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 is a 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.

 Odds comparison

Odds comparison

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.

 Sharp vs Soft Bookie Odds and Probability

Sharp vs Soft Bookie Odds and Probability

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.

 Arbitrage Bet / Surebet

Arbitrage Bet / Surebet

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. Surebets are also called arbitrage bets and have been covered in even more detail in this article. While this article covers some practical experiences of using arbitrage betting from Vida, a guest contributor at the Trademate blog

However, the majority of surebets will occur at the soft bookmakers (will be defined later), which can lead to several practical disadvantages:

  1. Soft bookmakers limit sports traders who are able to win consistently.

  2. You need to find high enough odds on all of the outcomes for it to add up to a surebet.

  3. 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. (If you are unfamiliar with the statistical concept of expected value (EV), read this short article) 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).

  4. 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.

 Difference in estimated probability between soft and sharp bookmaker

Difference in estimated probability between soft and sharp bookmaker

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 the Asian Bookmaker's odds accurately reflect the true probability of a game’s outcome, which is covered in this article. 



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. 

 How value occurs in sports betting markets

How value occurs in sports betting markets

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 in this article


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

  1. Market inefficiencies enable arbitrage opportunities.

  2. Shorter investment cycles provide a higher potential for profit growth and reduced capital tied up in investments.

  3. Faster feedback loop on strategy performance.

Written by: Marius Meling Norheim

Disclosure: Neither I, nor Tradematesports have any affiliation or receive any form of compensation what so ever from any of the bookmakers, websites or companies mentioned in this article.


Value bets: How does value occur in sports betting?

Learn what value bets are and how it can improve your sport betting strategies today!

Read More

Staying under the radar - the Trademate guide to avoid getting limited by the Soft books

The biggest struggle profitable bettors taking on the "soft" books have is not getting limited from them. We have put together a set of guidelines you can follow to extract even more value from the "soft" bookmakers.

 Staying under the bookies radar

Staying under the bookies radar

Follow our recommended leagues

Trademate has a filter called recommended leagues. By selecting this, you'll only be presented with opportunities from the leagues with the highest betting limits. This includes Premier League, Primera Divisione, NBA, NFL and many more. These leagues are the ones that most people bet on - so it's easy to hide in the mass of all the non-profitable betters.

Bet whole amounts

Arbitrage betting is very usual in sports betting (A topic covered in this article) - so bookmakers look out for bet sizing out of the ordinary. Instead of placing the exact recommended kelly amount of $162, bet $160. The Kelly Criterion as a stake sizing strategy for bankroll management in sports betting has been covered in this article

Never cash out before you have to

Never cash out from a bookmaker before you're limited. Bookmakers are paying fees whenever you cash out, so that's an easy way for them to do a second look at your account. So you've tripled your bankroll in the past 3 weeks? Let's take an even closer look..

Don't push the max limits

Let's say you try to place a bet of $250 on a game. The bookmaker may tell you that you can only place $238 on the particular bet. Instead of putting the $238, bet 60-70% of the max stake, in this case $150.

Some bookmakers even give you the opportunity to automatically put the max limit of $238 and send the remaining $12 for manual clearance. Never do that. 

Add in some accumulators with a lower bet size. This will make you look more of a "recreational bettor" and its something bookmakers appreciate. Lower your bet size for these as the variance is higher.

One bet per game

Bookmakers place betting limits for a reason. The reason is usually that they're not really sure if their odds in a particular game are any good. If someone comes in and places bets on Over 198.5, Over 199.5, Over 200.5 and Over 201.5 - it's pretty clear that they're trying to get value. Bookmakers don't like that.

Also - placing more than one bet on a game has a great impact on your variance, but that's a whole other discussion, we'll touch upon in another blog post.

Make your first deposit small

Try to look like a hobby Sports bettor. Depositing $10,000 in a brand new account is an obvious way to tell bookmakers that you're trying to beat them.

Wanna be really clever? Throw in an accumulator once in a while.

In general you want to avoid accumulators as covered in this article. Bookmakers make most of their money from accumulators. Their margins increases for each bet in the accumulator. But matching different value bets will still give a positive expected value, however  it will increase your variance. So use it carefully. By doing this though, you look more like a non-profitable player to the bookmakers.

Nothing lasts forever

Unfortunately, by continuously placing profitable bets and beating the bookmakers - chances are they will limit you eventually. After all - they are losing money on you. 

