Systematic Trading research and development, with a flavour of Trend Following
Au.Tra.Sy blog – Automated trading System header image 2

Why Trend Following works: Autocorrelation?

February 24th, 2010 · 13 Comments · Data, Strategies, Trend Following

some Autocorrelation representation by kylemcdonald@flickr (CC)

some Autocorrelation representation by kylemcdonald@flickr (CC)

Is it important to understand why Trend Following works (ie what are the sources of its profitability)?
 
I believe yes. Because markets are non-stationary (changing all the time), their characteristics – including those at the root of Trend Following profits – are changing too.
 
Understanding these market characteristics is a first step towards being able to identify and measure them. This, in turn should be a step to linking Trend Following performance to the state of these market characteristics. Finally, this might be a step towards devising a way for a Trend Following strategy to adapt to these changing market characteristics (this last point makes a very big assumption: market characteristic changes can be predicted with some degree of accuracy).

Kurtosis only?

In an earlier post, I discussed how fat-tails are a reason for Trend Following success (or in technical terms: the excess kurtosis of price distributions).

However, there is something unsatisfying in that explanation: if the kurtosis was the sole source of Trend Following success:

  • Random entries should work as well as any other entries
  • Strategies such as buying Out-of-The-Money (OTM) options (think Nassim Taleb for example) should exhibit similar performance to Trend Following (with the advantage of being a rather simpler strategy)

Something Extra?

I recently came across this paper (PDF) explaining that Trend Following and OTM options buying are strategies exhibiting similar performance profiles. However, the conclusion of this paper was that Trend Following showed superior performance.

Additionally, there is definitely a measurable edge to Trend Following entries (such as this Donchian breakout e-ratio calculation shows). Random entries would not show such an edge.

So, there must be something extra to the kurtosis story explaining Trend Following success…

Autocorrelation

One hypothesis that I want to investigate further is autocorrelation (also referred to serial correlation).

One of the main principles of Trend Following entries – in the face of conventional wisdom – is:

Buy High and Sell Low

Well, it should really say “Buy High, Sell Higher and Sell Short Low, Buy Back Lower”. The point is that Trend Following entries are made at extremes, in the direction of the extremes.

If market exhibit positive autocorrelation at extremes, it can be derived that following the direction of the extreme moves should provide an edge (positive expectancy). This would explain why Trend Following entries perform better than random entries and why Trend Following is a superior strategy to buying Out-of-The-Money options.

Calculation Project

Now, this sounds all well and fine in theory but does this stack up to verification?

To check this, I am planning to run some calculations on historical prices and see if markets exhibit such autocorrelation at extremes. Another aspect that will be interesting to look into is whether this autocorrelation evolves over time and whether these autocorrelation levels are autocorrelated themselves (ie is there some degree of predictability in the autocorrelation evolution).

Now, please note that I am stepping out of my comfort zone here: my “heavy maths” days are quite far behind me and I know that using statistics can be a minefield (because it is so easy to use it in an incorrect manner). For example, the “standard” correlation calculation (Pearson’s correlation coefficient) only determines linear dependence – although market data is non-linear. Might set myself up for some hardship but as we say in French: “Qui ne risque rien n’a rien” (no pain, no gain).

I am also thinking of getting one or two Econometrics books to give me a headstart on this. But if any of you clever readers have any suggestions or tips on any of the above, please let me know.

Please bear with me and stay tuned.

Related Posts with Thumbnails

Tags: ····

13 Comments so far ↓

  • Sam

    Your theory is correct on average. Trading in the direction of a fat-tailed move has proved to be a generally good strategy.

    Generally is the key word, though. In real time you will need a lot of trades to prove this word, “generally.” Trend following can be rough in this case because some times “generally” takes many months and many trades to work itself out.

    One of my fat-tailed models, which was profitable in actual trading for the past four years and profitable in all prior testing back to 2000 fell to pieces over the course of last year and if you examine the the model from Jan 2009-Present “generally” does not work itself out.

    Long story short in trend following you are working with the law or large numbers and to get to those large number in many cases you will need to have an iron stomach.

    All the best.

  • Jez

    Completely agree Sam. Survival is key!

