Monday, February 05, 2007

Index tracking, arbitrage, and cointegration

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.)


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9 comments:

  1. AnonymousThursday, March 26, 2009 at 9:54:00 PM EDT

    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.

    ReplyDelete
  2. Ernie ChanFriday, March 27, 2009 at 7:41:00 AM EDT

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

    ReplyDelete
  3. AnonymousFriday, March 18, 2011 at 12:30:00 PM EDT

    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.

    ReplyDelete
  4. Ernie ChanFriday, March 18, 2011 at 1:58:00 PM EDT

    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

    ReplyDelete
  5. AnonymousFriday, March 18, 2011 at 2:04:00 PM EDT

    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.

    ReplyDelete
  6. Ernie ChanTuesday, March 22, 2011 at 3:26:00 PM EDT

    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

    ReplyDelete
  7. JPSMonday, May 11, 2015 at 12:54:00 AM EDT

    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?

    ReplyDelete
  8. Ernie ChanMonday, May 11, 2015 at 6:59:00 AM EDT

    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

    ReplyDelete
  9. JPSFriday, May 15, 2015 at 1:49:00 AM EDT

    Thanks Ernie for the prompt reply

    ReplyDelete