Module 10   Trading SystemsChapter 3

Pair Trading, Method 1, Chapter 1 (PTM1, C1) -Tracking Pairs

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3.1 – Getting you familiar with Jargons

Like I had mentioned in the previous chapter, there are two techniques based on which you can pair trade. The first technique that we will discuss starting now, is usually referred to as the correlation based technique. I consider this as a fairly standard approach as many traders get their pair trading handholding of sorts using this approach.

We need to learn few jargons before we get started on the actual technique, so let’s get to that straight. The jargons we will talk about in this chapter are related to tracking pairs. At this stage, I just want you to know what is what. We will connect the dots as we proceed.

Spreads – The spread, is perhaps the most versatile jargon used in the trading world. For example, if you are scalping the market then the word spread refers to the Rupee differential between the bid price and the ask price. Now, if you are doing an arbitrage trade, then the word spread refers to the difference between the prices of the same asset across two different markets. In the pair trading world (actually, just correlation-based technique), the word spread refers to the difference between the closing prices of two stocks.

The spread is calculated 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

Please note, both 6.1 and 3.85 represents a change in stock price with respect to the previous close. Also, both the numbers are positive here. Now, for a moment assume, the closing price of ICICIGI was negative 3.85, in this case, the spread would turn out to be –


= 9.95

I’ve calculated the spread for the last couple of trading days, this should give you an idea of how the spread ‘runs’. Also, since I’ve calculated the spread on a daily basis, traders refer to this as the ‘historical spread’.

As you can see, the spread varies on a daily basis. Also, here is an interesting (general) observation –

  1. The spread expands if the closing value of S1 is positive and S2 is negative
  2. The spread contracts if the closing value of S1 is positive and S2 is also positive

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

Differential – Unlike spreads, the differential measures the difference in the stock prices. The differential measures the absolute difference in the closing stock prices of two stock. The formula is as below –

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

So if a stock 1 has closed at Rs.175 and stock 2 has closed at 232, the differential is –

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 –

Here is something you need to know about differentials – if you are using spreads to track pairs, then you can use it on an intraday basis. But unlike spreads, the ‘differentials’ is not a great technique to track pairs on an intraday basis, its best used at an end of day basis.

Of course, more on these things later. For now, let’s just focus on busting some jargons.

Ratio – I find the ratio bit quite interesting. The ratio is essentially dividing the stock price of stock 1 over the price of stock 2. Or it can be the other way round as well.

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

I’ve calculated the ratio of the same two stocks, here is how it looks –

The Ratio as you can see is a bit more consistent (or at least appears) when calculated as a time series. I’ve represented all the three variables on graph –

So what are these things that we just looked at – spread, differential, and ratios and how are they related to pair trading?

Well, as you can imagine, these are the different variable which helps us measure or quantify the relationship between two stocks, which we consider as pairs. The graph tells us how the two stocks move with respect to each other. For instance, if we consider the spread, we know it expands if the closing value of S1 is positive and S2 is negative and the spread contracts if the closing value of S1 is positive and S2 is also positive.

Likewise in the ratio – the ratio between two stocks decrease if the stock prices of both the stock decline and the ratio increases if the stock prices of both the stocks increases. Of course, there are other variations possible – for example, the ratio can increase if stock 1 declines heavily and stock 2 stays flat or the other way round. Alternatively, stock 2 can increase a lot more compared to stock 1 or the other way round J

Confusing isn’t it?

Hence, for this reason, we need to look at the chart of the variable we are following, the variable could be spread, differential, or the ratio. We need to track the movement of the variable and figure out if the spread is expanding or contracting. This leads us to the next two jargons.

Divergence – If the ratio or the spread between the two stocks is expected to move apart or alternatively, you expect the graph to move up, then this translates to something called a divergence. When you expect your variable to diverge, you can make money (or at least attempt to make) by setting up a divergence trade.

Convergence – If the ratio or the spread between the two stocks is expected to move closer or alternatively, you expect the graph to move down, then this translates to something called as a convergence. When you expect your variable to converge, you can make money (or at least attempt to make) by setting up a convergence trade.

Now here is the big question – what makes you believe the variable can either converge or diverge? When do you decide to set up a trade? What are the triggers? How do you set up a trade? What if the trade does not work out? What is the stop-loss for such trades?

Well, even before we answer these questions, how do we qualify two stocks as a pair? Just because two stocks belong to the same sector, does that mean they qualify as a pair? For instance, does ICICI Bank and HDFC Bank qualify as a pair because they both belong to private sector banking?