    An edge is not enough if your Risk/Money management does not keep you in the game during the bad times…

  • Joost

    Hi,

    Love to see the result from the autocorrelation calc. Did it myself, but had not enough time to do it correctly.
    Had a hard time to get a much different number then zero in stocks(0-10 minutes intraday).
    I think the result will be a bit different when comparing stocks to indices where in my opinion trendfollowing and mean reversal is different too(prob. range of vola related). Maybe intraday and interday have a different profile as well.

    To Sam: a lot of strategies had a hard time in 2009 not only your trendfollowing but short term (at least what in my mind is short term)mean reversal as well.

  • Jez

    Joost-
    Was thinking a bit more in detail about how to calculate this correctly. As you say it might be a bit more complicated than it sounds to do it correctly but I am planning to do it (at some point). I have quite a few other things on my plate also but I’ll definitely pubish my findings (just dont hold your breath too much ;-)
    Jez

  • Jez

    Readers interested in the above might also be interested in a paper/study mentioned on the CXOAG blog (Amplifying Momentum Returns with Idiosyncratic Volatility)

  • Cap't Moe

    You might want to double check some things, i’m a signals analyst, and the tiemseries autocorrelation that we use is only applicable for stationary signals. If its the same autocorrelation that you’re using, your results will be useless. Unless your signal is at least piece-wise stationary. If it is, try using a forier transform of your autocorrelation data (spectral analysis) plotted in loglog time and magnitude. You should get some pretty interesting results if piecewise stationality is valid

  • Jez

    @Cap’t Moe
    Thanks for the advice – it is indeed more complicated than textbook examples where data is stationary…
    Any recommendations on which direction you would look at for non-statinoray data autocorrelation studies?
    ps: I have to admit this issue has been in the “backburner” for a bit…

  • Artur

    So if Pearson’s correlation coefficient is inadequate, how woud you measure correlation??

  • Jez Liberty

    Artur, I do not think there is any answer to that question (ie how to measure non-linear correlations).
    See this page that gives a bit more explanation on the subject.

  • Ravi Annaswamy

    The highlighted sentence is a great insight in itself:
    “Trend following entries are made at extremes, in the direction of the extremes.” Bravo!

    I do not think you need autocorrelation measurements etc etc, are you hoping that the strength of the autocorrelation will tip you whether to take a trade, etc?

    I think the corollary of your sentence is that:
    ‘Market when it reaches extremes of previous range, sometimes goes to further and further extremes, far beyond anyone can believe’.
    But this happens only some of the times, I would say less than 2/3 of the times.

    So the profitability of trend followers is only partly from the ‘enter at the extremes, in the direction of the extremes’ (another way of saying buy new highs and short new lows.
    The big part of their success is that they cut their losses when the market retraces from the extremes. The willingness to scratch a trade with a loss is the big part of ‘trend following’. So in my opinion, trend-following is actually ‘trend-following, loss-limiting, profit-running’ in the correct description.

    Anyways, your two posts, this one and the other one that describes how tf hangs on the positive fat tail, avoids the negative fat tails are very nice insights, thanks for sharing. Novice trading, even when done by experienced people who have been successful in the past, is to hang onto negative fat tails (big losses) and cut the positive fat tails.

    I once wrote to myself. First enemy: big losses.
    Next enemy: small profits (because they prevent big profits). Good friend: big profits (but they are not in your control to initiate).
    Best friend: small losses (because they prevent big losses)

  • Ravi Annaswamy

    Range expansion from extremes: I meant to say less than 1/3 of the time.

  • Jez Liberty

    Ravi,
    Thanks for your comments.

    I have to say your comment came as a good reminder about this old post (and project idea). I have not pushed this much further for now, but indeed the underlying idea was to check if the strength of the autocorrelation prior to the extreme is a good predictor of continuation of the move (so that it could be used in some sort of regime filtering: take the trade in favourable auto-correlation conditions and do not otherwise).

    I am still not 100% convinced on regime trading for long-term trend following, which is one of the main reasons I have left it “on the back-bruner” for now…

  • Paul

    You have a point. Indeed, if price behavior changes at the extremes (say, LT support and resistance) trend following strategies could have an edge.
    There is evidence the sup and res could act as attractors. The argument is that there are order clusters in those regions and statistical tests support this claim.
    BTW, forget these econometric books. What you need is: Analysis of Financial Time Series by Ruey S. Tsay
    I’m looking in similar issues in my own academic research. I will send you an email.

Leave a Comment