OPTIMAL PRICE SETTING IN FIXED‐ODDS BETTING MARKETS UNDER INFORMATION UNCERTAINTY

This paper develops a model of optimal pricing under information uncertainty for fixed‐odds betting markets. The model suggests that bookmakers require a premium for quoting the odds several days before an event. This premium reflects the uncertainty of public information that can be exploited by expert bettors. The model predicts that when bookmakers set optimal prices, expected returns to bettors increase as a monotonic function of winning probabilities. In this manner, an information‐based explanation is given for the celebrated favourite‐longshot bias in fixed‐odds. Using an extensive data‐set of football odds from two major European bookmakers, we estimate the probability of informed betting.     

What drives intermediation costs? A case of tennis betting market

We demonstrate that there is a considerable variation in bookmaker margins across matches, time and bookmakers. Our results imply that using match, tournament and players’ characteristics explains the variations in margins hence, they can be helpful in managing intermediation cost in a market of state-contingent assets: fixed-odds betting markets. We also provide evidence that bookmakers protect themselves by increasing odds on the favourite player, thus attracting more bettors to the favourite player, while deterring bettors from betting on the underdog by reducing the odds. By that process, bookmakers are possibly sacrificing a portion of their margin.     

Game,set and match: the favourite-long shot bias in tennis betting exchanges

We test for the existence of Favourite-Longshot Bias (FLB) in tennis betting exchanges. Despite these being order-driven markets, with no direct participation from bookmakers, we have found very similar results to those obtained by Lahvi?ka (2014) for bookmakers’ betting markets: the bias is stronger in matches between lower-ranked players, in later round matches and in high profile tournaments. This suggests that bookmakers’ adjustments to respond to informed betting are not the main driver of FLB. The varying magnitude of the bias across different types of event in the main market also weakens arguments linking FLB to gamblers’ risk preferences, and suggests the need to consider the microstructure features of the market together with the cognitive biases highlighted in the behavioural finance literature.     

The house doesn’t always win: Evidence of anchoring among Australian bookies

We examine Australian horseracing bookmakers’ responses to late scratches, instances in which a horse is abruptly withdrawn after betting has commenced. Our observed bookies exhibit anchoring on the original odds and fail to re-adjust odds fully on the remaining horses after a scratch, thereby earning lower profit margins and occasionally creating nominal arbitrage opportunities for bettors. We also examine which horses’ odds bookies adjust after a scratch and demonstrate diminished profit margins even after controlling for these endogenous adjustments. Our results indicate that bookies’ adjustments recover approximately 80% of lost profit margin but that bookies forgo the remaining 20% due to systematic under-adjustments.     

Do bookmakers possess superior skills to bettors in predicting outcomes?

In this paper we test the hypothesis that bookmakers display superior skills to bettors in predicting the outcome of sporting events by using matched data from traditional bookmaking and person-to-person exchanges. Employing a conditional logistic regression model on horse racing data from the UK we find that, in high liquidity betting markets, betting exchange odds have more predictive value than the corresponding bookmaker odds. To control for potential spillovers between the two markets, we repeat the analysis for cases where prices diverge significantly. Once again, exchange odds yield more valuable information concerning race outcomes than the bookmaker equivalents.     

An explanation of each-way wagers in three models of risky choice

Punters may engage in betting on both a selection in an event to finish first or in one of the number of places, e.g. second, third or fourth. When the amounts staked with bookmakers at fixed odds on the win and place are equal, it is called an each-way bet. Each-way bets are apparently popular with punters but inconsistent with prominent models of wagering which assume gamblers are everywhere risk-seeking. In this note, we derive the conditions for win and place bets to be optimal in these three models of risky choice. The mathematical conditions for the each-way wager to be optimal, as opposed to a win and place wager with different stakes, are complicated and appear likely to occur rarely in practice. However, bettors obviously see the attraction in giving themselves two ways to bet on the one horse or two ways to win and betting each way. We suggest part of the ‘each-way’ betting attraction is that they are quick and easy to compute – a heuristic – to solve an otherwise complex betting strategy.     

Betting market inefficiencies are short-lived in German professional football

In this article, we argue that potential inefficiencies on betting markets are more likely to exist at the very beginning of a season, when the available information on the teams’ playing strength is difficult to evaluate. This lack of reliable information should be particularly large in the case of recently promoted teams that have typically undergone major changes in the composition of their roster following their promotion. Without any information on the latter teams’ potential performance, they are particularly difficult to evaluate, which may eventually lead to inefficiencies and positive returns on investment in the betting market. We analyse odds from German first division Bundesliga soccer for the seasons from 2002/03 to 2015/16 to find betting market inefficiencies at the start of the season. As expected, betting on recently promoted team wins generates temporarily positive returns, especially for away games. These results suggest bookmakers to underestimate promoted teams’ ability to familiarize with the conditions in the new league, such as having to play in front of larger, often hostile crowds.     

