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Arbitrage strategies

Arbitrage (arbitrage trading, arbitrage strategies) is a trading style based on "squeezing" profit from the immediate price difference of assets posing some level of connection. The core of all arbitrage strategies is seeking price imbalances in a group of interconnected financial instruments, and opening simultaneous trading positions in the direction of elimination of these discrepancies. Arbitrage strategies are almost unanimously characterized by high profitability, low risk (the usual selling point), neutrality in accordance to market dynamics and the ability to formalize trading, making it essentially automatic or semi-automatic. In this article, we will examine main arbitrage trading strategy types that withstood the test of time and are still in use and high regard among the best investors in the world.

So, basically arbitrage is speculation on the price difference of related financial instruments. Depending on the nature of this relationship, arbitrage can be deterministic or statistical.

Deterministic arbitrage implies that a fundamental connection between the instruments exists. This guarantees that this relationship will continue into the future. An example is a stock share and the same shares futures contract, shares and depositary receipts, same assets represented in different markets, etc.

Statistical arbitrage relies on just a statistical relationship between instruments, based usually solely on historical observations and backtesting, it does not by any means guarantee the preservation of such a connection in future. Examples include shares in the same market sector, different crude oil types etc.

Above is a most common arbitrage strategies' classification, basically just a binary one. Yet, depending on the types of financial instruments used and trading strategy, different subclasses of strategies can be branched out. Let's immerse into some of the most popular and known options below.

Classical arbitrage

Classical arbitrage this is one of the simplest arbitrage strategies in essence, based on using a fundamental relationship between any underlying asset and its derivative financial instrument (derivative). The most common example is just conducting arbitrage trading on a pair consisting of shares (or "spot", some immediate delivery asset) and futures (or - assets with deferred delivery).

Where does the price difference come from if we're literally trading the same asset? The quirk is that futures, comparing with shares, require significantly less funds to open a trading position (just the margin, usually calculated with the SPAN method), with the remaining money "laying free", as in "free to deposit while getting additional income". With the market considering this additional profit opportunity, expected additional income from the deposit is included in the futures' contract price. Therefore, usually futures price is always higher than the share price by the premium amount, and this difference decreases over time, reaching zero at the time of contract expiration. However, market participants' expectations regarding interest rates and the value of the underlying asset vary (not a surprise by any means in such a field riddled with complex inter-relationships, predictions, fear, greed and deep data analysis) provide additional price "noise". As a result, constant fluctuations appear in the difference between futures and the spot prices, the "spread", allowing arbitrage traders to earn their cash.

Below is an example of a typical spot-futures price difference (spread) chart:

spot-futures arbitrage

This strategy is suitable for cautious traders, because of its low-risk nature and, if used correctly, capability of bringing up to 30% per annum ROI. However, it should be noted that because of its "popularity" and sheer algorithmical simplicity, a high degree of competition among traders on the absolute majority of trading instruments persists, therefore, as a rule, speedy connection while being colocated with the exchange is needed not to sink (because this pond is mostly inhabited by sharks and marlins).

Сross-exchange arbitrage

As it often happens, the same or roughly equivalent financial instruments are traded on different market exchanges; for example, most commodity futures. For various reasons, ones objective, with the others being so complex we'd sign them off as purely random, there are regular price differences between exchanges that can be used for biting off quick (for sure - otherwise they'd dissapear switfly) and (almost) risk-free profit. This is the basis of cross-exchange arbitrage.

The algorithm behind this strategy is almost as simple: on one exchange's asset price becoming higher (lower) than the other, simultaneous opposite transactions are made on both exchanges in the direction on both exchange prices returning to some mean value. Cheap instrument is bought, while the expensive one is sold, so it's just another personification of traders' mantra "buy low, sell high", only now it's performed with almost crystalline certainty. Since the same asset is traded, after some (usually quite short, in the second-minute ballpark at most) time the prices equalize (or jump in another direction), and the trader can exit his double-fork position with a small but guaranteed profit. An interesting thing to note is that surebets or value bets are in reality conducted using the same "algorithm".