To qualify two stocks as a pair we need to rely upon the good old statistical measure, called the ‘Correlation’. I guess, we have discussed correlation multiple times on varsity. Here is a quick explanation –

Correlation between two variables gives us a sense of how two variables move with respect to each other. Correlation is measured as a number which varies between -1 to +1. For example, if the correlation between two stocks is +0.75, then it tells us two things –

  1. The plus preceding the number tells us that they both are positively correlated i.e when they move in the same direction
  2. The actual number gives us a sense of the strength of this movement. In a loose sense, the closer it is to +1 (or -1) the higher is the tendency for the two variable to move in tandem.
  3. A correlation of 0 suggests that the two variables are not related to each other.

From the above, we know a correlation of +0.75 suggests that the two variables move not only in the same direction but also tend to move together closely. Note, the correlation does not suggest the extent of the move, all it suggests is that the move in the same direction is likely to happen. For example, if Stock A moves 3%, and the correlation between stock A and stock B is +0.75, then it does not mean that Stock B will also move by 3%, all that the correlation suggests is that Stock B will move up positively, just like Stock A.

But, there is another twist here – suppose stock A and Stock B are correlated at 0.75, and the daily average return on Stock A and Stock B is 0.9% a 1.2%, then it can be said that on any given day, if Stock A moves above its daily average return of 0.9%, then stock B is also likely to move higher than its daily average return of 1.2%.

Likewise, a correlation of -0.75 indicates that the two variables move in opposite direction (-ve sign) but they both tend to move in opposite direction. Suppose stock A moves up by +2.5%, then by virtue of correlation we know that Stock B is likely to come down, but by what degree will it come down will not be known.

While we are at it, one more point on correlation. This bit is only for those interested in the math part of correlation. The correlation data makes sense only if the data series is ‘stationary around the mean’. What does this mean? – Well, it simply means that the data set should be sticking close the average values.

Keep this line ‘stationary around the mean’ in the back of your mind, don’t forget it. This will come back to again, when we discuss the 2nd technique to pair trade, much later in this module.

We will proceed with correlation as a measure to understand how tightly two stocks are coupled. In the next chapter, we will figure out how to calculate two different varieties of correlations.

For now, I want you to be clear on Spread, Differentials, Ratios, Divergence Trading, Convergence Trading, and Correlations!

Download the Excel sheet used in this chapter here.

Key takeaways from this chapter

  1. Spread measures the difference between the closing values of two stocks
  2. Differentials measures the difference between the closing prices of two stock
  3. Ratio between the two stocks essentially requires you to divide stock 1 over stock 2
  4. Divergence is when you expect the two stocks to move apart
  5. Convergence is when you expect the two stocks closer to each other
  6. Correlation is like a glue which tells how tightly two stocks move together. ­­


  1. Sujeet Raj says:

    Things are getting interesting. Thank you!!!

    Any approximation on the number of chapters you are planning for this module?

  2. KUMAR MAYANK says:

    Hello sir
    As i got it:
    Convergence= i) spread approaches zero (from both the sides ie -ve and +ve) ii) ratio tains to one. iii) graph of spread moves towards y(vertical axis)=0 from y= -ve ie upward and from y= +ve to y=0 ie downward.
    Am i correct?
    Thank you

  3. NARASIMHA says:

    Since zerodha is not allowing all stocks for intraday(eventhough they are eligible for intraday),Can we use cnc order type with full margin and square it off on the same day?Will it consider as intraday or stt charges are more???

    • Yes, you can use CNC order type and take long(buy) intraday positions and square it off the same day except for Trade to Trade segment stocks. However, you cannot take short positions due to liquidity risk(Read about auction penalties on short delivery here).
      Brokerage, STT and other charges will be charged on intraday basis only

      • NARASIMHA says:

        THANK you faisal sir.I hope zerodha will provide intraday mis order type facility to all stocks.I am loosing opportunities due to this issue.Feeling very sad to say that Iam changing from zerodha…:(

  4. Sashidhar. L says:

    Sir I’m very excited to see this module live. When you say pairs tracking can be used on intraday basis what does it mean? And while we are on the subject, can you suggest one good book on intraday trading techniques? Thanks a ton.

  5. Sashidhar. L says:

    Sir what is the significance of the reference to Jordan Belfort and pairs trading in your tweet?

    • Karthik Rangappa says:

      Hahah, nothing really. The illustration used in this chapter is Leonardo DiCaprio, so thought we;d say something relevant 🙂

  6. Umer Azam says:

    “By stationery around the mean, it simply means that the data set should be sticking close the average values”

    Sir, can you kindly elaborate a bit on this.

  7. Sashidhar. L says:

    Sir I recently discovered something called option adjustment. Do you think you’ll be writing about that or you think it’s not necessary? If you can point me toward a book regarding the same. Thanks in advance.

