IDEAS home Printed from https://ideas.repec.org/p/mit/sloanp/3540.html
   My bibliography  Save this paper

Evaluating Portfolio Policies: A Duality Approach

Author

Listed:
  • Kogan, Leonid
  • Haugh, Martin
  • Wang, Jiang

Abstract

The performance of a given portfolio policy can in principle be evaluated by comparing its expected utility with that of the optimal policy. Unfortunately, the optimal policy is usually not computable in which case a direct comparison is impossible. In this paper we solve this problem by using the given portfolio policy to construct an upper bound on the unknown maximum expected utility. This construction is based on a dual formulation of the portfolio optimization problem. When the upper bound is close to the expected utility achieved by the given portfolio policy, the potential utility loss of this policy is guaranteed to be small. Our algorithm can be used to evaluate portfolio policies in models with incomplete markets and position constraints. We illustrate our methodology by analyzing the static and myopic policies in markets with return predictability and constraints on short sales and borrowin

Suggested Citation

  • Kogan, Leonid & Haugh, Martin & Wang, Jiang, 2003. "Evaluating Portfolio Policies: A Duality Approach," Working papers 4329-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    • Handle: RePEc:mit:sloanp:3540
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/1721.1/3540
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. John Y. Campbell & Yeung Lewis Chanb & M. Viceira, 2013. "A multivariate model of strategic asset allocation," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 39, pages 809-848, World Scientific Publishing Co. Pte. Ltd..
    2. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    3. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    4. Yeung Lewis Chan & Leonid Kogan, 2002. "Catching Up with the Joneses: Heterogeneous Preferences and the Dynamics of Asset Prices," Journal of Political Economy, University of Chicago Press, vol. 110(6), pages 1255-1285, December.
    5. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    6. Jérôme B. Detemple & Ren Garcia & Marcel Rindisbacher, 2003. "A Monte Carlo Method for Optimal Portfolios," Journal of Finance, American Finance Association, vol. 58(1), pages 401-446, February.
    7. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    8. 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.
    9. Kandel, Shmuel & Stambaugh, Robert F, 1996. "On the Predictability of Stock Returns: An Asset-Allocation Perspective," Journal of Finance, American Finance Association, vol. 51(2), pages 385-424, June.
    10. 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.
    11. Yacine AÏT‐SAHALI & Michael W. Brandt, 2001. "Variable Selection for Portfolio Choice," Journal of Finance, American Finance Association, vol. 56(4), pages 1297-1351, August.
    12. Yihong Xia, 2001. "Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation," Journal of Finance, American Finance Association, vol. 56(1), pages 205-246, February.
    13. Pastor, Lubos & Stambaugh, Robert F., 2000. "Comparing asset pricing models: an investment perspective," Journal of Financial Economics, Elsevier, vol. 56(3), pages 335-381, June.
    14. Balduzzi, Pierluigi & Lynch, Anthony W., 1999. "Transaction costs and predictability: some utility cost calculations," Journal of Financial Economics, Elsevier, vol. 52(1), pages 47-78, April.
    15. Andrew Ang & Geert Bekaert, 1999. "International Asset Allocation with Time-Varying Correlations," NBER Working Papers 7056, National Bureau of Economic Research, Inc.
    16. Ioannis Karatzas & John P. Lehoczky & Suresh P. Sethi & Steven E. Shreve, 1986. "Explicit Solution of a General Consumption/Investment Problem," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 261-294, May.
    17. M. J. Brennan, 1998. "The Role of Learning in Dynamic Portfolio Decisions," Review of Finance, European Finance Association, vol. 1(3), pages 295-306.
    18. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, June.
    19. Schroder, Mark & Skiadas, Costis, 2003. "Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursive preferences," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 155-202, December.
