Greed, Leverage, and Potential Losses: A Prospect Theory Perspective

Abstract

This paper quantifies the notion of greed, and explores its connection with leverage and potential losses, in the context of a continuous-time behavioral portfolio choice model under (cumulative) prospect theory. We argue that the reference point can serve as the critical parameter in defining greed. An asymptotic analysis on optimal trading behaviors when the pricing kernel is lognormal and the S-shaped utility function is a two-piece CRRA shows that both the level of leverage and the magnitude of potential losses will grow unbounded if the greed grows uncontrolled. However, the probability of ending with gains does not diminish to zero even as the greed approaches infinity. This explains why a sufficiently greedy behavioral agent, despite the risk of catastrophic losses, is still willing to gamble on potential gains because they have a positive probability of occurrence whereas the corresponding rewards are huge. As a result an effective way to contain human greed, from a regulatory point of view, is to impose a priori bounds on leverage and/or potential losses.

Keywords: Cumulative prospect theory, greed, leverage, gains and losses, reference point, portfolio choice

JEL Classification: C61, G11