However, by following these steps we are confident that your accounts will last longer, thus making more money from each and every soft book! And hey, once they're all used up, you can always transition to the Asian markets.

Remember if you have any questions, we're only an e-mail or message away. Good luck and happy betting!

Closing line: The most important metric in sports trading

As part of any form of investing it is important to have a benchmark that you can compare your performance against. Otherwise, you do not know whether the results you are getting are because you have made smart decisions or luck. Professional poker players use analysis software to track their hand history, enabling them to review whether they make decisions with a positive expected value. E.g. calling hands where they have pot odds. For stock investors, a suitable benchmark is how you perform against the S&P 500, an index fund consisting of the 500 US companies with the highest market cap (Stock price x volume of shares). For sports traders, the benchmark is the odds at the time the match kicks-off, what is known as the closing line. This article covers the topic of whether sports betting markets are efficient. A key assumption about the accuracy of the closing line,  is that because it has been shaped by all the bets placed at the bookmakers, and because they know where the rest of the market have their odds, the sports betting markets are very efficient at the time the games start. Or in other words the closing line is a great benchmark. 

The goal for sports traders is to beat the vig-free closing line of the sharpest bookmakers

No one is able to accurately predict the outcome of every sporting event. However, this does not imply that it is impossible to become a profitable sports trader nor that those who are profitable are merely lucky. The goal when trading sports is not to win every bet you place, but to make decisions that have a positive expected value (+EV). E.g placing trades that have a larger chance of winning than implied by the odds. This article explains the concept of expected value. Over a small sample size of trades anything can happen or in other words variance will have a large impact on your results,. However, over a large volume of trades the variance will even out (the reason for which is explained in this article) and only sports traders who are able to consistently beat the vig-free closing lines at the sharp bookmakers will be profitable. In the sports market, the sharp bookmakers’ closing lines are considered to be the expected value. Meaning that If you traded at a higher odds than the closing line you have made a +EV trade, while if the odds you traded at is lower than the closing line you have a -EV trade. Now obviously at the time you decide on whether to place a trade or not, you do not know what the closing line will be. However there are multiple factors that impact the movement of the odds and thus the closing line, such as the time before kick-off, the bookmakers payout rate and the liquidity in the market, which will be discussed next.


Time before kick-off

The odds are a reflection of the information possessed by the market. Thus the longer before kick-off you place a trade, the more information might appear that can affect the odds one way or the other. Therefore trades that are placed closer to kick-off will most likely experience less fluctuations.


Payout rate and liquidity - The difference between edges (+EV trades) at soft vs sharp bookmakers

The main difference between the soft and the sharp bookmakers is their payout rate and liquidity. An edge occurs in the market, when there are differences in the odds offered by the various bookmakers. This is commonly referred to as a value bet, which you can read more about here. The majority of the soft bookmakers have a lower payout rate than the sharps. So for instance the odds at Manchester United winning at home vs Arsenal this weekend is 2.50 at Ladbrokes and 2.68 at a Sharp Bookmaker Their respective payout rates are at the time of writing, 92,6% and 98%.

Because the Sharp Bookmaker has a higher payout rate and allow larger bets to be placed on the outcome of this game than Ladbrokes, more money is placed on the game through the Sharp Bookmaker. The result being that the Sharp Bookmaker has more liquidity. More liquidity means more information, which means that odds at the Sharp Bookmaker is a better reflection of the true odds (the true probability of the game’s outcome). Now let’s imagine the scenario where news gets out 1 hour before kick-off that Alexis Sanchez, Arsenal’s best player is injured. The sharp traders know that this decreases the likelihood of Arsenal winning the game, so they will place a large bet of $1 000 000 on a Manchester United win, the result being that the odds of United winning at the Sharp Bookmaker drops to 2.30. If we look at the vig-free odds (removing the Sharp Bookmaker’s margin of 2%), the odds is 2.346 (2.30 * 1.02). The odds at Ladbrokes remains at 2.50, meaning that there now exists an edge in the market of 6.56% [ ((2.50 / 2.346)-1)*100 ]. The market movement from 2.68 to 2.30 is a fluctuation of 16.5%. For the Sharp Bookmaker's odds to swing the other way and eliminate the edge, it is going to take new information. This information must then convince bettors to place hundreds of thousands of dollars on a draw or away win to change the odds. Now there is only 1 hour before kick-off so we can assume that the probability of this occurring is rather low. This implies that what is an edge 1 hour before kick-off is also likely to remain an edge at the time of kick-off. Or in other words if we had placed that trade 1 hour before kick-off at 2.50, it is likely that we would have beat the closing line of the sharp bookmaker, thus it is a +EV trade.

