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Portfolio selection with mental accounts and background risk

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  • Baptista, Alexandre M.

Abstract

Das et al. (2010) develop a model where an investor divides his or her wealth among mental accounts with motives such as retirement and bequest. Nevertheless, the investor ends up selecting portfolios within mental accounts and an aggregate portfolio that lie on the mean–variance frontier. Importantly, they assume that the investor only faces portfolio risk. In practice, however, many individuals also face background risk. Accordingly, our paper expands upon theirs by considering the case where the investor faces background risk. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we show that these portfolios lie away from the mean–variance frontier under fairly general conditions. Third, we find that the composition and location of such portfolios can differ notably from those of portfolios on the mean–variance frontier.

Suggested Citation

  • Baptista, Alexandre M., 2012. "Portfolio selection with mental accounts and background risk," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 968-980.
    • Handle: RePEc:eee:jbfina:v:36:y:2012:i:4:p:968-980
    DOI: 10.1016/j.jbankfin.2011.10.015
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    References listed on IDEAS

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    3. Xi Zhang & Xu Wu & Linlin Zhang & Zhonglu Chen, 2022. "The Evaluation of Mean-Detrended Cross-Correlation Analysis Portfolio Strategy for Multiple risk Assets," Evaluation Review, , vol. 46(2), pages 138-164, April.
    4. 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.
    5. 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.
    6. 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.
    7. Huang, Hung-Hsi & Wang, Ching-Ping, 2013. "Portfolio selection and portfolio frontier with background risk," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 177-196.
    8. 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).
    9. Brandtner, Mario & Kürsten, Wolfgang & Rischau, Robert, 2020. "Beyond expected utility: Subjective risk aversion and optimal portfolio choice under convex shortfall risk measures," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1114-1126.
    10. Kuo-Hwa Chang & Michael Nayat Young, 2019. "Portfolios Optimizations of Behavioral Stocks with Perception Probability Weightings," Annals of Economics and Finance, Society for AEF, vol. 20(2), pages 817-845, November.
    11. Brandtner, Mario, 2018. "Expected Shortfall, spectral risk measures, and the aggravating effect of background risk, or: risk vulnerability and the problem of subadditivity," Journal of Banking & Finance, Elsevier, vol. 89(C), pages 138-149.
    12. Huang, Xiaoxia & Yang, Tingting, 2020. "How does background risk affect portfolio choice: An analysis based on uncertain mean-variance model with background risk," Journal of Banking & Finance, Elsevier, vol. 111(C).
    13. Asgar Ali & K. N. Badhani, 2023. "Tail risk, beta anomaly, and demand for lottery: what explains cross-sectional variations in equity returns?," Empirical Economics, Springer, vol. 65(2), pages 775-804, August.
    14. 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.
    15. 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.
    16. Maxime MERLI & Antoine PARENT, 2022. "Portfolio Diversification During the Belle Époque: When the Actual Portfolios of French Individual Investors Met Behavioral Finance," Working Papers of LaRGE Research Center 2022-01, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    17. Huang, Xiaoxia & Di, Hao, 2016. "Uncertain portfolio selection with background risk," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 284-296.
    18. Silva, Emmanuel Marques & Moreira, Rafael de Lacerda & Bortolon, Patricia Maria, 2023. "Mental Accounting and decision making: a systematic literature review," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 107(C).
    19. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "An analysis of portfolio selection with multiplicative background risk," MPRA Paper 51331, University Library of Munich, Germany.
    20. Hübner, Georges & Lejeune, Thomas, 2021. "Mental accounts with horizon and asymmetry preferences," Economic Modelling, Elsevier, vol. 103(C).

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    More about this item

    Keywords

    Portfolio selection; Mental accounts; Background risk; Behavioral finance;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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