    20. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585, Elsevier.
    21. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
    22. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 3-17.
    23. Rust, John, 1996. "Numerical dynamic programming in economics," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 14, pages 619-729, Elsevier.
    24. John Y. Campbell & Luis M. Viceira, 1999. "Consumption and Portfolio Decisions when Expected Returns are Time Varying," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 433-495.
    25. H. M. Amman & D. A. Kendrick & J. Rust (ed.), 1996. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 1, number 1.
    26. Lynch, Anthony W., 2001. "Portfolio choice and equity characteristics: characterizing the hedging demands induced by return predictability," Journal of Financial Economics, Elsevier, vol. 62(1), pages 67-130, October.
    27. Hua He & Neil D. Pearson, 1991. "Consumption and Portfolio Policies With Incomplete Markets and Short‐Sale Constraints: the Finite‐Dimensional Case1," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 1-10, July.
    28. Munk, Claus, 2000. "Optimal consumption/investment policies with undiversifiable income risk and liquidity constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(9), pages 1315-1343, August.
    29. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    30. Stanley R. Pliska, 1986. "A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 371-382, May.
    31. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    32. Ľuboš Pástor, 2000. "Portfolio Selection and Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(1), pages 179-223, February.
    33. 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.
    34. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    35. 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.
    36. Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
    37. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
    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. Michele Longo & Alessandra Mainini, 2017. "Welfare effects of information and rationality in portfolio decisions under parameter uncertainty," Papers 1709.04387, arXiv.org.
    2. Hong, Yi & Jin, Xing, 2018. "Semi-analytical solutions for dynamic portfolio choice in jump-diffusion models and the optimal bond-stock mix," European Journal of Operational Research, Elsevier, vol. 265(1), pages 389-398.
    3. Kasper Larsen & Oleksii Mostovyi & Gordan Žitković, 2018. "An expansion in the model space in the context of utility maximization," Finance and Stochastics, Springer, vol. 22(2), pages 297-326, April.
    4. Castañeda, Pablo & Reus, Lorenzo, 2019. "Suboptimal investment behavior and welfare costs: A simulation based approach," Finance Research Letters, Elsevier, vol. 30(C), pages 170-180.
    5. Björn Bick & Holger Kraft & Claus Munk, 2013. "Solving Constrained Consumption-Investment Problems by Simulation of Artificial Market Strategies," Management Science, INFORMS, vol. 59(2), pages 485-503, June.
    6. Thomas Breuer & Martin Jandačka, 2008. "Portfolio selection with transaction costs under expected shortfall constraints," Computational Management Science, Springer, vol. 5(4), pages 305-316, October.
    7. Cheng-Der Fuh & Yanwei Jia & Steven Kou, 2023. "A General Framework for Importance Sampling with Latent Markov Processes," Papers 2311.12330, arXiv.org.
    8. Kasper Larsen & Oleksii Mostovyi & Gordan v{Z}itkovi'c, 2014. "An expansion in the model space in the context of utility maximization," Papers 1410.0946, arXiv.org, revised Aug 2016.
    9. Min Dai & Steven Kou & Shuaijie Qian & Xiangwei Wan, 2022. "Nonconcave Utility Maximization with Portfolio Bounds," Management Science, INFORMS, vol. 68(11), pages 8368-8385, November.
    10. Paolo Guasoni & Gu Wang, 2020. "Consumption in incomplete markets," Finance and Stochastics, Springer, vol. 24(2), pages 383-422, April.
    11. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    12. Thijs Kamma & Antoon Pelsser, 2019. "Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading Constraints," Papers 1906.12317, arXiv.org, revised Oct 2019.
    13. Larsen, Linda Sandris & Munk, Claus, 2012. "The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts," Journal of Economic Dynamics and Control, Elsevier, vol. 36(2), pages 266-293.
