Multi-factor Loading Uncertainty and Expected Returns Open Access

Abstract

β is notoriously difficult to measure, and the direction of the relationship between beta uncertainties and expected returns is a priori not obvious. This paper demonstrates that stocks with high factor-loading uncertainty exhibit significant underperformance compared to those with lower factor-loading uncertainty, and systematic risk factors in the canonical multi-factor models cannot account for this negative premium. Our findings show that uncertainty surrounding non-market factor loadings have significantly larger impact than the market beta uncertainty, and additionally, the former subsumes the latter. Investors’ uncertainty on the CAPM market beta alone does not have significant explanatory power over expected returns. Additionally, our results indicate that the pricing implications of factor-loading uncertainties are driven by large-cap stocks.

Table of Contents

1 Introduction 1

2 Data and Methodology 6

2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Estimation Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Benchmark Pricing Models . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.2 Fama-MacBeth Two-Step Regressions . . . . . . . . . . . . . . . . . . 8

2.2.3 Portfolio Sorts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.4 Quadruple Sorts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Results 15

3.1 Revisiting the CAPM Beta Uncertainty Risk Premium . . . . . . . . . . . . 15

3.2 Multi-factor Loading Uncertainty and Expected Returns . . . . . . . . . . . 17

3.3 Portfolio Sorts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4 Do Non-Market Factor Loading Uncertainties Subsume the CAPM Beta Uncertainty? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4 Conclusion 24

5 Appendix: Variable Definitions 26

About this Honors Thesis

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School	Emory College
Department	Economics
Degree	B.A.
Submission	Honors Thesis
Language	English
Research Field	Economics, General Economics, Finance
Keyword	Asset Pricing
Committee Chair / Thesis Advisor	Jeong-Ho (John) Kim, Emory University
Committee Members	Caroline Fohlin, Emory University Kaiji Chen, Emory University

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