In general the odds at the soft bookmakers is way lower than the sharp bookmakers, because their payout rate is lower. Thus for an edge to occur at the soft bookmakers, the market must drop by approximately 10% (because of the soft vig). The probability that the market will swing back to its original position is then fairly low. Whereas a 2-3% drop between the sharp bookmakers will create an edge, it then takes a lot less new information for the market to move out of your favor as opposed to the 10-13% drop at the soft bookmakers. The point being that if an edge occurs at a soft bookmaker, it is much more likely to remain an edge versus the closing line when the game starts, than an edge that occurs between sharp bookmakers.


Which bookmaker is the sharpest?

The bookmaker with the consistent highest liquidity in a particular market is considered to be the sharpest within that market. This is because more liquidity attracts sharper traders. Sharper trades possess information. Once they place a trade the market reflects the information possessed by this trader. Close to kick-off in a high liquidity market all of the sharp traders will have placed their trades and thus the market reflects the sum of the information possessed by the individual traders. The closing line represents what the market believes to be the true odds and thus probability for the different game outcomes.

Pinnacle usually has the highest liquidity and is therefore most often the sharpest of the bookmakers. Thus when edges occur between the sharp bookmakers it is usually because a sharp trader is placing a lot of money on a line at Pinnacle. This causes the odds to drop by 2-3 % and a 1% edge to occur versus the rest of the market. When this happens other traders will compete to capture the same liquidity on the other sharp bookmakers before someone else does.

When an edge occurs in the asian market, the sharp traders will keep betting the line until the value is on the other side, hence equilibrium is usually not the lowest-most point on the graph. Thus if you are able to place your trades at the peak edge it is very likely that the line will stabilize slightly lower than the odds you placed at. By placing trades on edges, you are placing your money on what is the right side of the market. Therefore it is more likely than not that the market will move in your favor.

Trademate is a valuable tool for sports traders, because it allows you to monitor market movements. Sometimes “false deviations” will occur at the sharp bookmakers, meaning that the line is pushed back to its original position, by someone taking a large position on the other side of the market. The result would then be that what was a +EV trade at the time you placed it, becomes a -EV trade 2 minutes later. As more money is placed on a game, meaning that the liquidity increases, it requires more money to shift the odds. Thus placing trades closer to kick-off means increases the likelihood of your trade being a +EV trade at the time the line closes.


Low liquidity vs high liquidity sport markets

In general, bookmakers only allow smaller stakes to be placed on lower leagues and smaller sports. Thus these leagues have lower liquidity than the major leagues such as PL, CL, NBA, NFL and MLB. As a sports trader this is important to know, because if there is a 5% edge on both a Premier League game and a game in English League 2, it is going to take a lot less money to shift the odds in the L2 game and thus turning your +EV trade into a -EV trade. Now, this could swing both ways, so your +EV trade could be even higher. The point is that the only thing that is guaranteed is that the lower liquidity markets are much more volatile than high liquidity markets. Therefore they can be considered to be riskier. In an example where you place both trades close to kick-off (<1 hour) then most likely both of the trades will end up as +EV trades versus the closing line. However, let us assume that you place both trades 4 hours before the game. Then it is much more likely that the L2 game is going to swing out of your favor than the PL game. Thus as a sports trader, you have to weigh up whether placing that trade at that edge is worth the risk.


Key takeaways

  • As a sports trader your goal is to place trades that beat the vig-free closing line of the sharpest bookmakers. Over a high volume of trades, only traders who are able to consistently beat the closing line will be profitable.

  • The closing line in high liquidity markets reflects the true odds, because it incorporates all of the information that exists in the market.

  • At the soft bookmakers it is likely that more often than not edges that occur pre-game are likely to remain +EV trades versus the closing line, because in order for the edge to occur in the first place the market needs to move a lot. This decreases the possibility of it swinging the other way and out of your favor.

  • Placing trades close to kick-off reduces the likelihood that the edge will change dramatically.

  • Lower liquidity markets are much more volatile and thus riskier than high liquidity markets.