Portfolio Risks under Estimation Uncertainty and Price Movement

Risk decomposition is a standard tool for analyzing investment portfolio risk. The portfolio is divided into notional parts—e.g., individual securities, holdings by sector or region, factor exposures—whose contributions to net risk are estimated and reported. Convention regards the inputs—portfolio weights and covariance—as fixed and known, but portfolio composition changes with price movement and estimates have errors. Since behavior only in the direction of net risk is counted, hedged effects are invisible regardless of size. What if numbers aren’t exact? Hedge instability manifests in proportion to underlying gross (not net) exposure, akin to leverage. For example, in a market-neutral portfolio, market is the largest risk in each side, conventionally uncounted since hedged, and extremely consequential under small deviations. To solve the problem, this paper models weights and parameters as uncertain. Evaluating a portfolio across the range of possibility measures risks better and surfaces latent fragility. No longer point-estimated, contributions are reported with a center and spread