Classical Pairs Trading Using MatLab

Performs the classical pairs trading strategy with user defined parameters

Description

This function performs the classical pairs trading framework in a given set of prices
  
From Wikipedia, the free encyclopedia:
“The pairs trade was developed in the late 1980s by quantitative analysts and pioneered by Gerald Bamberger while at Morgan Stanley. With the help of others at Morgan Stanley at the time, including Nunzio Tartaglia, Bamberger found that certain securities, often competitors in the same sector, were correlated in their day-to-day price movements. When the correlation broke down, i.e. one stock traded up while the other traded down, they would sell the outperforming stock and buy the underperforming one, betting that the "spread" between the two would eventually converge.”

Source: http://en.wikipedia.org/wiki/Pairs_trade#Algorithmic_pairs_trading
See also the great book “Demon of Our Own Design” by Richard Bookstaber, which provides an interesting background for the pairs trading strategy.

There are many ways you can implement the pairs trading framework. For this package, I used a very simple set of rules. Details can be found within code’s comments.

Please note that this package has been developed over the years and it will no longer exactly replicate the results from my 2007 paper.

Qualities of the package:
- Handles any number of assets
- Outputs separately the plot for the total cumulative profit from the long, short and combined positions.
- Outputs all trades, including traded prices and time of trades.
- Provides the user a large amount of input choices for the pairs trading algorithm, including:
* amount of money to put in each position (long and short)
* value of transaction cost (in money unit)
* size of moving window for finding the pairs over the price data
* periodicity of pairs updates
* maximum number of days to keep any trade (without convergence).
* value of threshold variable
  
Main references related to the pairs trading strategy are:
  
NATH, P. (2003) "High Frequency Pairs Trading with U.S. Treasury Securities: Risks and Rewards for Hedge Funds", Working Paper, London Business School.

GATEV, E., GOETZMANN, W. N., ROUWENHORST, K. G. (1999) ‘Pairs Trading: Performance of a Relative Value Arbitrage Rule’, Working Paper, Yale School of Management. Available at SSRN: http://ssrn.com/abstract=141615.
  
PERLIN, M. S. (2009) ‘Evaluation of Pairs Trading Strategy at the Brazilian Financial Market’
Journal of Derivatives & Hedge Funds, V. 15, N. 2, pp. 122-136.

PERLIN, M. S. (2007b) "M of a Kind: A Multivariate Approach at Pairs Trading". Working Paper. available at SSRN: http://ssrn.com/abstract=952782.

• Required Products: Statistics Toolbox
• MATLAB release: MATLAB 7 (R14)

[vincent leclercq]

hi Marcelo,

Good work, well explained. Could you please tell where the data provided with the example is coming from ?

[Marcelo Perlin]

The data is from the brazilian equity Market (the paper at SSRN).

But not the full period of the research, just a small part and for a portion of the assets.

Honestly, this was a long time ago. I don't remember which period and which assets were included, but the data is from real assets (not simulated).

[Gabri Jo]

Excellent

[Jon Zimmerman]

I think there is an error in pairs.m when the correlation method is used as many stocks seem to be paired with themselves.

you may want to replace:

    corr=corrcoef(x);
    [idx1,idx2]=find(corr==1);
    corr(idx1,idx2)=0;

with corr = corr - diag(diag(corr)) to zero out the diagnol;
    

[Marcelo Perlin]

Hi Jon,

You're right. I wrote this function for using it in the ssrn paper. In there I didn't used the correlation method. And I never bother to check if it was working. The 'correlation' method is not even an option to the main algortihm. If you wanted to change it, you would had to go to the m file and write it.

Somehow the line corr(idx1,idx2)=0; doesn't take the diagonal out as it should be. Your approach will work, but I'm changing it to corr(corr==1)=0; which I think its a little more intuitive. The new files whould be up tomorrow.

Thanks for your message and rating. I really appreciate it.

Cheers.
Marcelo.

[Jia Geng]

Hey, Marcelo,
 this is a great program. And I am working on this topic too. I always have a question about the data. As Gatev mentioned in his paper, he used the data covering from 1962 to 2002. How did he(how did you)handle the missing values? There got to be some missing values(for example, trading closed for a particular stock). Thanks again for your grogram.

[Modiri Kgomari]

 

[bob]

hello everybody,

marcelo you normalise equities values by ''(value-mean)/std deviation'' it seems to me it's not realistic since all equities do not follow a normal distribution.

how can you justify such a behavior ??

nevertheless the technical code are very well done, congratulations.

maxime

[Marcelo Perlin]

Hi Bob,

Thanks for you comment.

