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## May 04, 2005

### Loss Aversion

WHAT IS LOSS AVERSION?:

Loss aversion, or the tendency for people to prefer avoiding losses over acquiring equivalent gains, is a much-cited psychological concept receiving more and more attention in economic analysis. A recent article presents a behavioral definition of loss aversion and dicusses implications for original and cumulative prospect theory.

ABSTRACT:

"A behavioral definition of loss aversion is proposed and its implications for original and cumulative prospect theory are analyzed. Original prospect theory is in agreement with the new loss aversion condition, and there utility is capturing all effects of loss aversion. In cumulative prospect theory loss aversion is captured by both the weighting functions and the utility function. Further, some restrictions apply for the weighting functions involved in the latter model."

QUOTES:

"It has first been proposed by Kahneman and Tversky (1979) in the framework of prospect theory, and later it has also been defined for choice under certainty by Tversky and Kahneman (1991). The popularity of loss aversion is due to the fact that it can explain many phenomena which remain paradoxes in traditional choice theory. Well-known examples are the endowment effect (Thaler, 1980), the equity premium puzzle (Benartzi and Thaler, 1995), and the status quo bias (Samuelson and Zeckhauser, 1988). In recent years loss aversion has also frequently been applied in behavioral finance (cf. Barberis et al., 2001; Barberis and Huang, 2001; Berkelaar and Kouwenberg, 2000a, b; Roger, 2003; Gomes, 2003). A further important aspect of loss aversion is the fact that it can resolve the criticism on expected utility put forward by Rabin (2000) and Rabin and Thaler (2001)who showed that reasonable degrees of risk aversion for small and moderate stakes imply unreasonable high degrees of risk aversion for large stakes."

"Kahneman and Tversky's (1979, p. 279) view of loss aversion is as follows: An individual is loss averse if she or he dislikes symmetric 50–50 bets and, moreover, the aversiveness to such bets increases with the absolute size of the stakes. This clearly is a behavioral concept defined entirely in terms of preferences. As such, the concept is model independent. Kahneman and Tversky (1979) showed that, in the framework of prospect theory, this definition of loss aversion is equivalent to a utility function which is steeper for losses than for gains. As probability weighting played no role in the derivation of this result, it appears that the effect of loss aversion is captured solely by the utility function. It is, therefore, not surprising that nearly all work on loss aversion employed utility as the carrier of loss aversion. For instance, Tversky and Kahneman (1992, p. 303) assume that utility is steeper for losses than for gains. Wakker and Tversky (1993) propose a preference condition based on a cardinal utility index independent of probability weighting. The latter condition has empirically been confirmed in a recent test in Schmidt and Traub (2002). In a review of non expected utility theories Starmer (2000) highlights the descriptive advantages of rank and sign dependent models, and summarizes loss aversion as utility being steeper for losses than for gains. Benartzi and Thaler (1995) view loss aversion as a property of utility exhibited at the status quo. This view is also adopted in K¨ obberling and Wakker (2003), where an index of loss aversion is defined as the ratio of the left and right derivative of utility at the status quo. All the previous conditions employ a comparison of utility differences between gains and losses of equal absolute size. In contrast Neilson (2002) suggests stronger conditions by dropping this symmetry requirement."

"The way loss aversion is currently understood, it is essential to identify utility independent of probability weights prior to any analysis of loss attitudes. Moreover, given that most definitions of loss aversion are not formulated in terms of pref erences, it follows that loss aversion is no longer model independent. Since most studies mentioned above do not use original prospect theory but the modern cumulative prospect theory instead, their notion of loss aversion does no longer agree with the behavioral concept proposed by Kahneman and Tversky (1979)."

ABOUT THE AUTHORS:

ULRICH SCHMIDT

Lehrstuhl fuer Finanzmarkttheorie, University of Hannover, Germany. The research interets of Ulrich Schmidt are decision theory, public economics, finance and experimental economics. He has publshed more than thirty articles in journals like Management Science, Journal of Public Economics, Journal of Mathematical Economics, Journal of Risk and Uncertainty und Journal of Mathematical Psychology. He is member of the editorial board of Theory and Decision and officer of the Economic Science Association. Homepage.

HORST ZANK

"Horst Zank teaches at the School of Economic Studies, The University of Manchester, UK. Horst received his Master's degree in mathematics from the University of Technology Aachen (Germany) in 1994. He was a PhD student at Maasticht University (the Netherlands) between 1995 and 1999. The topic of his PhD study was "Individual Decision Making under Risk/Uncertainty." From Horst's homepage at the University of Manchester.

Posted by DSN at May 4, 2005 10:50 AM