OPTIMAL PRICE SETTING IN FIXED‐ODDS BETTING MARKETS UNDER INFORMATION UNCERTAINTY
| Date | 01 September 2011 |
| DOI | http://doi.org/10.1111/j.1467-9485.2011.00557.x |
| Published date | 01 September 2011 |
OPTIMAL PRICE SETTING IN
FIXED-ODDS BETTING MARKETS
UNDER INFORMATION UNCERTAINTY
Vasiliki Makropoulou
n
and Raphael N. Markellos
n
Abstract
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.
Since Fama (1970) first formalized the concept of information efficiency, several
studies have evaluated relevant hypotheses in markets spanning the entire range
of real and financial assets. Of particular interest to academics and laymen alike,
are investigations of efficiency in the betting industry. Indeed, as has been
pointed out in the literature (e.g. Thaler and Ziemba, 1988; Vaughan Williams,
1999), there are special features of gambling markets that make them
particularly relevant for studying market efficiency. In particular, they possess
many of the attributes of financial markets: future outcomes are uncertain, there
are many investors (bettors) and historical information is widely available.
However, there is a well-defined point in time where the actual value of each bet
is revealed, in contrast to financial assets, which tend to have infinite duration
and at no point in time reveal their true value with certainty.
Most studies of betting markets have focused on pari-mutuel systems.
In pari-mutuel betting, the bettors do not know the payoff odds until all bets are
placed. The winners receive the share of the betting pool, after taxes and market
maker’s costs are removed, in proportion to their stake. On the contrary, in
fixed-odds betting, the odds are set by the market makers, i.e. bookmakers, and
the payoff is agreed at the time the bet is placed, rather than determined by the
pool when all betting has been completed. The latter is the most common form
of football betting in Europe and particularly in the United Kingdom, and
n
Athens University of Economics and Business
Scottish Journal of Political Economy, Vol. 58, No. 4, September 2011
r2011 The Authors. Scottish Journal of Political Economy r2011 Scottish Economic Society. Published by Blackwell
Publishing Ltd, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA, 02148, USA
519
traditionally it was implemented via coupons offered by bookmakers several
days before the event (Pope and Peel, 1989; Kuypers, 2000).
1
In more recent
years, fixed-odds betting is increasingly carried out online. Since the payoff to
each bet is fixed at the time the bet is placed, fixed-odds bets are more prone to
exploitation by informed bettors.
The present paper develops a model of optimal pricing for fixed odds that
accounts for the possibility of changes in publicly available information after the
odds have been set. The model accounts for asymmetries in the information
utilised by bettors, by assuming two distinct groups of bettors; informed and
uniformed. The concept of heterogeneously informed market participants is not
new in the literature and has been considered, for example, in the context of
financial markets and the bid-ask spread (e.g. Copeland and Galai, 1983) and
prediction markets (e.g. Wolfers and Zitzewitz, 2006; Ottaviani and Srensen,
2010). In the context of betting markets, Shin (1991, 1992, 1993) and Ottaviani
and Srensen (2005) drew upon analogies with financial markets – where prices
are set by the market maker and the informational source of the bid-ask spread
– and focused on the determination of prices by bookmakers in the racetrack
betting market in the presence of insiders, i.e. bettors that possess private
information unknown to the bookmaker. In this paper, we also provide an
informational model of price determination, but we focus on football betting.
There are significant differences between football and racetrack betting. In
football betting bookmakers offer odds around 1 week before the event.
Once the odds are determined, they remain largely unchanged throughout the
betting period, especially for fixed-odds coupons, since any change would
constitute a considerable expense to the bookmaker (Cain et al., 2003;
Levitt, 2004). On the contrary, the racetrack betting market convenes typically
for thirty minutes before the race starts and during this time, bookmakers
may change their odds very easily, and typically do so, according to the
flow of bets. This means that changes in public information are irrelevant,
since they can almost instantly be incorporated into the new odds; in this
case, the main risk for the racetrack bookmaker arises from insiders. In this
paper, rather than dealing with insiders who possess private information, we
deal with expert or informed bettors who exploit public information that
arrives after the declaration of the odds. Bookmaker pricing behaviour in fixed-
odds betting on UK football has only been modelled once before. Kuypers
(2000) derived prices by assuming a profit-maximizing strategy of a book-
maker who exploits the bias in the expectations of bettors. In this context,
information asymmetries are ignored since Kuypers assumes that all market
participants, i.e. bookmakers and bettors, are equally able to evaluate publicly
available information.
The motivation for our model is threefold. The first stems from the a priori
reasonable assumption that a bookmaker who quotes fixed-odds several days
1
In UK racetrack betting, a considerable amount of bets are settled at the official Starting
Price (SP), i.e. the price that prevails on-course at the start of the race. In this respect it differs
from fixed-odds betting since SP is not known to bettors at the time of betting.
VASILIKI MAKROPOULOU AND RAPHAEL N. MARKELLOS520
Scottish Journal of Political Economy
r2011 The Authors. Scottish Journal of Political Economy r2011 Scottish Economic Society
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