The Favourite-Longshot Bias and Market Efficiency in UK Football betting

It is shown that the individual fixed-odds betting market on UK football exhibits the same favourite-longshot bias as that found in horse-racing. The bias appears both in betting on results (home win, away win or draw) and in betting on specific scores, and there are certain trading rules which appear to be profitable. Poisson and Negative Binomial regressions are carried out to estimate the mean number of goals scored by a team in a match with given market odds for the various outcomes. Tables of odds for individual scores are derived and these appear to fit the actual outcomes far better than those of the bookmaker.     

Is there an optimistic bias on betting markets?

Bettors are subject to an optimistic bias when betting on the team they support. This paper shows that this individual bias does not affect betting odds on British teams in association football (soccer), as it is often argued.     

Searching for the favourite-longshot bias down under: an examination of the New Zealand pari-mutuel betting market

This paper tests for the presence of the favourite-longshot bias in a new setting. This bias #150 the tendency for bettors to underbet favourites and overbet longshots #150 has been found in most studies of pari-mutuel and bookmaking betting markets in the USA, the UK and Australia. However, there is growing evidence that in at least some pari-mutuel betting markets there is no favourite-longshot bias. This paper examines the previously unexplored New Zealand pari-mutuel betting market on horse races for evidence of this bias. Utilizing a large sample of recent New Zealand thoroughbred horse races, it is found that while early, off-track bettors price this bias into odds, late (on-and off-track) bettors eliminate much of the bias by the close of betting. That is, the results reinforce the view that not all pari-mutuel betting markets are characterized by a favourite-longshot bias at the close of betting. Evidence is also found that late bettors in this market are smart bettors.     

New light on the longshot bias

The longshot bias is the tendency for bettors to put more money on horses with long odds than is justified by their objective probability of winning: thus favourites win more often than projected by their odds. This challenges normative assumptions as it means the return increases with the probability of winning. Even though the longshot bias is well-known, it has defied authoritative explanation. This article draws on studies of the longshot bias over 50 years across four continents to show that its nature is consistent with two bettor populations. One is risk-averse, knowledgeable about winners, backs favourites, believes in the gambler's fallacy, and has a positive expected return. The other, a larger group is risk loving, backs longshots, believes in hot hands, and has a significant, negative expected return. The crossover between the two groups occurs where the probability of a positive result is about 0.2. This matches the transition from risk aversion to risk embrace which has been found in a variety of behavioural studies.     

Betting on weight loss … and losing: personal gambles as commitment mechanisms

Professional bookmakers rarely accept bets from individuals who directly control the outcome of the bet. We analyse a unique exception to this rule and a potential policy innovation in the battle against obesity: a weight loss betting market. If obese individuals have time-inconsistent preferences then commitment mechanisms, such as personal gambles, should help them restrain their short-term impulses and lose weight. Correspondence with the bettors confirms that this is their primary motivation. However, it appears that the bettors in our sample are not particularly skilled at choosing effective commitment mechanisms. Despite payoffs of as high as $7350, approximately 80% of people who spend money to bet on their own behaviour end up losing their bets. Empirical analysis of the betting market yields further insights. Males are treated very differently compared to females: being male is considered equivalent to having an extra 6 months to lose the same amount of weight. Movements in the market price also confirm the belief that rigidity is preferred to flexibility in setting successful weight loss targets.     

The elasticity of demand for wagering in an unregulated market

The literature estimating the take-out rate (price) elasticity of horse race wagering has consistently found values far above one. The persistence of these apparently inefficiently high prices can be attributed to institutional factors of the US market where federal taxes are imposed on the total amount wagered, and not on the bookmakers’ revenue. By investigating all horse races in New Zealand from August 1993 to April 2009, our article is the first one to consider price setting for wagering in an unregulated market where taxes for a monopolistic betting agency are based on revenues. In such a setting, one would expect elasticities close to one, but in all econometric specifications, we find values well below one. We identify two reasons why higher prices could nevertheless reduce profits: cross price elasticities are negative and, due to the specific features of parimutuel betting, international competitors may only be attracted when take-out rates are above a critical threshold.     

Why are some favourite-longshot biases positive and others negative?

Most studies of both pari-mutuel and fixed-odds betting markets have shown a systematic tendency for the expected return to bets at lower odds to exceed those at higher odds. Some work, however, has revealed in certain markets the absence or even reversal of this bias. We present a model which distinguishes two separate types of bettor, and use this to demonstrate how transactions costs, the extent of public information, and consumption benefits of betting can explain the disparities. Our empirical evidence, taken from a fixed-odds market, lends support to our theoretical conclusions.     

