Revisiting the investment anomaly: Financing constraints or limits‐to‐arbitrage?

• Published date: 01 October 2020
• Author: Kyungyeon (Rachel) Koh
• Date: 01 October 2020
• DOI: http://doi.org/10.1002/rfe.1098

Rev Financ Econ. 2020;38:655–673. wileyonlinelibrary.com/journal/rfe

|

655

© 2020 University of New Orleans

1

|

INTRODUCTION

Firm investments have negatively predicted future stock returns in cross sections after controlling for the standard risks. There

are two prominent hypotheses for this pervasive return predictability: (a) prolonged mispricing due to limits to arbitrage and (b)

financing constraints (FCs) affecting the link between the corporate investment process and the discount rate.

The mispricing hypothesis suggests that certain behavioral biases, such as over- or under-reaction to information, lead to

stock overvaluation following large investments undertaken by firms. Although arbitrageurs in an efficient market should

promptly correct the mispricing, limits to arbitrage due to capital shortage, excessive transaction costs and/or information

risk may discourage the arbitrageurs from fully acting on the overvaluation (Shleifer & Vishny, 1997). For instance, previous

studies have attributed the persistence of the momentum and post-earnings drift anomalies long after their discovery to such

risks borne by the arbitrageurs (Mendenhall, 2004; Sadka, 2006). The arguments for the effect of limits to arbitrage on the

investment-related anomalies are mixed. Some studies document the evidence that the anomalies exist due to high barriers to

arbitrage (Lakonishok, Shleifer, & Vishny, 1994; Li & Sullivan, 2011); others associate the anomalies with the systematic risk

related to the firm's growth options (Li, Livdan, & Zhang, 2009; Zhang, 2006). If the return predictability of firm investments

is statistically and economically stronger in firms with higher arbitrage costs, then the expected return-investment relation is

likely attributable to the limits to arbitrage.

Alternatively, a non-behavioral explanation for the return predictability can bring insights from the Q-theory of investment

(Cochrane, 1991, 1996) extended with the inclusion of FCs by Li and Zhang (2010). In imperfect markets with informational

asymmetry, agency costs and transaction costs, internal and external financing are not perfect substitutes, and smoothing in-

vestments becomes more challenging for firms (Fazzari, Hubbard, Petersen, Blinder, & Poterba, 1988; Kaplan & Zingales,

1997). Then, the investment anomaly may likely be the byproduct of a firm's investment optimization process: firms increasing

Received: 8 July 2019

|

Revised: 16 December 2019

|

Accepted: 17 December 2019

DOI: 10.1002/rfe.1098

ORIGINAL ARTICLE

Revisiting the investment anomaly: Financing constraints or

limits-to-arbitrage?

Kyungyeon (Rachel)Koh

Department of Finance, California State

University—Channel Islands, Thousand

Oaks, CA, USA

Correspondence

Kyungyeon (Rachel) Koh, Department

of Finance, California State University—

Channel Islands, Thousand Oaks, CA, USA.

Email: rachel.koh@csuci.edu

Abstract

The investment anomaly refers to the pervasive negative predictability in future stock

returns following large firm investments. I re-investigate two competing hypotheses

for the potential source of the anomaly: (a) prolonged mispricing due to limits to

arbitrage and (b) financing constraints in the context of Q-theory of investments.

The analyses employ new proxies for financing constraints, the text-based measures

developed by Hoberg and Maksimovic (2014). While the evidence supporting the

limits-to-arbitrage hypothesis is stronger, there is a fair amount of evidence that fi-

nancing constraints also reinforce the anomaly effect.

KEYWORDS

financing constraints, investment anomaly, limits to arbitrage, mispricing

JEL CLASSIFICATION

G12; G31

656

|

KOH

investments must have low discount rates, especially if they face high FCs. I empirically test this theoretical outcome by using

proxies for FCs and examining whether the return predictability is stronger in more financially constrained firms.

