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4.1

Up until here, the concepts we looked at were quite different from what we saw during the discussion for the first pair trading technique. But from here on, it’s quite similar to what we did earlier. Remember what we did towards the end of the first technique? Let’s recap.

• We identified the variable with which we were going to identify trade triggers. In this case, it was the price ratio.
• We calculated the density curve for the price ratio.
• We identified trigger points based on normal distribution.
• And we also identified the type of trade.

The manner of identifying trades using regression is also pretty much the same. The only difference is that we will be using the residual as the basis for calculating the density curve, since that’s the metric here that connects both the variables, just like the price ratio did earlier.

So, without further ado, let’s get started.

### Calculating the density curve

Since the error for the scenario with TCS as the dependent variable was lower, let’s go ahead with that. The regression function gave us the residuals for the price points chosen. We can calculate the density curve for the residuals using the normal distribution function, as you’ll recall.

Here’s a screenshot.

And here’s the table we saw in an earlier chapter, that you can quickly refer to in order to make sense of the density curve.

 Density curve Number of standard deviations to mean Probability of mean reversion 0.0015 -3 SD 99.7% 0.0250 -2 SD 95% 0.1600 -1 SD 68% 0.8400 +1 SD 68% 0.9750 +2 SD 95% 0.9985 +3 SD 99.7%

### Identifying the trigger points

The guide to identifying trigger points remains the same. You will need to identify density curves that are -3 SD to -2 SD from the mean, or 2 SD to 3 SD from the mean. Here’s the guide to initiating a pair trade based on this method.

 Density curve range SD range Trade Target density curve Stop loss 0.0015 to 0.0250 -3 SD to -2 SD Long 0.025 or higher 0.0015 or lower 0.9750 to 0.9985 2 SD to 3 SD Short 0.975 or lower 0.9985 or higher

And a short trade on a pair means going long on the X and short selling the Y.

### Setting up a long trade

To set up a long trade, the trigger range for the density curve is from 0.0015 to 0.0250. Let’s take up some hypothetical data to understand what the trigger and the target scenario look like for a long trade.

• In the row coloured green, the density curve is 0.05. While it’s not in the range 0.0015 to 0.025, it’s the lowest we have in our data set, and it’s quite close to the trigger range.
• Now, say you initiate your pair trade at this point.
• Since this is a long trade, you will buy TCS at Rs. 2248.40 and sell Infosys at Rs. 947.05.
• Recall from the table we saw earlier that the target density curve for a long trade is 0.025 or higher.
• The row coloured yellow meets our requirement.
• With a density curve of 0.35, that’s the target point.
• At this point, you will sell TCS at Rs. 2327.05 and buy Infosys at Rs. 925.05.

So, what’s the net gain or loss from this trade? Let’s check it out.

 Trigger action Cash flow Target action Cash flow Net TCS Buy -2,248.40 Sell +2,327.05 78.65 Infosys Sell +947.05 Buy -925.05 22.00 100.65

So, this trade gives you a net profit of Rs. 100.65.

### Setting up a short trade

To set up a short trade, the trigger range for the density curve is from 0.9750 to 0.9985. Again, let’s take up some hypothetical data to understand what the trigger and the target scenario look like for a short trade.

• In the row coloured green, the density curve is 0.98. This falls in the trigger range.
• Now, say you initiate your pair trade at this point.
• Since this is a short trade, you will sell TCS at Rs. 3203.45 and buy Infosys at Rs. 1271.25.
• Recall from the table we saw earlier that the target density curve for a short trade is  0.975 or lower.
• The row coloured yellow meets our requirement.
• With a density curve of 0.86, that’s the target point.
• At this point, you will buy TCS at Rs. 3176.90 and sell Infosys at Rs. 1305.55.

So, what’s the net gain or loss from this trade? Let’s check it out.

 Trigger action Cash flow Target action Cash flow Net TCS Sell +3,203.45 Buy -3,176.90 26.55 Infosys Buy -1,271.25 Sell +1,305.55 34.30 60.85

So, this trade gives you a net profit of Rs. 60.85.

#### Wrapping up

As you may have observed, the final method of identifying the trigger is common. But the basis for the identification varies. In this method, it is the residuals. And again, as with the previous method, do keep in mind that since pair trading involves short selling, you can only execute pair trades in those market segments that support shorting. So, in the spot market, you can short sell if you’re executing intraday trades. If you want to pair trade in the spot market, you’ll need to execute the two trades within the trade day, and also close your positions in the same session. Or, you could pair trade in the futures market.

#### A quick recap

• A long trade is triggered when the residuals touch the -2SD range.
• A short trade is triggered when the residuals touch  the +2SD range.
• Here, a long trade on a pair implies going long on the Y and short selling the X.
• And a short trade on a pair means going long on the X and short selling the Y.