Attributing Forecast Gaps to Component Models in Complex Model Suites

Abstract

Complex model suites composed of multiple interacting component models are widely used in financial forecasting and risk management. In model performance testing, including in-sample backtesting (BT) and out-of-sample ongoing performance monitoring (OPM), a material gap between a model-suite forecast and the realized outcome must often be attributed to individual component models for development, validation, and regulatory review. This paper studies this gap-attribution problem in the expected loss framework, where exposure at default (EAD), prepayment or single monthly mortality (SMM), probability of default (PD), and loss given default (LGD) interact multiplicatively and are aggregated across loans and projection periods. We first formalize standard walk analysis and show why its attribution is generally order dependent. We then adapt two order-independent attribution frameworks: an augmented Logarithmic Mean Divisia Index (LMDI) approach tailored to the expected-loss structure, and a more general Shapley value approach based on averaging marginal contributions over all component orderings. We derive both elementwise and vectorized formulas to support efficient implementation, with the additional computation time for gap attribution typically limited to a few seconds in practical portfolio-scale examples. Finally, we discuss the connections among walk analysis, LMDI, and Shapley attribution, and show how the attribution framework extends to model suites with an additional Monte Carlo simulation layer.