Mr. Lange, a reader of mine from Germany, alerted me to the following paper regarding a strategy related to index arbitrage that involves the EUROStoxx50 index. It is a nice illustration of a common application of cointegration techniques to statistical arbitrage trading. I have written an exposition of this paper, together with an additional index arbitrage strategy not discussed in the original paper, which I posted to my subscribers only area. (Mr. Lange has graciously allowed me to share this exposition with other readers of this blog.)

## Monday, February 05, 2007

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## 9 comments:

I am not sure who is copying whom, but at least another (different) set of authors have written on this exact topic, with very similar applications and results.

See, for example, here: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=315619

"The Cointegration Alpha: Enhanced Index Tracking and Long-Short Equity Market Neutral Strategies", by Carol Alexander and Anca Dimitriu, June 2002, ISMA Finance Discussion Paper No. 2002-08.

I could not access the Ingenta link (paid subscription required) but an alternate search yielded the following copy for Dunis and Ho:

http://www.ljmu.ac.uk/AFE/AFE_docs/ARTCDRH_01051.PDF

In fact, the articles are so similar, that one of the author sets ought to accuse the other of plagiarism.

Hi Anonymous,

It is quite possible that they did the research independently. This type of models is not exactly earth-shatteringly novel.

Ernie

Hi Erine,

First off great blog.

I have a question - I have read through the paper by Alexander and Dimitriu and then compared the methodology they use to test for cointegration with that of used by Paul Teetor descibed in his paper below

(http://epchan.blogspot.com/2009/08/using-r-to-test-for-cointegration.html).

Alexander/Dimitriu run the ADF on a regression that uses log prices and has a constant. While Paul uses prices and removes the constant term.

I am trying to test for cointegration between and ETF and a select basket of components but am confused with what methodology is best.

Any guidance would be greatly appreciated.

Hi Anon,

I prefer regression without logs and without constant offset.

If you regress using log prices, the hedge ratios will apply to the relative capital of the 2 sides. That means you have to constantly buy and sell shares to keep that ratio constant even if there is no entry/exit signal. Regression using raw prices gives you the ratio between number of shares.

As for the constant offset, it is an additional free parameter to be fitted, and the more free parameters there are, the poorer the out-of-sample fit.

Best,

Ernie

Thanks Ernie for your comment on the regression form. I will follow your suggestion and use raw prices.

I had another question - I am using R and I have read your your book as well as Paul Teetor's cointegration guide listed below -

http://quanttrader.info/public/testForCoint.html

My question is - would I have to detrend the spread before running the ADF or does the ADF test in R automatically take care of this?

Appreciate the guidance.

Hi Anon,

Generally, you can set certain parameters in the adf test to allow for trends. But if you spread has a trend, that means it isn't stationary!

Ernie

Hi Ernie,

How important is the Serial Correlation gets after applying the VECM to the two Cointegrating stocks( though the spread is pretty stationary as indicated by the ADF unit root test?

If one finds that there is Serial Correlation in the VECM model,is there a method to remove it?

Hi JPS,

If the serial correlation in the residuals is negative, that enhances a mean-reverting strategy! We only want to make sure it is not positively correlated.

Ernie

Thanks Ernie for the prompt reply

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