ORIGINAL ARTICLE
Shortfall aversion
Paolo Guasoni,
Gur Huberman,
Dan Ren,
Corresponding Author
Paolo Guasoni
School of Mathematical Sciences, Dublin City University, Dublin, Ireland
Correspondence
Paolo Guasoni, School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, D09 W6Y4, Ireland.
Email: paolo.guasoni@dcu.ie
Search for more papers by this authorGur Huberman
Columbia Business School, Columbia University, New York, New York
Search for more papers by this authorDan Ren
Department of Mathematics, University of Dayton, Dayton, Ohio
Search for more papers by this authorPaolo Guasoni,
Gur Huberman,
Dan Ren,
Corresponding Author
Paolo Guasoni
School of Mathematical Sciences, Dublin City University, Dublin, Ireland
Correspondence
Paolo Guasoni, School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, D09 W6Y4, Ireland.
Email: paolo.guasoni@dcu.ie
Search for more papers by this authorGur Huberman
Columbia Business School, Columbia University, New York, New York
Search for more papers by this authorDan Ren
Department of Mathematics, University of Dayton, Dayton, Ohio
Search for more papers by this authorFunding information:
Partially supported by the ERC (279582), NSF (DMS-14-12529), and SFI (16/IA/4443, 16/SPP/3347).
All authors have contributed equally to this study.
Abstract
Shortfall aversion reflects the higher utility loss of spending cuts from a reference than the utility gain from similar spending increases. Inspired by Prospect Theory's loss aversion and the peak-end rule, this paper posits a model of utility from spending scaled by past peak spending. In contrast to traditional models, which call for spending rates proportional to wealth, the optimal policy in this model implies a constant spending rate equal to the historical peak when wealth is relatively large. The spending rate increases when wealth reaches a model-determined multiple of peak spending. In 1926–2015, shortfall-averse spending is smooth and typically increasing.
CONFLICT OF INTEREST
The authors do not declare any conflicts of interest.
Open Research
DATA AVAILABILITY STATEMENT
This paper did not generate new data sets. The historical analysis uses data from the Ibbotson yearbook, which is published annually by Ibbotson and Associates.
REFERENCES
- Ang, A., Bekaert, G., & Liu, J. (2005). Why stocks may disappoint. Journal of Financial Economics, 76(3), 471–508.
- Bell, D. E. (1982). Regret in decision making under uncertainty. Operations Research, 30(5), 961–981.
- Blavatskyy, P. (2018). A second-generation disappointment aversion theory of decision making under risk. Theory and Decision, 84(1), 29–60.
- Bleichrodt, H., & Wakker, P. P. (2015). Regret theory: A bold alternative to the alternatives. The Economic Journal, 125(583), 493–532.
- Borodin, A. N., & Salminen, P. (2002). Handbook of Brownian motion: Facts and formulae. Berlin: Springer.
10.1007/978-3-0348-8163-0 Google Scholar
- Bowman, D., Minehart, D., & Rabin, M. (1999). Loss aversion in a consumption–savings model. Journal of Economic Behavior & Organization, 38(2), 155–178.
- Brav, A., Graham, J. R., Harvey, C. R., & Michaely, R. (2005). Payout policy in the 21st century. Journal of Financial Economics, 77(3), 483–527.
- Brown, J., Dimmock, S., Kang, J., & Weisbenner, S. (2014). How university endowments respond to financial market shocks: Evidence and implications. American Economic Review, 104, 931–962.
- Campbell, J. Y., & Cochrane, J. H. (1999). By force of habit: A consumption based explanation of aggregate stock market behavior. Journal of Political Economy, 107(2), 205–251.
- Constantinides, G. (1990). Habit formation: A resolution of the equity premium puzzle. The Journal of Political Economy, 98(3), 519–543.
- Davis, M., & Varaiya, P. (1973). Dynamic programming conditions for partially observable stochastic systems. SIAM Journal on Control, 11(2), 226–261.
- De Neve, J. E., Ward, G., De Keulenaer, F., Van Landeghem, B., Kavetsos, G., & Norton, M. I. (2018). The asymmetric experience of positive and negative economic growth: Global evidence using subjective well-being data. Review of Economics and Statistics, 100(2), 362–375.
- Detemple, J. B., & Karatzas, I. (2003). Non-addictive habits: Optimal consumption-portfolio policies. Journal of Economic Theory, 113(2), 265–285.
- Detemple, J. B., & Zapatero, F. (1991). Asset prices in an exchange economy with habit formation. Econometrica: Journal of the Econometric Society, 59(6), 1633–1657.
- Detemple, J. B., & Zapatero, F. (1992). Optimal consumption-portfolio policies with habit formation1. Mathematical Finance, 2(4), 251–274.
