Sports Arbitrage

Although sport and financial markets are seemingly two different worlds, arbitrage trading and sports betting have a lot in common. Trading strategies and risk-management techniques used in financial markets can be applied to sports betting and vice versa. As in financial markets, pricing inefficiencies do exist in the sport bookmaking markets which result in opportunities for arbitrageurs.

Sports arbitrage can be loosely categorized into two main types:

  • Inter-bookmaker arbitrage which exploits bookmakers’ different opinions on sport events’ outcomes or plain pricing errors.
  • Intra-bookmaker arbitrage which exploits the relative mispricing, based on the actual and implied odds, of a sport event.

Of the two types of sports arbitrage, the latter is being used by us. It is in a sense very similar to the options volatility trading strategy where one seeks an edge by taking advantage of the discrepancy between historical and implied volatilities of an underlying asset. To see how sports arbitrage work, let’s go through a real-life example.

Soccer is unarguably one of the most popular sports in the world. At the club level, UEFA Champions League is the most prestigious competition for a European soccer club. The final this year will be held on May 25 at the Wembley stadium. As of this writing there are four clubs remain in the competition, two from Germany and two from Spain. The draw for the semi-finals was held last Friday and the following match up will occur:

Bayern Munich – Barcelona        

Borussia Dortmund – Real Madrid

The first leg of the Bayern Munich- Barcelona match will be played on April 23 in Bayern’s homeland. As of this writing, the implied probability of a Bayern Munich win is 40%. It is calculated from the posted odds of 2.5 on Ladbrokes, a well-known bookmaker.

Note, however, that this price is not static; it can vary from now until the end of the match, thus creating short-term trading opportunities.  The actual probability of winning for Bayern Munich, calculated based on its past and recent performance, is 45.9% (2.18 in decimal form).  Consequently, there is an opportunity for arbitrage. If we place a bet on Ladbrokes now, we’ll have an edge of 5.9 %.

As can be seen from the example above, the goal of sports arbitrage is to find as many as possible this kind of mispricing opportunity and repeat the betting process over and over again. This way we play a positive expectation game and will make money in the long run.

Relative Pricing

Many popular trading strategies are based on some forms of fundamental or technical analysis. They attempt to value securities based on some fundamental multiples or technical indicators. These valuation techniques can be considered “absolute pricing”. Arbitrage trading strategies, on the other hand, are based on a so-called relative pricing. So what is relative pricing?

The theory and practice of relative pricing are derived from the principle of no arbitrage. Stephen A. Ross, a renowned professor of finance, is known for saying:

You can make even a parrot into a learned political economist—all he must learn are the two words “supply” and “demand”… To make the parrot into a learned financial economist, he only needs to learn the single word “arbitrage”.

What he was referring to is what financial economists call the principle of no risk-free arbitrage or the law of one price which states that: “Any two securities with identical future payouts, no matter how the future turns out, should have identical current prices.”

Relative pricing based on the principle of no risk-free arbitrage underlies most of the derivative pricing models in quantitative finance. That is, a security is valued based on the prices of other securities that are as similar to it as possible. For example an over-the-counter interest-rate swap is valued based on the prices of other traded swaps and not on, for example, some macro-economic factors. A bespoke basket option is valued based on the prices of its components’ vanilla options.

The principle of no risk-free arbitrage is employed in its original form in trading strategies such as convertible and volatility arbitrage. In statistical arbitrage  it is, however, relaxed; it normally involves stocks  which are similar but not 100% identical.

In summary, relative pricing based on the principle of no risk-free arbitrage is very different from absolute pricing. It is the foundation of many derivative pricing models and quantitative trading strategies.