# Exploiting arbitrage opportunities: From trading stocks to sports.

“Arbitrage is the simultaneous purchase and sale of an asset to profit from a difference in the price. It isa trade that profits by exploiting the price differences of identical or similar financial instruments on different markets or in different forms.Arbitrage exists as a result of market inefficiencies”

- Investopedia

# HOW HIGH-FREQUENCY TRADING FIRMS EXPLOIT ARBITRAGE OPPORTUNITIES IN THE STOCK MARKET

With today’s technology, the pricing of stocks is updated within a few milliseconds of real-time. This is way faster than a human is able to perform calculations, which makes it difficult to find arbitrage opportunities in financial markets. As a result, firms who are performing day trading are now using computers to perform algorithmic electronic trading at a speed that is impossible for humans to match. The way this works is that you give the computer a set of instructions, which will trigger it to buy or sell stocks. These instructions can be related to price, timing, volume or a mathematical model. For instance, you write an algorithm that tells the computer to buy 1000 Tesla stocks whenever the price goes above $200 and sell if the stock price increases by 10% above the purchase price. For more reading on arbitrage and algorithmic trading, check out the links.

The non-fiction book “Flash Boys” by Michael Lewis, tells the story of how high-frequency trading (HFT) firms used a super fast fiber optic cable that connected the financial markets of New York with Chicago to perform arbitrage trading. This $300m cable reduced the journey time for data from 17 to 13 milliseconds. An advantage, which enabled the HFT firms to obtain better prices on their trades compared to their competitors.

To illustrate how this works in practice let’s imagine that a hedge fund wants to buy a 100 000 shares of Tesla stock. This purchase will be spread out on multiple stock exchanges to ensure that they get the best possible price on their purchase. As a result 60 000 shares are purchased on Nasdaq for $200 per share, but once someone buys stocks in a company, the price will increase. Thus there are only a limited amount of shares are available for $200. Once the purchase has been made the stock price of Tesla increases to $202 on Nasdaq. Therefore the hedge fund will look at buying the remaining 40 000 shares at a better price on a different stock exchange. At the London Stock Exchange (LSE) Tesla is still trading at $201 because the price has not been updated yet. What happens is that the HFT firm will notice that someone has purchased a large amount of Tesla shares on Nasdaq and therefore they will leverage their faster cable connection to purchase Tesla shares at the London Stock Exchange before the price increases to $202. So let’s say the HFT firm manages to buy Tesla shares at $201 per share at LSE. They then sell the stocks to the hedge fund for $201.99 and pocket a 99 cent profit per share. All of these events take place within a couple of milliseconds and are enabled by the firms using complex computer algorithms to perform their trading. In reality, the pricing difference is more likely down to 1 cent or less, rather than the 99 cents used in this example. However, if the HFT firm is able to perform thousands of trades like this during a day, then the profits will add up to huge sums in the end. According to the article at Harvard Politics, the HFT market produced profits of $5 billion in 2009, but declined to 1.25 billion in 2014. Also, HFT trading accounted for 73% of the total daily market volume on U.S. exchanges in 2014. A possible explanation for this decline can be found in the macroeconomics principle of perfect competition, which states that the existence of economic profits within an industry will attract new firms to the industry. The increased competition will result in diminishing returns for the firms and in the long run the industry will reach the state of perfect competition, an equilibrium where the industry profits equal zero. A second possible explanation is that the stock exchanges have improved their own connections, which reduced the relative edge that the faster connection provided the HFT firms.

According to Investopedia’s definition, arbitrage opportunities exist as a result of market inefficiencies, which allow investors to exploit price differences. Therefore it is not limited to just investments in stocks, but really any market where such opportunities exist. As a result the HFT firms also trade other types of securities such as bonds, futures and foreign exchange contracts. The rest of this article will focus on price inefficiencies within sports markets.

