A new decomposition approach to modeling financial returns: Conditioning sign on magnitude

Ars\`ene Brou and Richard Luger

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Abstract: Changes in volatility contain valuable information about the likelihood of positive versus negative returns. We propose a new approach to modeling financial returns that exploits this insight by decomposing returns into sign and magnitude (absolute value) components, with magnitude closely related to volatility. The joint distribution used to compute expected returns combines a model for the marginal distribution of magnitude with a model for the distribution of the sign, conditional on the contemporaneous magnitude. Unlike traditional linear predictive regressions, this decomposition framework captures nonlinear predictability in return dynamics. An out-of-sample forecasting evaluation using monthly U.S. stock market excess returns demonstrates substantial statistical and economic gains relative to linear regression and complete subset regression, while delivering performance that is competitive with copula-based return-decomposition methods and other nonlinear benchmarks.

Date: 2026-06
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