Regularization adds a penalty term to the OLS loss to discourage large coefficients, trading bias for variance.
Ridge regression uses an penalty:
It shrinks all coefficients toward zero and has a closed-form solution. Especially useful when predictors are correlated.
Lasso uses an penalty:
Lasso drives some coefficients to exactly zero, doubling as variable selection. The optimization is convex but lacks a closed form (use coordinate descent).
Elastic Net combines and penalties — better than Lasso when groups of correlated predictors should all enter or none.
Regularization trades a small bias for a much larger reduction in variance, which usually improves out-of-sample MSE. That's exactly what matters in trading: prediction quality on tomorrow's data, not in-sample .