# ARBITRAGE OPPORTUNITIES IN SPORTS MARKETS

Within the world of sports betting there exists bookmakers where you bet against the house and betting exchanges where you bet against other people. The latter can be compared to a regular stock exchange, the main difference being that the traders buy and sell bets on the outcome of events such as a football game rather than stocks. What makes the sports market interesting from a trading perspective is that it is more inefficient than the financial markets, which in turn creates arbitrage opportunities. At the free site oddsportal.com, one can compare the odds of a game provided by different bookmakers and betting exchanges, which enables you to see the inefficiencies that exist within the sports market with your own eyes. I’ve included a screenshot of the odds from different bookmakers on the Liverpool — Manchester United game that was played on 17.10.2016.

The odds of a game’s outcome reflect what the bookmaker believes to be the probability of that outcome. The probability of an outcome equals the inverse of the odds, in addition one has to adjust for the bookmaker’s payout rate, which is the amount of money that they pay back to their customers. For instance Mybet has a 90% payout rate, which means that they take a 10% cut of the money that is placed on this game. Next let’s compare the odds provided by two different bookies.

What we can see here is that the two bookies differ greatly in what they believe will be the outcome of the game. Now this leaves us with the question of which bookmaker is right and are either of them able to accurately predict the game’s outcome? The earlier screenshot above shows that Mybet’s odds for a home win is 2.40, while the closest bookmaker is at 2.27. This large deviation from the rest of the market indicates that Mybet is the bookmaker who underestimates the probability of a Liverpool win. The consequence of Mybet having mispriced the probability of a Liverpool win, by placing their odds at a higher level than the rest of the market, is that it creates an arbitrage opportunity. More specifically it makes it possible to put money on the outcome of a draw and an away win at two other bookmakers with a guaranteed ROI of 2.62% as can be seen in the screenshot below.

This is what is referred to as a surebet. The advantage of surebets is that in theory you are guaranteed a profit without any risk. However, the majority of surebets will occur at the soft bookmakers (will be defined later), which can lead to several practical disadvantages:

- Soft bookmakers limit sports traders who are able to win consistently.
- You need to find high enough odds on all of the outcomes for it to add up to a surebet.
- If the odds deviate too much from the rest of the market, bookmakers are able to void bets placed on that game. Imagine the following scenario: you are following the recommendation in the screenshot above, by placing money on a home win at Mybet, a draw at Vulkan bet, but when you are trying to place a money on an away win at Leonbet, you are limited to place a maximum of $1. You are now unable to complete the surebet, which results in a huge negative expected value on the bet. Now whether you are investing in stocks or sports the most important principle is to avoid loosing money, because if you loose 50% of your capital ($10 000 → $5000), you will need to increase it by 100%, just to return to the starting point ($5000 → $10 000).
- You will need to distribute your capital and thus tie up your capital across a very wide range of bookmakers to take advantage of the surebet opportunities.

Because of the disadvantages with arbitrage trades (surebets) listed above, a better strategy is to place a high volume of +EV trades. An example of a value trade would be to place money on a home win to Liverpool, which has a +6.06% EV. Over a large sample size placing +EV trades should be a profitable strategy in theory. This is based on the assumption that Pinnacle odds accurately reflect the true probability of a game’s outcome, which will be discussed next.

# HOW EFFICIENT IS THE SPORTS MARKET?

## HOW DO BOOKMAKERS DECIDE ON THEIR ODDS?

Typically an odds line will be placed by a bookmaker after they have performed a statistical analysis, which takes all the information they have available into consideration, for instance the team’s lineup, injuries and historical performance. Once the initial odds line has been set it will be adjusted based on market movements, meaning how much money is put on the different outcomes. The efficient market hypothesis used in financial markets states that it is impossible to beat the market, because the existing asset prices always incorporate and reflect all relevant information. So if an asset is underpriced in the stock market, it will lead to investors buying the stock until it returns to its intrinsic value or in other words a fair price. The same applies to the sports market, if a bookmaker underpriced the odds of a particular outcome, let’s say a home win to Liverpool, then smart sports traders will put money on this outcome until it is priced at a fair value. So for instance if someone places a $1 million on Liverpool to win, the odds will shift. If another person believes that the odds are now mispriced and that there is value on the other side, they might place $1 million on Manchester United to win and the odds will shift again and thus eliminating the inefficiency. The more money that is put on the outcome of a game, the more likely it is that the all of the inefficiencies have been eliminated. Thus the odds at the time the match kicks off will reflect all of the information that is in the market. This odds at the kick-off time is referred to as the closing odds.

