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A collective investment problem in a stochastic volatility environment: The impact of sharing rules

Author

Listed:
  • An Chen

    (Institute of Insurance Science, Ulm University)

  • Thai Nguyen

    (École d’Actuariat, Université Laval)

  • Manuel Rach

    (Institute of Insurance Science, Ulm University)

Abstract

It is typical in collectively administered pension funds that employees delegate fund managers to invest their contributions. In addition, many pension funds still need to sustain guarantees (prescribed by law) in spite of the current low interest environment. In this paper, we consider an optimal collective investment problem for a pool of investors who (implicitly) demand minimum guarantees by deriving utility from the wealth exceeding their guarantees in two financial market settings, one with a stochastic and one with a constant volatility. We find that individual investors’ well-being will not be worsened through the collective investment in both financial markets, as individual optimal solutions are attainable if a financially fair state-dependent sharing rule is applied. When more prevailing sharing rules like linear rules are applied, this holds no longer. Furthermore, the degree of sub-optimality imposed by linear sharing rules is more pronounced in the stochastic volatility market than in the constant volatility market.

Suggested Citation

  • An Chen & Thai Nguyen & Manuel Rach, 2021. "A collective investment problem in a stochastic volatility environment: The impact of sharing rules," Annals of Operations Research, Springer, vol. 302(1), pages 85-109, July.
    • Handle: RePEc:spr:annopr:v:302:y:2021:i:1:d:10.1007_s10479-021-03983-8
    DOI: 10.1007/s10479-021-03983-8
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    as
    1. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    2. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    3. Chen, An & Nguyen, Thai & Rach, Manuel, 2021. "Optimal collective investment: The impact of sharing rules, management fees and guarantees," Journal of Banking & Finance, Elsevier, vol. 123(C).
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Bjarne Astrup Jensen & Carsten Sørensen, 2001. "Paying for Minimum Interest Rate Guarantees: Who Should Compensate Who?," European Financial Management, European Financial Management Association, vol. 7(2), pages 183-211, June.
    6. Sven Balder & Antje Mahayni, 2010. "How Good Are Portfolio Insurance Strategies?," World Scientific Book Chapters, in: Rüdiger Kiesel & Matthias Scherer & Rudi Zagst (ed.), Alternative Investments And Strategies, chapter 10, pages 227-257, World Scientific Publishing Co. Pte. Ltd..
    7. Schumacher, Johannes M., 2018. "Linear Versus Nonlinear Allocation Rules In Risk Sharing Under Financial Fairness," ASTIN Bulletin, Cambridge University Press, vol. 48(3), pages 995-1024, September.
    8. Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," The Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
    9. Huang, Chi-fu & Litzenberger, Robert, 1985. "On the Necessary Condition for Linear Sharing and Separation: A Note," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(3), pages 381-384, September.
    10. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    11. Branger, Nicole & Muck, Matthias & Seifried, Frank Thomas & Weisheit, Stefan, 2017. "Optimal portfolios when variances and covariances can jump," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 59-89.
    12. Pazdera, Jaroslav & Schumacher, Johannes M. & Werker, Bas J.M., 2016. "Cooperative investment in incomplete markets under financial fairness," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 394-406.
    13. Bühlmann, Hans & Jewell, William S., 1979. "Optimal Risk Exchanges," ASTIN Bulletin, Cambridge University Press, vol. 10(3), pages 243-262, December.
    14. Ioannis Karatzas & John P. Lehoczky & Steven E. Shreve, 1990. "Existence and Uniqueness of Multi-Agent Equilibrium in a Stochastic, Dynamic Consumption/Investment Model," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 80-128, February.
    15. Holger Kraft, 2005. "Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 303-313.
    16. Dumas, Bernard, 1989. "Two-Person Dynamic Equilibrium in the Capital Market," The Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 157-188.
    17. Zieling, Daniel & Mahayni, Antje & Balder, Sven, 2014. "Performance evaluation of optimized portfolio insurance strategies," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 212-225.
    18. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous‐Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    19. Jianming Xia, 2004. "Multi-agent investment in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 241-259, May.
    20. Kim, Hugh Hoikwang & Maurer, Raimond & Mitchell, Olivia S., 2016. "Time is money: Rational life cycle inertia and the delegation of investment management," Journal of Financial Economics, Elsevier, vol. 121(2), pages 427-447.
    21. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    22. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    23. Torben G. Andersen & Luca Benzoni, 2009. "Stochastic volatility," Working Paper Series WP-09-04, Federal Reserve Bank of Chicago.
    24. Bjarne Astrup Jensen & Jørgen Aase Nielsen, 2016. "How suboptimal are linear sharing rules?," Annals of Finance, Springer, vol. 12(2), pages 221-243, May.
    25. Hambardzumyan, Hayk & Korn, Ralf, 2019. "Dynamic hybrid products with guarantees—An optimal portfolio framework," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 54-66.
    26. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    27. Chen, An & Nguyen, Thai & Stadje, Mitja, 2018. "Optimal investment under VaR-Regulation and Minimum Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 194-209.
    28. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    29. Branger, Nicole & Schlag, Christian & Schneider, Eva, 2008. "Optimal portfolios when volatility can jump," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 1087-1097, June.
    30. Escobar, Marcos & Ferrando, Sebastian & Rubtsov, Alexey, 2018. "Dynamic derivative strategies with stochastic interest rates and model uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 86(C), pages 49-71.
    31. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    32. Basak, Suleyman, 2002. "A comparative study of portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1217-1241, July.
    33. Busra Zeynep Temocin & Ralf Korn & A. Sevtap Selcuk-Kestel, 2018. "Constant proportion portfolio insurance in defined contribution pension plan management under discrete-time trading," Annals of Operations Research, Springer, vol. 260(1), pages 515-544, January.
    34. Black, Fischer & Perold, AndreF., 1992. "Theory of constant proportion portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 403-426.
    35. Weinbaum, David, 2009. "Investor heterogeneity, asset pricing and volatility dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 33(7), pages 1379-1397, July.
    36. Busra Zeynep Temocin & Ralf Korn & A. Sevtap Selcuk-Kestel, 2018. "Constant proportion portfolio insurance in defined contribution pension plan management," Annals of Operations Research, Springer, vol. 266(1), pages 329-348, July.
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    2. M. Escobar-Anel & M. Kschonnek & R. Zagst, 2023. "Mind the cap!—constrained portfolio optimisation in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 23(12), pages 1793-1813, November.
    3. Nicole Branger & An Chen & Antje Mahayni & Thai Nguyen, 2023. "Optimal collective investment: an analysis of individual welfare," Mathematics and Financial Economics, Springer, volume 17, number 5, February.

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    More about this item

    Keywords

    Collective investment problems; Stochastic volatility; portfolio insurance; Sharing rules;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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