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

Mathematical Finance

25 Pages Posted: 21 Nov 2009 Last revised: 5 Jan 2011

Hanqing Jin

Mathematical Institute; Oxford-Man Institute of Quantitative Finance; St. Peter's College

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: January 4, 2011

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

Suggested Citation

Jin, Hanqing and Zhou, Xun Yu, Greed, Leverage, and Potential Losses: A Prospect Theory Perspective (January 4, 2011). Mathematical Finance. Available at SSRN: https://ssrn.com/abstract=1510167

Hanqing Jin (Contact Author)

Mathematical Institute ( email )

Andrew Wiles Building
Radicliff Observatory Quarter, Woodstock Road
Oxford, oxfordshire OX2 6GG
United Kingdom

HOME PAGE: http://www.maths.ox.ac.uk

Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Raod
Oxford, Oxfordshire OX2 6ED
United Kingdom

St. Peter's College ( email )

New Inn Hall Street
Oxford, Oxfordshire OX1 2DL
United Kingdom

HOME PAGE: http://www.spc.ox.ac.uk

Xunyu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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