Inferring Risk Preferences Using Synthetic Win Bets in Horse Betting “Exotic” Markets
AbstractExotic bets: exactas, trifectas and superfectas are complicated gambles that depend on the ordering of horse in a race that can be studied by converting them into “synthetic” or “virtual” win bets. Using two ways of constructing synthetic win bets, it is shown that the favorite-longshot bias is a poor description of the returns of the trifecta and superfecta synthetic win bet. Rather, consistent with financial markets, the standard deviation of the payout of the synthetic win bet better describes the different returns of synthetic win bets.It is found that the synthetic win market dislikes standard deviation and kurtosis (and other higher-order even moments) and likes skewness (and other higher order odd moments), implying participants conform to standard utility theory in their choice between win and synthetic win bets and are not risk-loving. A co-efficient of relative risk aversion of about 3 is estimated. Including higher-order moments strongly affects the magnitude of utility function estimates.
Ali, M. (1977) “Probability and utility estimates for racetrack bettors.” Journal of Political Economy, 84, 803-815.
Asch, P, and B. Malkiel (1987), “Efficiency and profitability in Exotic Bets,” Economica 54, 453-464.
Asch, P, B. Malkiel, R.E. Quandt (1984), “Market Efficiency in Racetrack Betting,” Journal of Business 57, 164-174.
Barberis, N and M. Huang (2004), “Stocks as Lotteries: The Implications of Probability Weighting for Security Prices,” Yale University working paper.
Cain, M. and D. Peel. (2004) “Utility and the Skewness of Return in Gambling,” Geneva Papers on Risk and Insurance Theory. Dec 2004. Vol. 29, Iss. 2; p. 145
Cain, M., D. Law, and D. Peel (2003), “The Favorite-Longshot Bias, Bookmaker Margins and Insider Trading in a Variety of Betting Markets,” Bulletin of Economic Research, 55(3), 307
Coleman (2004), “New Light on the Longshot Bias,” Applied Economics, 36, 315-326.
Eeckhoudt, L., and H. Schlesinger (2006), “Putting Risk in Its Proper Place,” The American Economic Review, 96(1), March:280-289.
Eisenhauer, J. G. (2005) "Estimating prudence." Eastern Economic Journal 26(4): 379.
Fama, E., K. French (1992) “The Cross-Section of Expected Stock Returns,” Journal of Finance, 47(2), 427-465.
Golec and Tamarkin (1998) “Bettors want Skewness not Risk at the Racetrack,” Journal of Political Economy, 106(1), 205-26.
Gramm, M, C.N McKinney, and D. Owens “The Efficiency of Exotic Wagers in Racetrack Betting,” forthcoming Applied Economics.
Harvey, C. and A. Siddique (2000), “Conditional Skewness in Asset Pricing Tests,” Journal of Finance, 55, 1263-1295.
Harville, D. (1973) “Assigning Probabilities to the Outcomes of Multi-Entry Competitions,” Journal of the American Statistical Association, 68, 312-316.
Hausch, D., V. Lo, and W. Ziemba “Pricing Exotic Racetrack Wagers,” reprinted in Efficiency of Racetrack Betting Markets, 1994, Academic Press, 469-484.
Hausch, D., V. Lo, and W. Ziemba “Introduction to Psychological Studies,” in Efficiency of Racetrack Betting Markets, 1994, Academic Press, pp. 7-8.
Hausch, D., V. Lo, and W. Ziemba “Introduction to Utility Preferences of Racetrack Bettors,” in Efficiency of Racetrack Betting Markets, 1994, Academic Press, pp. 39-40.
Hlawitschka, W. (1994), “The Empirical Nature of Taylor-Series Approximations to expected Utility,” American Economic Review, 84(3), June: 713-719.
Ingersoll, J.E. Jr. (1987), Theory of Financial Decision Making, Rowman & Little Publishers, Inc.
Kanto, A, and G. Rosenqvist “On the Efficiency of the Market for Double (Quinella) Bets at a Finnish Racetrack, in Efficiency of Racetrack Betting Markets, 1994, Academic Press, pp.485-498.
Mehra, R., and E. Prescott (1985), “The Equity Premium: a Puzzle” Journal of Monetary Economics, 15, 145-161.
O'Connor, P., (June 2007) "The Economic Significance of the Longshot Bias in Horse Race Wagering". Available at SSRN: http://ssrn.com/abstract=997789
Post and Levy (2005), “Does Risk Seeking Drive Stock Prices? A Stochastic Dominance Analysis of Aggregate Investor Preferences and Beliefs”, Review of Financial Studies, 18(3), 925-953.
Thaler, R, and W. Ziemba (1998) “Parimutuel Betting Markets: Racetracks and Lotteries,” Journal of Economic Perspectives, 2, 161-174.
Vannebo, O. (1980), “Horse Racing: Testing the Efficient Markets Model: Comment,” Journal of Finance, 35, 201-202.
Wolf, C., and L. Pohlman (1983), “The recovery of risk preferences from actual choices" Econometrica, 51(3), 843-850.