Consumption and Portfolio Choice Under Loss Aversion and Endogenous Updating of the Reference Level

Abstract

We explicitly derive and explore the optimal consumption and portfolio policies of a lossaverse individual who endogenously updates his reference level over time. We find that he protects his current consumption by delaying painful reductions in consumption after a drop in wealth, and increasingly so with higher degrees of endogeneity. The incentive to protect current consumption is stronger with a medium wealth level than with a high or low wealth level. Furthermore, this individual adopts a conservative investment strategy in normal states and typically a more aggressive strategy in good and bad states. Endogeneity of the reference level increases overall risk-taking and generates an incentive to reduce risk exposure with age even without human capital. The welfare loss that this individual would suffer under the conventional CRRA consumption and portfolio policies typically exceeds 10%.

Consumption and Portfolio Choice under Internal Multiplicative Habit Formation

“…Several authors have explored the implications of these alternative preference theories for optimal investment decisions or intertemporal consumption behavior (see, e.g., Bowman, Minehart, and Rabin (1999), Berkelaar, Kouwenberg, and Post (2004), Ang, Bekaert, and Lui (2005), Muermann, Mitchell, and Volkman (2006), Guasoni, Huberman, and Ren (2015), Pagel (2017), and Bilsen et al (2020)). Most relevant to our baseline model are Zapatero (1991), (1992), Schroder and Skiadas (2002), Bodie, Detemple, Otruba, and Walter (2004), and Munk (2008), who analyze the optimal consumption and investment behavior of an individual who derives utility from the difference between consumption and an internal habit level rather than some ratio of these, as we do.…”

“…More specifically, the individual in our baseline model lowers the share of his portfolio invested in the risky stock as he becomes older. Indeed, the available time to adjust current and future consumption levels in response to a stock return shock declines with age.11 For the classical implications of human capital on the optimal portfolio allocation, seeBodie, Merton, and Samuelson (1992) andCocco, Gomes, and Maenhout (2005).12 The second effect may explain why not many young individuals include long-term bonds in their investment portfolios; seeMorningstar (2017) for the investment behavior of long-term investors.13 The closest to the current paper in this respect isSchroder and Skiadas (1999), who analytically study Epstein-Zin utility but do not consider multiplicative internal habits.14 See, for example,Bilsen, Laeven, and Nijman (2020), who employSchroder and Skiadas (2002) to explicitly derive the optimal consumption and portfolio policies under loss aversion and endogenous updating of the reference level, two key features of prospect theory(Tversky and Kahneman (1992)). …”