Chapter 14

# Live Example – 2

## 14.1 – Position Sizing

I know, the discussion on pair trading was to end with the previous chapter, but I thought I had to discuss a special case before we finally wrap up. I’ll also try and keep this chapter really short ☺

So here you go.

I ran through the pair trading algo y’day evening (28th May) and found a very interesting trade. Here are the regression parameters –

• Stock X = ICICI Bank
• Stock Y = HDFC Bank
• Beta = 0.79
• Intercept = 1626
• Std_err = 2.67

What do you think of it? Perfect isn’t it? Its ICICI and HDFC, two of the largest private sector banks, both have similar business landscape, both have a similar revenue stream, both regulated by RBI. Perhaps the perfect candidate for a pair trade, right?.

The Adf value is 0.048, which means there is only 4.8% chance that the residual is non-stationary or about 95.2% chance of the residuals being stationary, which is fantastic.

The std_err is +2.67, which is a perfect residual value to initiate a short pair trade. The trade here is short HDFC and go long on ICIC.

So, how do we position size this? Here are the price and lot size details –

• HDFC Fut Price = 2024.8
• HDFC Lot size = 500
• ICICI Fut price = 298.8
• ICICI Lot size = 2750

Remember we discussed position size in the previous chapter. We look at the beta and estimate the number of shares required for this trade.

The beta is 0.79, this means, every 1 share of Y needs to be offset with 0.79 shares of X. The lot size of HDFC (Y) is 500, this means to offset the beta, we need 395 shares of ICICI (X).

Do you see the problem here? The lot sizes simply do not match.

We cannot simply trade 1 lot each here like we did in the TATA Motors and Tata Motors DVR example, discussed in the previous chapter. If we do, then this won’t be a beta neutral trade.

Hence to position size this, we need to work around with the lot sizes –

The lot size of ICIC is 2750, beta is 0.79, lot size of HDFC is 500. Given this, that the lot size is higher than HDFC, what should be the minimum number of HDFC shares which will beta neutral 2750 shares of ICICI.

To figure this out, we simply divide –

2750/0.79

= 3481.01

Since the lot size of HDFC is 500, we can round this off to 3500. Considering the lot size of HDFC is 500, this will be 7 lots of HDFC against 1 lot of ICICI.

## 14.2 – Intercept

Alright, now that we know the position size as well, here is the big question – will you take this trade?

Everything seems perfect, right? ADF has a desirable value, residual is at 2.67 SD, the two stocks are highly correlated, the business is similar. So what can go wrong?

Yes, I agree, everything looks good, but on a closer look, the intercept reveals a slightly different story.

To understand this, we need to quickly revisit the regression equation –

y = Beta * x + Intercept + Residual

If you think about this equation, we are trying to explain the stock price of Y in terms of the stock price of X multiplied by its beta. The intercept is essentially that portion of the y’s stock price which the model cannot explain, and the residual is the difference between predicted y and actual y.

Going by this, a large intercept implies that a large portion of Y’s stock price cannot be explained by the regression model.

In this case, the intercept is 1626. The stock price of HDFC is 2024 per share, this means, 1626 out of 2024 cannot be explained by the regression equation. This means, the regression equation cannot explain nearly 80% (1626/2024) of Y’s stock price or in other words the equation can explain only 20% of the equation, which according to me is quite tricky.

This further implies, that if we are trading this pair, then we are essentially trading a very small probability here. I’d rather avoid this and look for another opportunity than trade this. Of course, I know traders who would love to jump in and take this trade, but for someone like me, I’d look at risk first and then the reward ☺

Good luck!

Module 10

#### Chapters

1. Kalpana says:

Thanks for the further insight

• Karthik Rangappa says:

Good luck, Kalpana.

2. KUMAR MAYANK says:

Hello sir
I have a doubt.
HDFC= 0.79*ICICI+ INTERCEPT+RESD
For every 100 shares of ICICI we need 79 shares of HDFCBANK. 1 Lot (ICICI)= 2750. Thus we require 2750*0.79 or 2172 shares of HDFCBANK. Therefore we need 2172/500 or 4 lots (approx) of HDFC to trade.
1 lot of ICICIBANK and 4 lots of HDFCBANK, i think, is a combination.
Thanks

• Karthik Rangappa says:

For every 0.79 shares of ICICI, we need 1 share of HDFC. Given the lot size of ICICI as 2750, we need 2750/0.79 = 3481 shares of HDFC, therefore rounded off at 3500.

• KUMAR MAYANK says:

Thank you, sir. I got it.

• Karthik Rangappa says:

Cheers!

3. Thirumal Sharma says:

Hi Sir. Thanks for bringing in another angle which we couldn’t think of. Its like inhaling a trading wisdom!

