Advanced Search
MyIDEAS: Login to save this paper or follow this series

Dynamic Mean-Variance Asset Allocation

Contents:

Author Info

  • Basak, Suleyman
  • Chabakauri, Georgy

Abstract

Mean-variance criteria remain prevalent in multi-period problems, and yet not much is known about their dynamically optimal policies. We provide a fully analytical characterization of the optimal dynamic mean-variance portfolios within a general incomplete-market economy, and recover a simple structure that also inherits several conventional properties of static models. We also identify a probability measure that incorporates intertemporal hedging demands and facilitates much tractability in the explicit computation of portfolios. We solve the problem by explicitly recognizing the time-inconsistency of the mean-variance criterion and deriving a recursive representation for it, which makes dynamic programming applicable. We further show that our time-consistent solution is generically different from the pre-commitment solutions in the extant literature, which maximize the mean-variance criterion at an initial date and which the investor commits to follow despite incentives to deviate. We illustrate the usefulness of our analysis by explicitly computing dynamic mean-variance portfolios under various stochastic investment opportunities in a straightforward way, which does not involve solving a Hamilton-Jacobi-Bellman differential equation. A calibration exercise shows that the mean-variance hedging demands may comprise a significant fraction of the investor's total risky asset demand.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.cepr.org/pubs/dps/DP7256.asp
Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 7256.

as in new window
Length:
Date of creation: Apr 2009
Date of revision:
Handle: RePEc:cpr:ceprdp:7256

Contact details of provider:
Postal: Centre for Economic Policy Research, 77 Bastwick Street, London EC1V 3PZ.
Phone: 44 - 20 - 7183 8801
Fax: 44 - 20 - 7183 8820

Order Information:
Email:

