Are Asset Pricing Models Sparse?

Description

While conditional asset pricing modeling permits time variation in factor premia/price, betas, and explanatory power (e.g., Bollerslev et al., 1988; Ferson and Harvey, 1999; Nagel and Singleton, 2011; Gagliardini et al., 2016), the illusion of sparsity still dominates the empirical literature searching for the small but fixed set of factors or characteristics for the entire history of observations. However, a recent paper by Giannone, Lenza, and Primiceri (2021) applies Bayesian sparsity predictive models in various economics fields and finds a very low posterior probability for sparsity. Time-varying sparsity can also be motivated as a particular case of a model with heterogeneous structural breaks. For instance, Smith and Timmermann (2022) distinguish between market-wide and style-specific breaks in stock returns panels due to different impacts on industry or characteristic-sorted portfolios. Evidence of time-varying sparsity and heterogeneous structural breaks (e.g., Cui et al., 2023) in the factor or characteristic performance indicates that the level of the sparsity changes over time. This project directly relates to the literature on time-varying sparse models and reevaluates whether asset pricing models are sparse, providing further economic and statistical solutions to the accumulating “zoo” of factors or characteristics. In particular, we develop a Bayesian latent factor model that combines structural break detection (Smith and Timmermann, 2021) and instrumental PCA (Kelly et al., 2019). One crucial methodology contribution of our project is the nonlinear (regime-switching) sparse extension for IPCA, which is exactly needed to answer our research question. Our project primarily focuses on making an empirical contribution to understanding the “zoo” of characteristics in U.S. equities and corporate bonds. The time-varying characteristics-based factor betas are modeled with sparsity using spike-and-slab priors within structural breaks driven by macroeconomic predictors. Following Giannone et al. (2021), we also consider the posterior probability for sparsity, which helps us determine the existence and level of sparsity in each detected regime. We expect to find macroeconomic-driven structural breaks that explain the time-varying explanatory power in the cross section of U.S. equity and corporate bond returns.