MATLAB Examples

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

## 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.