10.1111/j.1467-9965.1992.tb00032.x Google Scholar
- Deusenberry, J. (1949). Income, saving and the theory of consumer behaviour. Cambridge : Harvard University Press.
- Dybvig, P. H. (1995). Dusenberry's ratcheting of consumption: Optimal dynamic consumption and investment given intolerance for any decline in standard. Review of Economic Studies, 62, 287–313.
- Dybvig, P. H. (1999). Using asset allocation to protect spending. Financial Analysts Journal, 55, 49–62.
10.2469/faj.v55.n1.2241 Google Scholar
- Gilbert, T., & Hrdlicka, C. (2012). Fairness and risk-sharing across generations: An application to university and nonprofit endowments. University of Washington Working Paper.
- Gilbert, T., & Hrdlicka, C. (2015). Why are university endowments large and risky? The Review of Financial Studies, 28(9), 2643–2686.
- Guasoni, P., & Huberman, G. (2016). Asset pricing with shortfall aversion. Working Paper.
- Gul, F. (1991). A theory of disappointment aversion. Econometrica, 59(3), 667–686.
- Kahneman, D. (2011). Thinking, fast and slow. New York, NY: Macmillan.
- Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica: Journal of the Econometric Society, 47(2), 263–291.
- Karatzas, I., Lehoczky, J. P., Shreve, S. E., & Xu, G.-L. (1991). Martingale and duality methods for utility maximization in an incomplete market. SIAM Journal on Control and optimization, 29(3), 702–730.
- Karatzas, I., & Shreve, S. E. (1991). Brownian motion and stochastic calculus (Graduate texts in mathematics) (2nd ed., Vol. 113). New York: Springer.
- Kőszegi, B., & Rabin, M. (2006). A model of reference-dependent preferences. Quarterly Journal of Economics, 121(4), 1133–1165.
- Kőszegi, B., & Rabin, M. (2007). Reference-dependent risk attitudes. The American Economic Review, 97(4), 1047–1073.
- Kőszegi, B., & Rabin, M. (2008). Choices, situations, and happiness. Journal of Public Economics, 92(8), 1821–1832.
- Kőszegi, B., & Rabin, M. (2009). Reference-dependent consumption plans. American Economic Review, 99(3), 909–936.
- Lintner, J. (1956). Distribution of incomes of corporations among dividends, retained earnings, and taxes. American Economic Review, 46(2), 97–113.
- Loomes, G., & Sugden, R. (1982). Regret theory: An alternative theory of rational choice under uncertainty. Economic Journal, 92(368), 805–824.
- Markowitz, H. (1952). The utility of wealth. Journal of Political Economy, 60(2), 151–158.
- Menzly, L., Santos, T., & Veronesi, P. (2004). Understanding predictability. Journal of Political Economy, 112(1), 1–47.
- Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economics and Statistics, 51(3), 247–257.
- Merton, R. C. (1993). Optimal investment strategies for university endowment funds. In Studies of supply and demand in higher education (pp. 211–242). University of Chicago Press.
- Merton, R. C. (1971). Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3, 373–413.
- Pagel, M. (2017). Expectations-based reference-dependent life-cycle consumption. Review of Economic Studies, 84(2), 885–934.
- Pagel, M. (2018). A news-utility theory for inattention and delegation in portfolio choice. Econometrica, 86(2), 491–522.
- Rogers, L. C. G., & Williams, D. (2000). Diffusions, Markov processes, and martingales: Volume 1, foundations. Cambridge: Cambridge University Press.
- Routledge, B. R., & Zin, S. E. (2010). Generalized disappointment aversion and asset prices. The Journal of Finance, 65(4), 1303–1332.
- Ryder, H. E., & Heal, G. M. (1973). Optimal growth with intertemporally dependent preferences. The Review of Economic Studies, 40(1), 1–31.
- Santos, T., & Veronesi, P. (2010). Habit formation, the cross section of stock returns and the cash-flow risk puzzle. Journal of Financial Economics, 98(2), 385–413.
- Stutzer, A. (2004). The role of income aspirations in individual happiness. Journal of Economic Behavior & Organization, 54(1), 89–109.
- Sundaresan, S. M. (1989). Intertemporally dependent preferences and the volatility of consumption and wealth. Review of financial Studies, 2(1), 73–89.
- Thillaisundaram, A. (2012). The Merton problem with a drawdown constraint on consumption (Technical report). Cambridge: University of Cambridge.
- Tobin, J. (1974). What is permanent endowment income? American Economic Review, 64(2), 427–432.
- Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and uncertainty, 5(4), 297–323.
- van Bilsen, S., Laeven, R., & Nijman, T. (2019). Consumption and portfolio choice under loss aversion and endogenous updating of the reference level. Management Science.
