IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v419y2022ics0096300321009346.html
   My bibliography  Save this article

Another look at portfolio optimization with mental accounts

Author

Listed:
  • Chiu, Wan-Yi

Abstract

Das et al. (2010, 2018)[11,12] numerically solve the portfolio optimization with mental accounts (POMA) problem, which maps the mean-variance theory and mean-variance utility into a behavioral portfolio theory. We derive a POMA closed-form solution based on the maximum Sharpe ratio and minimum value-at-risk (VaR) rule. The extension offers an alternate equivalence between the POMA problem, the mean-VaR model, and the generalized Sharpe measure. From the manageable VaR-measure perspective, our evidence indicates that many efficient portfolios are statistically equivalent to the global minimum variance portfolio under the estimation risk.

Suggested Citation

  • Chiu, Wan-Yi, 2022. "Another look at portfolio optimization with mental accounts," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    • Handle: RePEc:eee:apmaco:v:419:y:2022:i:c:s0096300321009346
    DOI: 10.1016/j.amc.2021.126851
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321009346
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126851?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. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    2. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    3. Guiso, Luigi & Sapienza, Paola & Zingales, Luigi, 2018. "Time varying risk aversion," Journal of Financial Economics, Elsevier, vol. 128(3), pages 403-421.
    4. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July.
    5. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2020. "Portfolio selection with mental accounts: An equilibrium model with endogenous risk aversion," Journal of Banking & Finance, Elsevier, vol. 110(C).
    6. Taras Bodnar & Yarema Okhrin & Valdemar Vitlinskyy & Taras Zabolotskyy, 2018. "Determination and estimation of risk aversion coefficients," Computational Management Science, Springer, vol. 15(2), pages 297-317, June.
    7. Gabriel Frahm, 2010. "Linear statistical inference for global and local minimum variance portfolios," Statistical Papers, Springer, vol. 51(4), pages 789-812, December.
    8. Das, Sanjiv & Markowitz, Harry & Scheid, Jonathan & Statman, Meir, 2010. "Portfolio Optimization with Mental Accounts," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(2), pages 311-334, April.
    9. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    10. Alexander Kempf & Christoph Memmel, 2006. "Estimating the global Minimum Variance Portfolio," Schmalenbach Business Review (sbr), LMU Munich School of Management, vol. 58(4), pages 332-348, October.
    11. Taras Bodnar & Taras Zabolotskyy, 2017. "How risky is the optimal portfolio which maximizes the Sharpe ratio?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 1-28, January.
    12. Shefrin, Hersh & Statman, Meir, 2000. "Behavioral Portfolio Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 35(2), pages 127-151, June.
    13. 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.
    14. Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, February.
    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. Taras Bodnar & Yarema Okhrin & Valdemar Vitlinskyy & Taras Zabolotskyy, 2018. "Determination and estimation of risk aversion coefficients," Computational Management Science, Springer, vol. 15(2), pages 297-317, June.
    2. Baptista, Alexandre M., 2012. "Portfolio selection with mental accounts and background risk," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 968-980.
    3. Omid Momen & Akbar Esfahanipour & Abbas Seifi, 2020. "A robust behavioral portfolio selection: model with investor attitudes and biases," Operational Research, Springer, vol. 20(1), pages 427-446, March.
    4. Chiu, Wan-Yi, 2022. "Stepwise expanding the frontier one asset at a time," Finance Research Letters, Elsevier, vol. 46(PA).
    5. Xu Guo & Raymond H. Chan & Wing-Keung Wong & Lixing Zhu, 2019. "Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk," Risk Management, Palgrave Macmillan, vol. 21(2), pages 73-98, June.
    6. Bodnar Taras & Schmid Wolfgang & Zabolotskyy Tara, 2012. "Minimum VaR and minimum CVaR optimal portfolios: Estimators, confidence regions, and tests," Statistics & Risk Modeling, De Gruyter, vol. 29(4), pages 281-314, November.
    7. Li, Ting & Zhang, Weiguo & Xu, Weijun, 2013. "Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment," Economic Modelling, Elsevier, vol. 31(C), pages 12-17.
    8. Taras Bodnar & Taras Zabolotskyy, 2017. "How risky is the optimal portfolio which maximizes the Sharpe ratio?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 1-28, January.
    9. Muhinyuza, Stanislas & Bodnar, Taras & Lindholm, Mathias, 2020. "A test on the location of the tangency portfolio on the set of feasible portfolios," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    10. Bodnar, Taras & Lindholm, Mathias & Niklasson, Vilhelm & Thorsén, Erik, 2022. "Bayesian portfolio selection using VaR and CVaR," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    11. Alexander, Gordon J. & Baptista, Alexandre M., 2011. "Portfolio selection with mental accounts and delegation," Journal of Banking & Finance, Elsevier, vol. 35(10), pages 2637-2656, October.
    12. Brandtner, Mario, 2013. "Conditional Value-at-Risk, spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5526-5537.
    13. Luiz Vitiello & Ser-Huang Poon, 2022. "Option pricing with random risk aversion," Review of Quantitative Finance and Accounting, Springer, vol. 58(4), pages 1665-1684, May.
    14. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2014. "Bank regulation and international financial stability: A case against the 2006 Basel framework for controlling tail risk in trading books," Journal of International Money and Finance, Elsevier, vol. 43(C), pages 107-130.
    15. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679, arXiv.org.
    16. Righi, Marcelo Brutti & Borenstein, Denis, 2018. "A simulation comparison of risk measures for portfolio optimization," Finance Research Letters, Elsevier, vol. 24(C), pages 105-112.
    17. 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.
    18. Ukhov, Andrey D., 2006. "Expanding the frontier one asset at a time," Finance Research Letters, Elsevier, vol. 3(3), pages 194-206, September.
    19. Taras Bodnar & Mathias Lindholm & Erik Thorsén & Joanna Tyrcha, 2021. "Quantile-based optimal portfolio selection," Computational Management Science, Springer, vol. 18(3), pages 299-324, July.
    20. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2013. "International portfolio selection with exchange rate risk: A behavioural portfolio theory perspective," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 648-659.

    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:apmaco:v:419:y:2022:i:c:s0096300321009346. 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/applied-mathematics-and-computation .

    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.