEAS

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    1. Csóka, Péter & Bihary, Zsolt & Kondor, Gábor, 2018. "A részvénytartás spektrális kockázata hosszú távon [On the spectral measure of risk in holding stocks in the long run]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 687-700.
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    3. Josa-Fombellida, Ricardo & López-Casado, Paula, 2023. "A defined benefit pension plan game with Brownian and Poisson jumps uncertainty," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1294-1311.

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    More about this item

    Keywords

    Coherent Risk Measures; Spectral Risk Measures; Lévy processes; Finite Moment Log Stable Model; Time Diversification;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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