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Portfolio Optimization with Mental Accounts

Author

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  • 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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    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. James M. Poterba & Lawrence H. Summers, 1984. "The Persistence of Volatility and Stock Market Fluctuations," Working papers 353, Massachusetts Institute of Technology (MIT), Department of Economics.
    3. Pong, Shiuyan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2004. "Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2541-2563, October.
    4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, pages 579-625.
    5. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
    6. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, pages 478-539.
    7. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    8. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, pages 83-106.
    9. Deo, Rohit & Hurvich, Clifford & Lu, Yi, 2006. "Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 29-58.
    10. Chip Heath & Steven Huddart & Mark Lang, 1999. "Psychological Factors and Stock Option Exercise," The Quarterly Journal of Economics, Oxford University Press, vol. 114(2), pages 601-627.
    11. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    12. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    13. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, pages 127-158.
    14. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    15. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    16. Karolyi, G. Andrew, 1993. "A Bayesian Approach to Modeling Stock Return Volatility for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(04), pages 579-594, December.
    17. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    18. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    19. Poterba, James M & Summers, Lawrence H, 1986. "The Persistence of Volatility and Stock Market Fluctuations," American Economic Review, American Economic Association, pages 1142-1151.
    20. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    21. Huddart, Steven & Lang, Mark, 1996. "Employee stock option exercises an empirical analysis," Journal of Accounting and Economics, Elsevier, vol. 21(1), pages 5-43, February.
    22. Carpenter, Jennifer N & Remmers, Barbara, 2001. "Executive Stock Option Exercises and Inside Information," The Journal of Business, University of Chicago Press, vol. 74(4), pages 513-534, October.
    23. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
    24. repec:bla:joares:v:36:y:1998:i:2:p:231-255 is not listed on IDEAS
    25. Lev, Baruch, 1983. "Some economic determinants of time-series properties of earnings," Journal of Accounting and Economics, Elsevier, vol. 5(1), pages 31-48, April.
    26. Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September.
    27. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    28. Huddart, Steven & Lang, Mark, 2003. "Information distribution within firms: evidence from stock option exercises," Journal of Accounting and Economics, Elsevier, vol. 34(1-3), pages 3-31, January.
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    Cited by:

    1. Johansen, Kathrin & Singer, Nico, 2012. "Chasing rainbows: On the relationship between lottery tickets and common stocks," Thuenen-Series of Applied Economic Theory 129, University of Rostock, Institute of Economics.
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2017. "Portfolio selection with mental accounts and estimation risk," Journal of Empirical Finance, Elsevier, pages 161-186.
    9. Julián David García-Pulgarín & Javier Gómez-Restrepo & Daniel Vela-Barón, 2015. "An Asset Allocation Framework with Tranches for Foreign Reserves," Borradores de Economia 899, Banco de la Republica de Colombia.
    10. repec:dau:papers:123456789/9297 is not listed on IDEAS
    11. Chiu, Wan-Yi & Jiang, Ching-Hai, 2016. "On the weight sign of the global minimum variance portfolio," Finance Research Letters, Elsevier, vol. 19(C), pages 241-246.
    12. Das, Sanjiv R. & Statman, Meir, 2013. "Options and structured products in behavioral portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 137-153.
    13. Singer, Nico, 2010. "Safety-first portfolio optimization: Fixed versus random target," Thuenen-Series of Applied Economic Theory 113, University of Rostock, Institute of Economics.
    14. Li Xie & Wing Thye Woo & Zhichao Zhang & Zhuang Zhang, 2015. "A Multiple-Goal Investment Strategy for Sovereign Wealth Funds: An Application to China," Asian Economic Papers, MIT Press, vol. 14(1), pages 78-97, Winter/Sp.
    15. 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.
    16. Jason Scott & John Watson, 2013. "The Floor-Leverage Rule for Retirement," Discussion Papers 13-013, Stanford Institute for Economic Policy Research.
    17. Baptista, Alexandre M., 2012. "Portfolio selection with mental accounts and background risk," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 968-980.
    18. 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.
    19. 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.
    20. Cai, Jun & Ge, Chenliang, 2012. "Multi-objective private wealth allocation without subportfolios," Economic Modelling, Elsevier, vol. 29(3), pages 900-907.
    21. Singer, Nico, 2011. "A behavioral portfolio analysis of retirement portfolios," Thuenen-Series of Applied Economic Theory 104, University of Rostock, Institute of Economics.
    22. Behrens, Kristian & Bougna, Théophile, 2015. "An anatomy of the geographical concentration of Canadian manufacturing industries," Regional Science and Urban Economics, Elsevier, pages 47-69.

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