Industry Costs of Equity: Incorporating Prior Information

Published date01 February 2018
Date01 February 2018
The Financial Review 53 (2018) 153–183
Industry Costs of Equity: Incorporating
Prior Information
Ping McLemore
The Federal Reserve Bank of Richmond
I examine whether incorporating economically motivated prior information yields more
accurate forecasts of industry costs of equity. I find that incorporating the long-run mean
of the Capital Asset Pricing Model (CAPM) parameters and the industry characteristics in
the cross section produces more accurate parameter estimates, which subsequently translate
into more accurate out-of-sample forecasts of industry costs of equity. The outperformance
of this method over rolling-window estimates becomes larger as the forecast horizon extends
into the future. These findings provide evidence that the CAPM parameters have a long-run
mean-reversion property and correlate with the industry characteristics in a systematic way.
Keywords: C APM,industry costs of equity, prior information, forecast error
JEL Classifications: C11, G10, G12
Corresponding author: The Federal Reserve Bank of Richmond, 502 S. Sharp Street, Baltimore, MD
21201; Phone: (410) 951-4683; Fax: (410) 951-4651; E-mail:
I would like to thank Richard Warr (Editor) and twoanonymous referees for their helpful comments and
suggestions that greatly improved the paper.I also thank Scott Cederburg, George Jiang, Christopher Lam-
oureux, Marco Rossi, Matthew Serfling, conference participants at the 2013 Northern Finance Association
Annual Meeting, the 2013 Southern Finance Association Annual Meeting, and the 2013 Southwestern
Finance Association Annual Meeting, as well as workshop participants at the University of Arizona. The
views expressed herein are those of the author and do not necessarily reflect the position of the Federal
Reserve Bank of Richmond or the Federal Reserve System. All errors are my own.
C2018 The Eastern Finance Association 153
154 P.McLemore/The Financial Review 53 (2018) 153–183
1. Introduction
Fama and French (1997) show that the estimates of the cost of equity for
industries are imprecise using the Capital Asset Pricing Model (CAPM) of Sharpe
(1964) and Lintner (1965). However,in practice, managers commonly use the CAPM
to estimate expected returns and use the industry costs of equity as a benchmark when
making capital budgeting decisions.1Start-ups commonly use the industry costs of
equity as a proxy for firm-level measures, as theydo not have enough historical return
data to calculate the firm’s cost of equity. Thus, having more precise estimates of
industry costs of equity is critical for decision making by practitioners. This paper
aims to achieve this goal by bringing economically motivated prior information into
the estimation of the CAPM parameters and translating these parameter estimates
into a more accurate estimate of industry costs of equity.
Vasicek (1973) proposes the use of shrinkage to estimate the market beta of
the CAPM model, with the value-weighted (VW) mean and cross-sectional variance
of rolling betas used as the prior. Karolyi (1992) brings industry information into a
firm’s market beta estimation. Specifically, he tests an approach that shrinks a firm’s
rolling-window market beta estimate to the market beta of its industry. Cosemans,
Frehen, Schotman and Bauer (2016) apply the shrinkage approach to incorporate the
cross-sectional, firm-specific information into rolling-window market beta estimates
at the firm level. The authors find that their approach of incorporating firm-level
priors outperforms incorporating either the market-level prior or the industry-level
In line with these studies, I examine whether incorporating economically moti-
vated prior information into parameter estimation yields a more accurate forecast of
industry costs of equity using the CAPM. Specifically, I incorporate two sets of prior
information. The first set is the long-run mean of the model parameters. This set of
priors is motivated by the work of Blume (1975), where the author demonstrates the
long-run mean-reversion property of the market beta. I incorporate the long-run mean
of zero for the CAPM alpha and one for the market beta. These are common priors
for all 49 industries. The second set is the industry characteristic information in the
cross section. This prior is unique to individual industries, and its selection is moti-
vated by the theoretical work of Gomes, Kogan and Zhang (2003), where the authors
derive an explicit model for the relation between market beta and cross-sectional size
and book-to-market equity ratio in a general equilibrium setting. I incorporate the
industry size and book-to-market information via a Bayesian hierarchical model. The
hierarchical model produces the hybrid estimates that combine the information from
the time series returns and the cross-sectional characteristics.
Prior mean and prior variance are two inputs feeding into the Bayesian frame-
work. I apply a grid search for the optimal prior variance for two reasons (Doan,
1See Bruner, Eades, Harris and Higgins (1998); Brealey, Myers and Allen (2013); Graham and Harvey
(2001); and Da, Guo and Jagannathan (2012).

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