More features than observations

You have 400 candidate signals and 120 training dates. Why is unrestricted least squares fragile, and what alternatives would you compare?

The design matrix cannot have full column rank, so unrestricted coefficients are non-identifiable and may interpolate noise. Compare simple baselines, ridge, elastic net and dimension reduction using time-respecting nested validation. Select preprocessing and hyperparameters inside training folds. More rows from correlated assets do not necessarily supply equivalent independent information. Report out-of-sample performance and sensitivity to the regularisation choice.