# Statistical Arbitrage Strategies

Arbitrage in trading is the exploitation of price differences in the financial markets of e.g. foreign exchange, raw materials and crypto currencies for one's own benefit.

Arbitrage comes in handy for traders as it can both benefit from a mispricing and help rebalance the price of the underlying asset and the overall market. It is a short term trading strategy that can enable low risk investments. However, as with all strategies, there are always some risks to consider.

### What is arbitrage?

Arbitrage means making profit from price differences between identical or related financial instruments, although this usually does not allow for a large percentage return. The greater the mispricing of market inefficiency, the greater the potential return and the faster traders will try to take advantage of it. This reduces the margin potential and brings the underlying back into line with other market prices or information.

An arbitrage opportunity often becomes apparent by comparing underlying assets. For example, if the prices of two currency pairs often behave the same, but then diverge, this can lead to arbitrage in forex trading - assuming that the two pairs will then find each other again. If two very similar underlyings are valued differently for no reason, this can also represent an arbitrage opportunity.

This means that small incorrect assessments, in contrast to large inefficiencies, tend to persist for a longer period of time because the cost-benefit ratio is less attractive.

### Arbitrage Pricing Theory

The arbitrage pricing theory assumes that the return on underlying assets can be predicted as the sum of macroeconomic and other influencing risk factors. In this theory, a trader could find inefficiency in trading and possibly take advantage of the difference between the "wrong" price and the theoretical fair price.

Arbitrage is often referred to as "risk-free profit" when in reality there are very few trades without risk. Arbitrage pricing theory is based on assumptions such as the expected rate of return, that interest rates will not change and that we can identify all of the variables that affect the price of the underlying asset. This cannot be done with a high level of accuracy, but it can alert a trader to a potential opportunity.

Arbitrage pricing theory seeks to identify such opportunities and also assumes that price will return to its historical tendencies. Things that are mispriced tend to revert to more realistic prices over time (mean reversion). Whether or not the theory is used, the concept is important in understanding this type of trading.

### How does arbitrage work?

Arbitrage takes advantage of the financial markets and the fundamental factors that determine the price of an underlying asset, such as supply and demand. This is done in a number of ways. There are statistical arbitrage, which corresponds to a mean reversion, or triangular arbitrage for currency markets. Some more specific arbitrage trading strategies include risk arbitrage, fixed income arbitrage, and covered rate arbitrage, all of which are discussed below.

In all cases, a trader does research to use evidence to uncover mispricing of one or more underlying assets.

### Statistical arbitrage

Statistical arbitrage involves analyzing the normal behavior of certain underlying assets in order to identify possible deviations. A high positive correlation between underlying assets is a commonly used statistic that is often combined with another short-term trading strategy called pair trading.

Using the example of the stock market, a trading opportunity can arise if the prices of e.g. Ford and General Motors normally correlate, but then suddenly deviate from one another. The "normal behavior", the correlation, offers reason to assume that the two prices will move in the same way again in the future.

This assumption is based on the mean reversion model. This means that although markets tend to exaggerate temporarily, they always return to their mean in the long term.

With statistical arbitrage, on the two deviant stocks, a trader could buy the one that is moving down and short the one that is moving up. The stocks selected should move in opposite directions or they are still correlated. In this way, the trader does not rely on the overall direction of both stocks, but on the anticipated correction of a market exaggeration.

Popular commodity products like West Texas Crude and Brent Crude usually move together too. However, the prices are different. So if the typical spread between them decreases or increases, it can present a statistical possibility of arbitrage. This is shown in the following chart.

Source: CMC Markets, WTI Chart

### Triangle arbitrage

Triangle arbitrage is often used in the Forex market when there are price differences between three related exchange rates. Triangle arbitrage involves three transactions: the first currency is swapped for a second, the second currency for a third, and then the third is swapped back for the first. If these transactions create a profit margin, then there is arbitrage.

The magnitude of this arbitrage is usually small, although the potential may increase in moments of high volatility or for currencies that are not traded as often.

For example, if the bid rate for EUR / USD is 1.0847 and the bid rate for GBP / USD is 1.4808, this would imply a bid rate for EUR / GBP of 0.7325. If the price were different, especially by more than a few pips, there would be the potential for profitable arbitrage trading.

### Retail arbitrage

Retail arbitrage tends to take place outside of the financial markets. If you buy an item on the flea market for 5 euros and then sell it on eBay or Amazon for 6 euros, this is a retail arbitrage. You are taking advantage of a disparity in different markets.

Another example: Imagine that all the houses on a new building street are similar, but one house is offered significantly cheaper. The house is likely to sell quickly as a homeowner may want to get a bargain. In that case, that mispriced asset will be withdrawn from the market. However, someone may buy the property at the lower price and resell it at the same price as the other homes in the market to siphon off the difference. This is known as retail arbitrage and can be done in many ways and in different markets.

