The bias of growth opportunity

• Published date: 01 September 2022
• Author: Cynthia M. Gong,Xindan Li,Di Luo,Huainan Zhao
• Date: 01 September 2022
• DOI: http://doi.org/10.1111/eufm.12323

Eur Financ Manag. 2022;28:926–963.wileyonlinelibrary.com/journal/eufm926

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© 2021 John Wiley & Sons Ltd.

DOI: 10.1111/eufm.12323

ORIGINAL ARTICLE

The bias of growth opportunity

Cynthia M. Gong

1

|Xindan Li

2

|Di Luo

3

|Huainan Zhao

1

1

Accounting and Finance Group, School

of Business and Economics,

Loughborough University,

Loughborough, UK

2

School of Management and

Engineering, Nanjing University,

Nanjing, Jiangsu, China

3

Department of Banking and Finance,

Business School, University of

Southampton, Highfield Campus,

Southampton, UK

Correspondence

Di Luo, Department of Banking and

Finance, Business School, University of

Southampton, Highfield Campus,

Southampton, SO17 1BJ, UK.

Email: d.luo@soton.ac.uk

Abstract

The bias of growth opportunity (BGO), measured as

the difference between market and fundamental values

of a firm's growth opportunity, has an ability to predict

future stock returns. In the portfolio sort, downward‐

biased BGO firms earn higher returns than upward‐

biased ones, which is unexplained by the common

asset pricing models. Cross‐sectional regression results

also confirm BGO's power in predicting stock returns.

To explain the anomaly, we show that the BGO pre-

mium is more pronounced when investor sentiment is

high or when limits‐to‐arbitrage is severe, which sug-

gests that the

B

G

O

is more likely to capture beha-

vioural biases than systematic risk.

KEYWORDS

anomaly, asset pricing, behavioural finance, bias of growth

opportunity

JEL CLASSIFICATION

G12, G14, G30

The behavioural perspective allows for the possibility that market prices do not

coincide with fundamental values. …It is nonetheless important to estimate the gap

between market price and fundamental value, because the speed with which the

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FINANCIAL MANAGEMENT

We thank John Doukas (the Editor) and two anonymous referees for their insightful comments and suggestions. We

are grateful to Pu Gong, Hong Liu, Hersh Shefrin, Avanidhar (Subra) Subrahmanyam, Wei Zhang and seminar and

conference participants at Tianjin University, University of Aberdeen, the Behavioural Finance Working Group

(BFWG) 2019 Conference at Queen Mary University of London and Southern Finance Association (SFA) 2019 meeting

for helpful comments and suggestions. We are grateful for financial support from the National Natural Science

Foundation of China (Grant No. 71991473 and No. 71671076). All remaining errors are our own.

difference converges to zero in the future depends on their difference in the

present.

—Hersh Shefrin (2014, p. 15)

1|INTRODUCTION

Although it is clear that a firm's growth opportunity (GO) is a key driver of its fundamental and

market valuations, it is still not so clear on how to correctly measure a firm's GO, as it is the

‘yet‐unexercised future‐oriented growth option’which is not directly observable and common

proxies used to capture it are prone to errors.

1

Consequently, growth opportunities can,

sometimes, be misjudged by investors. If investors act irrationally to a firm's GO (i.e., overly

optimistic or pessimistic) and if the misjudgment becomes large and persistent, it can have a

lasting impact on the firm's valuation and returns.

2

Prior studies have reported evidence that the difference between firms' market and fun-

damental valuations predict stock returns (Bartram & Grinblatt, 2018; Doukas et al., 2010; Lee

et al., 1999). The difference between a firm's market and fundamental valuations is, however,

likely to be mainly driven by the divergence on growth opportunities (i.e., present value of

growth opportunity [PVGO]), as it is unobservable, hard to estimate and normally constitutes

the largest proportion of a firm's value. In recognising the significance of GOs in valuation and

returns, Trigeorgis and Lambertides (2014) study the role of growth option in explaining the

cross‐sectional stock returns. They find that growth options (GO) is negatively related to future

returns.

However, as stated above, we know that the difference between firms' market and funda-

mental valuations predicts stock returns, but we do not know how the difference between

firms' market growth opportunity (MGO) and fundamental growth opportunity (FGO) affects

stock returns. Following Trigeorgis and Lambertides (2014), we measure

M

GO

as the pro-

portion of a firm's market value arising from its future growth opportunities (PVGO) and

measure

F

GO by using the same ‘eight empirically observable growth option‐related variables’

of Trigeorgis and Lambertides (2014), which determine a firm's fundamental value of GO.

