Rationality on the rise: Why relative risk aversion increases with stake size

Abstract

How does risk tolerance vary with stake size? This important question cannot be adequately answered if framing effects, nonlinear probability weighting, and heterogeneity of preference types are neglected. We show that the increase in relative risk aversion over gains cannot be captured by the curvature of the utility function. It is driven predominantly by a change in probability weighting of a majority group of individuals who exhibit more rational probability weighting at high stakes. Contrary to gains, no coherent change in relative risk aversion is observed for losses. These results not only challenge expected utility theory, but also prospect theory.

Stake effects on ambiguity attitudes for gains and losses

“…For risky losses, we found no evidence of stake effects. This goes towards further clarifying the previous findings, with, e.g., (Schoemaker 1990) finding no effect of stakes on risk attitudes for losses, while Fehr-Duda et al (2010) found inconclusive effects of stakes and Bosch-Domènech and Silvestre (2006) found rather strong effects. Vieider (2012) found some effects of stake size on probability weighting functions for losses, which were however counteracted by opposite effects on utility, with the overall effect thus tending towards no difference.…”

“…Kachelmeier and Shehata (1992) ran high stakes experiments in China, finding that risk seeking for small probabilities was reduced relative to smaller stakes, a result that was replicated by Lefebvre et al (2010) in France using a between subjects design. Holt and Laury (2002) supplied further evidence on how subjects become more risk averse as stakes increase, and Fehr-Duda et al (2010) showed with Chinese subjects how, in a prospect theory framework, such stake effects will affect the probability weighting function as well as the utility function, thus violating the separability precept by which attitudes towards money are supposed to be reflected purely in utility (although this may, to some extent, depend on the functional form of utility-see Scholten and Read (2014), and Bouchouicha and Vieider (2016)). …”

“…Bosch-Domènech and Silvestre (2006), on the other hand, found large increases in risk aversion for both small and large probabilities of losses as stakes increased. Fehr-Duda et al (2010) found inconclusive effects in the loss domain. Moreover, there exist several papers investigating the issue of whether hypothetical choice differs from choices for real money under losses (Etchart-Vincent and L'Haridon 2011; Laury et al 2009;Schoemaker 1990;Vieider 2011), which is, however, quite a different issue.…”

Beware of black swans: Taking stock of the description–experience gap in decision under uncertainty

“…Experimental evidence suggests that the probability weighting function is systematically affected by specific characteristics of the decision situation, whereas the curvature of the utility function is not (Fehr-Duda and Epper 2012). For example, departures from linear weighting are more pronounced for more emotional consequences such as an electric shock than for less emotional consequences such as a financial payment (Rottenstreich and Hsee 2001), and high-stake prospects are evaluated less optimistically than low-stake prospects (Fehr-Duda et al 2010). People typically exhibit aversion to betting on ambiguous events (Ellsberg 1961), particularly when they feel relatively ignorant or incompetent assessing those events (Heath and Tversky 1991;Fox and Tversky 1995;Fox and Weber 2002) although ambiguity seeking is occasionally observed, especially for losses (Camerer and Weber 1992).…”

Selling Money on Ebay: A Field Study of Surplus Division

“…34 The regression results do not support this hypothesis (see Tables 4-9 in Appendix). Similarly, the paper by Fehr-Duda et al (2010) demonstrates that for amounts similar to our stakes the risk aversion is not identifiable in the data.…”