If a trend-following system is too slow, you risk a Type II error by missing a turning point.If a trend-following system is too fast, you risk a Type I error by reacting to noise.
The Holy Grail of trend following is a dynamic system to adjust
speed depending on market/economic conditions.
- from Campbell Harvey Regimes Notes
I think this is the best way to think about the trend-following problem - a choice between making a type II or type I. You cannot escape this problem. Reduce type II and you take on more type I risk. Statisticians will often try and to set the type I to 5% and then have a suitable type II at 10-20%. Traders have to ask the question of what are the cost differences between type I and type II errors. If you are too fast, you will increase trading costs while if too slow, you will miss opportunities. Harvey in his regime work looks at four states of the world based on observable market regimes which fits nicely into the idea that trend-following only focuses on price information. The bull market has short and long-term returns both moving higher. A bear market has short and long-term returns moving lower. The rebound has short returns positive while long-returns are negative, and corrections have short returns negative versus long-term rates.
His work on regimes shows that return performance can be sorted by these four states, yet further work can be developed to account for other state variables.
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