Spectral risk measure of holding stocks in the long run

Zsolt Bihary (), Péter Csóka and Dávid Szabó ()
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Zsolt Bihary: Corvinus University of Budapest

Annals of Operations Research, 2020, vol. 295, issue 1, No 4, 75-89

Abstract: 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 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.

Keywords: Coherent risk measures; Downside risk; Lévy processes; Finite moment log stable model; Time diversification (search for similar items in EconPapers)
JEL-codes: G11 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Working Paper: Spectral risk measure of holding stocks in the long run (2018)
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DOI: 10.1007/s10479-020-03678-6

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