Systematic Trading research and development, with a flavour of Trend Following
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Why Trend Following works: look at the Distribution

October 21st, 2009 · 7 Comments · Strategies, Trend Following

One of the most important underlying concepts that contribute to the success of Trend Following is the fact that the strategy is based on the non-normality of market returns. Let me explain.

Trend followers position themselves to profit from and capture the “fat tails” exhibited in market returns distribution. In a fat-tail distribution (Power law, Levy or Mandelbrotian distributions), extreme occurrences occur with a probability greater than normal.

Fat-tail vs. normal distribution: notice the thickness of both extremes on the Levy distribution." title="Distributions: Normal v. Levy

Fat-tail vs. normal distribution: notice the thickness of both extremes on the Levy distribution.


As Dave Harding of Winton Capital puts it:

If you put in stops and run your profits and trade randomly you make money; and if you put in targets and no stops, and you trade randomly you lose money. So the old saw about cutting losses and running profits has some truth to it.

The basics of trend following is to ride the trend until the end (when it bends) and to protect yourself on the downside by cutting your losses.

This ensures that the location of your trades in the returns distribution will:

  • Never venture on the left fat-tail (i.e. no extreme negative return)
  • Not be bounded on the right-hand side of the distribution (i.e. allow for extreme positive returns)

As the markets are mostly random, most of the trades will end up in the centre of the distribution curve either side of the horizontal axis – and their return should cancel each other out.

Trend Following’s alpha (the actual strategy return) is generated by extreme movements: By letting trades run on the right-hand side fat-tail and stopping them from “wandering” on the left-hand side one, an overall positive return is generated. This outlines the fact that Trend Following relies on rare extreme returns (outliers) whereas the bulk of trades cancel each other out.

Note that this post simplifies matters to illustrate the fundamental point. Other parameters such as trading costs, etc. obviously need to be considered.

UPDATE: For those readers wanting to investigate this concept a bit further, a later post presents a research paper investigating the effects of the 4 first moments of the price distributions on the return of a Trend Following system. Please read here

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7 Comments so far ↓

  • Millward

    A very clear and layman like discription of how a fat tail can be conducive to a traders overall alpha.
    Cheers

  • Jez

    @Millward
    Thanks – I tried to break it down in a simpe manner because I think it is primordial to understand and be in full agreement of the underlying philosophy behind a trading system.
    Re-reading Trend Following by Covel made me understand that trading philosophy is as important as the actual strategy.

  • jack

    i don’t agree with your assertion that the market is mostly random with some extreme movements, especially the extreme movement part, because it implies that only in rare occasions will you ride on the trend correctly.

    the overall market is a reflection of the economy and a particular stock price is a reflection of the health of that company. if we agree on this then the stock price is not a random walk down the street. if a company is enjoying 30% growth year over year, the stock price should rise year over year to reflect that growth. so in good times you should see a lot of trending stocks.

  • Jez

    Jack – I understand your point of view, although I believe in your specific case, a stock growing at 30% a year might have this aspect already “priced in” and any future price variation will depend on other factors (ie beating expectations, unforeseen events – black swans, etc.). One could argue that these factors can not be known and therefore price changes will appear “random” in the future (as random as events that will influence it). This in essence the philosophy of the Efficient Market Hypothesis. In this scenario prices are distributed under a gaussian (normal distribution).

    However there is also a behavioral aspect to investing/trading which generates these fat-tails (maybe similar to the reflexivity concept described by Soros) which proves that the gaussian does not apply to the price distribution.

    One way of looking at this is if you picked stocks randomly, most of them wouldd randomly “err” on the positive or negative side but more stocks than “predicted” by the normal distribution would exhibit extreme movements. And this is shown by Trend Followers performance with more losing trades than winning ones (albeit winning trade gains far exceed losing trade losses).

    I hope this clarifies my point… I was not trying to say that stock movement is completely random – it is definitely linked to the fundamentals (in the long term); but the change in the fundamentals is random from an investor point of view (even though it might result from excellent management from the Company directors).

    This post was mostly inspired from various readings (mostly these books) as well as Trend Following by Michael Covel (and there are a few more posts coming regarding this!)

  • Alex

    Hi,

    your blog is very interesting.

    Concerning TF and fat tail, we often hear that TF profits from fat tails, but can we conclude that it is “The” reason why it works? What about a distribution with fat tails but where the daily returns are strongly negatively autocorrelated? What about a distribution without fat tail where the daily returns are positively autocorrelated? I was never able to demonstrate that fat tails is “The” reason. Would be enough to find a theoretical distribution without fat tail that is profitable with TF to demonstrate that fat tails is not the reason. Read a research once where the impact on TF of the different moments and other features of the distribution were analysed. I think, the conclusion was that fat tails had a negative impact. More important was the path of the daily returns (“directional volatility”). Have to find where I have this research.

  • Jez

    Would be very interested in that research Alex, please keep us posted if you find it again.

    Thanks for your comments – and you make a very valid point. I think the main point I was trying to illustrate that “cutting losses short and letting winners run” (which is one of the main concepts of trend following) in a fat tails distribution should yield positive returns – because fat tails mean that there will be “relatively speaking” many extreme movements (ie. long trends).

    Agree that there is a bit more to trend following than that (otherwise you really only need random entries with tight stop-losses…). The main “extra” is that the actual entry provides a positive edge compared to a random entry and as you point out this implies auto-correlation

  • Ravi Annaswamy

    Very nice summary that ties together the cut your losses and run your profits and shows it visually on the distribution.

    The motto of every trader should be: avoid big losses.

    Two causes of big losses: big position, no stop.

    Defining big loss, big position, right stop in a quantitative uniform way across market moods, instruments, one’s own moods is what takes me from ‘logically-I-get-it’ to ‘actually-I-make-it’.

    Hite’s 1% rule and the ATR are nice ways to quantify these.

    Regarding the extreme fat tails, they happen either because (a) market has to adjust to a real fact, a company made huge profits (b) a bluff feeds on itself (c) bluff has been called and market has to reset and overcorrect

    Mandelbrot does note that there are events that drive prices in a predictable direction, just that one cannot predict WHEN. Hence, a company announces increased earnings and on that day, stock tanks.

    This is why, Buffett model of time-agnostic buying value at a discount, when you can patiently wait UNTIL it appreciates, assuming the company does not go bankrupt in the meantime, is also a solid framework for moneymaking on stock investments, though the analysis, patience and ability to weed out bad ideas is hard. TF on the other hand is a simple framework but to grasp and implement it in its detail is so hard, on a trade by trade basis. Until trades are sized so small that one can be indifferent to the outcome of a given trade, TF is hard to implement.

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