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Optimal Dynamic Portfolio Risk with First-Order and Second-Order Predictability

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  • Gollier Christian

    (U of Toulouse, gollier@cict.fr)

Abstract

We consider a two-period portfolio problem with predictable assets returns. First-order (second-order) predictability means that an increase in the first period returns yields a first-order (second-order) stochastically dominated shift in the distribution of the second period state prices. Mean reversion in stock returns, Bayesian learning, stochastic volatility and stochastic interest rates (bond portfolios) belong to one of these two types of predictability. We first show that a first-order stochastically dominated shift in the state price density reduces the marginal value of wealth if and only if relative risk aversion is uniformly larger than unity. This implies that first-order predictability generates a positive hedging demand for portfolio risk if this condition is met. A similar result is obtained with second-order predictability under the condition that absolute prudence be uniformly smaller than twice the absolute risk aversion. When relative risk aversion is constant, these two conditions are equivalent. We also examine the effect of exogenous predictability, i.e., when the information about the future opportunity set is conveyed by signals not contained in past asset prices.

Suggested Citation

  • Gollier Christian, 2004. "Optimal Dynamic Portfolio Risk with First-Order and Second-Order Predictability," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 4(1), pages 1-35, September.
    • Handle: RePEc:bpj:bejtec:v:contributions.4:y:2004:i:1:n:4
    DOI: 10.2202/1534-5971.1070
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    Cited by:

    1. Hui Chen & Nengjiu Ju & Jianjun Miao, 2014. "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 799-823, October.
    2. Blake, David & Cairns, Andrew & Dowd, Kevin, 2008. "Turning pension plans into pension planes: What investment strategy designers of defined contribution pension plans can learn from commercial aircraft designers," MPRA Paper 33749, University Library of Munich, Germany.
    3. Christian Gollier & Edward Schlee, 2011. "Information And The Equity Premium," Journal of the European Economic Association, European Economic Association, vol. 9(5), pages 871-902, October.
    4. Gollier, Christian, 2005. "Optimal Portfolio Management for Individual Pension Plans," IDEI Working Papers 298, Institut d'Économie Industrielle (IDEI), Toulouse.
    5. Gollier, Christian, 2008. "Understanding saving and portfolio choices with predictable changes in assets returns," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 445-458, April.
    6. Gollier, Christian, 2007. "Assets Relative Risk for Long-term Investors," IDEI Working Papers 466, Institut d'Économie Industrielle (IDEI), Toulouse.

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