Abstract

Empirical asset pricing relies heavily on conditioning sets--industry groupings, size buckets, valuation screens, and other researcher-defined partitions--to structure cross-sectional tests and portfolio construction. While intuitive, such partitions risk blending heterogeneous firms, masking latent exposures, and introducing omitted-variable bias. This thesis develops an objective, mathematically grounded conditioning pipeline that replaces subjective groupings with latent-factor extraction, Kalman-based data techniques, and probabilistic clustering via Gaussian hidden Markov models (HMMs). Using CRSP monthly returns, the framework stabilizes noisy return data, extracts systematic structure through principal component analysis (PCA), identifies homogeneous stock cohorts through HMM clustering, and models regime persistence using Markov transition matrices. These objectively derived clusters form the basis for evaluating mean-variance efficiency (MVE) and out-of-sample performance relative to equal-weight benchmarks. The results demonstrate that objective conditioning sharpens inference, improves portfolio stability, and reveals persistent latent structure in the cross-section of U.S. equities. In-sample alphas are economically zero and statistically insignificant, while out-of-sample realized alphas are positive across all regimes.

Degree

MS

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2026-03-26

Document Type

Thesis

Keywords

Melanie Neller, Kalman filter, Kalman smoothing, Gaussian HMM, PCA, objective, empirical asset pricing, applied mathematics

Language

english

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