Information and Attitudes to Risk at the Track

Abstract There have been many attempts, theoretical and empirical, to explain the persistence of a favorite-longshot bias in various horse betting markets. Most recently, Snowberg and Wolfers (2010) have shown that the data for the US markets support a misperceptions of probability approach in line with prospect theory over a neoclassical approach of the Quandt (1986) type. However, their paper suffers from two basic difficulties which beset much of this literature. First, the theoretical model used fails to allow for the existence of horse betting markets which either display no such bias (or a reverse bias) as in Hong Kong and at least one large Australian market (Busche and Hall, 1988, Schnytzer, Shilony and Thorne, 2003 and Luppi and Schnytzer, 2008). Second, econometric testing and theoretical modeling are facilitated by the highly unrealistic assumption that the betting population is homogeneous with respect to either information or attitude to risk or (usually) both. Our purpose is to show that allowing for heterogeneous betting populations (in terms of both attitude to risk and access to information) permits the explanation for the different biases (or their absence) observed in different markets within a strictly neoclassical framework of rational bettors. We conclude with empirical support for our model.

A General Index of Inherent Risk

We extend the pioneering work of Aumann and Serrano by presenting an index of inherent riskiness of a gamble having the desirable properties of their index, while being applicable to gambles with either positive or negative expectations. As such, our index provides a measure of riskiness which is of use for both risk lovers and risk aversive gamblers, and is defined for all discrete and a large class of continuous gambles. We analyze abstract properties of our index, and present in addition three empirical applications - roulette, horse betting market and US options traded on financial stocks between 2005 and 2007.

Attitudes to Risk and Roulette

We present an empirical framework for determining whether or not customers at the roulette wheel are risk averse or risk loving. Thus, we present a summary of the Aumann-Serrano (2007) risk index as generalized to allow for the presence of risk lovers by Schnytzer and Westreich (2010). We show that, for any gamble, whereas riskiness increases for gambles with positive expected return as the amount placed on a given gamble is increased, the opposite is the case for gambles with negative expected return. Since roulette involves binary gambles, we restrict our attention to such gambles exclusively and derive empirically testable hypotheses. In particular, we show that, all other things being equal, for gambles with a negative expected return, riskiness decreases as the size of the contingent payout increases. On the other hand, riskiness increases if the gamble has a positive expected return. We also prove that, for positive return gambles, riskiness increases, ceteris paribus, in the variance of the gamble while the reverse is true for gambles with negative expected returns. Finally, we apply these results to the specific gambles involved in American roulette and discuss how we might distinguish between casino visitors who are risk averse and those who are risk loving as well as those who may suffer from gambling addictions of one form or another.

False Consciousness in Financial Markets: Or is it in Ivory Towers?

In general, models in finance assume that investors are risk averse. An example of such a recent model is the pioneering work of Aumann and Serrano, which presents an economic index of riskiness of gambles which is independent of wealth and holds (as might be understood from the adjective “economic”) for exclusively risk averse investors. In their paper, they discuss gambles with positive expected returns which will be accepted or rejected by agents which different levels of risk aversion. The question never asked by the authors (and in most of the finance literature) is: Who is offering these attractive gambles? To arrive at an answer, we extend the Aumann-Serrano risk index in such a way that it accommodates gambles with either positive or negative expectations and is thus suitable for both the risk averse and risk lovers. Once we allow for the existence of risk lovers, it may be shown that in financial markets, many gambles with negative expectations are taken either knowingly or unknowingly so that there are always people that act as if they are risk lovers. The paper concludes with a brief discussion of the implications of our result, in particular that gambling is by no means restricted to the casino or the track.