Set out the techniques used to forecast volatility and covariance

The sample covariance matrix is simple but becomes unreliable when the number of assets is large relative to observations. Factor models impose structure, estimating each asset's exposure to a few common factors, which reduces estimation error at the cost of possible misspecification. Shrinkage estimation blends the sample matrix with a structured target, improving accuracy. Volatility clusters, so ARCH-type models let today's variance depend on yesterday's variance and the latest shock, for example σ²ₜ = γ + α × σ²ₜ₋₁ + β × ηₜ². Appraisal-based series must be unsmoothed: rₜ = (Rₜ − λ × Rₜ₋₁) ÷ (1 − λ), where λ is the smoothing weight. The trap is using smoothed private-asset data, which understates both volatility and correlation.