[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/127311.html
   My bibliography  Save this paper

Downside Risk Aversion vs Decreasing Absolute Risk Aversion: An Intuitive Exposition

Author

Listed:
  • Hammitt, James K.
Abstract
Downside risk aversion (downside RA) and decreasing absolute risk aversion (DARA) are different concepts that describe preferences for which the harm from bearing risk is lessened by an increase in wealth. This note presents some intuitive explanations of the difference between the two concepts using simple lotteries and graphical analysis. All risk-averse utility functions exhibit downside risk aversion, except those that exhibit sufficiently strong increasing absolute risk aversion (IARA). In a sense, downside RA is to be expected: adding downside risk to a baseline lottery is analogous to increasing risk while adding upside risk is analogous to decreasing risk. The difference between the two concepts can be attributed to the use of different measures of the harm from risk bearing: downside RA measures harm using the utility premium and DARA measures harm using the risk premium. The two premia can change at different rates and even in different directions as wealth increases.

Suggested Citation

  • Hammitt, James K., 2022. "Downside Risk Aversion vs Decreasing Absolute Risk Aversion: An Intuitive Exposition," TSE Working Papers 22-1359, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:127311
    as

    Download full text from publisher

    File URL: https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/wp/2022/wp_tse_1359.pdf
    File Function: Full Text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    2. Menegatti, Mario, 2001. "On the Conditions for Precautionary Saving," Journal of Economic Theory, Elsevier, vol. 98(1), pages 189-193, May.
    3. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    4. Gollier, Christian, 2021. "A general theory of risk apportionment," Journal of Economic Theory, Elsevier, vol. 192(C).
    5. Paan Jindapon & Liqun Liu & William S. Neilson, 2021. "Comparative risk apportionment," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 91-112, April.
    6. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
    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. James K. Hammitt, 2023. "Downside risk aversion vs decreasing absolute risk aversion: an intuitive exposition," Theory and Decision, Springer, vol. 95(1), pages 1-10, July.
    2. Menegatti, Mario, 2011. "The risk premium and the effects of risk on agents utility," Research in Economics, Elsevier, vol. 65(2), pages 89-94, June.
    3. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2020. "The theory of precautionary saving: an overview of recent developments," Review of Economics of the Household, Springer, vol. 18(2), pages 513-542, June.
    4. Baiardi, Donatella & De Donno, Marzia & Magnani, Marco & Menegatti, Mario, 2015. "New results on precautionary saving under two risks," Economics Letters, Elsevier, vol. 130(C), pages 17-20.
    5. Eeckhoudt, Louis & Schlesinger, Harris, 2008. "Changes in risk and the demand for saving," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1329-1336, October.
    6. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    7. Michel M. Denuit & Louis Eeckhoudt, 2010. "A General Index of Absolute Risk Attitude," Management Science, INFORMS, vol. 56(4), pages 712-715, April.
    8. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2014. "Precautionary saving under many risks," Journal of Economics, Springer, vol. 113(3), pages 211-228, November.
    9. Eeckhoudt, Louis & Schlesinger, Harris, 2009. "On the utility premium of Friedman and Savage," Economics Letters, Elsevier, vol. 105(1), pages 46-48, October.
    10. Mario Menegatti, 2014. "Optimal choice on prevention and cure: a new economic analysis," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 15(4), pages 363-372, May.
    11. Wang, Hongxia & Wang, Jianli & Li, Jingyuan & Xia, Xinping, 2015. "Precautionary paying for stochastic improvements under background risks," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 180-185.
    12. Loubergé, Henri & Malevergne, Yannick & Rey, Béatrice, 2020. "New Results for additive and multiplicative risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 140-151.
    13. Christophe Courbage & Henri Loubergé & Béatrice Rey, 2018. "On the properties of high-order non-monetary measures for risks," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 77-94, May.
    14. Danau, Daniel, 2020. "Prudence and preference for flexibility gain," European Journal of Operational Research, Elsevier, vol. 287(2), pages 776-785.
    15. David Crainich & Louis Eeckhoudt, 2008. "On the intensity of downside risk aversion," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 267-276, June.
    16. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    17. Vergara, Marcos & Bonilla, Claudio A., 2021. "Precautionary saving in mean-variance models and different sources of risk," Economic Modelling, Elsevier, vol. 98(C), pages 280-289.
    18. Baiardi, Donatella & Manera, Matteo & Menegatti, Mario, 2013. "Consumption and precautionary saving: An empirical analysis under both financial and environmental risks," Economic Modelling, Elsevier, vol. 30(C), pages 157-166.
    19. Marco M. Sorge, 2024. "Even imprudent risk lovers may engage in precautionary saving," Journal of Economics, Springer, vol. 143(1), pages 101-109, September.
    20. Liu, Liqun & Meyer, Jack, 2013. "Substituting one risk increase for another: A method for measuring risk aversion," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2706-2718.

    More about this item

    Keywords

    risk aversion; prudence; risk apportionment; utility premium;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:tse:wpaper:127311. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tsetofr.html .

    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.