Distributionally Robust Recovery of Omitted Factors from Forecast Residuals with Application to Interest Rate Risk Management

Abstract

A forecasting model compresses its predictors into an estimate of a conditional mean, and the systematic structure that estimate omits survives in the second moment of its forecast errors. Accuracy comparisons do not measure this structure, and variance-based extraction does not recover the part of it that a given decision bears. In this paper, we propose a distributionally robust framework that recovers the omitted structure from the residuals of a fixed forecaster: a decision is made robust over a two-layer moment ambiguity set on the standardized residual cross-section, and the discovery statistic is the covariance forcing, the component of the decision's residual risk transverse to its exposure. We demonstrate that the forcing is invariant to shrinkage and to isotropic inflation of the covariance, so the recovered direction is a property of the residuals rather than of the regularization, the sense in which the recovery is ground truth. This is confirmed on monthly U.S. Treasury zero-coupon yields from 2006 to 2025, where the recovered factor is named by factor-adjusted robust selection against a panel of 111 macroeconomic, Treasury supply-and-demand, and financial indicators. From the residuals of the linear factor-augmented dynamic Nelson-Siegel benchmark the factor names as a leading business-cycle factor, anchored on the Conference Board leading index and certified by a block-permutation test; from those of the more accurate nonlinear random forest benchmark the same procedure selects the same real-activity family without certification. A neutralization test completes the evidence: removing the recovered factor from the deployed duration position leaves volatility essentially unchanged and worsens the tail, so the factor is a material systematic risk the position bears.