Just wanted to find out below;

– What are chances of getting stopped out say for ex: out of 100 trades (Just to asess success rate) both in 1st method pair trade method (correlation) and 2nd method (regression).

• Karthik Rangappa says:

I’ve stopped using the first method long ago, Thirumal, and for the 2nd method, I think the success ratio is fairly higher something around the region of 6 of 10 trades working in your favor. The key here is to keep a sharp eye on risk parameters.

• Thirumal Sharma says:

Thank you for the information sir

• Karthik Rangappa says:

Welcome!

4. Akshay Hire says:

What intercept value is right you think?? Pair I am tracking explains 71.83 of NIFTy(y).

• Karthik Rangappa says:

70-80% or higher is a good equation according to me. I’d be hesitant below that.

• Akshay Hire says:

In today’s session it fell down to 63% , Do you think I should wait before it jumps back above 70% to take the trade.

• Karthik Rangappa says:

Yes, that would be better, Akshay. Better safe than sorry 🙂

• Akshay Hire says:

Hey Karthik,
Just wanted so Thank You, since you started this pair trading chapter I spent most of my time thinking about perfect pair trade setup.
I have finally found out using multiple regression method an equation that explains almost 99% of dependent variable.
Is it too perfect to be true?

• Karthik Rangappa says:

99% seems too good to be true, Akshay 🙂
Which pair is this?

• Akshay Hire says:

I am using more than one independent variable to predict just one dependent variable, like using few heavy weights to predict Index.

• Karthik Rangappa says:

Yes, this is possible in a multivariate regression. But we have not really discussed that here 🙂

• Akshay Hire says:

I tried using regression concept between two stocks but it was quite difficult to find stationarity, so I reduced my time frame & used multivariate regression. This is providing better results & stationarity.

• Karthik Rangappa says:

Nice, good luck Akshay!

5. Deepu says:

Hi Karthik,

Amazing write-up!!!

Just a query on hdfc hdfc bank pair. In last 15 days there was a deviation but it never reverted which is strange given it is a highly co-integrated pair.

Request your detailed analysis as a live example on this pair:

1. Whether trade was there in the first place ?
2. Which date would have been the best entry ?
3. Did it hit the stop loss? What should be the SL in such cases ?
4. Is averaging suggested if it moves against you ?

Regards
Deepu

• Karthik Rangappa says:

Deepu, I don’t track HDFC and HDFC Bank as a pair so I wont be able to answer this question.
On your query with averaging, no its not a good idea to average it out. Not just with pair, but every other trade.

6. KUMAR MAYANK says:

Hello sir
I too run the regression b/w HDFCBANK(y) & ICICIBANK(x) for last 200 days starting from 7 Aug,2017. On 28-May-18 i got the following data:
Beta= 0.75, intercept=1639, std.error=67.74
But the ADF value was 0.732
On seeing the graph of residual it is clearly evident that the plot was continuously diverging from the mean from last 50-60 days.
Thanks

• Karthik Rangappa says:

Hmmm, there is a big difference in the ADF values.

• Kumar Mayank says:

If you wish i could show you the plot. On seeing the plot i couldn’t convince myself that the ADF value could be that low.

• Karthik Rangappa says:

Sure Mayank, but currently too many things on the plate. Maybe I’ll look at it one of these days. Thanks for your co operation.

• Kalpana says:

Hello Karthik,

I have been trying to develop the script as you have motivated, currently, i am also getting the same results as KUMAR MAYANK posted above. If you could provide few things from your side, it would be great help to develop my code :
(1) Any 200 Day data of Any two stocks
(2) Output of Linear Regression on these data
(3) Output of ADF Test from your script for these particular data,

If you could provide these then it would be helpful to find out if my script is generating right data or not.
Thanks

7. MOHIT CHANGANI says:

Hello, KarthikJi.
Good Evening,
gone through the last example you shared and it helps me a lot to accurate my trade decisions.
as u mentioned : In this case, the intercept is 1626. The stock price of HDFC is 2024 per share, this means, 1626 out of 2024 cannot be explained by the regression equation. This means, the regression equation cannot explain nearly 80% (1626/2024) of Y’s stock price or in other words the equation can explain only 20% of the equation, which according to me is quite tricky.

what if Intercept Value is negative (-) or sometimes greater than Value of Y stock Price ?

kindly go through the sheet i shared once pls

thanks
Mohit

• Karthik Rangappa says:

Interesting point on intercept being -ve. I will get back to you on that soon. Meanwhile, if the beta is -ve, you cannot really trade the pair.

8. Mani says:

Enjoyed the whole module sir, is there a book or two that you can recommend to further my learning in advanced statistics?