However now, usually the price difference for most liquid instruments is either very small, or dissapearing so quickly that it is almost impossible to use it to earn, among the vast majority of private traders. Mostly, this is due to the high popularity of this strategy among large players using high-frequency trading systems (damn you millisecond-zero-commission arbitrage guys!), continuously monitoring even the slightest price differences between exchanges. These robots dictate an absurdly high level of competition, constantly competing with each other over being first getting quotes and submitting orders. Therefore, for an ordinary trader without significant infrastructure investment - entering this pitfight is just meaningless at the very least, usually - detrimental to his trading account (and emotional status, for sure!).

But, despite all these difficulties, it is still quite possible to earn with cross-exchange arbitrage if one excercises his imagination in using young exchanges, where price discrepancies are oft-happening, and big players are rare, on the contrary; or exotic/illiquid instruments (be sure to include a market-making algorithm too) that for various reasons are not of big players' interest. As an example, we can include forex broker CFD contract vs. real asset arbitrage. Another good example is Bitcoin arbitrage. A couple of years ago, in the era of rapid growth of crypto-hype, may we say so, a lot of cryptocurrency exchanges began to pop up, with the price difference sometimes reaching tens of percent in times of volatility and news (in that particular case - almost all the day). But even now the cross-exchange cryptocurrency arbitrage "spread" often remains extremely attractive for excercising one's arbitrage skills.

Calendar arbitrage

Calendar arbitrage as a strategy applies to instruments with deferred delivery (most derivatives belong to this category), primarily - to futures (although there are vanilla option calendar arbitrageurs, to be honest; though this is one of the most "math-y" fields of trading). The gist of the strategy is also quite simple (as always, with devil hiding in details). Suppose we have two futures contracts, with different expiration times. With the constant market participants' expectations on interest rate, the price difference between those would surely remain constant and equal to the amount of additional income obtained in case of placing the funds remaining in free posession (remember - if we buy futures instead of the spot, we do retain control over spot minus margin lump sum) on an interest account for a period equal to the number of days between the expiration dates of said futures contracts. However, as in the case of classical arbitrage, due to various expectations of traders, unexpected (same with expected) news, the price difference between contracts makes constant fluctuations around the theoretical "fair" value, providing us, traders, with the opportunity to conduct arbitrage trades.

As an example, here's a Gazprom (MOEX blue chip) futures calendar spread chart:

calendar arbitrage
Statistical arbitrage

Statistical arbitrage stems from its very name, "statistical". All the types of arbitrage strategies above are based on an unconditional, fundamental relationship between financial instruments, yet statistical arbitration is only (huh) relying on statistics, i.e. on historical correlation or cointegration (there are several more non-causal relationship types though) showing some degree of relationship between assets. The main task picking a synthetic spread of two or more financial instruments so the price difference between them (the spread) would make constant oscillatory movements with a presence of some average value, a mean value, and that which would be constant or vary slowly enough compared to the frequency of oscillations. By finding (or checking for, algorithmically of course) such a combination, one can use these fluctuations to profit with mean-reversion trading.

As an example of statistical arbitrage, we below provide a spread chart representing a relationship between the NASDAQ100 index futures and its two largest constinuent companies: Apple and Google.

statistical arbitrage

The main statarb advantage is a much greater degree of variability: within an almost infitite number of possible combinations of instruments lies a guarantee of absence of serious competition from other traders. Indeed, thousands and thousands of different financial instruments are traded on modern stock and derivative exchanges. If only considering just possible pairs (with weights = 1) of all those instruments, the sheer quantity of those combinations will soar to tens and hundreds of thousands, and there are still three, four-constinuent synthetic spreads, etc. Among such a number of options, one can always find statistically stable combinations suitable for arbitrage trading. However, the reverse side of such a variable coin is a need for specialized software and both computationally and knowledge-intensive (you don't write something like that with one hand on a keyboard and the other holding a bottle of beer during your weekend, although everything can happen, we admit) algorithms to find presumably profitable combinations, since it is all but impossible to do this manually. Imagine checking a thousand of combinations of NASDAQ vs APPLE, and that would only be one combination, with just the weights changed! This is where the computers got us, humans, totally dead to rights.

