The applications of spectral factor model in the financial markets

Abstract

This thesis develops and applies spectral methods, based on the extended Wold representation, to asset pricing across corporate bonds and equities in the U.S. market and equities in Chinese market. The central premise is that conventional time-domain factor models obscure horizon-specific pricing signals by averaging across business cycle frequencies, whereas spectral decomposition isolates these signals and reveals their distinct contribution to risk premia.

Chapter 2 establishes the theoretical foundation of the extended Wold repre sentation and demonstrates how stationary time series can be decomposed into orthogonal frequency components. This framework allows risk factors to be stud ied at horizons that align with business cycle dynamics, thereby improving both interpretation and empirical performance.

Chapter 3 applies this framework to the U.S. corporate bond market. By decomposing the bond market, term, and default factors into frequency-specific components, the analysis shows that the spectral term factor (16–32 months) and spectral default factor (8–16 months) carry substantial pricing information that is masked in aggregate models. The spectral factor model significantly outperforms traditional specifications in cross-sectional tests and exhibits robust links with macroeconomic indicators, highlighting its relevance for business cycle-sensitive bond pricing.

Chapter 4 extends the three-moment CAPM by introducing spectral coskew-ness in the U.S. equity market. Unlike conventional coskewness models that treat skewness risk as time-invariant, the spectral approach reveals that high-frequency components (2–4 months) are priced in the cross-section of returns, consistent with quarterly earnings cycles. The spectral three-moment CAPM dominates tradi tional models, showing that investor sensitivity to skewness varies across horizons and that spectral coskewness is a critical dimension of risk beyond mean–variance tradeoffs.

Chapter 5 applies the spectral CAPM to the Chinese stock market. While the extended Wold representation remains valid in this context, the results indicate that no single frequency component dominates pricing as in U.S. markets. Instead, joint regressions using multiple spectral components deliver substantially higher explanatory power for anomaly returns, underscoring the segmented structure of the Chinese market and the importance of considering multiple business cycle horizons in emerging economies.

Overall, the thesis demonstrates that spectral factor models provide a powerful extension to conventional asset pricing by uncovering horizon-specific risk premia that are otherwise hidden in aggregated factors. The findings establish spectral decomposition as a robust framework for advancing our understanding of factor structures in both developed and emerging financial markets.

Date of Award	1 Jul 2026
Original language	English
Awarding Institution	University of Nottingham
Supervisor	Ying Jiang (Supervisor), Yuan Wang (Supervisor), Peipei Li (Supervisor) & Bruno Deschamps (Supervisor)