IDEAS home Printed from https://ideas.repec.org/a/eee/jebusi/v109y2020ics0148619519302097.html
   My bibliography  Save this article

Mean-variance-time: An extension of Markowitz's mean-variance portfolio theory

Author

Listed:
  • Fahmy, Hany

Abstract

In finance, investment decisions are commonly based on Markowitz's ex-ante mean-variance (MV) portfolio problem. The static ex-post trading problem, however, is completely absent. In this paper, we propose a theoretical extension of the MV framework by adding a time dimension so that the construction of a portfolio is thought of as an activity that consists of n monetary outcomes, i.e., rates of return on n risk assets, and the portfolio duration time t, which is the investor's optimal trading strategy time. Under a set of axioms, we show the existence and uniqueness of a utility function that represents investors’ preference over different time horizons. The analytical solution over the extended field yields an expression where optimal portfolio duration time depends explicitly on various sources of uncertainty; a key result that distinguishes this paper from the existing literature. We demonstrate empirically that our proposed model can explain many of the observed time-related anomalies of stock returns. Finally, we show that long-term trading strategies are more profitable for rational investors under perfect information.

Suggested Citation

  • Fahmy, Hany, 2020. "Mean-variance-time: An extension of Markowitz's mean-variance portfolio theory," Journal of Economics and Business, Elsevier, vol. 109(C).
    • Handle: RePEc:eee:jebusi:v:109:y:2020:i:c:s0148619519302097
    DOI: 10.1016/j.jeconbus.2019.105888
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0148619519302097
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconbus.2019.105888?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Jeanblanc, Monique & Martellini, Lionel, 2008. "Optimal investment decisions when time-horizon is uncertain," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1100-1113, December.
    2. Ron Kaniel & Gideon Saar & Sheridan Titman, 2008. "Individual Investor Trading and Stock Returns," Journal of Finance, American Finance Association, vol. 63(1), pages 273-310, February.
    3. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    4. repec:bla:jfinan:v:53:y:1998:i:6:p:1839-1885 is not listed on IDEAS
    5. Lioui, Abraham & Poncet, Patrice, 2001. "On optimal portfolio choice under stochastic interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1841-1865, November.
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    7. Bruce N. Lehmann, 1990. "Fads, Martingales, and Market Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 1-28.
    8. Lionel Martellini & Branko Uroševi'{c}, 2006. "Static Mean-Variance Analysis with Uncertain Time Horizon," Management Science, INFORMS, vol. 52(6), pages 955-964, June.
    9. Nils H. Hakansson, 1971. "Optimal Entrepreneurial Decisions in a Completely Stochastic Environment," Management Science, INFORMS, vol. 17(7), pages 427-449, March.
    10. Fama, Eugene F & French, Kenneth R, 1996. "Multifactor Explanations of Asset Pricing Anomalies," Journal of Finance, American Finance Association, vol. 51(1), pages 55-84, March.
    11. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    12. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    13. Jegadeesh, Narasimhan, 1990. "Evidence of Predictable Behavior of Security Returns," Journal of Finance, American Finance Association, vol. 45(3), pages 881-898, July.
    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. Hany Fahmy, 2017. "Testing the Empirical Validity of the Adaptive Markets Hypothesis," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 9(2), pages 169-184, December.
    16. Roberto C. Gutierrez & Eric K. Kelley, 2008. "The Long‐Lasting Momentum in Weekly Returns," Journal of Finance, American Finance Association, vol. 63(1), pages 415-447, February.
    17. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    18. Chan, Wesley S., 2003. "Stock price reaction to news and no-news: drift and reversal after headlines," Journal of Financial Economics, Elsevier, vol. 70(2), pages 223-260, November.
    19. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-317, June.
    20. Hakansson, Nils H, 1969. "Optimal Investment and Consumption Strategies under Risk, an Uncertain Lifetime, and Insurance," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(3), pages 443-466, October.
    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. Oleg S. Sukharev, 2020. "Portfolio Theory in Solving the Problem Structural Choice," JRFM, MDPI, vol. 13(9), pages 1-21, September.
    2. Bin Meng & Shuiyang Chen & Haibo Kuang & Hercules Haralambides & Xin Zhang, 2024. "Advances in risk management: optimum investment portfolios in tanker shipping," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 26(4), pages 572-591, December.
    3. Fahmy, Hany, 2022. "Clean energy deserves to be an asset class: A volatility-reward analysis," Economic Modelling, Elsevier, vol. 106(C).
