Does q-theory with investment frictions explain anomalies in the cross section of returns?☆
Introduction
Initiated by Cochrane, 1991, Cochrane, 1996, asset pricing based on the q-theory of investment argues that real investment explains cross-sectional differences in expected returns. Intuitively, all else equal, low costs of capital imply high net present values of new projects and high investment, and high costs of capital imply low net present values of new projects and low investment. The literature has so far applied the negative expected return–investment relation predicted by q-theory to explain a wide range of capital markets anomalies (empirical relations between average stock returns and firm characteristics that cannot be explained by traditional asset pricing models).1 In this paper we derive and test a novel implication of q-theory on cross-sectional returns—the expected return–investment relation should be steeper in firms with high investment frictions than in firms with low investment frictions. By exploring the previously ignored interaction between the expected return–investment relation and investment frictions, our tests address whether these anomalies can be attributed to q-theory.
With frictions, investment entails deadweight costs, which cause investment to be less elastic to changes in the discount rate than when frictions are absent. Using a simple model, we show that the magnitude of this elasticity decreases with investment costs. The higher are the investment costs that firms face, the less elastic firms’ investments are in responding to variation in the discount rate. Equivalently, a given change in investment corresponds to a larger change in the discount rate, meaning that the expected return–investment relation is steeper for firms with high investment frictions than for firms with low investment frictions. If q-theory does explain a particular investment related anomaly, the relation between expected returns and the anomaly variable must satisfy this prediction.
To test this prediction, we identify investment frictions with firm-level proxies of financing constraints. The premise is that if there are investment costs such as adjustment costs of capital, frictions in capital markets induce additional financing costs at the margin. We use three financing constraints proxies: asset size, payout ratio, and bond ratings. Firms with small asset, low payout ratios, and unrated public debt are more financially constrained than firms with big asset, high payout ratios, and rated public debt. We use six investment-related anomaly variables: investment-to-assets (Lyandres, Sun, and Zhang, 2008), asset growth (Cooper, Gulen, and Schill, 2008), investment growth (Xing, 2008), net stock issues (Fama and French, 2008), abnormal corporate investment (Titman, Wei, and Xie, 2004), and net operating assets (Hirshleifer, Hou, Teoh, and Zhang, 2004). We estimate Fama and MacBeth (1973) cross-sectional regressions of returns on a given anomaly variable within extreme subsamples split by a given financing constraints proxy. Under the q-theory logic, the slope should be negative. With investment frictions, the negative slope should be greater in magnitude in the more constrained subsample than in the less constrained subsample.
Overall, the news is not good for q-theory as an explanation of the anomalies. First, we show some evidence in support of the q-theory interpretation of the investment-to-assets and the asset growth effects. Their slopes are significantly greater in magnitude in the more constrained subsample than in the less constrained subsample. For example, the investment-to-assets slope is −0.85 in the small asset tercile and −0.33 in the big asset tercile, and the difference is more than 2.1 standard errors from zero. This slope is −0.93 in the low payout ratio tercile and −0.39 in the high payout ratio tercile, and the difference is more than 2.4 standard errors from zero. The investment-to-assets slope is −0.86 in the subsample without bond ratings and −0.47 in the subsample with bond ratings, and the difference is more than 2.4 standard errors from zero. The difference in the asset growth slope is significant across extreme asset size terciles and across the subsamples with and without bond ratings, but it is insignificant across extreme payout ratio terciles. However, the evidence is not robust to controlling for the January effect and to controlling for size, book-to-market, and momentum in cross-sectional regressions.
Second, no evidence exists that q-theory with investment frictions explains the investment growth, net stock issues, abnormal corporate investment, or net operating assets anomalies. Their slopes do not differ significantly across extreme financing constraints subsamples. For example, the difference in the investment growth slope is only −0.04 across the extreme asset size terciles and is within 0.9 standard errors from zero. The difference in the net stock issues slope across the subsamples with and without bond ratings is −0.04, which is within 0.2 standard errors from zero. The difference in the abnormal corporate investment slope across extreme payout ratio terciles is −0.05, which is within 1.3 standard errors from zero. The slope difference sometimes even goes in the wrong direction from the prediction of q-theory. In particular, the net operating assets slope in the high payout ratio tercile is higher in magnitude than that in the low payout ratio tercile by 0.06, although the difference is insignificant.
Third, and more important, limits-to-arbitrage proxies dominate financing constraints measures in explaining the magnitude of the investment-to-assets and asset growth anomalies.2 We show that proxies for investment frictions are correlated with those for limits-to-arbitrage (idiosyncratic volatility and dollar trading volume). Firms with stocks that are more costly to trade face higher investment frictions. However, in direct comparisons financing constraints proxies are largely insignificant after we control for limits-to-arbitrage, but limits-to-arbitrage proxies (in particular, idiosyncratic volatility) remain significant after we control for financing constraints. If the empirical proxies have sufficiently high quality, the overall evidence suggests that the q-theory explanation for the investment-to-assets and asset growth anomalies is not robust to controlling for limits-to-arbitrage and that the mispricing hypothesis seems to better explain the anomalies in question. However, no evidence exists that arbitrage costs affect the magnitude of the investment growth, net stock issues, or abnormal corporate investment anomalies from the prediction of the mispricing hypothesis.