• Mani says:

is it prudent to pair HDFC with Nifty, since it has high weight-age in index calculations, also is there any rule that has to be followed while selecting pairs sir?

• Mani says:

Hope I am not bugging you with too many questions, I see that you have split automobile segment in 2-wheeler and 4-wheeler, like that is there any sub category in IT and FMCG space?

• Karthik Rangappa says:

No Mani, you are not bugging me 🙂

IT can be split as IT large enterprises like HCL, TCS, Wipro, Infy and medium enterprises like Mindtree, Sonata, etc. Same with FMCG.

• Karthik Rangappa says:

Mani, we will have to run through the regressing to test to identify if this is worth as a pair.

9. Mohit Changani says:

Hello Karthik ji,
As mentioned above in this case we had 1626 Intercept for Y stock HDFCBANK price at 2024.
In some cases I had negative values of intercept and in some cases it is more than Y stock Price .
Kindly suggest on how to interprete it.

Thanks

• Karthik Rangappa says:

Negative values cant be traded I guess. Will get back on that. Dont think it can be more that y’s price.

• Mohit Changani says:

Hello Karthikji,
Pls clarify the doubt about it, m confused still …

Thanks

• Karthik Rangappa says:

What is the doubt, Mohit?

10. KUMAR MAYANK says:

Hello sir
You said that the intercept should be much lower with respect to “y” or “beta times X”. I have a doubt. What if the intercept is low but the variance of it is very high or the value of t-stat is very low? Will you take a trade if all parameters are fine save this?
If intercept is high but its variance is quite low or the value of t-stat is very very high. Will you trade it if all other conditions are met?
Thanks

• Karthik Rangappa says:

This is the reason we filter them with the ‘Error Ratio’ 🙂

11. Sivan says:

Sir
Next topic can be on Personal finance
Thanks

• Karthik Rangappa says:

Thanks Siva, will give this a thought.

12. Thirumal Sharma says:

Hi sir, could you please share the latest pair data sheet
Thanks

13. ARUN says:

Hi karthik,
How many modules do u plan to write???

• Karthik Rangappa says:

I’m tempted to write 2 more – Mutual Funds and Financial Modelling 🙂

• Ravi says:

Is there a Chapter on above topic?

• Karthik Rangappa says:

This is quantitative, Ravi 🙂

• Ravi says:

I think, you are missing a module on Qualitative Analysis.

14. Atharva says:

Hello Karthik Sir ,
Will you please consider to write a few chapters on “The ugly side of the markets” like the operators circle , the fake multibagger messages and how prices are manipulated by biggies . If possible how to identify it , either for our benefit or to completely stay away from it . And would also completely love to hear some of stories about this.

• Karthik Rangappa says:

Interesting suggestion, Atharva 🙂

15. Jitender Rajput says:

Hi,
Can the ADF plug in utility can be have for a price or can I get in touch with the developer?

• Karthik Rangappa says:

Suggest you find a developer for building the algo.

16. Pramod Doke says:

Dear Karthik,
I saw tweet about finishing of this module.
I request you to please consider module regarding excel modeling for analysing stocks, options, futures etc.

Thank you
Pramod

• Karthik Rangappa says:

The discussion on Pair Trading is done, Pramod. There is more to discuss in this module. We already have enough content on Futures & Options in Varsity – https://zerodha.com/varsity/

17. Pritam Shetty says:

Hello Sir, Thanks for all the modules of the varsity. I am a regular varsity reader and all this materials have just increased my confidence to trade. Was curious to know if this is the last module or you plan to introduce some more concepts?
Also, kudos to Zerodha for attaining the most number of active traders in such a short span. Its a pleasure to have brokers who are great mentors too.

• Karthik Rangappa says:

Pritam, I’m so glad you liked the content here. I plan to discuss few more trading systems in the module. Post this module, I may stop adding new content for a while. But I do intend to have a module on financial modeling and personal finance sometime soon.

18. Kumar Mayank says:

Hello sir
I got a trade opportunity b/w SBI(X) and Baroda(Y) on 5 June with 200 data points.
Beta= 0.438
Intercept= 28.76 (22% of Y)
Z-Score= -2.678
But i faced a problem with the position sizing. If i long 2 lots (8000) of Baroda then ideally i should have shorted 3504 shares of SBI whereas one lot of SBI has 3000 shares. If i try to balance the size then capital (8 lacs) requirement goes beyond my reach. Still i have been tracking it on paper with 2 lot of Baroda and one lot of SBI.
I want to know your views on the 1) Trading signal 2) Position size.
Btw, the trade is in green 🙂 and touched the profit of Rs 2600 when zscore was at -2.255. Got some relief after a setback in Baroda-IndianBank pair.
Thank you very much, sir 🙂

