MATLAB Examples

Intraday Pairs trading

This demo shows how functionality within Econometric Toolbox can be used to identify and calibrate a simple, intraday pairs trading strategy.

Copyright 2010-2011, The MathWorks, Inc. All rights reserved.

Contents

Load intraday data from a database

We will download intraday data for Brent Crude (LCO) from our database. We will also download data corresponding to West Texas Intermediate (WTI).

LCO = getMinuteDataFromDB('LCO');
WTI = getMinuteDataFromDB('WTI');

pairsChart(LCO, WTI)

% These two time series have historically tracked each other, but since
% December 2010, LCO has consistently traded higher than WTI.  It would
% seem that a pairs trading strategy would not work in 2011, but if we are
% willing to actively recalibrate our model on an intraday basis, we may
% find profitable opportunities.

Let's focus on the last 11 days' of data:

series = [LCO(end-4620+1 : end, 4) WTI(end-4620+1 : end, 4)];
plot(series)
legend('LCO','WTI')

The cointegration test framework

Econometrics Toolbox supports both the Engle-Granger and the Johansen cointegration frameworks. Engle-Granger is the older model, and Johansen is particularly useful for analyzing more than two time series at a time. We will use Engle-Granger for our trading model.

% First, we note that the last 11 days are not cointegrated as a whole
egcitest(series)
% (A zero indicates failure to reject the null hypothesis that no
% cointegrating relationship exists.)
ans =

     0

Even so, there are smaller windows of time where a cointegrating relationship does exist.

[h, ~, ~, ~, reg1] = egcitest(series(1700:2000, :));
display(h)
h =

     1

The test estimates the coefficients of the cointegrating regression as well as the residuals and the standard errors of the residuals: all useful information for any pairs trading strategy.

display(reg1)
reg1 = 

       num: 301
      size: 301
     names: {2x1 cell}
     coeff: [2x1 double]
        se: [2x1 double]
       Cov: [2x2 double]
    tStats: [1x1 struct]
     FStat: [1x1 struct]
       yMu: 110.7448
    ySigma: 0.3043
      yHat: [301x1 double]
       res: [301x1 double]
    DWStat: 0.1891
       SSR: 13.0123
       SSE: 14.7666
       SST: 27.7789
       MSE: 0.0494
      RMSE: 0.2222
       RSq: 0.4684
      aRSq: 0.4666
        LL: 26.6152
       AIC: -49.2304
       BIC: -41.8162
       HQC: -46.2636

The pairs trading strategy

The following function describes our pairs strategy.

edit pairs

We may test this strategy as we do our other rules:

pairs(series, 420, 60)
% Note that this strategy will not trade if the most recent minutes do not
% show signs of cointegration and that the size of the long/short positions
% are dynamically scaled with the volatility of the cointegrating
% relationship.  Many other customizations can be made.

We can use our existing parameter sweep framework to identify the best combination of calibration window and rebalancing frequency.

if matlabpool('size') == 0
    matlabpool local
end

window = 120:60:420;
freq   = 10:10:60;
range = {window, freq};

annualScaling = sqrt(250*7*60);
cost = 0.01;

pfun = @(x) pairsFun(x, series, annualScaling, cost);

tic
[~,param] = parameterSweep(pfun,range);
toc

pairs(series, param(1), param(2), 1, annualScaling, cost)
Starting matlabpool using the 'local' configuration ... connected to 8 labs.
Elapsed time is 32.812738 seconds.

Despite the fact that these historically-tracking time series have diverged, we can still create a profitable pairs trading strategy by frequently recalibrating.