    • Karthik Rangappa says:

      Option adjustment? Can you share the context, please? Thanks.

      • Sashidhar. L says:

        If the positions we have taken, goes against our target, we take an additional position either to break even or top contradict our earlier view, since we were wrong in our prediction in first place.

        • Karthik Rangappa says:

          No, we have to cut the loss. Will discuss this in detail as we proceed.

          • Sashidhar. L says:

            Sir I will take it at face value if you say taking an additional position to break even in case our positions go wrong is a bad idea. But can you shed some light into why it’s bad thing? After all, breaking even is better than booking a loss right? Thank you.

          • Karthik Rangappa says:

            What if you do not breakeven as expected? Under such a scenario, you will be making a further loss, only with a greater quantity.

  8. gopal says:

    how to download this

  9. Sashidhar. L says:

    Hi sir. Can you please tell me how to get started with NSIM certification? Thanks in advance.

    • Karthik Rangappa says:

      Register for the certification and start reading! You can read the content here as well for additional knowledge 🙂

      • Sashidhar. L says:

        It says in the certification portal that first one is current derivatives. Is that right? Am I registering for the right exam? Also, I’ve already read varsity multiple times sir. Printed out all the modules and gave it to few of my friends as well.. Thanks for the treasure..

  10. Isaac kraho says:

    Zerodha Varsity alone has given me more knowledge than all the other combined studies I have done related to trading. Thank you.

  11. Ganesh Rajput says:

    Very nice,
    Eagerly waiting more on pair trading.

    • Karthik Rangappa says:

      New chapter next week.

      • Umer Azam says:

        Sir, Im having a real problem drawing the graphs, can you please tell me the whole procedure?

        I have downloaded the sheet, the graph is already drawn but If Im trying to remake it I cant!

        • Karthik Rangappa says:

          Which version of excel are you using? YOu need to select the data and click on the insert graph option and select line chart as the graph type.

  12. neerav1234 says:

    While doing the calculations taking two stocks..what is the basis of keeping a particular stock as Stock 1 and the other as stock 2 and not vice versa ?
    Is there any criteria or rule which defines between the pair that this particular stocks will be placed as stock 1 and 2 ?

  13. Pratheesh Karthikeyan says:

    Hi Karthik,

    Great work as usual.

    I have a doubt – at what point does your portal charge the brokerage, stt, etc. Why i ask this is – i had 1.71 lacs on Feb 20,2017 in my account. Till today from that day, I have made a net profit of around 2.78 Lacs on that amount. This means my total account value (if charges are not deducted) should be 4.49 Lacs but it is only 4.22 Lacs now.

    1) I assume the difference is due to the charges (brokerage, stt, etc). Please confirm if that is the case.
    2) Are they deducted whenever we square off positions? Or?


    • Brokerages and taxes are charged at the end of trading for all your trades for the day. You will also receive a contract note in your email with the details.
      You can also these details in Q- Backoffice under Reports>> P&L
      I cannot confirm what all deductions have been made in your account, you can confirm them yourself following the above method

  14. Deepu says:

    Hi Karthik,

    One query for the below statement :
    ” if you are using spreads to track pairs, then you can use it on an intraday basis”
    How to use spreads on intraday basis and what are the setups for the intraday trade based on spreads ? Whats is the success ratio for such spreads setup ?

    Thanks in advance.

    • Karthik Rangappa says:

      I’m not a big fan of spreads to track pair, I find the ratio a better deal. Anyway, the spread is just Stock 1 – Stock 2. Use the LTP to track this.

  15. Manish says:

    Hi Karthik

    Based on the data given in excel, I’ve calculated the Coorelation for HPCL and BPCL. Correlations arrived by correl() excel function are 0.82909, 0.198854 & 0.184658 for Close, % Return and Absolute Change respectively.
    1) Why is there such significant difference in values themselves?
    2) What can be inferred on the relationship between HPCL and BPCL based on figures above.

    Kindly correct me if my calculation is wrong.

    • Karthik Rangappa says:

      Which % return are you measuring, Manish? Also, the correlation seems to be good @ 0.82.

      • Manish says:

        Thanks for your response Karthik.

        Im referring to correlation arrived from data points % return (% return for today = today close/yesterday close – 1) taken for all the dates given in the excel of HPCL and BPCL. Please refer sample data below
        Close %Return Close %Return
        5 Dec 16 432.05 604.2
        6 Dec 16 438.3 1.45% 612.95 1.45%
        7 Dec 16 447.85 2.18% 632.15 3.13%
        8 Dec 16 453.25 1.21% 638.05 0.93%
        9 Dec 16 454.3 0.23% 634.65 -0.53%
        12 Dec 16 433.55 -4.57% 611.85 -3.59%

        I’ve arrived at the correlation value on data points of %return on HPCL and BPCL prices as 0.198854.
        I’m confused on how can the correlation be so less.