• Kumar Mayank says:

ahh.it was a profit of Rs 26000 on paper. Have missed to add one more ‘zero’ 🙂

• Karthik Rangappa says:

Hope this translates to real money soon 🙂

• Kumar Mayank says:

Hello sir
I have been tracking the SBI and BOB pair and logging the details. On 11 June the trade was at 28000+ profit with Z-score of -2.11. Now today 18-06-18 the trade ended with the loss of -19500 and z-score 3.11 (dynamic Z-score is -2.84). I checked the adf value and it was 0.1214.
Thank you

• Karthik Rangappa says:

Kumar, its just unfortunate that this pair is taking so much time to converge. This is, in fact, the drawback of pair trading – you need liquidity and patience to hold the pair.

This should also give you a sense of optimizing each pair – not all pair may be worth initiating at 2.5/2.7 and closing at the mean, sometimes, based on the pair, you may want to initiate and close quicker.

• Karthik Rangappa says:

Yes, this seems like a valid trade and the best possible position size is 2:1 on BOB:SBIN.

1) Perfectly valid signal
2) 8000 BOB vs 3000 SBI

Ideally, you should close the position when you hit ard -1 on Z-Score.

• Mani says:

Is it advisable to track the pairs live during trading hours or end of day better?

• Karthik Rangappa says:

Yes, it does. You need to track the Z-score.

19. shiva says:

hi karthik where can we find the trading pairs list, like u said u will publish the same every week

• Karthik Rangappa says:

Will upload the file today in this chapter.

20. Manoj says:

Hi Sir,
Thanks for such a wonderful chapter about pair trading. The way you teach is quite remarkable. Eagerly waiting for the next trading system.

Could you please suggest some books (not pure statistics books) for multivariate regression which is applied for trading along with any case study.

• Karthik Rangappa says:

Manoj, unfortunately, there isn’t much content on Pair trading itself, forget Multivariate 🙂
All you can find is few SSRN papers on the concept.

I will probably discuss an easy way to trade calendar spreads next 🙂

21. Pritam Shetty says:

Hello Sir,
This was an excellent module, enjoyed reading it.
I wanted to know, while looking at the intercept, what percent do you consider should be explained by equation for Y (dependent variable) ?

• Karthik Rangappa says:

Glad you liked it, Pritam. Intercept should explain at least 70% of Y.

Thank you for writings..
What will be the next module Karthik gaaru

• Karthik Rangappa says:

Next chapter will be on Calendar spreads, hopefully next week 🙂

23. siva pavan kumar gummalla says:

• Karthik Rangappa says:

I think Mayank Kumar had suggested few links in one of his comments, maybe you can check that.

24. Pratik Sahindrakar says:

Hi Karthik,

You have mentioned in this post that, this post is risky because 80% of HDFCBANK cannot be explained. Can you specify below what % of Std. Error it is safe to trade on the pair. I get that 80% is definitely high. But below how much % would you have considered this trade as safer?

Thanks for the brilliant post on this topic. You have really simplified the paid trading topic.

• Karthik Rangappa says:

Pratik, I prefer pairs where the intercept explains at least 70% of the dependent variable.

25. sankar says:

Hi Karthik,

Thank you for the fantastic work but the topics are very heavy for the common people. Your creation of any topic and teaching method is fantastic. Your way of viewing in each topic always stunned me and I learnt a lot. My small suggestion is Personal finance for the next chapter with lesser math but with new idea.

• Karthik Rangappa says:

Sankar, thanks for the kind words and suggestion. I have always wanted to do a module on PF, will try and do the same shortly. Thanks.

26. Keshav says:

In 12 Jun pairdata list y stock bank Baroda and x stock sbin beta neutrality 4000/0.44=9090
Then we need to sell 3 lots of sbin for every 1 lot bank Baroda buy, Is it right?

• Karthik Rangappa says:

Nope, 2 lots of BoB with 1 lot of SBIN.

27. Shiva says:

Hi Karthik.when can we expect financial modeling…

• Karthik Rangappa says:

Sometime this year, Shiva 🙂

28. Shivu says:

Is it possible for you to upload the sheet where we can get the trade signals?

• Karthik Rangappa says:

Trying to do that, Shivu. May take some time.

29. Sumit says:

Hi Karthik, The entire strategy series was lovely. I had read linear regression earlier but thanks to you now I am learning to apply them on trading setup. One request/suggestion on the next topic in the line of many such requests. There are many traders who are using Market Profile but there is not very good study material available on web. Can you plan some chapters on this topic & its usability along with price action.

Thanks!!

