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The riskiness of stock versus money market investment with stochastic rates

Author

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  • Dávid Zoltán Szabó

    (Corvinus University of Budapest)

  • Zsolt Bihary

    (Corvinus University of Budapest)

Abstract

To efficiently assess the performance of investing in stocks rather than in a bank account for the long run, stochastic interest rate modelling is advocated. We introduce a correlated stochastic interest rate model that addresses this problem. We derive analytic formulas for general spectral risk measures in our setting, and apply our results to Value at Risk, Expected Shortfall and GlueVaR. We characterize the short- and long-term behaviour of these risk measures. We fit our model to financial markets, perform an empirical study and evaluate risk numbers for realistic scenarios in the future. Our results reveal sizeable sensitivities on parameter estimation, but we may conclude that holding stocks for less than a few decades bears significant risk.

Suggested Citation

  • Dávid Zoltán Szabó & Zsolt Bihary, 2023. "The riskiness of stock versus money market investment with stochastic rates," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(2), pages 393-415, June.
    • Handle: RePEc:spr:cejnor:v:31:y:2023:i:2:d:10.1007_s10100-022-00814-4
    DOI: 10.1007/s10100-022-00814-4
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    1. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. repec:bla:jfinan:v:58:y:2003:i:2:p:753-778 is not listed on IDEAS
    4. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    5. Hung Nguyen & Uyen Pham & Hien Tran, 2012. "On some claims related to Choquet integral risk measures," Annals of Operations Research, Springer, vol. 195(1), pages 5-31, May.
    6. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    7. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    8. Labreuche, Christophe & Grabisch, Michel, 2018. "Using multiple reference levels in Multi-Criteria Decision aid: The Generalized-Additive Independence model and the Choquet integral approaches," European Journal of Operational Research, Elsevier, vol. 267(2), pages 598-611.
    9. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    10. Ľuboš Pástor & Robert F. Stambaugh, 2012. "Are Stocks Really Less Volatile in the Long Run?," Journal of Finance, American Finance Association, vol. 67(2), pages 431-478, April.
    11. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    12. Robert Elliott & Rogemar Mamon, 2002. "An interest rate model with a Markovian mean reverting level," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 454-458.
    13. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    14. Jan Willem van den End, 2011. "Statistical evidence on the mean reversion of interest rates," DNB Working Papers 284, Netherlands Central Bank, Research Department.
    15. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    16. Saralees Nadarajah & Bo Zhang & Stephen Chan, 2014. "Estimation methods for expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 271-291, February.
    17. Miloš Kopa & Vittorio Moriggia & Sebastiano Vitali, 2018. "Individual optimal pension allocation under stochastic dominance constraints," Annals of Operations Research, Springer, vol. 260(1), pages 255-291, January.
    18. Zsolt Bihary & Péter Csóka & Dávid Zoltán Szabó, 2020. "Spectral risk measure of holding stocks in the long run," Annals of Operations Research, Springer, vol. 295(1), pages 75-89, December.
    19. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, February.
    20. Brandtner, Mario, 2013. "Conditional Value-at-Risk, spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5526-5537.
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    More about this item

    Keywords

    Asset allocation; Spectral risk measures; Vasicek process; Time diversification; GlueVaR;
    All these keywords.

    JEL classification:

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

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