What is the bias-variance trade-off?

Prediction error splits into bias squared, variance and irreducible noise. Simple models have high bias and low variance; complex models the reverse. Total error is minimised between the extremes.

Why do quant researchers prefer simple models?

Because financial data has a very low signal-to-noise ratio, so flexible models fit noise and the variance term dominates. The error-minimising complexity is much lower than in high-signal domains.

Statistics

The Bias-Variance Trade-off

NeetQuant · August 2026 · 4 min read

The decomposition

Expected prediction error at a point splits into three parts:

Bias squared - error from your model being systematically wrong. Variance - error from your model being sensitive to which data you happened to see. Irreducible noise - the part nothing can fix.

You control the first two, and they pull in opposite directions.

The trade-off

A simple model (a straight line) has high bias and low variance: it may be wrong, but it is wrong consistently.

A complex model (a high-degree polynomial) has low bias and high variance: it fits your sample beautifully and a different sample would give completely different predictions.

Total error is minimised somewhere in between, and finding that point is most of applied modelling.

Why finance sits at the simple end

Financial return data has a very low signal-to-noise ratio. When most of what you see is noise, a flexible model fits the noise - the variance term dominates, and the optimum sits much further toward simplicity than in domains like image recognition.

This is why linear models remain competitive in quant research long after they were abandoned elsewhere, and it is a good thing to be able to explain.

Regularisation

Ridge and lasso deliberately shrink coefficients toward zero. That introduces bias - the estimates are systematically too small - in exchange for a large reduction in variance.

When the reduction outweighs the bias introduced, total error falls. Lasso additionally sets some coefficients exactly to zero, giving feature selection for free.

Overfitting in practice

The symptom: excellent in-sample performance, poor out-of-sample. The cause is usually more parameters than the data can support, or - just as often - repeated model choices made after looking at the test set, which is multiple testing in disguise.

The interview question

"Your model has 95% in-sample accuracy and 55% out-of-sample. What is wrong?"

Overfitting: variance dominates. Fixes are regularisation, fewer features, more data, cross-validation, and being honest about how many model variants were tried.

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Frequently asked questions

What is the bias-variance trade-off?: Prediction error splits into bias squared, variance and irreducible noise. Simple models have high bias and low variance; complex models the reverse. Total error is minimised between the extremes.
Why do quant researchers prefer simple models?: Because financial data has a very low signal-to-noise ratio, so flexible models fit noise and the variance term dominates. The error-minimising complexity is much lower than in high-signal domains.