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

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  • Gollier, Christian

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

Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 250.

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Date of creation: 2003
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Publication status: Published in Contributions to Theoretical Economics, vol.�4, n°1, 2004.
Handle: RePEc:ide:wpaper:608

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  1. John Y. Campbell & Luis M. Viceira, 2000. "Who Should Buy Long-Term Bonds?," Harvard Institute of Economic Research Working Papers 1895, Harvard - Institute of Economic Research.
  2. 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.
  3. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, 02.
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  7. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  8. Christian Gollier & Richard J. Zeckhauser, 1997. "Horizon Length and Portfolio Risk," NBER Technical Working Papers 0216, National Bureau of Economic Research, Inc.
  9. Brennan, Michael J. & Schwartz, Eduardo S. & Lagnado, Ronald, 1997. "Strategic asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1377-1403, June.
  10. Treich, Nicolas, 1997. "Risk tolerance and value of information in the standard portfolio model," Economics Letters, Elsevier, vol. 55(3), pages 361-363, September.
  11. Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2000. "A Monte-Carlo Method for Optimal Portfolios," CIRANO Working Papers 2000s-05, CIRANO.
  12. Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, December.
  13. Miles S. Kimball, 1989. "Precautionary Saving in the Small and in the Large," NBER Working Papers 2848, National Bureau of Economic Research, Inc.
  14. Campbell, John, 1996. "Understanding Risk and Return," Scholarly Articles 3153293, Harvard University Department of Economics.
  15. Gennotte, Gerard, 1986. " Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-46, July.
  16. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
  17. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-61.
  18. Gollier, C., 1997. "Wealth Inequality and Asset Pricing," Papers 97.486, Toulouse - GREMAQ.
  19. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
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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. "Understanding Saving and Portfolio Choices with Predictable Changes in Assets Returns," IDEI Working Papers 430, Institut d'Économie Industrielle (IDEI), Toulouse.
  3. Christian Gollier, 2003. "Collective Risk-Taking Decisions with Heterogeneous Beliefs," CESifo Working Paper Series 909, CESifo Group Munich.
  4. Gollier, Christian, 2005. "Optimal Portfolio Management for Individual Pension Plans," IDEI Working Papers 298, Institut d'Économie Industrielle (IDEI), Toulouse.
  5. Gollier, Christian, 2002. "Optimal Prevention of Unknown Risks: A Dynamic Approach with Learning," IDEI Working Papers 139, Institut d'Économie Industrielle (IDEI), Toulouse.
  6. Gollier, Christian, 2003. "Who Should we Believe? Collective Risk-Taking Decisions with Heterogeneous Beliefs," IDEI Working Papers 201, Institut d'Économie Industrielle (IDEI), Toulouse.
  7. 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.

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