Optimal Betting Odds Against Insider Traders

“For the favourite-longshot bias phenomena there exist a variety of explanations such as risk attitudes in form of risk-loving utility of gamblers (Ali (1977), Quandt (1986)) or insider trading introduced by Shin (1991, 1993).”

“The market microstructure literature (e.g. Glosten and Milgrom (1985) for financial markets, and Shin (1991, 1992, 1993) for betting markets) would suggest that as the proportion of informed traders declines, ceteris paribus, the odds will increase.”

“9 Thus, our model accommodates models of both heterogeneous risk attitudes, such as Weitzman (1965) and Quandt (1986), and heterogeneous beliefs, such as Ali (1977), Blough (1994), and Watanabe (1997).”

“Potential reasons for the longshot bias can be risk-hedging pricing strategies of betting providers against insider trading (Cain et al. 2003, Shin 1991, 1992, 1993), bettors’ overconfidence or image effects (Direr 2011, Golec & Tamarkin 1995, Williams 1999), bettors’ willingness to especially make…”

“Second, Shin (1991, 1992, 1993) shows that bookmakers may deviate from the true prices to hedge themselves from bettors with superior information.”

“There are studies on reverse FLB in other sports betting markets outside of horse tracks, including Swidler and Shaw (1995) and Schnytzer and Weinberg (2008).”

“In particular, we obtain the probability to be champion of each national team from different bookmakers using the Shin (1993) procedure, and given that just two teams achieve the final match, we standardize the probability between each possible final match combination, so we get 496 combinations for four bookmakers.”

“In a series of papers Shin (1991, 1992, 1993) has provided an explanation for the favourite± longshot bias in betting markets where bookmakers set odds.”

“Proposed explanations include risk-loving preferences over longshots [13], bookmaker behavior in the presence of insider traders [14], and bookmaker risk aversion in competitive fixed-odds markets [16].”

“Consequently, we develop the following CL function to test hypothesis 3, which includes an interaction term between Shin z and the betting volume on each horse in the race: In order to determine the appropriate function, f ( z ), to include in Equation (8) , we seek to confirm Shin's (1991) prediction of a linear rela…”

“…to the classical account of bookmaker margins, in which both the margin and the favorite–longshot bias arise from the threat of privately informed insiders [Shin, 1991, 1992]; here no informed trader is required, only a marginal taste for favorites meeting a handicap that makes that taste costly.”

“Shin [6,8,9] proposed Shin probabilities based on the assumption that bookmakers quote odds that maximize their expected profit in the presence of uninformed bettors and a known proportion of “insider” traders.”

“Among explanations that involve private information, we find the idea (Shin, 1991) that bookmakers have customers with insider information whom they cannot distinguish from customers with only public information.”

“In the case of fixed-odds bookmakers’ markets, a f/l bias is uniformly observed (see, for example, Shin, 1991, 1992 and 1993, Vaughan Williams and Paton 1997 and Schnytzer and Shilony, 2003 and 2005).”

“An advantage of employing bookmaker odds is that Shin (1991, 1992, 1993) has developed a theoretical model of the manner in which bookmakers set odds that generates the favourite–longshot bias and enables computation of winning probabilities that correct for the favourite– longshot bias conditional…”