IDEAS home Printed from https://ideas.repec.org/a/bpj/bejtec/vcontributions.4y2004i1n4.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

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
    as

    Download full text from publisher

    File URL: https://www.degruyter.com/view/j/bejte.2004.4.1/bejte.2004.4.1.1070/bejte.2004.4.1.1070.xml?format=INT
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    3. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    4. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    5. John Y. Campbell & Luis M. Viceira, 1999. "Consumption and Portfolio Decisions when Expected Returns are Time Varying," The Quarterly Journal of Economics, Oxford University Press, vol. 114(2), pages 433-495.
    6. Treich, Nicolas, 1997. "Risk tolerance and value of information in the standard portfolio model," Economics Letters, Elsevier, vol. 55(3), pages 361-363, September.
    7. 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.
    8. Kevin F. McCardle & Robert L. Winkler, 1992. "Repeated Gambles, Learning, and Risk Aversion," Management Science, INFORMS, pages 807-818.
    9. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    10. Leonid Kogan & Raman Uppal, "undated". "Risk Aversion and Optimal Portfolio Policies in Partial and General Equilibrium Economies," Rodney L. White Center for Financial Research Working Papers 13-00, Wharton School Rodney L. White Center for Financial Research.
    11. 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.
    12. LuisM. Viceira & John Y. Campbell, 2001. "Who Should Buy Long-Term Bonds?," American Economic Review, American Economic Association, pages 99-127.
    13. LuisM. Viceira & John Y. Campbell, 2001. "Who Should Buy Long-Term Bonds?," American Economic Review, American Economic Association, pages 99-127.
    14. M. J. Brennan, 1998. "The Role of Learning in Dynamic Portfolio Decisions," Review of Finance, European Finance Association, vol. 1(3), pages 295-306.
    15. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    16. Gennotte, Gerard, 1986. " Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-746, July.
    17. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, February.
    18. Detemple, Jerome B, 1986. " Asset Pricing in a Production Economy with Incomplete Information," Journal of Finance, American Finance Association, vol. 41(2), pages 383-391, June.
    19. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
    20. Brennan, Michael J & Xia, Yihong, 2001. "Assessing Asset Pricing Anomalies," Review of Financial Studies, Society for Financial Studies, pages 905-942.
    21. Brennan, Michael J & Xia, Yihong, 2001. "Assessing Asset Pricing Anomalies," Review of Financial Studies, Society for Financial Studies, pages 905-942.
    22. LuisM. Viceira & John Y. Campbell, 2001. "Who Should Buy Long-Term Bonds?," American Economic Review, American Economic Association, vol. 91(1), pages 99-127, March.
    23. Michael J. BRENNAN & Yihong XIA, 1999. "Assessing Asset Pricing Anomalies," FAME Research Paper Series rp10, International Center for Financial Asset Management and Engineering.
    24. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    25. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, pages 247-257.
    26. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, pages 141-161.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. Gollier, Christian, 2007. "Assets Relative Risk for Long-term Investors," IDEI Working Papers 466, Institut d'Économie Industrielle (IDEI), Toulouse.
    4. 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.

    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:bejtec:v:contributions.4:y:2004:i:1:n:4. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Golla). General contact details of provider: https://www.degruyter.com .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.