        • Karthik Rangappa says:

          Got it. The correlation should be applied to % return, which I think is quite low. Correlation on price should not be considered.

  16. Learning says:

    Thank you for the good read content

  17. Hina says:

    Sir, how can I obtain the data regarding open and close prices of various companies.

  18. Ravi says:

    Sir when module 10 will be available in pdf…. Eagerly waiting for it?

  19. sahil swaroop says:

    hii Karthik
    sahil here as discussed the strategy of pair I wanted to ask how can someone pair trade nifty and sgx nifty as sometimes both they act differently and then again then start moving in the same direction so there is an arbitrage opportunity so wanted to ask how can one place orders in Singapore exchange ?

  20. Deepak says:


    In the data you mentioned in the attached excel, the correll come at -0.21. Is it correct?

    Kindly guide if i am wrong.


  21. Chirag says:

    Hi, data as on 03-04-19 for goldm silverm gave me 0.952 as density output. However, when i inserted today’s close (assumed) and got a new density output, the data for 03-04-19 changed from 0.952 to 0.947.

    Is that fine? I don’t think so. Guess something is wrong

    • Chirag says:

      I now think there is nothing wrong. The mean had to be changed and so did SD and so the density curve too will change.

    • Karthik Rangappa says:

      No, that is absolutely fine. Two possibilities – ether gold or silver or both made a decent move y’day. Or the oldest data point (which gets replaced by y’day’s new data point) was a large value. Please do check for this.

  22. Tejus Reddy says:

    Hi Karthik
    Iam not able to compare same stock at different exchanges.
    For Eg Tatasteel in NSE and Tatasteel BSE.
    If it is not possible, why.
    I want to take Arbitrage opportunity in the intraday, pair of
    stocks in the two exchanges.

  23. A.Latif says:

    Hi Karthik !
    Hv Gone Thru Your Modules.
    Very Well Presented And Understandable.
    I Was Not Able To Find Instructions How To Put The Data Of Two Shares Together On Excel After Downloading From Nse Individually To Proess Them To Find Spread Differential Price Ratio Mean Etc. Also An Full Example Of How To Choose Pairs And When Ready To Trade.
    Can You Please Put Up One Taking HDFC BANK / HDFC As Pair If They Are Suitable And Why ? Any Live Excel Possible To Track The Parameters Live For Intraday.
    Are You Taking Correlation And Cointegration Possibilities Together ?
    Appreciating The Way You Present The Course And Answer All Difficulties In Details.
    Best Rgds,


    • Karthik Rangappa says:

      Latif, you just have to copy-paste the data from two different excel sheets to one and start working on it. The rest of the procedure is explained in the chapter itself.

  24. Tejus Reddy says:

    Hi Karthik

    I forget mention it is in the Kite.
    I am not able to plot line chart with the compare option for the same stock in the different exchanges which has price diffrence.For e.g. Raymonds stock which has the 634 in NSE and 631 in BSE.

  25. KUSHAL SHAH says:

    Hi..I read all the chapters.. excellent concept .and very well explained.. thanks for this
    I have a query ..can we use the same density curve concept for single stock for swing trading..I mean if the stock goes far away from mean ..there wll be mean reversion..

    Plz reply

  26. Dr K Shaikh says:

    i just wanted to know whether the historical stock price data available on nse website are adjusted for splits, bonuses etc…if not then where can i find adjusted data???

  27. sachin amrut karande says:

    please, sir information Hindi me provide Kijiye.

  28. Abhay says:

    Two questions.

    How to get tick data EOD and hourly for backtesting the pair trading strategy? Is it possible to get the data from kite?
    Can you please suggest some books or other materials related to pair trading?
    Zerodha varsity is really good for someone who is into trading. I am thankful to Zerodha team for providing such material to all.

  29. Abhay says:

    Sir, thanks for the book that you suggested. Please suggest if zerodha provides adjusted close price historical data and if not then suggest some authorized vendors.

  30. C H Batraa says:

    Can you assist which stock has to be chosen as stock 1 and stock 2 respectively?
    Isi it mandate to choose the buying stock as stock 1 and the selling stock as stock 2?
    Please assist

  31. can arel says:

    Wow! What a gold mine for Stat Arb, amazing job! The thing about Pair Trading not being market neutral, could they not be it in some scenarios?

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