IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v310y2023i2p773-792.html
   My bibliography  Save this article

Portfolio selection with exploration of new investment assets

Author

Listed:
  • De Gennaro Aquino, Luca
  • Sornette, Didier
  • Strub, Moris S.

Abstract

We introduce a model for portfolio selection with an extendable investment universe where an agent with mean-variance preferences faces a trade-off between exploiting existing and exploring for new investment opportunities. When the agent chooses to explore, a new risky asset is discovered and the agent subsequently invests in the extended universe. We first provide conditions for wellposedness and characterize the optimal amount devoted to exploration. Our model shows that incremental exploration does not pay off, that it is increasingly worthwhile to explore in worse market environments, and that investment performance measured by the Sharpe ratio is increasing in the initial wealth of the agent indicating that richer agents can make better use of new investment opportunities. We further generalize our model and verify the robustness of the main findings with regard to various modeling assumptions.

Suggested Citation

  • De Gennaro Aquino, Luca & Sornette, Didier & Strub, Moris S., 2023. "Portfolio selection with exploration of new investment assets," European Journal of Operational Research, Elsevier, vol. 310(2), pages 773-792.
    • Handle: RePEc:eee:ejores:v:310:y:2023:i:2:p:773-792
    DOI: 10.1016/j.ejor.2023.03.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221723002230
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2023.03.017?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. Yan, Xuemin (Sterling), 2008. "Liquidity, Investment Style, and the Relation between Fund Size and Fund Performance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 43(3), pages 741-767, September.
    2. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2012. "Time-Inconsistent Stochastic Linear--Quadratic Control," Post-Print hal-00691816, HAL.
    3. Steven R. Grenadier & Andrey Malenko, 2010. "A Bayesian Approach to Real Options: The Case of Distinguishing between Temporary and Permanent Shocks," Journal of Finance, American Finance Association, vol. 65(5), pages 1949-1986, October.
    4. Ehrbar, Hans, 1990. "Mean-variance efficiency when investors are not required to invest all their money," Journal of Economic Theory, Elsevier, vol. 50(1), pages 214-218, February.
    5. James G. March, 1991. "Exploration and Exploitation in Organizational Learning," Organization Science, INFORMS, vol. 2(1), pages 71-87, February.
    6. Dang, D.M. & Forsyth, P.A., 2016. "Better than pre-commitment mean-variance portfolio allocation strategies: A semi-self-financing Hamilton–Jacobi–Bellman equation approach," European Journal of Operational Research, Elsevier, vol. 250(3), pages 827-841.
    7. Bi, Junna & Jin, Hanqing & Meng, Qingbin, 2018. "Behavioral mean-variance portfolio selection," European Journal of Operational Research, Elsevier, vol. 271(2), pages 644-663.
    8. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    9. Way, Rupert & Lafond, François & Lillo, Fabrizio & Panchenko, Valentyn & Farmer, J. Doyne, 2019. "Wright meets Markowitz: How standard portfolio theory changes when assets are technologies following experience curves," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 211-238.
    10. Tomas Björk & Agatha Murgoci, 2014. "A theory of Markovian time-inconsistent stochastic control in discrete time," Finance and Stochastics, Springer, vol. 18(3), pages 545-592, July.
    11. Gary Smith & Michael Levere & Robert Kurtzman, 2009. "Poker Player Behavior After Big Wins and Big Losses," Management Science, INFORMS, vol. 55(9), pages 1547-1555, September.
    12. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, vol. 70(3), pages 393-408, June.
    13. Haoran Wang & Xun Yu Zhou, 2020. "Continuous‐time mean–variance portfolio selection: A reinforcement learning framework," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1273-1308, October.
    14. Charles Cao & David Gempesaw & Timothy T Simin, 2021. "Information Choice, Uncertainty, and Expected Returns [A noisy rational expectations equilibrium for multi-asset securities markets]," Review of Financial Studies, Society for Financial Studies, vol. 34(12), pages 5977-6031.
    15. Xiangyu Cui & Li Duan & Jiaan Yan, 2015. "Classical mean-variance model revisited: pseudo efficiency," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(10), pages 1646-1655, October.
    16. Min Dai & Hanqing Jin & Steven Kou & Yuhong Xu, 2021. "A Dynamic Mean-Variance Analysis for Log Returns," Management Science, INFORMS, vol. 67(2), pages 1093-1108, February.
    17. Cui, Xiangyu & Gao, Jianjun & Li, Xun & Li, Duan, 2014. "Optimal multi-period mean–variance policy under no-shorting constraint," European Journal of Operational Research, Elsevier, vol. 234(2), pages 459-468.
    18. Oded Berger-Tal & Jonathan Nathan & Ehud Meron & David Saltz, 2014. "The Exploration-Exploitation Dilemma: A Multidisciplinary Framework," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-8, April.
    19. A. Dyck & L. Pomorski, 2016. "Investor Scale and Performance in Private Equity Investments," Review of Finance, European Finance Association, vol. 20(3), pages 1081-1106.
    20. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    21. Stijn Van Nieuwerburgh & Laura Veldkamp, 2010. "Information Acquisition and Under-Diversification," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 779-805.
    22. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    23. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    24. Didier Sornette & Spencer Wheatley & Peter Cauwels, 2019. "The fair reward problem: the illusion of success and how to solve it," Papers 1902.04940, arXiv.org, revised Apr 2019.
