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

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Author Info
Christian Gollier (U of Toulouse)

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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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Publisher Info
Article provided by Berkeley Electronic Press in its journal Contributions to Theoretical Economics.

Volume (Year): 4 (2004)
Issue (Month): 1 ()
Pages: 1070-1070
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Handle: RePEc:bep:thecon:v:4:y:2004:i:1:p:1070-1070

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Related research
Keywords: portfolio choice predictability mean-reversion learning bond portfolio stochastic volatility

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Find related papers by JEL classification:
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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  17. Gollier, Christian, 2001. "Wealth Inequality and Asset Pricing," Review of Economic Studies, Blackwell Publishing, vol. 68(1), pages 181-203, January.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Christian Gollier, 2003. "Collective Risk-Taking Decisions with Heterogeneous Beliefs," CESifo Working Paper Series CESifo Working Paper No. , CESifo GmbH. [Downloadable!]
  2. GOLLIER, Christian, 2002. "Optimal Prevention of Unknown Risks: A Dynamic Approach with Learning," IDEI Working Papers 139, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
  3. GOLLIER, Christian, 2003. "Who Should we Believe? Collective Risk-Taking Decisions with Heterogeneous Beliefs," IDEI Working Papers 201, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
  4. Christian Gollier, 2005. "Optimal Portfolio Management for Individual Pension Plans," CESifo Working Paper Series CESifo Working Paper No. , CESifo GmbH. [Downloadable!]
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