IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v81y2015i2p181-233.html
   My bibliography  Save this article

Downside loss aversion: Winner or loser?

Author

Listed:
  • Ines Fortin
  • Jaroslava Hlouskova

Abstract

We study the asset allocation of a quadratic loss-averse (QLA) investor. First, we derive conditions under which the QLA problem is equivalent to the mean-variance (MV) and conditional value-at-risk (CVaR) problems. Then we solve analytically the two-asset problem of the QLA investor for one risk-free and one risky asset. We find that the optimal QLA investment in the risky asset is finite, strictly positive, and minimal with respect to the reference point for a value strictly larger than the risk-free rate. Finally, we implement the trading strategy of a QLA investor who reallocates her portfolio on a monthly basis using 13 EU and 13 US assets. Using risk-adjusted performance measures that do not target specific types of utility we find that QLA portfolios mostly outperform MV and CVaR portfolios; and that incorporating a conservative dynamic update of the QLA parameters, which is based on the historical patterns of bull and bear markets, improves the performance of QLA portfolios. Compared with linear loss-averse portfolios, QLA portfolios display significantly less risk but they also yield lower returns. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Ines Fortin & Jaroslava Hlouskova, 2015. "Downside loss aversion: Winner or loser?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 181-233, April.
    • Handle: RePEc:spr:mathme:v:81:y:2015:i:2:p:181-233
    DOI: 10.1007/s00186-015-0493-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-015-0493-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-015-0493-1?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. Fortin, Ines & Hlouskova, Jaroslava, 2011. "Optimal asset allocation under linear loss aversion," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2974-2990, November.
    2. Berkelaar, Arjan & Kouwenberg, Roy, 2009. "From boom 'til bust: How loss aversion affects asset prices," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1005-1013, June.
    3. André Lucas & Arjen Siegmann, 2008. "The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 35(1‐2), pages 200-226, January.
    4. 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.
    5. Arjen Siegmann & André Lucas, 2005. "Discrete-Time Financial Planning Models Under Loss-Averse Preferences," Operations Research, INFORMS, vol. 53(3), pages 403-414, June.
    6. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(6), pages 808-817, December.
    7. Jaroslava Hlouskova & Jana Mikocziova & Rudolf Sivak & Peter Tsigaris, 2014. "Capital Income Taxation and Risk-Taking under Prospect Theory: The Continuous Distribution Case," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 64(5), pages 374-391, November.
    8. Neilson, William S, 2002. "Comparative Risk Sensitivity with Reference-Dependent Preferences," Journal of Risk and Uncertainty, Springer, vol. 24(2), pages 131-142, March.
    9. Bowman, David & Minehart, Deborah & Rabin, Matthew, 1999. "Loss aversion in a consumption-savings model," Journal of Economic Behavior & Organization, Elsevier, vol. 38(2), pages 155-178, February.
    10. Nicholas Barberis & Ming Huang, 2001. "Mental Accounting, Loss Aversion, and Individual Stock Returns," NBER Working Papers 8190, National Bureau of Economic Research, Inc.
    11. Siegmann, Arjen, 2007. "Optimal investment policies for defined benefit pension funds," Journal of Pension Economics and Finance, Cambridge University Press, vol. 6(1), pages 1-20, March.
    12. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    13. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    14. Robert Jarrow & Feng Zhao, 2006. "Downside Loss Aversion and Portfolio Management," Management Science, INFORMS, vol. 52(4), pages 558-566, April.
    15. Jaroslava Hlouskova & Panagiotis Tsigaris, 2012. "Capital income taxation and risk taking under prospect theory," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 19(4), pages 554-573, August.
    16. Hwang, Soosung & Satchell, Steve E., 2010. "How loss averse are investors in financial markets?," Journal of Banking & Finance, Elsevier, vol. 34(10), pages 2425-2438, October.
    17. O’Connell, Paul G. J. & Teo, Melvyn, 2009. "Institutional Investors, Past Performance, and Dynamic Loss Aversion," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(1), pages 155-188, February.
    18. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    19. Xue Dong He & Xun Yu Zhou, 2011. "Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment," Management Science, INFORMS, vol. 57(2), pages 315-331, February.
    20. André Lucas & Arjen Siegmann, 2008. "The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 35(1‐2), pages 200-226, January.
    21. 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.
    22. Nicholas Barberis & Ming Huang, 2001. "Mental Accounting, Loss Aversion, and Individual Stock Returns," Journal of Finance, American Finance Association, vol. 56(4), pages 1247-1292, August.
    23. Francisco J. Gomes, 2005. "Portfolio Choice and Trading Volume with Loss-Averse Investors," The Journal of Business, University of Chicago Press, vol. 78(2), pages 675-706, March.
    24. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.
    25. Enrico Giorgi & Thorsten Hens, 2006. "Making prospect theory fit for finance," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 20(3), pages 339-360, September.
    26. Zhang, Wenlang & Semmler, Willi, 2009. "Prospect theory for stock markets: Empirical evidence with time-series data," Journal of Economic Behavior & Organization, Elsevier, vol. 72(3), pages 835-849, December.
    27. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fortin, Ines & Hlouskova, Jaroslava & Tsigaris, Panagiotis, 2016. "The Consumption-Investment Decision of a Prospect Theory Household," Economics Series 322, Institute for Advanced Studies.
    2. Jesus Crespo Cuaresma & Ines Fortin & Jaroslava Hlouskova, 2018. "Exchange rate forecasting and the performance of currency portfolios," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 37(5), pages 519-540, August.
    3. Hlouskova, Jaroslava & Fortin, Ines & Tsigaris, Panagiotis, 2017. "The consumption–investment decision of a prospect theory household: A two-period model," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 74-89.
    4. Fortin, Ines & Hlouskova, Jaroslava, 2024. "Prospect theory and asset allocation," The Quarterly Review of Economics and Finance, Elsevier, vol. 94(C), pages 214-240.