    25. 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.
    26. Phillips, Blake & Pukthuanthong, Kuntara & Rau, P. Raghavendra, 2018. "Size does not matter: Diseconomies of scale in the mutual fund industry revisited," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 357-365.
    27. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    28. Josh Lerner & Antoinette Schoar & Jialan Wang, 2008. "Secrets of the Academy: The Drivers of University Endowment Success," Journal of Economic Perspectives, American Economic Association, vol. 22(3), pages 207-222, Summer.
    29. Bingyan Han & Hoi Ying Wong, 2019. "Mean-variance portfolio selection under Volterra Heston model," Papers 1904.12442, arXiv.org, revised Jan 2020.
    30. Langer, Thomas & Weber, Martin, 2008. "Does commitment or feedback influence myopic loss aversion?: An experimental analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 810-819, September.
    31. Didier Sornette & Spencer Wheatley & Peter Cauwels, 2019. "The Fair Reward Problem: The Illusion Of Success And How To Solve It," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-52, May.
    32. Gao, Jianjun & Xiong, Yan & Li, Duan, 2016. "Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time," European Journal of Operational Research, Elsevier, vol. 249(2), pages 647-656.
    33. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    34. Joseph Chen & Harrison Hong & Ming Huang & Jeffrey D. Kubik, 2004. "Does Fund Size Erode Mutual Fund Performance? The Role of Liquidity and Organization," American Economic Review, American Economic Association, vol. 94(5), pages 1276-1302, December.
    35. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    36. Pástor, Ľuboš & Stambaugh, Robert F. & Taylor, Lucian A., 2015. "Scale and skill in active management," Journal of Financial Economics, Elsevier, vol. 116(1), pages 23-45.
    37. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    38. Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
    39. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    40. Nicole Bäuerle & Stefanie Grether, 2015. "Complete markets do not allow free cash flow streams," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 137-146, April.
    41. Nathaniel D. Daw & John P. O'Doherty & Peter Dayan & Ben Seymour & Raymond J. Dolan, 2006. "Cortical substrates for exploratory decisions in humans," Nature, Nature, vol. 441(7095), pages 876-879, June.
    42. Wang, Ling & Chen, Kexin & Chiu, Mei Choi & Wong, Hoi Ying, 2023. "Optimal expansion of business opportunity," European Journal of Operational Research, Elsevier, vol. 309(1), pages 432-445.
    43. 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.
    44. Leippold, Markus & Stromberg, Jacob, 2017. "Strategic technology adoption and hedging under incomplete markets," Journal of Banking & Finance, Elsevier, vol. 81(C), pages 181-199.
    45. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    46. Didier Sornette & Spencer Wheatley & Peter Cauwels, 2019. "The Fair Reward Problem: The Illusion of Success and How to Solve It," Swiss Finance Institute Research Paper Series 19-25, Swiss Finance Institute, revised Apr 2019.
    47. Chiu, Mei Choi & Wong, Hoi Ying, 2011. "Mean-variance portfolio selection of cointegrated assets," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1369-1385, August.
    48. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2017. "Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium," Post-Print hal-01139343, HAL.
    49. Jianjun Gao & Duan Li, 2013. "Optimal Cardinality Constrained Portfolio Selection," Operations Research, INFORMS, vol. 61(3), pages 745-761, June.
    50. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    51. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2005. "Investment Timing Under Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 472-500, May.
    52. Zhang, Wenlang & Semmler, Willi, 2009. "Prospect theory for stock markets: Empirical evidence with time-series data," Journal of Economic Behavior & Organization, Elsevier, vol. 72(3), pages 835-849, December.
    53. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.
    54. Page, Lionel & Savage, David A. & Torgler, Benno, 2014. "Variation in risk seeking behaviour following large losses: A natural experiment," European Economic Review, Elsevier, vol. 71(C), pages 121-131.
    55. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    56. Jianming Xia, 2005. "Mean–Variance Portfolio Choice: Quadratic Partial Hedging," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 533-538, July.
    57. Christoph Czichowsky, 2013. "Time-consistent mean-variance portfolio selection in discrete and continuous time," Finance and Stochastics, Springer, vol. 17(2), pages 227-271, April.
    58. 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, April.
    59. Joshua M. Pollet & Mungo Wilson, 2008. "How Does Size Affect Mutual Fund Behavior?," Journal of Finance, American Finance Association, vol. 63(6), pages 2941-2969, December.
    60. Juha Uotila & Markku Maula & Thomas Keil & Shaker A. Zahra, 2009. "Exploration, exploitation, and financial performance: analysis of S&P 500 corporations," Strategic Management Journal, Wiley Blackwell, vol. 30(2), pages 221-231, February.
    61. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    62. Tomas Björk & Agatha Murgoci & Xun Yu Zhou, 2014. "Mean–Variance Portfolio Optimization With State-Dependent Risk Aversion," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 1-24, January.
    Full references (including those not matched with items on IDEAS)

