Required return on equity when capital structure is dynamic

• Author: Louis R. Piccotti,Na Dai
• Published date: 01 March 2020
• DOI: http://doi.org/10.1111/fima.12266
• Date: 01 March 2020

DOI: 10.1111/fima.12266

ORIGINAL ARTICLE

Required return on equity when capital structure

is dynamic

Na Dai1Louis R. Piccotti2

1Department of Finance in the School of

Business, University at Albany,SUNY, Albany,

New York

2Department of Finance in the Spears School of

Business, Oklahoma State University,Stillwater,

Oklahoma

Correspondence

LouisR. Piccotti, 370 Business Building, Rm. 460

Stillwater,OK 74078.

Email:Louis.r.piccotti@okstate.edu

Abstract

We link the firm's required return on equity to its target debt ratio.

We find that a firm's expected return on equity is increasing in the

product of the distance between its debt ratio and its target debt

ratio, its speed of adjustment, and the spread of the tax benefits of

its debt over its bankruptcy costs of debt. Our empirical tests vali-

date the testable implications of our model.

1INTRODUCTION

Proposition 2 of Modigliani and Miller (1958) states that a firm's required return on equity is linearly increasing in

its debt-to-equity ratio (DR) due to compensation for increased financial distress risk. Within this frictionless model,

there is no predictability in expected returns on equity other than the firms with higher DRs have higher expected

returns.1Recently, however, a number of researchers (Byoun, 2008; DeAngelo, DeAngelo, & Whited, 2011; Fama &

French, 2002; Faulkender,Flannery, Hankins, & Smith, 2012; Flannery & Rangan, 2006; Hovakimian, Hovakimian, &

Tehranian,2004; Hovakimian, Opler, & Titman, 2001; Huang & Ritter,2009; Leary & Roberts, 2005; Lemmon, Roberts,

& Zender, 2008; and Warr, Elliot, Koëter,and Öztekin, 2012) have determined that firms appear to have target debt

ratios (TDR)andthatDRsdisplay mean reversion.2The dynamic nature of corporatecapital structure is largely ignored

in the literatureregarding the relation between debt ratio and a firm's required return on equity. Our paper seeks to fill

this void by examiningwhether and how a firm's required return on equity is affected by its capital structure deviation

from its TDR and the cost of adjustment to that TDR.

Building upon the partial adjustment of the capital structure model (Flannery & Rangan, 2006; Hovakimian et al.,

2001; Leary & Roberts, 2005; Strebulaev,2007), we find that the presence of TDRs has important implications for the

required rates of return on equity. In the presence of TDRs, the required return on equity becomes a function of the

expecte d DRdistance from TDR and the speed of adjustment (SOA)tothatTDR.In our model, the relationship between

afirm's expected return and its distance from its target leverage level depends upon the tradeoff between the tax

benefits of debt and the bankruptcy costs of debt. If the tax benefits spread over bankruptcy costs is increasing in

the leverage level, then the relationship between expectedreturns and leverage distance is positive. However,if the

tax benefits spread is decreasing in the leverage level, then the relationship between expectedreturns and leverage

c

2019 Financial Management Association International

1Bhandari(1988) provides empirical support in favor of higher DR firms earning higher expected returns.

2Consistentwith this strand of the literature, Graham and Harvey (2001) also report that 81% of chief financial officers claim to have target debt ratios.

Financial Management. 2020;49:265–289. wileyonlinelibrary.com/journal/fima 265

266 DAI AND PICCOTTI

distance is negative. Thus, relatively over-levered firms are expectedto have lower required returns on equity as the

bankruptcy costs of leverage are expected to dominate the tax benefits of leveragein this region, whereas relatively

under-levered firms are expectedto have higher required returns as the tax benefits of leverage are expected to dom-

inate the bankruptcy costs of leverage in this region. Our hypotheses contrast with the traditional Proposition 2 of

Modigliani and Miller (1958). In the traditional case, equity holders’ expected claim to firm cash flows is constant and

the required return on equity remains a function of the firm's risk class and the firm's current DR.

