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. (more…)