    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. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    2. Chi Kin Lam & Yuhong Xu & Guosheng Yin, 2016. "Dynamic portfolio selection without risk-free assets," Papers 1602.04975, arXiv.org.
    3. Xue Dong He & Xun Yu Zhou, 2021. "Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation," Papers 2105.01829, arXiv.org.
    4. Cong, F. & Oosterlee, C.W., 2016. "On pre-commitment aspects of a time-consistent strategy for a mean-variance investor," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 178-193.
    5. Li, Yongwu & Qiao, Han & Wang, Shouyang & Zhang, Ling, 2015. "Time-consistent investment strategy under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 187-197.
    6. Van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2018. "Time-consistent mean–variance portfolio optimization: A numerical impulse control approach," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 9-28.
    7. Xiangyu Cui & Xun Li & Duan Li & Yun Shi, 2014. "Time Consistent Behavior Portfolio Policy for Dynamic Mean-Variance Formulation," Papers 1408.6070, arXiv.org, revised Aug 2015.
    8. Felix Fie{ss}inger & Mitja Stadje, 2023. "Time-Consistent Asset Allocation for Risk Measures in a L\'evy Market," Papers 2305.09471, arXiv.org, revised Jun 2023.
    9. Dong-Mei Zhu & Jia-Wen Gu & Feng-Hui Yu & Tak-Kuen Siu & Wai-Ki Ching, 2021. "Optimal pairs trading with dynamic mean-variance objective," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 145-168, August.
    10. Marcel Nutz & Yuchong Zhang, 2019. "Conditional Optimal Stopping: A Time-Inconsistent Optimization," Papers 1901.05802, arXiv.org, revised Oct 2019.
    11. Xiangyu Cui & Duan Li & Xun Li, 2014. "Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure," Papers 1403.0718, arXiv.org.
    12. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.
    13. Bingyan Han & Hoi Ying Wong, 2019. "Time-inconsistency with rough volatility," Papers 1907.11378, arXiv.org, revised Dec 2021.
    14. F. Cong & C. W. Oosterlee, 2017. "On Robust Multi-Period Pre-Commitment And Time-Consistent Mean-Variance Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-26, November.
    15. Shuzhen Yang, 2020. "Discrete time multi-period mean-variance model: Bellman type strategy and Empirical analysis," Papers 2011.10966, arXiv.org.
    16. Bingyan Han & Chi Seng Pun & Hoi Ying Wong, 2023. "Robust Time-inconsistent Linear-Quadratic Stochastic Controls: A Stochastic Differential Game Approach," Papers 2306.16982, arXiv.org.
    17. Xiangyu Cui & Xun Li & Duan Li & Yun Shi, 2017. "Time consistent behavioral portfolio policy for dynamic mean–variance formulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1647-1660, December.
    18. Cong, F. & Oosterlee, C.W., 2016. "Multi-period mean–variance portfolio optimization based on Monte-Carlo simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 23-38.
    19. Li, Bin & Li, Danping & Xiong, Dewen, 2016. "Alpha-robust mean-variance reinsurance-investment strategy," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 101-123.
    20. Zhou, Zhongbao & Xiao, Helu & Yin, Jialing & Zeng, Ximei & Lin, Ling, 2016. "Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 187-202.

    More about this item

    Keywords

    Portfolio optimization; Mean-variance preferences; Investment analysis; Exploration vs. exploitation;
    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

    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:ejores:v:310:y:2023:i:2:p:773-792. 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: http://www.elsevier.com/locate/eor .

    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.