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Optimal Portfolio Allocation under a Probabilistic Risk Constraint and the Incentives for Financial Innovation

Author

Listed:
  • Jón Daníelsson

    (London School of Economics)

  • Bjørn N. Jorgensen

    (Harvard Business School)

  • Casper G. de Vries

    (Erasmus University Rotterdam)

  • Xiaogang Yang

    (Chinese Academy of Sciences)

Abstract

We characterize the investor’s optimal portfolio allocation subject to a budget constraint and a probabilistic VaR constraint in complete markets environments with a finite number of states. The set of feasible portfolios might no longer be connected or convex, while the number of local optima increases exponentially with the number of states, implying computational complexity. The optimal constrained portfolio allocation may therefore not be monotonic in the state–price density. We propose a type of financial innovation, which splits states of nature, that is shown to weakly enhance welfare, restore monotonicity of the optimal portfolio allocation in the state-price density, and reduce computational complexity. This discussion paper resulted in a publication in Annals of Finance , 2008, 4(3), 345-67.

Suggested Citation

  • Jón Daníelsson & Bjørn N. Jorgensen & Casper G. de Vries & Xiaogang Yang, 2001. "Optimal Portfolio Allocation under a Probabilistic Risk Constraint and the Incentives for Financial Innovation," Tinbergen Institute Discussion Papers 01-069/2, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20010069
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    References listed on IDEAS

    as
    1. Franklin Allen, Douglas Gale, 1988. "Optimal Security Design," The Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 229-263.
    2. Miller, Merton H., 1986. "Financial Innovation: The Last Twenty Years and the Next," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(4), pages 459-471, December.
    3. Mark Grinblatt & Francis A. Longstaff, 2000. "Financial Innovation and the Role of Derivative Securities: An Empirical Analysis of the Treasury STRIPS Program," Journal of Finance, American Finance Association, vol. 55(3), pages 1415-1436, June.
    4. Grossman, Sanford J & Vila, Jean-Luc, 1989. "Portfolio Insurance in Complete Markets: A Note," The Journal of Business, University of Chicago Press, vol. 62(4), pages 473-476, October.
    5. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    6. Leland, Hayne E, 1980. "Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-594, May.
    7. Arzac, Enrique R. & Bawa, Vijay S., 1977. "Portfolio choice and equilibrium in capital markets with safety-first investors," Journal of Financial Economics, Elsevier, vol. 4(3), pages 277-288, May.
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    Cited by:

    1. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    2. Daníelsson, Jón & Jorgensen, Bjørn N. & Samorodnitsky, Gennady & Sarma, Mandira & de Vries, Casper G., 2013. "Fat tails, VaR and subadditivity," Journal of Econometrics, Elsevier, vol. 172(2), pages 283-291.

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    More about this item

    Keywords

    Portfolio Optimization; Value-at-Risk; NP-hard;
    All these keywords.

    JEL classification:

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

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