We conduct our main empirical testing using the following steps. First, we estimate the TDR and DIST for each firm

and the SOA coefficient. Significant mean reversion in DRs existswhere the half-life for log book DR (BDR)3deviations

from TDR is 2.421 years. The DIST half-lives that we estimate are similar to those found in Fama and French (2002)

and Hovakimian and Li (2011) when historical data is used, and those found in Flannery and Rangan (2006) when firm

fixed-effects are excludedfrom the SOA estimation.4We present the portfolio results in Appendix C when firm fixed

effects are included in the estimation of SOAsandTDRsand the portfolio return results are qualitatively unchanged.

We sort stocks into portfolios based on their DIST to determine how required returns on equity are affected by

capital structure adjustment. Our triple sorting procedure first sorts stocks into low and high portfolios based on stock

risk class. Stocks are then re-sorted based on their DR, and then re-sorted based on their DIST. For robustness, the

first sort on stock risk class is repeated on the market/book ratio (M/B), the marketvalue of equity (MVE), the realized

beta (BETA),and the Amihud (2002) price impact illiquidity (PI).5We find that the high DIST portfolios have significantly

greater expected returns than the low DIST portfolios broadly across DR levels,as well as across risk class levels.

We form the high-minus-low DIST (HDMLD) portfolios by buying the high DIST firms and selling the low DIST firms.

Across the risk classes used, the HDMLD portfolio attains annual alphas ranging from 3.0% to 6.0%, each significant at

the 1% level. These alphas are also highly persistent as the alphas continue to be significantly positive with a holding

period of up to 3 years. Significant HDMLD alphas are also consistently attained across the sample subperiods. More-

over, we continue to find significant HDMLD alphas when we excludeutility and financial firms from our sample and

firms with extremely low/high leveragelevels.

Our work builds on and combines several strands of the corporate finance and asset pricing literature. First, our

paper relates to the literature on the dynamic capital structure of corporations, which includes, but is not limited to,

Byoun (2008), DeAngelo et al. (2011), Fama and French (2002), Faulkenderet al. (2012),Flannery and Rangan (2006),

Hovakimian et al. (2001), Hovakimian et al. (2004), Huang and Ritter (2009), Leary andRoberts (2005), Lemmon et al.

(2008), and Warret al. (2012). These studies argue that corporations have TDR and that the debt ratio deviations from

the TDR display a mean reversion to zero. Our empirical design is built upon these findings. In addition, our paper

explores the relation between the required return of equity and the TDR. More specifically, the deviation from the

TDR. Thus, our paper adds to the literature on the relation between leverage and returns including Bhandari (1988),

Fama and French (1992), George and Hwang (2010), Gomes and Schmid (2010), Nielsen (2006), Obreja (2013), and

Penman, Richardson, and Tuna (2007).Moreover, our paper is also related to a growing literature that connects cor-

porate financing decisions to asset pricing. Some recent papers in this area include Bhamra, Kuehn, and Strebulaev

(2010a, 2010b), Chen (2010), Garlappi and Yan (2011), Gomes and Schmid (2010), Livdan,Sapriza, and Zhang (2009),

and Obreja (2013). Both Gomes and Schmid (2010) and Obreja (2013) also investigate the link between leverageand

returns. Obreja (2013) focuses on the role of leverage in generating the observed size and book-to-marketfactors in

cross-sectional equity regressions, whereas Gomes and Schmid (2010) concentrates on how the interaction of corpo-

rateinvestment and leverage decisions leads to different patterns in equity returns. In both papers, the leverage choice

is endogenous. Our work seeks to understand how the deviation from the TDR affects the required return on equity,

rather than the endogenous determinants of the TDR.

3BDR =ln(1+D

S).

4Quicker speeds for SOA havebeen found, by Warr et al. (2012), Hovakimian and Li (2011), and Flannery and Rangan (2006) when full sample firm fixed-

effectsa reincluded inthe SOA estimation. These shorter half-lives are approximately 1.609 years. In contrast,we only use information that is currently in an

investor'sinformation set when estimating TDR and the SOA coefficient.

5The realized beta is a realized covariance (an extensionof the r ealized variance of Andersen, Bollerslev,Diebold, and Labys, 2003) divided by the realized

varianceof Andersen et al. (2003).