    4. Vukovic, Darko B. & Maiti, Moinak & Frömmel, Michael, 2022. "Inflation and portfolio selection," Finance Research Letters, Elsevier, vol. 50(C).
    5. Fahmy, Hany, 2023. "Satiation, habit formation, and other temporal anomalies: Extending the choice theory to multiple neighborhoods of time," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 163-173.
    6. Spyridon D. Mourtas & Vasilios N. Katsikis, 2022. "V-Shaped BAS: Applications on Large Portfolios Selection Problem," Computational Economics, Springer;Society for Computational Economics, vol. 60(4), pages 1353-1373, December.
    7. Ossa González, Genjis A., 2023. "Comparación de los modelos de Black-Litterman, Markowitz y CAPM en la estimación de los rendimientos esperados en el mercado de renta variable en Colombia," Revista Estrategia Organizacional, Universidad Nacional Abierta y a Distancia, vol. 12(2), pages 29-53, 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. Huang, Zongyuan & Wang, Haiyang & Wu, Zhen, 2020. "A kind of optimal investment problem under inflation and uncertain time horizon," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    2. Adam Zaremba & Jacob Koby Shemer, 2018. "Price-Based Investment Strategies," Springer Books, Springer, number 978-3-319-91530-2, September.
    3. Cakici, Nusret & Zaremba, Adam & Bianchi, Robert J. & Pham, Nga, 2021. "False discoveries in the anomaly research: New insights from the Stock Exchange of Melbourne (1927–1987)," Pacific-Basin Finance Journal, Elsevier, vol. 70(C).
    4. Turan G. Bali & Robert F. Engle & Yi Tang, 2017. "Dynamic Conditional Beta Is Alive and Well in the Cross Section of Daily Stock Returns," Management Science, INFORMS, vol. 63(11), pages 3760-3779, November.
    5. Cakici, Nusret & Zaremba, Adam, 2022. "Salience theory and the cross-section of stock returns: International and further evidence," Journal of Financial Economics, Elsevier, vol. 146(2), pages 689-725.
    6. Jank, Stephan & Roling, Christoph & Smajlbegovic, Esad, 2021. "Flying under the radar: The effects of short-sale disclosure rules on investor behavior and stock prices," Journal of Financial Economics, Elsevier, vol. 139(1), pages 209-233.
    7. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
    8. Gabriel Hawawini & Donald B. Keim, "undated". "The Cross Section of Common Stock Returns: A Review of the Evidence and Some New Findings," Rodney L. White Center for Financial Research Working Papers 08-99, Wharton School Rodney L. White Center for Financial Research.
    9. Cakici, Nusret & Zaremba, Adam, 2021. "Liquidity and the cross-section of international stock returns," Journal of Banking & Finance, Elsevier, vol. 127(C).
    10. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    11. Mostafa Saidur Rahim Khan & Naheed Rabbani, 2017. "Momentum in stock returns: evidence from an emerging stock market," Macroeconomics and Finance in Emerging Market Economies, Taylor & Francis Journals, vol. 10(2), pages 191-204, May.
    12. Huang, Dashan & Zhu, Shu-Shang & Fabozzi, Frank J. & Fukushima, Masao, 2008. "Portfolio selection with uncertain exit time: A robust CVaR approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 594-623, February.
    13. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    14. Fernando Rubio, 2005. "Eficiencia De Mercado, Administracion De Carteras De Fondos Y Behavioural Finance," Finance 0503028, University Library of Munich, Germany, revised 23 Jul 2005.
    15. Cao, Ji & Rieger, Marc Oliver & Zhao, Lei, 2023. "Safety first, loss probability, and the cross section of expected stock returns," Journal of Economic Behavior & Organization, Elsevier, vol. 211(C), pages 345-369.
    16. Jungshik Hur & Mahesh Pritamani & Vivek Sharma, 2010. "Momentum and the Disposition Effect: The Role of Individual Investors," Financial Management, Financial Management Association International, vol. 39(3), pages 1155-1176, September.
    17. Cakici, Nusret & Zaremba, Adam, 2023. "Recency bias and the cross-section of international stock returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 84(C).
    18. Keunbae Ahn, 2021. "Predictable Fluctuations in the Cross-Section and Time-Series of Asset Prices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2021, January-A.
    19. Huang, Tao & Li, Junye, 2019. "Option-Implied variance asymmetry and the cross-section of stock returns," Journal of Banking & Finance, Elsevier, vol. 101(C), pages 21-36.
    20. Grinblatt, Mark & Keloharju, Matti & Linnainmaa, Juhani T., 2012. "IQ, trading behavior, and performance," Journal of Financial Economics, Elsevier, vol. 104(2), pages 339-362.

    More about this item

    Keywords

    Portfolio selection; Mean-variance portfolio theory; Uncertain time horizon; Overreaction; Portfolio duration;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G41 - Financial Economics - - Behavioral Finance - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making in Financial Markets

    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:eee:jebusi:v:109:y:2020:i:c:s0148619519302097. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/journal-of-economics-and-business .

    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.