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Portfolio Optimization with Mental Accounts

Author

Listed:
  • Das, Sanjiv
  • Markowitz, Harry
  • Scheid, Jonathan
  • Statman, Meir

Abstract

We integrate appealing features of Markowitz’s mean-variance portfolio theory (MVT) and Shefrin and Statman’s behavioral portfolio theory (BPT) into a new mental accounting (MA) framework. Features of the MA framework include an MA structure of portfolios, a definition of risk as the probability of failing to reach the threshold level in each mental account, and attitudes toward risk that vary by account. We demonstrate a mathematical equivalence between MVT, MA, and risk management using value at risk (VaR). The aggregate allocation across MA subportfolios is mean-variance efficient with short selling. Short-selling constraints on mental accounts impose very minor reductions in certainty equivalents, only if binding for the aggregate portfolio, offsetting utility losses from errors in specifying risk-aversion coefficients in MVT applications. These generalizations of MVT and BPT via a unified MA framework result in a fruitful connection between investor consumption goals and portfolio production.

Suggested Citation

  • 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(02), pages 311-334, April.
  • Handle: RePEc:cup:jfinqa:v:45:y:2010:i:02:p:311-334_00
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    5. 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.
    6. Singer, Nico, 2010. "Safety-first portfolio optimization: Fixed versus random target," Thuenen-Series of Applied Economic Theory 113, University of Rostock, Institute of Economics.
    7. Marie Brière & Bastien Drut & Valérie Mignon & Kim Oosterlinck & Ariane Szafarz, 2013. "Is the Market Portfolio Efficient? A New Test of Mean-Variance Efficiency when all Assets are Risky," Finance, Presses universitaires de Grenoble, vol. 34(1), pages 7-41.
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    9. Chiarawongse, Anant & Kiatsupaibul, Seksan & Tirapat, Sunti & Roy, Benjamin Van, 2012. "Portfolio selection with qualitative input," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 489-496.
    10. Jason Scott & John Watson, 2013. "The Floor-Leverage Rule for Retirement," Discussion Papers 13-013, Stanford Institute for Economic Policy Research.
    11. Zhang, Zhichao & Chau, Frankie & Xie, Li, 2012. "Strategic Asset Allocation for Central Bank’s Management of Foreign Reserves: A new approach," MPRA Paper 43654, University Library of Munich, Germany.
    12. Baptista, Alexandre M., 2012. "Portfolio selection with mental accounts and background risk," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 968-980.
    13. Huang, Xiaoxia & Zhao, Tianyi, 2014. "Mean-chance model for portfolio selection based on uncertain measure," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 243-250.
    14. Julián David García-Pulgarín & Javier Gómez-Restrepo & Daniel Vela-Barón, 2015. "An Asset Allocation Framework with Tranches for Foreign Reserves," BORRADORES DE ECONOMIA 013440, BANCO DE LA REPÚBLICA.
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    16. Xu, Guo & Wing-Keung, Wong & Lixing, Zhu, 2013. "Comparisons and Characterizations of the Mean-Variance, Mean-VaR, Mean-CVaR Models for Portfolio Selection With Background Risk," MPRA Paper 51827, University Library of Munich, Germany.
    17. 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.
    18. 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.
    19. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2017. "Portfolio selection with mental accounts and estimation risk," Journal of Empirical Finance, Elsevier, vol. 41(C), pages 161-186.
    20. Ahmed Ibrahim Mokhtar, 2016. "An Empirical Examination of the Behavioral CAPM," Journal of Finance and Investment Analysis, SCIENPRESS Ltd, vol. 5(3), pages 1-2.
    21. Cai, Jun & Ge, Chenliang, 2012. "Multi-objective private wealth allocation without subportfolios," Economic Modelling, Elsevier, vol. 29(3), pages 900-907.
    22. Singer, Nico, 2011. "A behavioral portfolio analysis of retirement portfolios," Thuenen-Series of Applied Economic Theory 104, University of Rostock, Institute of Economics.
    23. David Ardia & Kris Boudt, 2013. "Implied Expected Returns and the Choice of a Mean-Variance Efficient Portfolio Proxy," Cahiers de recherche 1328, CIRPEE.

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