Trigeorgis and Lambertides (2014) argue that, in contrast to previous studies using indirect

proxies for growth opportunities (e.g., book‐to‐market [ ∕

BM

] ratio, earnings‐to‐price [ ∕

E

P]

ratio, or Tobin's q), they use ‘more direct, theoretically based measures of the firm's growth

options’. Specifically, the yet‐unexercised growth option's value is obtained from a time series

cross‐sectional regression of eight empirically observable and option‐motivated variables for

each firm. In their study, they provide the theoretical rationale for each of the variables em-

ployed, which makes it the best method available to capture the FGO.

Next, we define the difference between MGO and FGO as the bias‐of‐growth opportunity

(BGO). A large BGO means the market valuation of a firm's GO is much higher than its

fundamental valuation of GO. Thus, the BGO picks up the difference or disagreement between

1

Some common proxies for estimating growth opportunities are research and development (

R

&D

), Tobin's q, debt‐to‐

equity ratio and capital expenditure (e.g., Cao et al., 2008; Kogan & Papanikolaou, 2014).

2

On the contrary, illustrated in a 'beauty contest', Keynes (1936) argues that investors do not necessarily base their

investment decisions on fundamental valuations, instead they base their decisions on the choices they predict others

are likely to make. Thus, misevaluations caused in the marketplace can also be intentional.

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market and fundamental valuations of GO.

3

We know from the behavioural finance literature

that when the market goes ahead of its fundamentals, it will typically adjust and its future

returns will be lower. On this basis, we predict a negative relation between a firm's BGO and its

future returns, that is, the further ahead of the MGO relative to the FGO, the lower the future

returns. In this study, we focus on testing this hypothesis.

Examining U.S. common stocks from 1977 to 2017,

4

we find a significant negative relation

between BGO and stock returns. Firms in the most downward‐biased BGO decile (i.e., growth

potentials are most underestimated) significantly outperform that of the most upward‐biased

BGO decile (i.e., growth potentials are most overestimated) by

0

.537

%

(

t

=4.9

7

) per month. The

BGO premium is unexplained by the Fama–French three‐factor model (FF3FM), momentum‐

extended FF3FM, Fama–French five‐factor model (FF5FM) and other commonly used asset

pricing models. For instance, under the FF5FM, the return difference (alphas) between the

most downward‐biased and upward‐biased BGO portfolios is

0

.543

%

(

t

=4.6

8

) per month.

Building on the portfolio sorts, we also perform the Fama–MacBeth (1973) regression

analysis to simultaneously control for

B

G

O

and key firm characteristics. We show that

B

G

O

is

significantly related to stock returns after adjusting for size, B/M, momentum, return‐on‐assets

(ROA) and asset growth (AG). Brennan et al. (1998) argue that using the risk‐adjusted returns

(rather than risk loadings) as the explained variable avoids errors‐in‐variable problem asso-

ciated with the Fama–MacBeth procedure. Following their study, we run the Fama–MacBeth

regressions using the risk‐adjusted returns and we show that

B

G

O

consistently predicts future

stock returns.

We submit our results to a battery of robustness tests including using a gross‐return

weighting method of Asparouhova et al. (2010,2013) to control for the potential bias caused in

the rebalance method; the characteristics‐adjusted returns of Daniel et al. (1997) and Wermers

(2004) to control for size, B/M and momentum; the double‐sorted portfolios on both

B

G

O

and

market capitalisation following Fama and French (2008). Given high

M

GO

indicates high

expected growth by the market and growth of the company measured by relative pricing ratios,

such as price‐to‐cash flow or price‐to‐earnings ratio, also has low future returns; we double‐sort

portfolios based on both BGO and one of the relative pricing ratios. We also employ additional

asset pricing models such as the Pastor and Stambaugh (2003) liquidity‐extended FF3FM, the

Liu (2006) liquidity‐augmented capital asset pricing model (LCAPM), the Hou et al. (2015)q‐

factor model (HXZqFM), the Stambaugh and Yuan (2016) mispricing factor model (SYmFM)

and the most recent Hou et al. (2021) augmented q‐factor model with expected investment

growth (HMXZq5FM). The BGO premium stands firm to all these tests.

Intuitively, the most upward‐biased (downward‐biased) BGO stocks are the ones that their

market values of GOs are much larger (smaller) than the estimates of their fundamental values. It is

possible that investors overreact (underreact) to the growth opportunities of these stocks, which

results in lower (higher) subsequent returns,

5

and, hence, driving the BGO premium. Berk et al.

(1999) argue that explanations for asset pricing anomalies fall in missing state variables in risk factors

or behavioural biases. Given the inability of the risk‐based methods in explaining the BGO premium,

we investigate whether the results are driven by behavioural biases such as investor sentiment or

3

Banerjee and Kremer (2010) and Banerjee (2011) provide theoretical foundations on how disagreement affects stock

returns.

4

Our sample starts from 1977 due to the availability of various COMPUSTAT annual data to calculate MGO and FGO

(discussed in Section 2).

5

Cooper et al. (2008) find evidence that investors tend to overreact to firms' past growth rates.

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