IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v52y2006i4p558-566.html
   My bibliography  Save this article

Downside Loss Aversion and Portfolio Management

Author

Listed:
  • Robert Jarrow

    () (Johnson Graduate School of Management, Cornell University, Ithaca, New York 14853)

  • Feng Zhao

    () (Rutgers Business School, Rutgers University, Newark, New Jersey 07102)

Abstract

Downside loss-averse preferences have seen a resurgence in the portfolio management literature. This is due to the increasing use of derivatives in managing equity portfolios and the increased use of quantitative techniques for bond portfolio management. We employ the lower partial moment as a risk measure for downside loss aversion and compare mean-variance (M-V) and mean-lower partial moment (M-LPM) optimal portfolios under nonnormal asset return distributions. When asset returns are nearly normally distributed, there is little difference between the optimal M-V and M-LPM portfolios. When asset returns are nonnormal with large left tails, we document significant differences in M-V and M-LPM optimal portfolios. This observation is consistent with industry usage of M-V theory for equity portfolios but not for fixed-income portfolios.

Suggested Citation

  • Robert Jarrow & Feng Zhao, 2006. "Downside Loss Aversion and Portfolio Management," Management Science, INFORMS, vol. 52(4), pages 558-566, April.
  • Handle: RePEc:inm:ormnsc:v:52:y:2006:i:4:p:558-566
    DOI: 10.1287/mnsc.1050.0486
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1050.0486
    Download Restriction: no

    References listed on IDEAS

    as
    1. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    2. Jun Liu & Francis A. Longstaff & Jun Pan, 2003. "Dynamic Asset Allocation with Event Risk," Journal of Finance, American Finance Association, vol. 58(1), pages 231-259, February.
    3. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    4. Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558, arXiv.org, revised Oct 2002.
    5. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(6), pages 808-817, December.
    6. James R. Melvin, 1974. "A Theory of Leisure," Eastern Economic Journal, Eastern Economic Association, vol. 1(4), pages 251-267, October.
    7. Robert Jarrow, 2002. "Put Option Premiums and Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 135-142, April.
    8. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    9. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    10. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    11. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Abstract: Capital Market Equilibrium in a Mean-Lower Partial Moment Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 635-635, November.
    12. Liu, Jun & Longstaff, Francis & Pan, Jun, 2001. "Dynamic Asset Allocation with Event Risk," University of California at Los Angeles, Anderson Graduate School of Management qt9fm6t5nb, Anderson Graduate School of Management, UCLA.
    13. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    14. D. A. L. Auld, 1974. "Advertising and the Theory of Consumer Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 88(3), pages 480-487.
    15. Frey, Rudiger & McNeil, Alexander J., 2002. "VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1317-1334, July.
    16. Bawa, Vijay S., 1978. "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(2), pages 255-271, June.
    17. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    18. Harlow, W. V. & Rao, Ramesh K. S., 1989. "Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(3), pages 285-311, September.
    19. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Capital market equilibrium in a mean-lower partial moment framework," Journal of Financial Economics, Elsevier, vol. 5(2), pages 189-200, November.
    20. Grootveld, Henk & Hallerbach, Winfried, 1999. "Variance vs downside risk: Is there really that much difference?," European Journal of Operational Research, Elsevier, vol. 114(2), pages 304-319, April.
    21. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
    22. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    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. Fulga, Cristinca, 2016. "Portfolio optimization under loss aversion," European Journal of Operational Research, Elsevier, vol. 251(1), pages 310-322.
    2. Anthonisz, Sean A., 2012. "Asset pricing with partial-moments," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2122-2135.
    3. Elie Matta & Jean McGuire, 2008. "Too Risky to Hold? The Effect of Downside Risk, Accumulated Equity Wealth, and Firm Performance on CEO Equity Reduction," Organization Science, INFORMS, vol. 19(4), pages 567-580, August.
    4. Zhangxin (Frank) Liu & Michael J. O'Neill, 2018. "Partial moment volatility indices," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 58(1), pages 195-215, March.
    5. Ayub, Usman & Shah, Syed Zulfiqar Ali & Abbas, Qaisar, 2015. "Robust analysis for downside risk in portfolio management for a volatile stock market," Economic Modelling, Elsevier, vol. 44(C), pages 86-96.
    6. Hildebrandt, Patrick & Knoke, Thomas, 2011. "Investment decisions under uncertainty--A methodological review on forest science studies," Forest Policy and Economics, Elsevier, vol. 13(1), pages 1-15, January.
    7. Bertsimas, Dimitris & Lauprete, Geoffrey J. & Samarov, Alexander, 2004. "Shortfall as a risk measure: properties, optimization and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1353-1381, April.
    8. León, Angel & Moreno, Manuel, 2017. "One-sided performance measures under Gram-Charlier distributions," Journal of Banking & Finance, Elsevier, vol. 74(C), pages 38-50.
    9. Basu, Anup K. & Drew, Michael E., 2010. "The appropriateness of default investment options in defined contribution plans: Australian evidence," Pacific-Basin Finance Journal, Elsevier, vol. 18(3), pages 290-305, June.
    10. Schuhmacher, Frank & Auer, Benjamin R., 2014. "Sufficient conditions under which SSD- and MR-efficient sets are identical," European Journal of Operational Research, Elsevier, vol. 239(3), pages 756-763.
    11. Chen, Zhiping & Wang, Yi, 2008. "Two-sided coherent risk measures and their application in realistic portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2667-2673, December.
    12. León, Ángel & Moreno, Manuel, 2015. "Lower Partial Moments under Gram Charlier Distribution: Performance Measures and Efficient Frontiers," QM&ET Working Papers 15-3, University of Alicante, D. Quantitative Methods and Economic Theory.
    13. Niv Nayman, 2018. "Shortfall Risk Minimization Under Fixed Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-29, August.
    14. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, Michael, 2006. "Master funds in portfolio analysis with general deviation measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 743-778, February.
    15. Cumova, Denisa & Nawrocki, David, 2011. "A symmetric LPM model for heuristic mean-semivariance analysis," Journal of Economics and Business, Elsevier, vol. 63(3), pages 217-236, May.
    16. Lwin, Khin T. & Qu, Rong & MacCarthy, Bart L., 2017. "Mean-VaR portfolio optimization: A nonparametric approach," European Journal of Operational Research, Elsevier, vol. 260(2), pages 751-766.
    17. De Giorgi, Enrico & Hens, Thorsten & Mayer, Janos, 2011. "A note on reward-risk portfolio selection and two-fund separation," Finance Research Letters, Elsevier, vol. 8(2), pages 52-58, June.
    18. Cumova, Denisa & Nawrocki, David, 2014. "Portfolio optimization in an upside potential and downside risk framework," Journal of Economics and Business, Elsevier, vol. 71(C), pages 68-89.
    19. Shushang Zhu & Duan Li & Shouyang Wang, 2009. "Robust portfolio selection under downside risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 869-885.
    20. Brogan, Anita J. & Stidham Jr., Shaler, 2008. "Non-separation in the mean-lower-partial-moment portfolio optimization problem," European Journal of Operational Research, Elsevier, vol. 184(2), pages 701-710, January.

    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:inm:ormnsc:v:52:y:2006:i:4:p:558-566. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Matthew Walls). General contact details of provider: http://edirc.repec.org/data/inforea.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.