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The Chairman
Victor Niederhoffer

3/15/2005
Why I Don't Believe in Trends

I am often asked why I donít believe in trends despite the great profits of some selected trend followers. The main reason is that standard measures in statistics like the serial correlation coefficient or runs or Goodman tests for m dependent time series, are designed to test trends. I have not found many market series that show consistent departures from randomness on such tests. Nor more importantly, have I ever found a series that looks like it has a trend, whether it be a moving average or lagged momentum type, that doesnít show some serious evidence for non-randomness as measured by the above mentioned tests.

More terribly, the human mind is very good and capable of finding order in chaos and randomness. And what looks like order and trend is often completely consistent with the above.

Two main points that lead to these optical illusions are the fact that the variance of the sum of n random components is n times the variance of a given random component. So as you get further along in time from the starting point of a random series, the movements away from the beginning seem to be very big and trendy, albeit strictly consistent with randomness. (e.g. see chart below, which is a simulated price process where returns are independently normally distributed with mean 0 and standard deviation of 1).

The second main area of deriving order from chance is the human mind's ability to make multiple comparisons. When it looks at a series, it is very good at finding a million stopping and starting points which taken in isolation do indeed show local non-random trends. However, with all these stopping and starting points, it's bound to happen that the straight line between the two points will seem to "explain".

I am well aware that some markets do show trends (in retrospect), and allow back tested systems to work. But merely because it worked back tested, why should the markets be so kind as to allow those who can draw a straight line between two points to make money in the future. Mr. Bacon would argue against it in the field of horse racing. Presumably the wisdom of the market is at least equal to the deceptive practices of the trainers and horsemen.

Well then, how do I explain the great results of the selected trend followers compared to my own? Those results that the great promoters of systems, seminars and books hold up to my discredit and shame. Well , more power to them. I guess I will always be scratching the back of such well to dos.

Tim Rudderow Brings Up an Important Counter-Point:

I think the returns to trend following are not, on average, "great" but are in fact reasonably close to the capital market line. That is, on a risk adjusted basis the returns to the activity are similar to the returns of other risky assets. The presumption here then is that there is some risk premium being earned for the activity, a shorthand of which could be the observation that hedgers are not permitted to lower their risk for free.

As to the lack of serial correlation in the data, I think the appropriate model is more of a regime shift or combination of distributions , with unknown state variable. Markets are often in equilibrium, with little or no serial correlation, which mucks up any test based on the entire sample.

Lastly, trend following does not work in stocks since everyone in the stock market has the same profile - profit maximizer. What is required is a happy loser in a market with fat tails due to inelasticity - e.g. hedgers.

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