Returns to scale and asset prices

• DOI: http://doi.org/10.1111/jbfa.12408
• Published date: 01 October 2019
• Author: Yanzhi Wang,Hung‐Kun Chen,Konan Chan
• Date: 01 October 2019

DOI: 10.1111/jbfa.12408

Returnstoscaleandassetprices

Hung-Kun Chen1Konan Chan2YanzhiWang3

1Department of Banking and Finance, Tamkang

University, New TaipeiCity, Taiwan

2Department of Finance, National Chengchi

University, Taipei,Taiwan

3Department of Finance, Center for Research in

Econometric Theory and Applications National

TaiwanUniversity, Taipei,Taiwan

Correspondence

YanzhiWang, Department of Finance, and Center

forResearch in Econometric Theory and Applica-

tions,National TaiwanUniversity, Taipei,Taiwan.

Email:yzwang@ntu.edu.tw

Fundinginformation

Centerfor Research in Econometric Theory

andApplications, Grant/Award Number:

108L900202;Featured Areas Research Cen-

terProgram; Ministry of Education (MOE) in

Taiwan;Ministryof Science and Technology in

Taiwan,Grant/AwardNumber: MOST 108-3017-

F-002-003

Abstract

The q-theory of investment is proposed to explain firm growth

effects, where previous papers identify a negative effect of firm

growth, including asset growth, real investment and net share

issuance, on future stock returns. This paper uses returns to scale

from the production function to test the dynamic q-theory, which

predicts that the firm growth effect is theoretically weaker for firms

with decreasing returns to scale (DRS) than for non-DRS firms.

Our empirical results generally support the prediction of dynamic

q-theory. However,we find that the dynamic q-theory explains little

of the value, momentum and ROE effects from the standpoint of

returns to scale.

KEYWORDS

asset growth, investment, net share issuance, q-theory, returns to

scale

JEL CLASSIFICATION

G12, G14

1INTRODUCTION

It has been widely argued that the stock market responds to firm growth with negativestock returns.1Recently, many

studies have suggested that an alternative asset pricing model based on the q-theory of investment can account for

the relationship between corporate investments and expected stock returns (Lam and Wei, 2011; Li & Zhang, 2010;

Li, Livdan, & Zhang, 2009; Liu, Whited, & Zhang, 2009; Lyandres,Sun, & Zhang, 2008).2In the dynamic q-theory model

of Li et al. (2009), they argue that greater decreasing returns to scale reduces the dispersion in risk, thus reducing

the expected returns in the cross-section. This implies that the market anomalies associated with firm growth effect

will be weaker for firms with decreasing returns to scale but stronger for firms with non-decreasing returns to scale.

However,no research paper has examined the relationship between returns to scale and firm growth anomalies. This

paper addresses that gap.

1See, for example,Baker and Wurgler (2000), Cooper, Gulen, and Scholl (2008), Loughran and Ritter (1995), Pontiff and Woodgate (2008) and Titman, Wei,

andXie (2004) in the US market; and Petrovic, Manson, and Coakley (2016) in the UK market.

2Hou,Xue, and Zhang (2015) used the idea of q-theory of investment to modify the market model. Firm growth and corporate investment were added as new

pricingfactors in the literature.

J Bus Fin Acc. 2019;46:1299–1318. wileyonlinelibrary.com/journal/jbfa c

2019 John Wiley & Sons Ltd 1299

1300 CHEN ET AL.

This paper uses a novel test on returns to scale from production function to examine whether dynamic q-theory

explains firm growth effects. Dynamic q-theory explainsthe effect of returns to scale on asset pricing through the cur-

vature of the production function (Li et al., 2009). That is, the higher the curvature (i.e., lower curvature parameter),the

greater the decreasing returns to scale. Li et al. (2009) suggest that decreasing returns to scale implies that firms grow

by recei more investment opportunities. Because better projects (i.e., with higher NPVs)are taken first, an increase in

productive scale causes the output to increase by a smaller proportion. Hence, the dynamic q-theory predicts weaker

firm growth effects under a DRS scenario.

