Price formation in parimutuel markets

Abstract

Two types of betting are common in sports betting: fixed odds betting and parimutuel betting. In fixed odds betting, the payout conditional on winning is fixed once the bet is placed and is not affected by the placing of subsequent bets. By contrast, winning bettors in a parimutuel contest share pro-rata in the total betting pool. This means that the payout to winning bettors in a parimutuel contest depends not only on selecting the winning outcome, but also on the amounts bet by other bettors (which cannot be observed at the time a bet is placed). Therefore a parimutuel contest can be viewed as a game at the level of individual bettors. Existing models in the parimutuel literature explain the data by either assuming a single, representative bettor with certain risk preferences or by assuming that a number of risk neutral bettors compete strategically within a game theoretic framework. Our contribution is to construct a novel theoretical framework of parimutuel markets in which we model both strategic interaction and risk preferences at the level of individual insiders, in the presence of exogenous outsiders. We solve this model analytically for the optimal insider betting amount in a static symmetric Nash equilibrium. Using a new dataset of 1.6 million individual horse race bets in New Zealand from 2006 to 2009, we document a strong inverse linear relationship between our model-implied insider risk preferences and the strength of insider beliefs relative to outsiders. That is, as the strength of insiders’ beliefs relative to that of outsiders decrease, implied risk sensitivity moves from risk averse to risk loving. At a level of insider beliefs congruent with actual performance in the data, average implied risk preferences are close to zero, that is, insiders are effectively risk neutral. While risk neutrality is a standard assumption in strategic interaction models of parimutuel betting, our study is the first to provide empirical support for this assumption. Finally, we document a strong relationship (not previously reported in the literature) between the average bet size and the average payout ratio, suggesting that bettors with inside information self-select by placing larger bets.