Trend-following works — but only if you don’t trust strong trends.

This paper shows that classic time-series momentum is misspecified. The optimal signal is nonlinear:

• Linear near zero (small trends matter),

• Muted at extremes (big trends get less weight),

• Exactly the S-shape predicted by portfolio theory.

Across 55 futures markets and equity factors, this nonlinear TSMOM:

• Beats linear and binary trend following out of sample,

• Delivers higher Sharpe with lower trading,

• And earns most of its edge during market crashes.

Even better: a neural network trained to maximize Sharpe independently learns the same S-curve.

papers.ssrn.com/sol3/pa…