# ARE BOOKMAKERS ABLE TO ACCURATELY PREDICT THE OUTCOME OF A GAME?

Now which bookmakers are the best at accurately predicting the outcome of a game? First, let’s define the bookmakers and exchanges into two main categories: 1) soft bookmakers, who have a low payout rate (>= 90%) and low limits on how much money can be placed on games. 2) Sharp bookmakers, who have a high payout rate (<97%) and high limits on games. What typically happens at the soft bookmakers is that they limit winning players in order to protect their profit margins. The sharp bookmakers however, choose the opposite strategy, they want to have smart bettors at their site because it makes their odds more accurate. The sharp bookmakers have much higher limits on the amount of money that can be placed on a game. This basically allows them to have more information incorporated into their odds, which makes the bookmaker able to more accurately predict the real world outcome of the game.

Through looking at the correlation between the expected probability of a game’s outcome and the actual outcome it is possible to determine how accurate a bookmakers’ odds are. From a sample size of 397,935 football games offered by Pinnacle Sports, a sharp bookmaker, there existed a high correlation (r-squared = 0.997) between the closing lines and the observed probabilities. In other words, Pinnacle’s odds accurately predicted the real world outcome 99.7% of the time. Meaning that that their odds are very efficient. In their business models, bookmakers make a tradeoff between their margin and the total turnover of bets that are placed through their service. Because Pinnacle is so confident in their odds being correct it enables their business model to rely on a high volume of money being placed on their games and them to have a low margin, 2 % and a 98% payout rate to their customers.

The majority of the soft bookmakers are European, while the sharp bookmakers operate in the Asian market. Because of the higher amount of money that is placed on games in the Asian market, it has higher liquidity. This attracts professional sports traders with large bankrolls, which increases the level of competition. The consequence being an efficient market because smart sports traders exploit any inefficiencies that occur. Now it is easier to finds arbitrage opportunities in the European market, however, the limits on how much money you can place on the game effectively puts a cap on potential earnings. Because the Asian market is more efficient, the best sports traders are only able to beat the market with a couple of +EV%. They counter-balance the lower edge by placing a high volume of trades at high sums. Because the soft bookmakers limit winning players, sports traders will eventually have to move into the Asian market.

# WHY INVESTING IN SPORTS OVER STOCKS MAKES SENSE FOR PRIVATE INVESTORS

A rational investor will attempt to maximize returns while minimizing risks. This implies that they will invest in the markets or financial instruments where the potential return / risk ratio is the highest. Investors in financial markets can broadly be divided into two categories: Long-term oriented investors who rely on fundamental analysis and short-term oriented investors who follow a trend or technical analysis. The former are often referred to as value investors, which means that they try to identify assets that are underpriced by the market. They also require the asset to be significantly underpriced, which provides a margin of safety, before they purchase a given asset. What I view as the main disadvantage for the value investors is that, because they are oriented towards the long-term, which can be anytime between 3–10+ years, it means that they will tie up their capital in investments for a long time before potentially reaching a positive return on investment. In the meantime, you do not know whether your hypothesis that the asset is underpriced holds true.

The opposite of strategy would be day trading, taking advantage of short-term price discrepancies in the market. Day traders apply different methods such as looking at chart patterns or technical indicators in order to predict future market movements. Now the main disadvantage with being a day-trader is that computers are superior to humans in performing statistical analysis and for discovering patterns in large datasets. Thus gaining an edge in the market when you are competing against HFT firms is very difficult. The gap in access to information held by hedge funds compared private investors have increased dramatically in the last decades. Today hedge funds can rely on real-time satellite images of the parking lots of JC Penney to predict their quarterly returns, while private investors rely on historical financial statements. The result being that it is very difficult for private investors to compete against the professional hedge funds, especially if they rely on technical analysis. This is because, if there does exist price inefficiencies in the stock market it will be exploited by the HFT firms way faster than any private investor is capable of, returning the market to an efficient state. Thus in practice, the day trader performing technical analysis is competing against HFT firms, with access to less information and using inferior methods.