• Karthik Rangappa says:

Glad you liked the content, Sumit. Content on market profile has been on the radar for a while, will try and put this up sometime soon, thanks 🙂

• Sumit says:

• Karthik Rangappa says:

Cheers!

30. Pramod says:

Dear Karthik,

Can you please tell me how to calculate change in bank nifty ( or any other index) due to change in stocks.
say HDFC bank having weightage around 34 %. If HDFC bank rose by Rs 25 how much likely change in bank nifty considering other stocks being constant.

• Karthik Rangappa says:

You can use the Nifty Sensitivity tool here – https://www.equitymaster.com/india-markets/nse-replica.asp?utm_source=submenu

• Pramod Doke says:

Thank u karthik ji .

But only has the nifty and sensex and not bank nifty.
Could please elaborate on how to calculate on excel

• Karthik Rangappa says:

Sorry, Pramod. I’m not sure if I understand your query. Can you kindly elaborate? Thanks.

• Pramod says:

I want to check which stock is driving bank nifty on any single day if bank nifty is in good momentum.
That is why i want to know how much points are contributed by any bank nifty constituent stock say ICICI bank.
Eg
If icici bank changes by 4 points how much change there will be in bank nifty is other stock are assumed to be constant.

Is this kind of working possible in excel? if yes.

Thanks you

• Karthik Rangappa says:

Equity Master has this sorted out already, check this (look for Nifty Sensitivity) – https://www.equitymaster.com/india-markets/nse-replica.asp?utm_source=submenu

31. vihar patel says:

I really like knowledge shared here on varsity. It is very useful to a trader like me to understand various aspect of trading.

I found something on ADF TEST.

I DID NOT KNOW SINGLE THIS ABOUT IT

BUT MAY BE MR. KARTHIK TELL US WEATHER IT IS USEFUL OR NOT.

• Karthik Rangappa says:

I’ve never used this, Vihar, so I really cannot comment on this. But sure does look good enough.

32. Sumit says:

Hi Karthik,

The two pair data sheets uploaded with last 2 chapters have got tata motors & tata motors dvrm pair as both (x & y) & (y & x) each. Does that mean we can trade both of these pair?

• Karthik Rangappa says:

Sumit, I think the only valid pair is TMDVR (X) and TM (Y).

33. Sumit says:

Hi Karthik,
I regressed Bank Nifty & Nifty using last 200 days data. The stats coming for 1) BKNifty(x) & Nifty(y) was intercept coeff = 2498 & Std error of intercept/Std error = 2.175. Other pair 2) BKNifty(y) & Nifty(x), intercept coeff = -1283 & Std error of intercept/Std error = 2.55. My q is If we go by smaller error ratio, pair 1) the value of intercept coefficient is big. The value of intercept coefficient is less for 2nd pair but error ratio is big. Should we still go ahead with pair 1)?

• Karthik Rangappa says:

We cannot go with a -ve intercept, so your 2nd option is not viable. The first one has a large intercept I guess. So either ways, it may not be a great pair to trade 🙂

34. Keshav says:

Sir please provide commodity pair data sheet too.. Thanks

• Karthik Rangappa says:

Have not developed one, Kehav. Will check if this is possible. Thanks.

35. sumit m says:

Hi Karthik, thanks for the prev response!!

I have set up few other trades using regression data from 12th june excel and am tracking the trades. Pardon me for a long post ahead.

My question are on another trade setup between Andhra – Allahabad bank pair. Set up – (Allahabad Bk = y & Andhra Bk = x, Beta = 0.76. Z score was -1.72 at the time of trade). To make a beta neutral pair, I did long on Andhra BK(10000 lot), short Allahabad Bk(10000 lot) and long stocks of allahabad Bk (2346 Stocks in spot). What happened is that trade moved in favour and z score changed to -1.68 but profit went down due to excessive loss in 2346 extra stocks I purchased for beta neutrality. If I remove this long position than my actual profit has gone up since the trade execution.

1: Is it that by using beta neutrality I did a trade off between risk of z-score going further away from mean & amount of profit that pair will make If z score goes toward mean ?
2: Should we make every pair beta neutral?
3: Practically how long can we use same set of regression data without calculating again?
4: If we find a particular pair has stationary residual, will the pair remain intact unless their is substantial change in fundamentals of any stock. In other words, do we need to keep on running adf test on a particular pair very often?

Thanks again

• Karthik Rangappa says:

1) Not really, Sumit. Beta neutrality ensures your risk is in check.
2) Yes, at least in this way to pair trade
3) Ideally for every new trade
4) Not really, all else equal, adf remains same.

36. Deepu says:

Hi Karthik,

Thanks for the excellent write up time and again.

