Expected prediction error decomposes as
Bias measures how far the average prediction is from truth. Variance measures how much predictions wiggle as the training set changes. Simple models have high bias and low variance — they consistently miss the target. Complex models have low bias and high variance — they fit every training set differently.
The trade-off: minimizing total error requires balancing the two. Too simple → underfit (training error and test error both high). Too complex → overfit (training error low, test error high).
Regularization, ensembling, and cross-validation are the main tools for managing the trade-off. In quant prediction, the noise component is enormous — total error is mostly irreducible — so the optimum tends toward simple, high-bias models that resist overfitting.