    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. Liu, Shuangzhe & Ma, Tiefeng & Polasek, Wolfgang, 2014. "Spatial system estimators for panel models: A sensitivity and simulation study," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 101(C), pages 78-102.
    2. Fortin, Ines & Hlouskova, Jaroslava, 2012. "Optimal Asset Allocation under Quadratic Loss Aversion," Economics Series 291, Institute for Advanced Studies.
    3. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    4. Fortin, Ines & Hlouskova, Jaroslava, 2011. "Optimal asset allocation under linear loss aversion," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2974-2990, November.
    5. Horst Zank, 2010. "On probabilities and loss aversion," Theory and Decision, Springer, vol. 68(3), pages 243-261, March.
    6. Fortin, Ines & Hlouskova, Jaroslava & Tsigaris, Panagiotis, 2016. "The Consumption-Investment Decision of a Prospect Theory Household," Economics Series 322, Institute for Advanced Studies.
    7. Hlouskova, Jaroslava & Fortin, Ines & Tsigaris, Panagiotis, 2017. "The consumption–investment decision of a prospect theory household: A two-period model," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 74-89.
    8. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    9. Michael Best & Robert Grauer & Jaroslava Hlouskova & Xili Zhang, 2014. "Loss-Aversion with Kinked Linear Utility Functions," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 45-65, June.
    10. Bernard, Carole & Ghossoub, Mario, 2009. "Static Portfolio Choice under Cumulative Prospect Theory," MPRA Paper 15446, University Library of Munich, Germany.
    11. Jaroslava Hlouskova & Panagiotis Tsigaris & Anetta Caplanova & Rudolf Sivak, 2017. "A behavioral portfolio approach to multiple job holdings," Review of Economics of the Household, Springer, vol. 15(2), pages 669-689, June.
    12. Fortin, Ines & Hlouskova, Jaroslava, 2024. "Prospect theory and asset allocation," The Quarterly Review of Economics and Finance, Elsevier, vol. 94(C), pages 214-240.
    13. Ghossoub, Mario, 2011. "Towards a Purely Behavioral Definition of Loss Aversion," MPRA Paper 37628, University Library of Munich, Germany, revised 23 Mar 2012.
    14. Fulga, Cristinca, 2016. "Portfolio optimization under loss aversion," European Journal of Operational Research, Elsevier, vol. 251(1), pages 310-322.
    15. Weining Niu & Qingduo Zeng, 2017. "Security issuance and price impact under loss aversion," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-9, June.
    16. Chi, Yichun & Zheng, Jiakun & Zhuang, Shengchao, 2022. "S-shaped narrow framing, skewness and the demand for insurance," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 279-292.
    17. Jaroslava Hlouskova & Jana Mikocziova & Rudolf Sivak & Peter Tsigaris, 2014. "Capital Income Taxation and Risk-Taking under Prospect Theory: The Continuous Distribution Case," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 64(5), pages 374-391, November.
    18. Mohammed Abdellaoui & Han Bleichrodt & Corina Paraschiv, 2007. "Loss Aversion Under Prospect Theory: A Parameter-Free Measurement," Management Science, INFORMS, vol. 53(10), pages 1659-1674, October.
    19. Fulga, Cristinca, 2016. "Portfolio optimization with disutility-based risk measure," European Journal of Operational Research, Elsevier, vol. 251(2), pages 541-553.
    20. Wang, Jianli & Liu, Liqun & Neilson, William S., 2020. "The participation puzzle with reference-dependent expected utility preferences," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 278-287.

    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:spr:mathme:v:81:y:2015:i:2:p:181-233. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.