Industry Costs of Equity: Incorporating Prior Information

• Published date: 01 February 2018
• DOI: http://doi.org/10.1111/fire.12156
• Date: 01 February 2018

The Financial Review 53 (2018) 153–183

Industry Costs of Equity: Incorporating

Prior Information

Ping McLemore

The Federal Reserve Bank of Richmond

Abstract

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: ping.mclemore@rich.frb.org.

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.

C2018 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

prior.

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).