Estimating the Capital Asset Pricing Model with Many Instruments: A Bayesian Shrinkage Approach

Abstract

This paper introduces an instrumental variable Bayesian shrinkage approach specifically designed for estimating the capital asset pricing model (CAPM) while utilizing a large number of instruments. Our methodology incorporates horseshoe, Laplace, and factor-based shrinkage priors to construct Bayesian estimators for CAPM, accounting for the presence of measurement errors. Through the use of simulated data, we illustrate the potential of our approach in mitigating the bias arising from errors-in-variables. Importantly, the conventional two-stage least squares estimation of the CAPM beta is shown to experience bias escalation as the number of instruments increases. In contrast, our approach effectively counters this bias, particularly in scenarios with a substantial number of instruments. In an empirical application using real-world data, our proposed methodology generates subtly distinct estimated CAPM beta values compared with both the ordinary least squares and the two-stage least squares approaches. This disparity in estimations carries notable economic implications. Furthermore, when applied to average cross-sectional asset returns, our approach significantly enhances the explanatory power of the CAPM framework.

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“…It formalizes mean-variance optimization of a risky portfolio given the presence of a risk-free investment such as government bonds, and it defines the price of financial assets according to the premium that the investors demand for bearing the risk. CAPM is perhaps the most renowned example of asset pricing models, owing to its theoretical simplicity and ease of interpretation (de Andrade and Laurini, 2023) [50].…”