We use US data between 1968 and 2017 to perform an empirical test of the dynamic q-theory. Wefirst estimate

returns to scale to identify DRS firms. Following ˙

Imrohoro˘

glu and Tüzel (2014), we use the semiparametric procedure

suggested by Olley and Pakes (1996)to estimate the returns to scale by the Cobb-Douglas production function. This

approach not only controls for selection bias but also endogenous biases associated with the simultaneous determina-

tion of inputs and productivity.As a result, we find that 44.4% of the industries use DRS technology, while 55.6% of the

industries use non-DRS technology. Wefirst analyze three firm growth anomalies: asset growth, real investment, and

net share issuance effects. We calculate monthly abnormal returns in the year after the end of June (i.e., the formation

month) of each year by constructing five value-weighted portfolios sorted by asset growth, real investment, and net

share issuance, respectively.Value-weighted monthly raw returns are calculated. The abnormal returns are estimated

based on the capital asset pricing model (CAPM), the Fama and French (1993) three-factor model, and the Carhart

(1997) four-factor model.

Under CAPM, the abnormal returns of the hedge portfolios for asset growth subgroups, real investmentsubgroups,

and net share issuance subgroups are all positive and significant, confirming the findings of Cooper,Gulen, and Scholl

(2008), Lyandres et al. (2008), Pontiff and Woodgate (2008) and Titman, Wei, and Xie (2004). We further split the

firms into DRS and non-DRS subsamples and calculate abnormal returns for the hedge portfolios. We find that firm

growth effects are weaker for DRS firms, which is consistent with the predictions of dynamic q-theory. Forexample,

using CAPM, mean monthly hedge portfolio return sorted by asset growth is 48 basis points for DRS firms and 65 basis

points for non-DRS firms, suggesting that the asset growth effect is weakerfor DRS firms. Hedge portfolio returns tend

to be lower for DRS subgroups when we construct hedge portfolio returns for real investment or net share issuance.

Using real investment as an example, by CAPM, the monthly hedge portfolio return for DRS firms is 32 basis points,

whereas the hedge portfolio return for non-DRS firms is 56 basis points. Our conclusions remain unchanged for the

tests based on abnormal returns from the Fama and French (1993) three-factor model and the Carhart (1997) four-

factor model.

We further examine the relationship between returns to scale and other marketanomalies, such as value, momen-

tum and return-on-equity (ROE) premiums (Fama & French, 1993; Hou, Xue, & Zhang, 2015; Jegadeesh & Titman,

1993). Again, we calculate monthly abnormal returns in the year after the end of June of each year by constructing

five value-weighted portfolios sorted by the book-to-marketratio (B/M), prior return and ROE. The abnormal returns

are also estimated based on the capital asset pricing model (CAPM), the Fama and French (1993) three-factor model

and the Carhart (1997) four-factor model. However,the excess returns for DRS firms are slightly higher than those of

non-DRS firms when we construct hedge portfolio returns according to the top- and bottom-quintile based on B/M,

and prior return. The ROE effect, in which returns to scale in part account for the ROE effect in the factor model anal-

ysis, is probably the only exception.While firm growth (or investment) anomalies are tightly related to the production

inputs,book-to-market, momentum and ROE are not directly embedded in the production function inputs. Accordingly,

returns to scale may play a weak role in explainingthe value, momentum and ROE effects.

Moreover,we perform a Fama and MacBeth (1973) regression with an interaction term over firm growth variables

(asset growth, real investmentand net share issuance) and a dummyvariable for DRS firms. We find significantly nega-

tive coefficients for firm growth variables and significantly positive coefficients for the interaction term between firm

growth and returns to scale. This result is again consistent with our main finding that firm growth effects are weaker