Thinking about trend-following using a binomial tree - Simple model shows strategy value

The binomial tree is a core tool for understanding option pricing. David Modest has written a very skillful simple paper on the value of trend-following using the binomial tree framework. This work takes away some of the aura and mystery of trend-following but also shows its fundamental usefulness. Trend-following generates return shaping through dynamic positioning even in an  efficient  markets. The nature of trend-following (time series  momentum) creates “crisis alpha” even if there is no trend.  (See "Some Observations on Trend Following: A Binomial Perspective")

With any binomial tree, there are well-defined and measurable paths for price moves. The tree can be extended for any number of steps with defined paths up and down. Trend-following can take positions based on the path along the tree. In the simplest case, the trend can just follow whatever happened last period. The distribution of returns can be calculated for trend-following and behold, the value of trend-following, better performance  under adverse market conditions, exists even if markets are efficient and follow a random walk. 

Trend-following changes the shape or timing for when profits occur. There will be more mass during market declines which others refer to as "crisis alpha". This return timing phenomena occurs even if there is no trend and expected profits are zero. Using the binomial tree also allows us to compare the differences between fast and slow trend models. Again, there will be different pay-off functions. A fast model will generate more crisis alpha than a slow trend model. 

Just follow the paths using trends and you will get a timing of returns that provides the desired effect. There is no secret skill or magic formula. A long-only investment, a call option, or a trend model can be compared to show different return patterns. Trend-following will generate the greatest amount of crisis alpha.

This may be a disappointment to managers who want to sell their trading skill or for investors who are expecting some high level of strategy complexity from trend-following. Nonetheless, this is a toy model that looks at some generalized features from trend-following. There are countless ways to fail with systematic trading especially as you increase the set of opportunities. The laws of entropy or trading failure are still alive. Modest has done a great job of cutting through much of the excess verbiage and focused on the critical issue of return reshaping through dynamic strategies.