Sorry for the late reply (vacation was great!).

I agree with you that the way I normalized the time series of prices is not realistic. At the time I wrote the paper (which produced the matlab code) that seemed to be a good way of bringing all stock prices to the same unit but, today, I can see the drawbacks.

I cannot change the paper (it is already published) but I'm going to add another option of normalization to the algorithm.

Regards,
Marcelo.

[V]

edited your "pairs.m" file. noticed that when you use the least-squares sum method, the matrix you get is symmetric. therefore, I calculated the lower triangular only, 'nan' on diagonals, and copied over the transpose cell pair. When I set ut very low, this speedup really shows:

for i=1:n2
    for j=1:(i-1)
        Qdist(i,j)=sum((x(:,i)-x(:,j)).^2);
        Qdist(j,i)=Qdist(i,j);
    end
    Qdist(i,i)=nan;
end

last note: i don't think you use pairs(:,2)=m'; anywhere in the parent scripts, maybe you could eliminate it.

[Marcelo Perlin]

Hi V,

Thanks for you comment.

Sorry for the late reply. I just realized you comment on file.

Yes, this would speed up the algorithm, but, it also degenerates the Qdist matrix with respect of the infomration I need to find the pairs with the pairs(:,1)=n; command. .

So, I employed a quick fix based on your idea. See new updated file for details.

Again, thanks.
Cheers.
Marcelo.

[Felipe]

Ola Marcelo,
gostei muito do seu trabalho, e como trabalho no mercado, gostaria de saber mais sobre sua metodolgia de aplicacao. Como estou apenas comecando a me aprofundar nos estudos talvez precise de sua ajuda futuramente. Tenho interesse em aplicar seus estudos na pratica.
Se tiver interesse de discutir algumas ideias ficaria grato.

Obrigado,

Felipe
[e-mail]

[Marcelo Perlin]

Oi Felipe,

Agradeco pelo interesse no programa.
Favor entrar em contato pelo meu email.

Abraco.
Marcelo.

[?ahinder]

And I have a problem about to creating mat-file . I must to use my excell data .How can I solve this problem. I think that "Creating Mat file in C "; but I can not solve my problem because I don't have enough source . Could you help me?? Thanks for your all attention.

Şahinder Kaya
İstanbul Technical University

Mathematical Engineer

[e-mail]

[?ahinder]

Hello Marcelo,
I am student in Turkey, at Istanbul Technical University.And I have a problem about to create mat-file . I must to use my excell data .How can I solve this problem. I think that "Creating Mat file in C "; but I can not solve my problem because I don't have enough source . Could you help me?? Thanks for your all attention.

Şahinder Kaya
İstanbul Technical University

Mathematics Engineering
[e-mail]

[Marcelo Perlin]

Hi Sahinder,

HAve a look in matlab help files. There you can find all the information about importing xls data into matlab.

Cheers.
Marcelo.

[Ahmet Seker]

Hi Marcelo,

I have a question or comment. In the main file, just after line 150 you check whether a position is open and enter a trade if not. It seems to me that if say 1 is paired with 3 and 3 paired with 1, then these will be entered as two different trades. You will enter the same trade twice. Isn't this problematic?

Thanks,

Erdal

[Ahmet Seker]

Another thing is that the t-parameter is not explained clearly in the code. Since all values are normalized and the difference of two standard normal is distributed N(0,2) so setting t=2 means spread is one standard deviation away from the mean, and t=4 two std away from mean. Am I right?

Thanks,

Erdal

[Ahmet Seker]

 

[Marcelo Perlin]

Hi Ahmet,

My replies by email.

Regards.

[Fuzhi Cheng]

Hi, Marcelo:

Would it better to build a cointegration analysis into the pair selection process? Basically you pick the pairs, triples or whatever, that are cointegrated. That seems to be more statistically sound.

Thanks. Fuzhi

[Marcelo Perlin]

Hi Fuzhi,

Econometrically speaking, yes, it would be more intuitive to pick pairs according to a cointegration analysis since it implies a stationary residual from the linear transformation.

But, what I set out to do in the code was to have the simplest case of pairs trading. This justify the use of quadratic error and correlation to find the pairs.

Regards,
Marcelo.

[Nicolasillo]

Hi Marcelo,

It may sound like a stupid question, as I just started using MatLab, but in the description of the algorith is says that "Outputs all trades, including traded prices and time of trades. "

Actually, I am having difficulties in finding the actual file that reports these.

Thank you!

[Nicolasillo]

Actually I found the info I needed.
Thank you!