Shrinkage
Pulling estimates (e.g. mean, covariance) toward a prior or global average to reduce estimation error.
Definition
Shrinkage means taking a noisy estimate (e.g. sample covariance matrix, or sample mean return) and shrinking it toward a more stable target (e.g. diagonal matrix, grand mean). Example: ( \hat{\Sigma} = (1-\lambda) S + \lambda F ), where ( S ) is sample covariance and ( F ) is the target.
Why it matters
- Sample covariance is very noisy with many assets; optimized weights are unstable.
- Shrinkage reduces extreme weights and improves out-of-sample risk estimates.
Common mistakes
- No shrinkage when ( N ) (assets) is large relative to ( T ) (observations).
- Shrinking too much (lose signal) or too little (keep noise).
Typical use
Covariance for risk parity or mean-variance; also used for expected return (shrink toward zero or cross-sectional average).