### Risk Arbitrage Strategy

Risk arbitrage is a speculative and event-driven trading strategy, which is also known as merger arbitrage (English: risk arbitrage or merger arbitrage). If companies in a merger or takeover are expected to subsequently improve their valuation, the arbitrageur will place a long position in these stocks.

A common example is when one company buys another publicly traded company. Let's say Company A agrees to take over Company B for \$ 10 per share. Typically, Company B's stock trades at € 9.75 on the stock exchange, not € 10.

The EUR 0.25 represents a risk arbitrage option. A trader could buy the stock at a price of EUR 9.75 because he knows that he will earn EUR 0.25 per share bought after the deal is closed. This is his expected risk-return premium or the compensation for the risk he has taken.

The risk is that the deal may not go through. In this case, Company B's share price will revert to what it was before the announcement of the buyout. Some of the risk could be offset by hedging. A hedging strategy could be to sell short shares in the company to be acquired (Company A) or to buy a put option on Company B, provided the premium does not level out all of the potential return.

### Fixed Income Arbitrage

Fixed income arbitrage is a strategy used by traders for fixed income securities such as government bonds to exploit the interest rate differentials. Institutional traders can also use this method for more complex interest rate products.

For example, let's say two countries offer government bonds. The states have very similar economies, debt burdens, revenues, expenditures, and unemployment rates. One bond has a 3% return and the other has a 2.85% return. A trader believes that the two bonds should produce the same return. So he sells the 3% bond short and buys the 2.85% yield bond. If he's right, and bond yields ultimately adjust, whether they go up, down, or meet in the middle, he'll pay off.

The same concept could apply to companies that issue bonds. If the companies are similar but the bonds offer different interest rates of return, an arbitrage option may exist. A trader could short the "overpriced" bond and buy the "undervalued" one.

The risk is that the returns will not converge or that the difference will become even greater. In the latter case, the trader begins to lose money.

### Interest rate arbitrage: covered and uncovered interest parity

Covered Interest Arbitrage takes advantage of the differences in interest rates for foreign currencies between countries. This is done via futures or forwards in order to reduce the exchange rate risk.

The futures market takes into account interest rate differentials between currencies. However, if these are not properly accounted for, a trader can benefit from them after the futures contract expires.

Covered interest parity involves a number of steps in order to be successful. Uncovered Interest Arbitrage is less complex, but carries a higher risk. With an uncovered interest parity strategy, there is no futures contract, so a trader simply borrows in a currency with a lower interest rate and invests in a currency with a higher interest rate. This works when the currency with the higher interest rate does not fall more than the interest rate differential. When that happens, the trader loses money as the conversion back is less than the original loan amount.

Read more about how you can use CFDs to hedge currency risks.

### Arbitrage calculator

An arbitrage calculator, or Arb calculator for short, calculates what the theoretical price of an underlying asset would be and how much you should put on a trade to generate a margin.

For example, a triangle arbitrage calculator needs the prices of two currency pairs to calculate the fair price of the third. When the real market price is different, the trader can decide whether this is a favorable arbitrage opportunity.

While an arbitrage calculator is likely to be based on sophisticated programming, traders should understand the math behind it. For example, if the calculator rounds it can eliminate or increase the arbitrage. Therefore, check the parameters of the calculator before relying on third-party calculations.

### How does arbitrage trading work?

• Compare the market price of the underlying asset with the forecast or historical price or trend or possibly with other comparable underlying assets.
• Calculate the potential profit from the arbitrage trade.
• Deduct fees and transaction costs. Take into account spreads, commissions, holding costs and interest.
• Consider the risks and apply an appropriate risk management strategy.
• Review the calculations and plan to execute your trades. Write it down and, if possible, have all orders ready for order at the same time.

Our Next Generation online trading platform allows you to use less complex arbitrage strategies such as forex trading or asset correlations for hedging and forwards, which are available across multiple markets and instruments. As a CFD broker, however, we only offer our customers the option of trading CFDs ("Contracts for Difference").

With CFDs you can trade the price movement of underlying financial values ​​(i.e. forex, commodities or cryptocurrencies). The trading result (profit or loss) is calculated from the difference between the entry and exit price. With CFDs you have the opportunity to move more capital in the markets with the same amount of capital than with a direct investment in an underlying asset. In addition, with CFDs you can participate in rising as well as falling prices of different underlyings.

You can also try automated arbitrage strategies through our internationally hosted MetaTrader 4 (MT4) platform, which offers algorithmic CFD trading options using Expert Advisors (EAs). The EAs can be created by yourself or downloaded from the platform to look for arbitrage opportunities. Open an MT4 demo account to start practicing.

When using an automated trading program, it is important to monitor its performance and understand exactly how it works. Such programs can contain coding or math errors that, in the worst case, can cause loss. Do your own careful review before using automated trading programs.