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The Stochastic Discount Factor: Extending the Volatility Bound and a New Approach to Portfolio Selection with Higher-Order Moments

Author

Listed:
  • Fousseni Chabi-Yo
  • René Garcia
  • Eric Renault

Abstract

The authors extend the well-known Hansen and Jagannathan (HJ) volatility bound. HJ characterize the lower bound on the volatility of any admissible stochastic discount factor (SDF) that prices correctly a set of primitive asset returns. The authors characterize this lower bound for any admissible SDF that prices correctly both primitive asset returns and quadratic payoffs of the same primitive assets. In particular, they aim at pricing derivatives whose payoffs are defined as non-linear functions of the underlying asset payoffs. The authors construct a new volatility surface frontier in a three-dimensional space by considering not only the expected asset payoffs and variances, but also asset skewness. The intuition behind the authors' portfolio selection is motivated by the duality between the HJ mean-variance frontier and the Markowitz mean-variance portfolio frontier. The authors' approach consists of minimizing the portfolio risk subject not only to portfolio cost and expected return, as usual, but also subject to an additional constraint that depends on the portfolio skewness. In this sense, the authors shed light on portfolio selection when asset returns exhibit skewness.

Suggested Citation

  • Fousseni Chabi-Yo & René Garcia & Eric Renault, 2005. "The Stochastic Discount Factor: Extending the Volatility Bound and a New Approach to Portfolio Selection with Higher-Order Moments," Staff Working Papers 05-2, Bank of Canada.
  • Handle: RePEc:bca:bocawp:05-2
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    References listed on IDEAS

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    1. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
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    3. Raymond Kan & Guofu Zhou, 2006. "A New Variance Bound on the Stochastic Discount Factor," The Journal of Business, University of Chicago Press, vol. 79(2), pages 941-962, March.
    4. Peñaranda, Francisco & Sentana, Enrique, 2012. "Spanning tests in return and stochastic discount factor mean–variance frontiers: A unifying approach," Journal of Econometrics, Elsevier, vol. 170(2), pages 303-324.
    5. Pascal St-Amour & Stephen Gordon, 2000. "A Preference Regime Model of Bull and Bear Markets," American Economic Review, American Economic Association, vol. 90(4), pages 1019-1033, September.
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    7. Nijman, T.E. & de Roon, F.A., 2001. "Testing for mean-variance spanning : A survey," Other publications TiSEM 0159f80a-c61b-4519-b004-a, Tilburg University, School of Economics and Management.
    8. Andrea Gamba & Francesco Rossi, 1998. "A three-moment based portfolio selection model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 21(1), pages 25-48, June.
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    12. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, February.
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    More about this item

    Keywords

    Financial markets; Market structure and pricing;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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