Factor-Based Performance Attribution: Structural Limits and Double Unidentifiability

Factor attribution reports are central to institutional investment practice. Portfolio managers use them to explain performance, risk officers use them to monitor systematic exposures, and investment committees use them to evaluate manager skill. In practice, however, these reports are often unstable, counterintuitive, and sensitive to the choice of factor risk model. The same portfolio can produce nearly identical volatility forecasts and factor risk decompositions across models yet materially different factor contributions to realized return. This article explains why. Factor attribution applies a factor model to a problem it was not designed to solve, yielding a return decomposition that is doubly unidentified: Factor returns are not uniquely pinned down by the estimated covariance structure, and the reference portfolios that define them are unconstrained replicators that real mandates cannot hold. These failures are structural, not statistical, and they generate predictable pathologies, including correlated factor and specific contributions and sensitivity to model specification. Factor attribution remains a useful reporting tool, but its outputs must be interpreted with the precision the structure warrants.