Pairs Trading Basics Understanding Spreads, Differentials, and Ratios

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As I had mentioned before, there are two methods for pair trading. The first, which we will explore now, is called the correlation based technique. This is a common approach used by traders to get their feet wet in this field.

Before we move on to the actual technique, it is important that we are acquainted with some of the jargon related to tracking pairs. I just want you to be aware of their meaning for now; as we go along, you can join up the pieces.

Spreads are a popular term in the trading world due to their versatility. Traders who scalp can refer to the Rupee difference between the bid and ask prices, whilst arbitrage traders use it for the difference between prices of the same asset across two different markets. In pair trading – a correlation-based technique – the spread represents the difference between closing prices of two stocks.

The spread is worked out as –

Spread = Closing value of stock 1 – closing value of stock 2

Take a look at this –

If I assume GICRE as a stock 1 and ICICIGI as stock 2, then the spread is calculated as –

Spread = 6.1 – 3.85

= 2.25

It is important to understand that 6.1 and 3.85 represent changes in the stock price relative to the prior close, both of which are positive in this example. However, if we suppose that ICICIGI’s closing price was -3.85, the spread would be reversed.


= 9.95

I’ve worked out the spread for the past two trading days, so you have an insight into how it moves. Traders typically call this the ‘historical spread’ since it is measured on a daily basis.

It varies day-to-day.

The spread will widen if S1’s closing value is up, while S2’s is down.

The spread decreases if both S1 and S2 have a positive closing value.

Of course, there are other possible combinations which lead to the expansion of contraction of the spreads. More on this later.

Differential- Rather than looking at spreads, the differential offers a measure of the absolute difference in closing stock prices for two securities. The formula to compute this is as follows:

Differential = Closing Price of Stock 1 – Closing Price of Stock 2

If a stock 1 ends at Rs.175 and stock 2 closes at 232.

175 – 232

= – 57

As you may have guessed, you can run this as a time series and calculate this on a daily basis, I’ve done this for GICRE and ICICIGI –

It is important to remember that differentials are best employed at the end of the day, rather than for intraday tracking of pairs. On the other hand, spreads are an effective tool to monitor such activity on a short-term basis.

We will delve deeper into this later, for the moment however let’s focus on demystifying some of the terminology.

Ratio – It’s captivating to me how the ratio works. Essentially, it divides either stock 1’s stock price by stock 2’s, or vice versa.

Ratio = Stock Price of stock 1 / stock price of stock 2

I’ve examined the proportion of two stocks, and this is what it appears to be.

The Ratio is relatively steady when charted over time. I depicted all three elements on the graph, clearly demonstrating this.

What of these concepts – spread, differential, and ratios – are relevant to pair trading? How do they connect?

As you can see, these variables are a helpful tool in gauging the rapport between stocks seen as pairs. Graphs provide insight into how each stock behaves in comparison with the other; for instance, examining the spread helps us determine whether S1 closed higher than S2, or vice versa. If S1 is positive and S2 is negative, the spread will grow larger, whereas if both close positively then it will decrease.

If the stock prices of both stocks decrease, their ratio will reduce; similarly, if they rise, their ratio will increase. Although these are not the only possibilities – for instance the ratio can climb if stock 1 drops considerably and stock 2 remains relatively stable, or vice versa. Alternatively, one of the stocks could jump higher than the other.

Confusing isn’t it?

Therefore, we must monitor the graph of the variable in question, which could be the spread, differentials or ratio. To do this, we have to observe any changes occurring and determine if it’s increasing or decreasing. This will lead us to further terms.

If you anticipate the gap between two stocks to expand or the graph to increase, this is referred to as divergence. With this expectation, you can attempt to make money by putting in place a divergence trade.

When you anticipate the two stocks’ ratio or spread to decrease, it is known as a convergence. This situation can be taken advantage of in a convergence trade where you can try to earn money.

The key query is what makes you certain the variable will converge or diverge? At what point do you initiate a trade? What are the prompts for this course of action? How is the trade implemented? When a trade proves unsuccessful, how do you react? What does your predetermined stop-loss dictate?

How do we decide if two stocks are a pair? Just because they come from the same sector, does it mean they qualify? For example, do ICICI Bank and HDFC Bank count as a pair as both are private banking institutions?

Correlation measures the degree of mutual interaction between two stocks. It helps us to identify and qualify two stocks that move in tandem.

The correlation between two variables gives us a feeling of how they move together. It’s expressed as a numerical value ranging from -1 to +1. For instance, if the correlation of two stocks is +0.75, this implies that:

The plus sign implies a positive correlation, indicating that they move in the same direction.

The actual figure provides an indication of the power of this movement. Closer to +1 (or -1) suggests a stronger correlation between the two variables.

A correlation of 0 implies that the two variables have no connection.

From the above, we can see that when two variables have a correlation of +0.75, they will more than likely be moving in tandem. This does not indicated how much either one moves up or down, only that the overall movement is similar. For instance, if Stock A increases by 3%, and its correlation to Stock B is +0.75, then we cannot predict exactly how much Stock B will move – only that it will increase like Stock A.

It can be expected that with a correlation of 0.75, if Stock A surpasses its average daily return of 0.9%, then it is likely that Stock B will also experience a greater than-average movement in its 1.2% daily return.

A correlation of -0.75 indicates that the two variables move in opposite directions; if stock A increases by 2.5%, we can assume Stock B will decrease, though to what extent is unknown.

Whilst talking about correlation, for those that find the math elements interesting, it is worth noting that for the correlation data to be accurate it must come from a stationary set of data which spends most of its time around an average value.

Keep ‘stationary around the mean’ in the back of your mind – it’ll be important for our discussion about the second technique for pair trading later on.