A Review: “Two Centuries of Trend Following”

日期:2014/04/28

The paper "Two Centuries of Trend Following" by Lemperiere, Derenble, Seager, et al of Capital Fund Management purports to show that trend following has been profitable, over a wide range of markets, consistently over 200 years. It deserves to be reviewed as it represents a case study of the statistical practices, and armchair explanations that are sometimes used to justify a system that in the most recent five year period has lost its mojo. Rocky has asked me to review it.

The amazing thing is that the authors seem to know how to compute hyperbolic tangent regressions, and compute the duration of a drawdown given a sharpe ratio, yet they seem completely unaware of the problem of multicollinearity, overlapping observations, and lack of independent observations.



In a nutshell, they compute hundreds of thousands of means, and they combine them and measure how far away from randomness they are. Recall that the average of two random observations is about 0.7 times as variable as one observations. The average of 100,000 observations is about 1/320 as variable as 1 observation.

They report t statistics of 5 to show that their results are non-random. But, but, but. If you have say an expectation of 1 with a standard deviation of 10, ( lets say 1% for a typical market ), and you divide 10 by 320 (i.e. sigma/sqrt of n), you come up with a t of 32… none of the markets they cover are independent. For example, they use 7 and 10 year interest markets, and 7 stock index markets, and apparently treat each observation as independent. Instead of dividing by the square root of thousands, they should be dividing by the square root of tens depending on the years they consider, and the overlap of the running 5 month values of the independent variable.

Their results, as biased as they are are not meaningful in any practical or economic sense. When they look for the effect of subsequent profits of trend following on past result, they come up with a slope of 0.04. What does that mean economically. If the profits of trend following in the last month was 1%, then the profits predicted in the next month would be 0.03%. The variability presumably is 330 times as great as the expectation.

The authors note that over all markets over the last 5 years, trend following has been flat. Considering that the market likes to give you a profit from a system on a market like lean hogs that trades 1/1000 as much as stock indexes in order to lure you in, the fact that it hasn't made money is very negative. Also, the performance of trend following funds tracked by all the services shows that in practice the trend followers have worse results than the averages.

Even though trend following doesn't work in the real world, the authors have several paragraphs on why it should work. They talk about the slow response to Fed actions, and the tendency of heuristics to follow what works in the past. These are arm chair explanations out of the bush with no statistical support, although their ideas that Fed qualitative actions show momentum is a valid one. The authors might benefit from reviewing Bacon on ever changing cycles or being behind the form. Perhaps I am missing some nuggets of gold in the above paper, and I am open to any corrections in my analysis, or areas that favor trend following that I have overlooked.