Is nonlinear momentum the answer?

I have been harping on about how life is nonlinear and that linear approaches to investing are bound to be inferior (see here for an example in economics and one in finance). Furthermore, I am always interested in finding ways to improve momentum investing, which, in its basic form, suffers from the risk of momentum crashes. So, is a new nonlinear momentum approach going to be useful?

Tobias Moskowitz has teamed up with people at US, Swedish and German universities to develop a nonlinear time series momentum approach.

To repeat, the traditional approach to momentum investing is to look at the price change over the last 12 months (minus the previous month). One can then standardise this number by dividing it by the average annual volatility of the share price, so one can compare momentum signals across stocks and asset classes. But of course, this is a linear approach. If Company A has twice the return of Company B, it will look roughly twice as attractive.

Instead of going with this simple approach, the researchers looked at nonlinear momentum, where extreme returns are ‘dampened down’ and given less of a weight than in a linear model. The hope is that this nonlinear approach will reduce the vulnerability of the approach to momentum crashes, where stocks that have gone vertical in the past suddenly crash.

Another nonlinear approach is much simpler and simply looks at the sign of past returns. It then makes a binary decision and overweights stocks with positive past returns and underweights (or shorts) stocks with negative past returns.

Long story short, here is the Sharpe Ratio of these nonlinear approaches for different time periods under investigation and compared to the simple linear model.

Sharpe ratio of momentum strategies

Source: Moskowitz et al. (2025)

It’s easy to see that the Sharpe Ratio of the nonlinear approaches tends to be higher than the traditional approach. The chart shows the results for a lookback period of 12 months, but for shorter lookback periods, it tends to do even better.

What’s more, the performance of the nonlinear model tends to be better when the linear model is struggling, for example, in bear markets.

Yet, I cannot help but wonder why I should bother with this complexity? As you can see in the chart, the performance advantage of the nonlinear momentum strategies becomes smaller in every period, and in the last 10 years, these nonlinear approaches have even underperformed the conventional linear momentum approach.

The authors of the study don’t really give an answer, but only say that this weak performance may be due to the generally much more difficult environment for momentum strategies in general. To which I say that one of the key requirements of a good investment approach is that it is robust to a changing environment. Because the one thing you can be sure about is that markets change all the time in unpredictable and unforeseeable ways. And what the chart above shows to me is that the nonlinear approach to momentum is simply less robust than the traditional approach we have been using for decades.