Minerva Investment Management Society

Quantitative Research Paper

Variance risk premia and stock return predictability

· Quantitative Research

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Summary

The Quantitative Research Division at the Minerva Investment Management Society is pleased to present our latest research paper: “Variance Risk Premia and Stock Return Predictability: Nonlinear Evidence from Polynomial and Spline Models” Can volatility markets help predict future stock returns - and are we missing key signals by assuming linear relationships? In this paper, we revisit the predictive power of the variance risk premium (VRP), a widely studied measure capturing compensation for bearing volatility risk. While much of the literature relies on linear models, we explore whether allowing for nonlinearities can uncover additional predictive information. Using U.S. equity data, we compare linear, polynomial, and spline-based specifications, as well as regime-dependent extensions. Our findings show that simple nonlinear models — particularly spline-based approaches — substantially improve out-of-sample forecasting performance, highlighting that the relationship between VRP and future returns is inherently nonlinear. At the same time, the results emphasize the importance of parsimony: more complex models improve in-sample fit but do not necessarily translate into better out-of-sample performance.

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Details

Published
8 April 2026
Division
Quantitative Research
Type
Quantitative Research Paper
Pages
10
Authors
2

Cite this report

Minerva Investment Management Society (2026). Variance risk premia and stock return predictability. Quantitative Research. https://minervaims.org/archive/variance-risk-premia-and-stock-return-predictability-2026

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