    14. Snezhana Kirusheva & Thomas S. Salisbury, 2023. "A greedy algorithm for habit formation under multiplicative utility," Papers 2305.04748, arXiv.org.
    15. David B. Brown & James E. Smith, 2011. "Dynamic Portfolio Optimization with Transaction Costs: Heuristics and Dual Bounds," Management Science, INFORMS, vol. 57(10), pages 1752-1770, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guidolin, Massimo & Timmermann, Allan, 2007. "Asset allocation under multivariate regime switching," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3503-3544, November.
    2. Mark E. Wohar & David E. Rapach, 2005. "Return Predictability and the Implied Intertemporal Hedging Demands for Stocks and Bonds: International Evidence," Computing in Economics and Finance 2005 329, Society for Computational Economics.
    3. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    4. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    5. Jessica A. Wachter, 2010. "Asset Allocation," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 175-206, December.
    6. Massimo Guidolin & Allan Timmermann, 2008. "Size and Value Anomalies under Regime Shifts," Journal of Financial Econometrics, Oxford University Press, vol. 6(1), pages 1-48, Winter.
    7. Jakub W. Jurek & Luis M. Viceira, 2011. "Optimal Value and Growth Tilts in Long-Horizon Portfolios," Review of Finance, European Finance Association, vol. 15(1), pages 29-74.
    8. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    9. John Y. Campbell & Yeung Lewis Chanb & M. Viceira, 2013. "A multivariate model of strategic asset allocation," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 39, pages 809-848, World Scientific Publishing Co. Pte. Ltd..
    10. Larsen, Linda Sandris & Munk, Claus, 2012. "The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts," Journal of Economic Dynamics and Control, Elsevier, vol. 36(2), pages 266-293.
    11. Rapach, David E. & Wohar, Mark E., 2009. "Multi-period portfolio choice and the intertemporal hedging demands for stocks and bonds: International evidence," Journal of International Money and Finance, Elsevier, vol. 28(3), pages 427-453, April.
    12. Engsted, Tom & Pedersen, Thomas Q., 2012. "Return predictability and intertemporal asset allocation: Evidence from a bias-adjusted VAR model," Journal of Empirical Finance, Elsevier, vol. 19(2), pages 241-253.
    13. Maenhout, Pascal J., 2006. "Robust portfolio rules and detection-error probabilities for a mean-reverting risk premium," Journal of Economic Theory, Elsevier, vol. 128(1), pages 136-163, May.
    14. Weidong Tian & Murray Carlson & David A. Chapman & Ron Kaniel & Hong Yan, 2017. "Specification Error, Estimation Risk, and Conditional Portfolio Rules," International Review of Finance, International Review of Finance Ltd., vol. 17(2), pages 263-288, June.
    15. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    16. Daniel Giamouridis & Athanasios Sakkas & Nikolaos Tessaromatis, 2017. "Dynamic Asset Allocation with Liabilities," European Financial Management, European Financial Management Association, vol. 23(2), pages 254-291, March.
    17. Castaneda, Pablo & Rudolph, Heinz P., 2011. "Upgrading investment regulations in second pillar pension systems : a proposal for Colombia," Policy Research Working Paper Series 5775, The World Bank.
    18. Ang, Andrew & Bekaert, Geert & Liu, Jun, 2005. "Why stocks may disappoint," Journal of Financial Economics, Elsevier, vol. 76(3), pages 471-508, June.
    19. Guidolin, Massimo & Hyde, Stuart, 2012. "Can VAR models capture regime shifts in asset returns? A long-horizon strategic asset allocation perspective," Journal of Banking & Finance, Elsevier, vol. 36(3), pages 695-716.
    20. Francisco Gomes & Alexander Michaelides & Yuxin Zhang, 2022. "Tactical Target Date Funds," Management Science, INFORMS, vol. 68(4), pages 3047-3070, April.

    More about this item

    Keywords

    Portfolio Choice; Duality; Dynamic Programming; Constraints; Monte Carlo; Simulation;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:mit:sloanp:3540. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: None (email available below). General contact details of provider: https://edirc.repec.org/data/ssmitus.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.