Another advantage of statistical arbitrage is an overall higher profitability potential compared to deterministic arbitrage strategies, also - it depends less (like, a lot) on such crucial for classical arbitage factors as the speed of one's internet channel as well as exchange latency. This is due to the fact that spread fluctuations usually "targeted" by statistical arbitrage algorithms tend to have a larger amplitude and duration, which not only results in an increase in each transaction's relative profitability, but also allows a comfortable market entry, without worries of orders slipping, and a millisecond's worth delay turning the potential profit into an air castle gone with the wind, things that have a crucial value in other types of arbitrage. The main drawback and risk (here it's not a technical one, rather being a statistical risk) of statistical is the fact that the relation of instruments can disappear over time, and will most certainly do so in future. Therefore, when trading "statistically", one should never forget about setting stop-losses, and other risk- and capital management best practices.

Index arbitrage

Index arbitrage involves working with some kind of an index (for example, a stock index futures contract) and a basket of instruments that are components of the said index. In addition to index futures, various ETFs, mutual funds, as well as any other financial instrument with its price calculated as a weighted spread of a group of another instruments can also be used. The trader's goal in this case is selecting a trading "basket" (or "spread") that fully or at least partially repeats the composition of the index itself. Then you can use the price differences between the real McCoy and your generated synthetic basket instrument for arbitrage trading. So it's nothing new - a spread between two instruments that fluctuates. Only now we're stepping a level above - our spread is made of spreads!

As an example of index arbitrage on Russian derivative exchanges, we can bring forth a combination of RTS index futures vs. a basket of blue chip stocks (Gazprom, Lukoil, Sberbank, etc.). On other exchanges, for example, EUREX, one can try a combination of DAX futures and a basket of its constinuents.

Usually, completely copying an index or a ETF is either very difficult because of the large number of its constinuents, not viable because of rapidly rising trading costs (remember, each instrument in your basket equals an opened position with all the commissions, eating up potential profit), or even impossible. Therefore, traders usually use only the instruments that carry the greatest weight in the index when modelling a basket. As a result, depending on how accurately the trader's model basket copies the "real" index constinuents and their weights - the strategy may come closer to either deterministic or statistical arbitrage, with all the pros and cons of the corresponding type.

One-legged arbitrage

Any of the forementioned strategies can be "turned" (no, not by magic) into so-called one-legged arbitrage if it is established that one of the instruments always shows behaviour that preceds the second one's (or a group of instruments in the case of statistical/index arbitrage). In this case, all or almost all the profits from arbitrage transactions will accumulate on the lagging instrument, and one can try trading only the lagging one while using the leading instrument as an indicator for opening positions. So, when the spread's deviation from the average value occurs, this basically means that the lagging instrument is currently, huh, lagging behind, which means that it is possibly profitable to open a position, expecting that in the near future it will make a move towards restoring (at least partly) the parity, "catching up". With the spread finally returning to its average value, and the lagging instrument basically restoring the equilibrium again, the position can be closed.

There are several ways to determine the leading and lagging instruments, but the simplest and most effective (usually) way is backtesting the straregy on each instrument separately. The instrument on which profits are consistently accumulated will usually be lagging behind, and, respectively, one that shows zero equity rise, or a loss - is the leader of the pack. As a rule, in an arbitrage instrument basket the leading instrument is the one that has greater liquidity. For example, when conducting calendar arbitrage, a futures contract closer to expiration usually comes ahead of a long-term futures contract. Another example is the well-known S&P500 futures contract, which is in world's top 10 most liquid assets, is often used as a leading instrument in many cases, both with index components, and also with securities not directly related to it.

Compared with standard, two-legged arbitrage, the advantages of one-legged arbitrage are obvious and numerous: it has higher yield, requires significantly smaller spread deviations to open positions, has lower transaction costs (at least cut in half). In addition, it poses no technical risk associated with simultaneous opening and closing positions on different markets and the need for them to be at least a bit synchronized in time. However, its shortcomings are also obvious: since transactions remain unhedged, the probability of temporary drawdowns increases substantially.

