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

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  • Gollier Christian

    ()
    (U of Toulouse)

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.

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Bibliographic Info

Article provided by De Gruyter in its journal The B.E. Journal of Theoretical Economics.

Volume (Year): 4 (2004)
Issue (Month): 1 (September)
Pages: 1-35

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Handle: RePEc:bpj:bejtec:v:contributions.4:y:2004:i:1:n:4

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  7. Gollier, Christian, 2001. "Wealth Inequality and Asset Pricing," Review of Economic Studies, Wiley Blackwell, vol. 68(1), pages 181-203, January.
  8. Xia, Yihong, 2000. "Learning About Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation," University of California at Los Angeles, Anderson Graduate School of Management qt3167f8mz, Anderson Graduate School of Management, UCLA.
  9. Treich, Nicolas, 1997. "Risk tolerance and value of information in the standard portfolio model," Economics Letters, Elsevier, vol. 55(3), pages 361-363, September.
  10. Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, December.
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  17. Gollier, Christian & Zeckhauser, Richard J, 2002. " Horizon Length and Portfolio Risk," Journal of Risk and Uncertainty, Springer, vol. 24(3), pages 195-212, May.
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Cited by:
  1. Hui Chen & Nengjiu Ju & Jianjun Miao, 2008. "Dynamic Asset Allocation with Ambiguous Return Predictability," Boston University - Department of Economics - The Institute for Economic Development Working Papers Series dp-179, Boston University - Department of Economics, revised Feb 2009.
  2. Gollier, Christian, 2007. "Assets Relative Risk for Long-term Investors," IDEI Working Papers 466, Institut d'Économie Industrielle (IDEI), Toulouse.
  3. Gollier, Christian, 2007. "Understanding Saving and Portfolio Choices with Predictable Changes in Assets Returns," IDEI Working Papers 430, Institut d'Économie Industrielle (IDEI), Toulouse.
  4. Christian Gollier, 2005. "Optimal Portfolio Management for Individual Pension Plans," CESifo Working Paper Series 1394, CESifo Group Munich.
  5. Christian Gollier, 2003. "Collective Risk-Taking Decisions with Heterogeneous Beliefs," CESifo Working Paper Series 909, CESifo Group Munich.
  6. 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.
  7. Gollier, Christian, 2002. "Optimal Prevention of Unknown Risks: A Dynamic Approach with Learning," IDEI Working Papers 139, Institut d'Économie Industrielle (IDEI), Toulouse.
  8. Gollier, Christian, 2003. "Who Should we Believe? Collective Risk-Taking Decisions with Heterogeneous Beliefs," IDEI Working Papers 201, Institut d'Économie Industrielle (IDEI), Toulouse.

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