Related research

Keywords: Dynamic Programming; Incomplete Markets; Mean-Variance Analysis; Multi-Period Portfolio Choice; Stochastic Investment Opportunities; Time-Consistency;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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.:
as in new window
  1. Peleg, Bezalel & Yaari, Menahem E, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 391-401, July.
  2. George CHACKO & Luis M. VICEIRA, 1999. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," FAME Research Paper Series rp11, International Center for Financial Asset Management and Engineering.
  3. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942, October.
  4. John Y. Campbell & Karine Serfaty-De Medeiros & Luis M. Viceira, 2010. "Global Currency Hedging," Journal of Finance, American Finance Association, vol. 65(1), pages 87-121, 02.
  5. Basak, Suleyman & Chabakauri, Georgy, 2011. "Dynamic Hedging in Incomplete Markets: A Simple Solution," CEPR Discussion Papers 8402, C.E.P.R. Discussion Papers.
  6. Isabelle Bajeux-Besnainou & Roland Portait, 1998. "Dynamic Asset Allocation in a Mean-Variance Framework," Management Science, INFORMS, vol. 44(11-Part-2), pages S79-S95, November.
  7. Tomasz R. Bielecki & Hanqing Jin & Stanley R. Pliska & Xun Yu Zhou, 2005. "Continuous-Time Mean-Variance Portfolio Selection With Bankruptcy Prohibition," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 213-244.
  8. Antonios Sangvinatsos & Jessica A. Wachter, 2005. "Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors?," Journal of Finance, American Finance Association, vol. 60(1), pages 179-230, 02.
  9. Bansal, Ravi & Dahlquist, Magnus & Harvey, Campbell R., 2004. "Dynamic Trading Strategies and Portfolio Choice," SIFR Research Report Series 31, Institute for Financial Research.
  10. Acharya, Viral V & Pedersen, Lasse Heje, 2004. "Asset Pricing with Liquidity Risk," CEPR Discussion Papers 4718, C.E.P.R. Discussion Papers.
  11. John Y. Campbell & Luis M. Viceira, 1998. "Consumption and Portfolio Decisions When Expected Returns Are Time Varying," Harvard Institute of Economic Research Working Papers 1835, Harvard - Institute of Economic Research.
  12. Cvitanic, Jaksa & Goukasian, Levon & Zapatero, Fernando, 2003. "Monte Carlo computation of optimal portfolios in complete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 971-986, April.
  13. Caplin, Andrew & Leahy, John, 2006. "The recursive approach to time inconsistency," Journal of Economic Theory, Elsevier, vol. 131(1), pages 134-156, November.
  14. Jaksa Cvitanic & Fernando Zapatero, 2004. "Introduction to the Economics and Mathematics of Financial Markets," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262532654, December.
  15. Christopher Harris & David Laibson, 1999. "Dynamic Choices of Hyperbolic Consumers," Harvard Institute of Economic Research Working Papers 1886, Harvard - Institute of Economic Research.
  16. Wachter, Jessica A., 2002. "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(01), pages 63-91, March.
  17. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan Storud, 2004. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," NBER Working Papers 10934, National Bureau of Economic Research, Inc.
  18. Steven R. Grenadier & Neng Wang, 2006. "Investment Under Uncertainty and Time-Inconsistent Preferences," NBER Working Papers 12042, National Bureau of Economic Research, Inc.
  19. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, 08.
  20. Harrison Hong & Jose Scheinkman & Wei Xiong, 2005. "Asset Float and Speculative Bubbles," NBER Working Papers 11367, National Bureau of Economic Research, Inc.
  21. Michael W. Brandt & Pedro Santa-Clara, 2006. "Dynamic Portfolio Selection by Augmentingthe Asset Space," Journal of Finance, American Finance Association, vol. 61(5), pages 2187-2217, October.
  22. 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.
  23. Yacine AÏT-SAHALIA, & Michael W. BRANDT, 2001. "Variable Selection for Portfolio Choice," FAME Research Paper Series rp34, International Center for Financial Asset Management and Engineering.
  24. Johnsen, Thore H & Donaldson, John B, 1985. "The Structure of Intertemporal Preferences under Uncertainty and Time Consistent Plans," Econometrica, Econometric Society, vol. 53(6), pages 1451-58, November.
  25. Michael W. Brandt, 1999. "Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach," Journal of Finance, American Finance Association, vol. 54(5), pages 1609-1645, October.
  26. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, 06.
  27. Leippold, Markus & Trojani, Fabio & Vanini, Paolo, 2004. "A geometric approach to multiperiod mean variance optimization of assets and liabilities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1079-1113, March.
  28. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-19, March.
  29. Beckers, Stan, 1980. " The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-73, June.
  30. Schweizer, Martin, 1999. "A minimality property of the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 27-31, March.
  31. Leonard MacLean & Yonggan Zhao & William Ziemba, 2011. "Mean-variance versus expected utility in dynamic investment analysis," Computational Management Science, Springer, vol. 8(1), pages 3-22, April.
  32. Lixin Huang & Hong Liu, 2007. "Rational Inattention and Portfolio Selection," Journal of Finance, American Finance Association, vol. 62(4), pages 1999-2040, 08.
  33. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
  34. Liu, Jun, 2001. "Dynamic Choice and Risk Aversion," University of California at Los Angeles, Anderson Graduate School of Management qt36v1d9zg, Anderson Graduate School of Management, UCLA.
  35. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  36. Cvitanic, Jaksa & Lazrak, Ali & Wang, Tan, 2008. "Implications of the Sharpe ratio as a performance measure in multi-period settings," Journal of Economic Dynamics and Control, Elsevier, vol. 32(5), pages 1622-1649, May.
  37. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
  38. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-61.
  39. 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.
  40. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  41. Duan Li & Wan-Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406.
  42. Jér�me B. Detemple & René Garcia & Marcel Rindisbacher, 2003. "A Monte Carlo Method for Optimal Portfolios," Journal of Finance, American Finance Association, vol. 58(1), pages 401-446, 02.
  43. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
  44. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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 in new window

Cited by:
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:cpr:ceprdp:7256. 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: ().

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.