To manage risk the principle of portfolio diversification is followed by both groups of investors. The short-term investor will typically mitigate risk, by making a high volume of smaller trades with low risk and low returns that add up and provide a positive ROI. In comparison, value investors will make a lower volume of investments, but with a higher potential ROI on each of them. Similar to the day trader a sports trader will perform a high volume of smaller investments on the sports market. With any strategy, it is important to set up a feedback loop that provides you with data on how your strategy is performing. Within sports trading, the natural benchmark is to measure whether the odds you are putting money on is able to consistently beat the closing lines of the sharp bookmakers. If so, you will have a positive expected value, which in theory should lead to profits over a large sample size of sports trades.

Poker players will be familiar with the difference between the short and the long term. In the short term is possible for anyone to win, regardless of skill. because luck or randomness has a large impact on the outcome. While in the long run, the random variance will even out and the players who have an edge will be the ones making a profit. The same holds true for people who trade in both the stock and the sports markets. Anyone can make a profit in the short term, but in the long term only traders who make decisions with a positive expected value will be profitable.

# HOW PRICE DIFFERENCES OCCUR IN THE SPORTS MARKET

The reason that computers running algorithms are used to trade in the financial markets is because in these markets prices are updated so fast that it almost impossible for humans to exploit. In the stock market the difference in price that you will be able to obtain when purchasing Tesla stock at Nasdaq versus LSE is close to identical since the updates happen within milliseconds across exchanges in different markets. While in the sports markets the same asset, the outcome in the game between Liverpool and Manchester United is priced differently at different bookmakers or exchanges. In addition, these inefficiencies are not necessarily corrected in real-time. For instance, in the game between Chelsea vs Manchester City on February 21st, 2016 it took the bookmaker Norsk Tipping almost 30 minutes to adjust their odds compared to the Asian market, as seen in the image below. You can read more about how value occurs in the sports market by clicking the link in the previous sentence.

Now compare this to the stock market, where the price would have been adjusted within milliseconds. These market inefficiencies create arbitrage opportunities that can be exploited by smart sports traders.

# BEING A SPORTS TRADER

For professional sports traders, the majority of work is put in during the weekends because this is when the majority of games are played. In a given weekend you can potentially run through your bankroll multiple times by placing a high volume of sports trades. Trades are typically placed within a couple of hours before the game starts to reduce the variance that may occur between the opening to closing lines of the bookmakers. Thus the capital of the investor is tied up in the investment for a shorter period of time. The result being that you can grow your fund much faster, than for long-term investments in the stock market.

For example, if your bankroll consists of $10 000 and you place sports trades with an average of + 3% EV per trade. +EV being the trades where you get a higher odds than the closing lines of the sharpest bookmakers. Now let’s assume that you place your trades with a flat structure* of $100 per bet and that over the weekend you place 100 bets. Then your expected profit would be: 100 (trades) x $100 * 1,03 (EV) — $10 000 = $300. Now obviously, whether you endure winning or losing streaks will have an impact on your actual profits . If we assume that there is no variance in the 100 trades we placed or in other words that we are neither lucky nor unlucky, our actual profits would be equal to our expected profits of $300. In reality, the variance will only even out if you are able to place a high amount of +EV trades.

*Your bet sizing is an important topic when trading in the sports market. You can read more about bet sizing on the following link and also run a simulation of how different input variables affect your potential profits.

# CONCLUSION

To sum it up there are 3 main advantages of trading in the sports market compared to the stock market:

- Market inefficiencies enable arbitrage opportunities.
- Shorter investment cycles provide a higher potential for profit growth and reduced capital tied up in investments.
- Faster feedback loop on strategy performance.