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Spectral risk measure of holding stocks in the long run

Bihary, Zsolt and Csóka, Péter and Szabó, Dávid Zoltán (2020) Spectral risk measure of holding stocks in the long run. Annals of Operations Research (295). pp. 75-89. DOI https://doi.org/10.1007/s10479-020-03678-6

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Official URL: https://doi.org/10.1007/s10479-020-03678-6

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Abstract

We investigate how the spectral risk measure associated with holding stocks rather than a riskfree 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 downside risk. However, using realistic models, we find numerically that spectral risk initially increases for a significant amount of time and reaches zero level only after several decades. Therefore, we conclude that holding stocks has spectral risk for all practically relevant periods.

Item Type:Article
Uncontrolled Keywords:coherent risk measures, downside risk, Lévy processes, finite moment log stable model, time diversification
Subjects:Finance
DOI:https://doi.org/10.1007/s10479-020-03678-6
ID Code:6093
Deposited By: Veronika Vitéz
Deposited On:26 Nov 2020 13:52
Last Modified:27 Nov 2020 14:29

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