Do you know what strategies hedge funds use? How to make money regardless of the direction of the market with a minimum risk for the deposit? The answer lies in the use of so-called **market-neutral strategies**. Private such a strategy is **arbitrage**. But unlike classical arbitrage, the use of which is available only to a limited number of persons, statistical arbitrage, of which **paired trading** is a variety, is available to all traders.

In the article we will talk about how to find statistical dependencies, what tools to use for this purpose, and what potential this technique has against the background of a more traditional single-currency trade.

**MARKET-NEUTRAL STRATEGIES**

Neutral strategy with respect to the market means that the profitability of the strategy does not directly depend on the direction of movement of the price of a particular instrument. This is achieved by creating a hedging position between two or more instruments, the profits and losses of which compensate each other.

One of the main characteristics of such a strategy is a minimal risk, since we exploit low-level market dependencies. Such strategies, for example, include market-making and arbitrage. However, unlike classical arbitrage, statistical arbitrage does not imply a risk-free profit.

In the context of statistical arbitrage, the main task is to create a market-neutral portfolio. To achieve the effect of neutrality, the portfolio must consist of highly dependent instruments, roughly speaking, so that the growth of one compensates for the fall of the other. That is, we need to create a semblance of a closed system where the funds are redistributed between portfolio instruments. Paired trading is a special case of statistical arbitrage and the most popular strategy of such a plan.

**PAIR TRADING**

By **pair trading** means simultaneous opening of positions on two interconnected instruments. Dependence is usually determined by their **correlation coefficient**. The most popular way to evaluate the relationship between two time series is to calculate the Pearson correlation. The stronger the correlation of instruments, the greater the probability of their movement in a single direction.

In this case, there is both a positive and a negative correlation. In the first case, the tools move in a co-direction. Example - GBPUSD and EURUSD.

With negative correlation, the instruments move in opposite directions. Example - EURUSD and USDCHF. Both cases are examples of strong dependence.

In pair trading, the pair's **spread** is traded, that is, the difference of the two instruments. Since we know that the instruments are moving in a single direction, it means that with the next discrepancy they will likely come back together with a high probability.

The easiest way to illustrate trading on the strategy of pair trading is based on the pair EURUSD and GBPUSD. So, if the spread (difference) between the two instruments is widened to a certain threshold, we buy a lagging instrument and sell it ahead of schedule. When the instruments come together again, we fix the profit.

The magnitude of the threshold discrepancy is determined by the statistical method, by analyzing the history of past discrepancies. For example, this may be an average discrepancy over the past year.

As a result, for us it is absolutely unimportant in which direction a separate tool will go. It is important for us that they come together, that is, their spread is returned to zero. At this point, we fix the profit equal to the size of the discrepancy.

To make this strategy profitable, there must be a constant relationship between the instruments. EURUSD and GBPUSD have a fairly strong positive correlation. However, this dependence is not constant, because of what the pair can disperse for a very long distance and do not converge back.

In fact, trading the spread of EURUSD and GBPUSD is similar to trading their cross - EURGBP.

If the pair had a permanent strong correlation, the EURGBP would always be in a flat state. However, the dependence periodically collapses, in connection with which trends are formed.

**DRAWING A SPREAD CHART**

Now we turn to the practical part - the construction of a spread of two instruments. There are different ways of calculating the spread, slightly differing in the final result. Which one should be chosen is a matter of individual preferences. The simplest way is to calculate the spread by the difference. That is, the spread formula for EURUSD and GBPUSD will look like EURUSD - GBPUSD.

You can also build a spread with respect to, for example, EURUSD / GBPUSD. It is worth considering that the resulting signals may vary depending on the chosen method, but they do not fundamentally differ.

Next, you need to decide when to enter the position. The task is to enter the market with a strong expansion of the spread, that is, when the connection between the instruments is temporarily lost. A strong expansion of the spread is an expansion more than average. Therefore, a good indicator for the entry can serve as the difference between the spread graph and the moving average.

Thus, we get the spread oscillator. To trade such a spread is extremely simple. When the line enters the overbought zone, that is, the spread has deviated significantly from the average - we sell the spread, when it enters the oversold zone, we turn the position.

In this case, to buy the spread, you need to buy EURUSD and sell GBPUSD. To sell the spread, the opposite is true: we sell euro and buy pounds.

Another method is to trade a spread from the borders of the Bollinger Channel. To do this, just add the Bollinger Bands indicator to the chart of the spread. In this case, the crossing of the canal boundaries will also indicate a significant deviation of the spread from the mean.

**CALCULATION OF THE SIZE OF ORDERS**

Another important point - the correct calculation of the size of orders for the pair position. It is logical to assume that two orders should be of equal volume, so it is enough to open two positions with the same number of lots. But not everything is so simple. If we consider the discrepancy between the instruments in points, then we assume that the points are equal for both instruments.

In fact, to equalize positions, we need to take into account the different cost of a point of two instruments relative to the dollar. Let's say you want to open a pair position for EURUSD and USDJPY. The cost of the item for EURUSD is $ 1. The value of the item on USDJPY at the moment is equal to 0.87788 $. Thus, to equalize the position sizes, the position volume for USDJPY should be 1.14 times larger than the volume for EURUSD (1 / 0.87788).

**CONCLUSION**

The most important part of the pair trading strategy is the proper selection of instruments for trading. It should be understood that the strategy itself is not a grail, but with the right selection of correlating assets it is able to produce a stable profit with minimal risk. If you want to start studying the statistical arbitrage, it's definitely worth starting with pair trading.