Quick observations:
1. The stop loss in most cases is given as 0.5 SD but what I have seen that it goes to+- 3 SD and reverses many a times so is it advisable to keep the stop loss as 3 SD ?
2. Further in highly co-integrated pair like Tatamotors the pairs does eventually reverts so should we hold on to the trade ?
3. Is it always ideal to enter at +-2.5 SD level or we should wait for reversal then make the entry ?
4. After reversal also many a times it does not sustain and starts travelling in the unfavorable direction ? How to identify proper reversal ?

Request your views on the above points.

Regards
Deepu

• Karthik Rangappa says:

1) Yes, keeping the SL at 3DS makes sense. So you usually initiate the trade around 2.5 and keep an SL at 3sd
2) Yes, for this you need both patience and conviction 🙂
3) It is best if you can enter around 2.5, things like ‘waiting for reversal’ can add subjectivity in your analysis
4) This is tough

Good luck.

37. Keshav says:

When can we expect another pair data sheet.
Thanks

• Karthik Rangappa says:

Keshav, I will try and upload the file sometime today or tomorrow.

38. Keshav says:

Sir have u uploaded the pair data file.?

• Karthik Rangappa says:

Ah, no. Will do today.

39. Ricky says:

hiii sir,
can you tell me how to calculate z score of pair stocks and how to calculate sigma and which intercept we have to take while pair trading??
is that intercept work which will revived after regression??

• Karthik Rangappa says:

Ricky, have explained this in the previous chapters. Can you please take a look? Thanks.

• Ricky says:

yes thanx for your help sir,
i have understand about intercept but still i cant figure out how to calculate Z score

• Karthik Rangappa says:

The latest residual divided by sigma gives you the Z-score.

• Ricky says:

thanx for such a help sir,
and m sorry if i m bothering you,

but how to find sigma

• Karthik Rangappa says:

No problem, Ricky.

Sigma = Residual/Standard Error. I’ve explained in this chapter.

• Ricky says:

i havent find any thing about sigma in this chapter sir,
but thanq so much for your help…
now i have new query.
which residual we have to use for calculation of Sigma??
is it RESIDUAL OUTPUT or ANOVA RESIDUAL which we had after liner Regression

• Karthik Rangappa says:

Look for it in the previous chapter.

Sigma = Today’s residual / Standard Error of the residual

40. Ricky says:

yeah i have found it..
its in one line so i have missed it.
and again thanx for your help sir..

• Ricky says:

sir i have read again previous chapter and from i have discover in that chapter you had take live example of Tata motors and Tata motors dvr. in which you calculate std_err as same as you comment me how to calculate sigma so sir my question is you are saying that we can take std_err as Z score to open/exit potions in trade…

do i understand correctly or wrong sir..

• Karthik Rangappa says:

Yes, that’s correct, Ricky.

• Karthik Rangappa says:

Good luck, Ricky!

• Ricky says:

thnq very much for your help sir,
this will help me complete my code…

• Karthik Rangappa says:

Good luck, Ricky!

Excellent contribution sir.. one query, why one can not perform pair trading using Options ?

• Karthik Rangappa says:

Pair trading works best when there is only 1 variable to tackle i.e the direction. When there are multiple variables like for an option, you can’t really set up a pair trade.

42. Keshav says:

43. Jayram says:

Hi Karthik,

Just wanted clarity on something. The time period of closing price data to analyse is for 2 years and this will be rolling 2 years right? In the sense, if today i measured the adf test value and residual for (say) HDFCBANK vs BajFinance for 2 years of data (6th September 2016 to 6th September 2018) then tomorrow I would repeat this for 7th September 2016 to 7th September 2018?

• Karthik Rangappa says:

Jayram, yes, this is the rolling data.

• Jayram says:

Thank You!

• Rajiv says:

Hi Karthik,
I find that the length of data series is significantly affecting the parameters. Is two years closing price the best for analysis ?

Regards.

• Karthik Rangappa says:

Rajiv, I know traders who work with last 6 months data. It is best if you can calibrate the model and figure out which time frame yields the best possible results.

• Rajiv says:

Thanks a lot for your response Karthik , I must say just like others have commented earlier , you have done an exceptional work with this varsity.
Keep it up 🙂

• Karthik Rangappa says:

Many thanks, Rajiv 🙂

Happy learning!

44. swapnil says:

Karthik,

Some trades close within a expiry but some takes more than 2 series to close.
Why this huge difference is? any way to guess how much time it will take to close the trade?

Thanks.

• Karthik Rangappa says:

Swapnil, no, predicting timelines against stock price movement is a very hard task 🙂

45. salim qureshi says:

You have mention that you would upload update pair data sheet in one week or 15 day interval, where i should look for it ? and that data sheet will include std|_err, sigma column.