One-legged arbitrage is very popular among high-frequency, or HFT traders and scalpers, because when transactions are made fast and come in thousands per day, the risk of drawdowns almost completely disappears, and the equity curve is a lot steadier (to the north, of course!). In this form, the strategy is also often called "latency arbitrage". However, with one-legged arbitrage it's still quite possible to make long-term transactions, but one should not forget to limit the maximum risks by setting stop-losses, either fixed or trailing/adaptive. Trade safe!

Forex arbitrage

On Forex, you can successfully implement all of the above types of arbitrage strategies (classic, cross-exchange, calendar, statistical, index, one-legged). However, it's usually latency arbitrage coined under the term of "forex arbitrage". This strategy, in fact, is one-legged arbitrage between the trading instruments provided by forex brokers and their "prototypes" traded on stock and derivative exchanges, but it has its own peculiarities.

The quirk of forex arbitrage is that there is no centralized exchange where traders meet. Forex brokers set quotes and execution prices themselves, based on data streams they are receiving from various liquidity providers (these, in turn, are getting prices from "real" exchanges and banks) and which can be subject to additional transformations: filtering the gaps, the spikes, and just plain smoothing. As a result, quotes make a long way from the liquidity provider to the client's terminal, as they pass through the forex broker's servers and undergo different transformations. All these factors often create situations where broker prices offered begin to lag behind real prices (remember lagging indicators such as MA? Well, it's exactly the point here.), and this can be used (surprise) to one's profit if a faster source of price data is available. Thus, the essence of forex arbitrage, as well as one-legged arbitrage, can be boiled down to tracking situations when there deviations between the broker's quotes and the leading data source occur, and opening positions in the direction of eliminating this difference. Again, trading for an equilibrium, or mean-reversion.

Below is a typical example of a EURUSD spread chart between a forex broker and some leading source. Price deviations are easily spottable here, seen in the form of strong fluctuations in the spread:

forex arbitrage

Degree of forex arbitrage success and profitability usually depends directly on the degree of forex broker quotes lagging behind the fast data source. Leading quotes can be obtained from one of the price data providers, taken directly from the exchange of interest or loaded from a "faster" forex broker. One should, however, bear in mind that the degree of data latency can be and usually will be greatly influenced by not only the data source choice, but also by the geographic location of the broker's servers, the client terminal and the leading source. A compromiss exhibiting the least sum latency should be found. If you get the data with a latency of 5 milliseconds, yet send orders with a roundtrip of 300 milliseconds - you're in for slippage, and vice versa - you're in for a grief.

Forex arbitrage is, of course, one of the most profitable trading strategies, allowing one to accumulate thousands of percent of profit in a short time. Another advantage is the lack of competition between traders - since one trades on streaming prices, not on an exchange-basis, traders do not need to compete with each other to be the first to "grab" a potentially profitable limit order. However, the dark side of this strategy is the tedious search for forex brokers with lagging quotes and the selection of a leading source. In addition, most forex brokers who do B-Book dealing (more information here) do not like traders whose equity rises fast (or at all) and after a while start actively "preventing" profitable trading: increasing the transaction execution time, introducing artificial slippage, expanding spread, etc., thereby forcing one to stop trading. Therefore, a trader needs to be prepared for the harsh truth that daily parabolic deposit growth will not last indefinitely (or any substantial time), and sooner or later he or she will have to stop and withdraw the (easy-?)earned funds, if that would be possible at all. And then - either open a new account with a new "identity", or look for a new broker to zorro up.

Conclusion

In this article, we've tried to outline and describe the main types of arbitrage strategies. All of them are possible to conduct by even an ordinary private trader, it would just take a bit of time to delve into the peculiarities and gather data/experience with the particular strategy. From a practical point of view all arbitrage strategy types without exception require special software that allows one to track the dynamics of several financial instruments, then promptly selling and buying groups of assets in the basket spreads in the event of arbitration situations occuring. With the help of Megatrader, one can implement all of the above types of arbitrage, as well as any other strategies that require simultaneous operation of several financial instruments (pair trading, spread trading, including seasonal spreads, basket trading and others).