The results contribute to the current state of research on the source of the investment anomaly, which remains inconclusive

to date. To preserve comparability with the previous two articles that have compared the two hypotheses, Li and Zhang (2010)

and Lam and Wei (2011), I use the same rigorous statistical and econometric methods. However, this research updates the

sample up to the year 2018, while previous studies examine up to 2009, which is meaningful because some market anomalies,

including the investment anomalies examined in this study, have weakened over time (Chordia, Subrahmanyam, & Tong, 2014).

In addition, this study tests the hypotheses with new and advanced FC variables, which no previous research has undertaken.

Specifically, the tests employ the text-based FC metrics developed by Hoberg and Maksimovic (2014); these new measures

have been shown to capture the degree of financing costs with less noise than the traditional measures based on firm charac-

teristics. It is important to re-investigate the hypotheses with the new development in the literature. In short, this research finds

stronger evidence that supports the limits to arbitrage as the source of the investment anomaly, but interestingly, there is a fair

amount of evidence that FCs also reinforce the anomaly effect.

2

|

HYPOTHESIS DEVELOPMENT

The return predictability due to mispricing can persist over a longer period if arbitrageurs are discouraged from acting on the

mispricing immediately due to high arbitrage costs (Shleifer & Vishny, 1997). Hence, we expect that the persistence of the

overpriced-ness following large firm investments will be greater in stocks with higher arbitrage costs. To test this concept em-

pirically, I employ idiosyncratic volatility (IVOL) of stock returns, a conventional measure for arbitrage costs (Ang, Hodrick,

Xing, & Zhang, 2006 and Stambaugh, Yu, & Yuan, 2015). The higher the idiosyncratic risk, the more difficult and expensive

the riskless arbitrage effort is.1

We expect to find a stronger inverse expected return-investment relation in the high IVOL firms

than in the low IVOL firms.

Another channel through which the inverse relation between the expected return and firm investments is the discount rate. In

the framework of the production-based asset pricing model by Cochrane (1991), corporate investment decisions reflect changes

in expected discount rates in the economy. All else equal, firms will invest more (less) when the cost of capital is lower (higher),

which potentially provides an explanation for the investment anomaly. In the extended version by Li and Zhang (2010), in-

vestment decisions are also influenced by the varying levels of FCs faced by firms. All else equal, firms with higher (lower)

constraints will have lower (higher) flexibility to adjust the level of investment in accordance with the cost of external capital.

The setup of the Q-theory with investment frictions by Li and Zhang (2010) is as follows. Each firm indexed by i chooses

the optimal investment level,

I∗

i0

to maximize the market value of the firm at the beginning of the period, t=0. Each firm faces

a gross discount rate Ri that are different across firms and also some degree of FCs

𝜆i

, that are also different across firms. A

firm's operating profit,

∏

, is assumed to be time-invariant and constant across firms. Each firm will maximize its market value

by varying

Ii0

at the beginning of each period t=0, and the following equation is the first-order condition of the optimization

problem with respect to

Ii0

arranged for

Ri

:

Assuming all else constant, the inverse relation between

Ri

and

I∗

i0∕Ki0

serves as a potential explanation for the investment

anomaly. The intensity of that relation depends on the degree of FCs,

𝜆i

. Figure 1 shows how

Ri

varies with

I∗

i0∕Ki0

for different

levels of

𝜆i

, holding

∏

constant at 0.15 and

𝛿

at 0 (rate of capital depreciation). Letting

I∗

i0∕Ki0

vary from −0.02 to 1 and

𝜆i

from

0 to 30, we obtain a steeper relation at higher levels of

𝜆i

.

The pattern in the plot suggests that firms increasing investments must have low discount rates, especially if they face high

FCs.

The limits-to-arbitrage and FC explanations motivate the following set of hypotheses:

Hypothesis 1a If mispricing is the source of the return predictability, then the investment anomaly will appear stronger in

higher limits-to-arbitrage firms than in lower limits-to-arbitrage firms.

Hypothesis 1b If the Q-theory is the source of the return predictability, then the investment anomaly will appear stronger in

more financially constrained firms than in less financially constrained firms.

Ri=

∏

+1−𝛿

1+𝜆

i

(I∗

i0

∕K

i0)