• Karthik Rangappa says:

Salim, for some reason that has not happened, will try and look at this again. Meanwhile, do check out the free link readers have submitted.

46. K Karthik Kaushal says:

Sir, How to use pair trading system to trade options rather than futures??
Can i get a detailed explanation?

• Karthik Rangappa says:

I’ve never explored that angle, Karthik. So I don’t think I can comment on this.

47. Avijit Paul says:

Dear Karthik, what do you suggest on which expiry we buy or short the futures of current or current +1 or current +2 months?

• Karthik Rangappa says:

This depends on the pricing of futures. As a thumb rule, you buy the cheaper futures and sell the expensive one.

48. Arun says:

Dear Karthik,

One thing is clear that -ve beta cannot be traded with a valid reason behind it but what issue -ve intercept is creating, i m not understanding? anyway we are minimising intercept (error ratio), hence whether it is +ve or -ve, it won’t matter as far as it is minimised.
Pls clarify

49. Arun says:

Dear Karthik,

reply is still awaited, pls clarify my issue.

One thing is clear that -ve beta cannot be traded with a valid reason behind it but what issue -ve intercept is creating, i m not understanding? anyway we are minimising intercept (error ratio), hence whether it is +ve or -ve, it won’t matter as far as it is minimised.

50. Arun says:

Dear Karthik,
Talking of beta neutral, we r using it for investing equal amount in both the paired stocks. But dont u think we also need to be neutral such as in the form of hedging. If one stock goes down by 10 points then another stock if pulled up by 10 points, I am at No Loss.
For this to happen, arent we suppose to invest equal lot size in both the pairs so that both stocks counter balance each other’s P&L and give us profit?

• Karthik Rangappa says:

Talking of beta neutral, we r using it for investing equal amount in both the paired stocks —-> No, this is not true, Arun. Beta neutrality ensures we are equal weight on risk, and not on the amount invested. Rupee neutrality on the other side ensures we are equally invested in both the paired stocks.

51. jaya says:

sir , bank nifty vs nifty has correlation 0.93 can we take as intraday 30 minutes data for last 60 days ?
as you mentioned in commodity topic , gold vs silver has good correlation above .80 for intraday purposes .
and what is your opinion sir ?

• Karthik Rangappa says:

Yes, Jaya. 0.93 is a strong correlation, you can consider this.

52. jaya says:

sir thank you so much .

• Karthik Rangappa says:

Welcome, Jaya!

53. jaya says:

sir weekly options on nifty
low cost ETF ICICI NIFTY VALUE 121
RATIOS 11420/121 = 94 UNITS MULTIPLE WITH 75 TOTAL 7050 UNITS
INVESTMENT VALUE NEARLY 853050/RS
SELLING OTM VALUE 100000
SIR IS THIS METHOD RIGHT ?
HOW CAN WE SELECT RIGHT STRIKE FOR SELLING OPTIONS ?
SIR WILL YOU INCLUDE THIS SPECIAL TOPIC FOR “PASSIVE INCOME STRATEGY” IN DETAIL ?

• Karthik Rangappa says:

Will probably include passive income in the personal finance module, Jaya. Btw, you can select the strikes based on 2-3 standard deviations away from the current market price.

54. rohit gupta says:

Dear Karthik,
As posted by Kumar Mayank on 31 May 2018 at 11.30 A.M. that ADF test is 0.732. I have run ADF test for the given period given by Kumar Mayank and found that this test is in constant only parameter. But I asked you some days back that which parameter should be chosen and you told me that no constant parameter should be chosen. I am very much confused. Pl clarify.

• Karthik Rangappa says:

Rohit, use the no constant and no trend parameter for ADF test (in the context of pair trading).

55. rohit gupta says:

Dear Karthik,
In spiderfinancial.com, there are four parameters for ADF test viz no const, const only, const + trend, const + trend + trend^2. Is no constant and no trend parameter is equivalent to no const which is given in spiderfinancial.com. Pl clarify me.

• Karthik Rangappa says:

Rohit, I’ve not really used spiderfinancial. I guess you should speak to them for support, especially since its a paid software. Please check with is the no constant, no trend equivalent on their application. Thanks.

56. rohit gupta says:

Dear Karthik,
If all parameters like z-score, adf test are fine, is it necessary to consider the explain of intercept of y variable which should be at least 70% before initiating pair trade? Pl reply me.

• Karthik Rangappa says:

Yes, you need to look at that as well.