A Meta-analysis of Hypothetical Bias in Stated Preference Valuation

Individuals are widely believed to overstate their economic valuation of a good by a factor of two or three. This paper reports the results of a meta-analysis of hypothetical bias in 28 stated preference valuation studies that report monetary willingness-to-pay and used the same mechanism for eliciting both hypothetical and actual values. The papers generated 83 observations with a median ratio of hypothetical to actual value of only 1.35, and the distribution has severe positive skewness. We find that a choice-based elicitation mechanism is important in reducing bias. We provide some evidence that the use of student subjects may be a source of bias, but since this variable is highly correlated with group experimental settings, firm conclusions cannot be drawn. There is some weak evidence that bias increases when public goods are being valued, and that some calibration methods may be effective at reducing bias. However, results are quite sensitive to model specification, which will remain a problem until a comprehensive theory of hypothetical bias is developed.JEL classifications: C9, H41, Q26, Q28     

行业分析师盈利预测偏差的新解释

对于卖方行业分析师(简称分析师)盈利预测偏差的现象,本文提出一个新假说,即作为理性投资的代表者——分析师的盈利预测偏差会受到投资者情绪或噪音交易的影响,并通过我国的数据证实了该假说。首先,通过实证研究,发现国内行业分析师盈利预测存在系统性的偏差。其次,构造月度投资者情绪指数,通过非参数和参数的统计方法,针对盈利预测偏差的时间序列和面板数据两组数据,证明了情绪是分析师盈利预测偏差的一个重要因素。国际文献中对分析师偏差的绝大多数理论解释通常是基于经典金融学的框架,即假设分析师是完全理性的,其偏差主要来自利益驱动(他们供职的机构或个人利益最大化)。而本文认为情绪和利益驱动因素相结合才能更好地解释分析师预测的偏差。     

An experimental study of persuasion bias and social influence in networks

In many areas of social life, individuals receive information about a particular issue of interest from multiple sources. When these sources are connected through a network, then proper aggregation of this information by an individual involves taking into account the structure of this network. The inability to aggregate properly may lead to various types of distortions. In our experiment, four agents all want to find out the value of a particular parameter unknown to all. Agents receive private signals about the parameter and can communicate their estimates of the parameter repeatedly through a network, the structure of which is known by all players. We present results from experiments with three different networks. We find that the information of agents who have more outgoing links in a network gets more weight in the information aggregation of the other agents than under optimal updating. Our results are consistent with the model of “persuasion bias” of DeMarzo et al. (2013. Q. J. Econ., 909) and at odds with an alternative heuristic according to which the most influential agents are those with more incoming links.     

Globalization, the output-inflation tradeoff and inflation

This paper provides comprehensive evidence on the relation between inflation and globalization, defined here as trade and financial openness, using a large cross-section of 91 countries over the period 1985-2004. We establish two main empirical regularities: both higher trade and financial openness (i) reduce central banks’ inflation bias, yielding lower average inflation and (ii) are associated with a larger output-inflation tradeoff. This evidence is at odds with the standard Barro-Gordon framework, which would require globalization to have a negative effect on the output-inflation tradeoff to yield lower equilibrium inflation, but it is consistent with a recent strand of new Keynesian models emphasizing the role of imperfect competition and nominal rigidities. Our findings also support the relevance of the time-inconsistency hypothesis, which underlies the theoretical models predicting a relation between globalization and inflation. For the OECD subsample, however, we do not find an effect of openness on inflation (the output-inflation tradeoff), suggesting that these countries have created an institutional framework for central banks that eliminates distortions due to the time-inconsistency problem.     

Hypothetical Bias in Risk Preferences as a Driver of Hypothetical Bias in Willingness to Pay: Experimental Evidence

This study provides new insight on the established issue of elicitation bias in hypothetical choice settings. In particular, using an experiment that elicits real and hypothetical willingness to pay for the protection of otters, we provide evidence that the observed bias is driven by those who are both uncertain about their value and exhibit hypothetical bias in risk attitudes. This finding provides a reason why calibration approaches based on follow-up certainty questions have proven useful, but also suggests a degree of caution in applying the approach. Our results favour combining uncertainty calibration with CVM-X in which hypothetical bias in risk attitudes is also taken account to correct for hypothetical bias in WTP.     

DOES ‘AGGREGATION BIAS’ EXPLAIN THE PPP PUZZLE?

Abstract. Recently, Jean Imbs and colleagues have claimed that much of the purchasing power parity puzzle can be explained by ‘aggregation bias’. This paper re‐examines aggregation bias. It clarifies the meaning of aggregation bias and its applicability to the PPP puzzle; demonstrates that the size of the ‘bias’ is much smaller than suggested if explosive roots in the simulations are ruled out; and shows that the presence of non‐persistent measurement error data can make price series appear less persistent than they are. After correcting for small‐sample bias, half‐life estimates indicate that heterogeneity and aggregation bias do not help to solve the PPP puzzle.