The rest of the paper is organized as follows. Section 2 develops the investment frictions hypothesis from q-theory and sets up limits-to-arbitrage as an alternative hypothesis. Section 3 describes our data. Section 4 presents our empirical results. Finally, Section 5 concludes.
Section snippets
Hypothesis development
We develop the investment frictions hypothesis based on q-theory in Section 2.1, and set up limits-to-arbitrage as an alternative hypothesis in Section 2.2.
Data
We obtain accounting data from Compustat and stock returns data from the Center for Research in Security Prices (CRSP). All domestic common shares trading on NYSE, Amex, and Nasdaq with accounting and returns data available are included except for financial firms, which have four-digit standard industrial classification (SIC) codes between 6000 and 6999. Following Fama and French (1993), we exclude closed-end funds, trusts, American Depository Receipts, Real Estate Investment Trusts, units of
Empirical results
Section 4.1 presents descriptive statistics, Section 4.2 tests the investment frictions hypothesis, and Section 4.3 examines the incremental effect of investment frictions relative to limits-to-arbitrage.
Conclusion
We make two contributions to the literature. First, we use a two-period q-theory model to show theoretically that the expected return–investment relation should be steeper in firms with high investment frictions than in firms with low investment frictions. With frictions, investment entails investment costs, and higher investment entails higher investment costs, causing investment to be less elastic to changes in the discount rate. The higher are the investment costs, the less elastic
References (40)
- et al.
Arbitrage risk and the book-to-market anomaly
Journal of Financial Economics
(2003) - et al.
Common risk factors in the returns on stocks and bonds
Journal of Financial Economics
(1993) - et al.
Evidence on the role of cash flow for investment
Journal of Monetary Economics
(1995) - et al.
Do investors overvalue firms with bloated balance sheets?
Journal of Accounting and Economics
(2004) - et al.
Market underreaction to open market share repurchases
Journal of Financial Economics
(1995) Size-related anomalies and stock return seasonality: further empirical evidence
Journal of Financial Economics
(1983)- et al.
Why is the accrual anomaly not arbitraged away? The role of idiosyncratic volatility and transaction costs
Journal of Accounting and Economics
(2006) - et al.
Financial constraints, asset tangibility, and corporate investment
Review of Financial Studies
(2007) - et al.
The cash flow sensitivity of cash
Journal of Finance
(2004) - et al.
Empirical evidence on capital investment, growth options, and security returns
Journal of Finance
(2006)
Production-based asset pricing and the link between stock returns and economic fluctuations
Journal of Finance
A cross-sectional test of an investment-based asset pricing model
Journal of Political Economy
Asset growth and the cross-section of stock returns
Journal of Finance
Investment behavior, observable expectations, and internal funds
American Economic Review
Market reactions to tangible and intangible information
Journal of Finance
Measurement error and the relationship between investment and q
Journal of Political Economy
Accrued earnings and growth: implications for future profitability and market timing
The Accounting Review
Dissecting anomalies
Journal of Finance
Risk, return, and equilibrium: empirical tests
Journal of Political Economy
Financing constraints and corporate investment
Brookings Papers on Economic Activity
Cited by (167)
The use of asset growth in empirical asset pricing models
2024, Journal of Financial EconomicsMomentum investing and a tale of intraday and overnight returns: Evidence from Taiwan
2023, Pacific Basin Finance JournalQuarterly investment spikes, stock returns, and the investment factor
2023, Journal of Financial MarketsTechnology spillover, corporate investment, and stock returns
2023, Journal of Empirical FinanceDoes the investment-profitability correlation affect the factor premiums? Evidence from China
2023, Pacific Basin Finance JournalChanges in firm profitability, heterogeneous investor beliefs, and stock returns
2023, Journal of Management Science and Engineering
- ☆
For helpful comments we thank Espen Eckbo, Gerald Garvey, Rick Green, Hui Guo, Kewei Hou, Prem Jain, Erica Li, Anil Makhija, Korok Ray, Tyler Shumway, Ingrid Werner, Neng Wang, Wei Xiong, Hong Yan, and other seminar participants at Hanqing Advanced Institute of Economics and Finance at Renmin University of China, McDonough School of Business at Georgetown University, Fisher College of Business at Ohio State University, the China International Conference in Finance, and the University of British Columbia's Phillips, Hager, and North Centre for Financial Research Summer Finance Conference. Bill Schwert (the Editor) and an anonymous referee deserve special thanks. This work supersedes our previous working papers under the titles “Costly external finance: Implications for capital markets anomalies” and “Do investment frictions affect anomalies in the cross section of returns?” All remaining errors are our own.