57. rohit gupta says:

Dear Karthik,
Thanks for reply. I have calculated pair trade of idbi and canbk as on 22-8-19 as under:
idbi(x) and canbk(y)
z-score – -2.14
beta – 0.361
Intercept – 242.77
spot of idbi – 24.45
spot of canbk – 209.8
All parameters are ok but Intercept is very high as compared to y stock. I want to ask you whether sometimes intercept can be higher than y stock price and I think that this type of pair trade should be avoided. Am I right?

• Karthik Rangappa says:

Yup, but please do backtest for the same before concluding.

58. rohit gupta says:

Dear Karthik,
Sorry for inconvenience to you.
The answers that you gave in this chapter asked by different persons which has created many confusions to me as under:
1. Pl refer to Dated June 11 2018 at 11.23 am in which you answered about position sizing that the possible position size is 2:1 on BOB:SBIN. This is contradiction because according to data i.e. SBIN(x) and BOB(y) and Beta is 0.438 which are given by Kumar Mayank on dated 11 June 2018 12.34 am, position size should be calculated according to the chapter of Live example -1 as: for every 1 stock of BOB(y), I need to have 0.438 of SBIN(x) which according to this, the lot size of BOB is 4000, so I need 4000*0.438 = 1752 shares of SBIN and lot size of SBIN is 3000. So according to this calculation, the ratio should be 1:2 on BOB:SBIN. Am I right?

2. Pl refer to 21 June 2018 at 11.36 am in which you answered that “the first one has a large intercept I guess. So either ways, it may not be a great pair to trade.” This also created my confusion because according to first pair of data given by Sumit on dated 20 June 2018 at 6.47 pm that Bknifty(x) and Nifty(y) and Intercept is 2498 and price of nifty was 10772 and Intercept of explain on Nifty is 76.8% then how can you say that intercept is large on nifty which cannot be explained. Pl clarify this.

Awaiting of responses would be appreciated.

59. rohit gupta says:

Response of above queries are awaiting. Pl reply me.

• Karthik Rangappa says:

Rohit, in terms of lot size it works out the same right? i.e. 2 lots of BOB versus 1 of SBIN? As far as the intercept is concerned, I’d suggest you look for a lower intercept and ignore the beta. A low intercept implies a better is the linear relationship between X & Y.

60. rohit gupta says:

Dear Karthik,
What is based on the low intercept? Pl clarify me and give one illustration.

• Karthik Rangappa says:

The regression equation should explain at least 70% of the variation of Y based on X. This, of course, is based on the trader’s perspective which is again dependent on the risk-reward temperament of the trader.

61. Ram says:

Hi Karthik,
I was reading a article by The Economist about Bridgewater and how it manages the hedge fund by doing Quantitative analysis. The article explained how Bridgewater and other Hedge Funds have now started using AI. So do you think that with the emergence of all this Quantitative analysis and AI, the way that Trading and Investing is done presently will get vanished in the future?

• Karthik Rangappa says:

The techniques and approach may change as it has for many decades now, but the core underlying fact i.e. the markets being driven by human’s greed and fear will remain the same 🙂

62. Ram says:

So do you think that Fundamental and Technical analysis will still strive in the coming decades?

• Karthik Rangappa says:

My guess is that both will continue till the foreseeable future 🙂

63. Ram says:

Thanks 🙂

64. rohit gupta says:

Dear Karthik,
Sorry for my silly questions. Last month i.e. September month, I got opportunity 3-4 different pair trades method 2. But now for the last more than 30 days, I am not getting suitable different pair trades of stocks of different sectors viz banking(psu & pvt), IT, oil, auto(2-wheelers & 4-wheelers). Is the same occurs with you as well? As I want to trade pair trade method 2 atleast one every month. But this time I am not getting one. Please help me.

• Karthik Rangappa says:

This is a common thing, Rohit. You can have many dry weeks, sometimes few months without a pair trade. The idea is to just wait patiently.

65. rohit gupta says:

Karithik,
Thanks for reply. Now my doubts have been cleared.

• Karthik Rangappa says:

66. tanishq says:

so what percentage of intercept is acceptable according to you?

67. JAI says:

SIR PLEASE, ADD NEW TOPICS ” HALF LIFE CALCULATION AND HURST EXPONENT ” IN PAIR TRADING THANK YOU SIR.

• Karthik Rangappa says:

I’m not sure about the relevance to the topic, I need to understand that first. Will do.

68. Romit Saigal says:

Hi Karthik – I am a member of Zerodha and I have gone through the approaches. I must say very well written and explained, thanks for these. I just wanted to enquire are you publishing any daily pair trade file identifying the pair trade opportunities which I can access ? Thanks.. .Romit

• Karthik Rangappa says:

No, Romit. We were unable to continue doing that.

15 chapters

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16 chapters