Innovative Capacity and the Asset Growth Anomaly
Innovative Capacity and the Asset Growth Anomaly* Praveen Kumara
Dongmei Lib
November 2011
Abstract Innovative capacity (IC) is the ability of firms to produce and commercialize a sequence of innovations. Expected returns need not fall following asset growth by high IC firms because investment can generate new growth options. Using patent intensity based IC measures we provide the first analysis of the effects of IC on financial markets' response to asset growth. We find that the well-known negative relationship between asset growth and subsequent excess returns holds only for the subset of firms with high asset growth and low IC, but in a stronger and more robust fashion than reported earlier. However, high IC firms with high asset growth rates not only do not suffer negative excess returns subsequent to asset growth, they actually earn significantly positive subsequent excess returns. Moreover, and as predicted by a model of optimal dynamic investment with sequentially arising growth options, changes in the market risk loadings of firms following asset growth episodes are positively related to their IC. Firms' innovative capacity therefore appears to play an important role in the dynamics between asset growth and returns. Keywords: Innovative capacity; Asset growth; Excess returns; Risk dynamics; Patents JEL classification codes: G12, G32, O31 *
We thank Jonathan Berk, Wayne Ferson, Michael Fishman, Paolo Fulghieri, Robert Goldstein, Joao Gomes, Richard Green, David Hirshleifer, Kewei Hou, Po-Hsuan (Paul) Hsu, Nisan Langberg, Robert Stambaugh, Jeremy Stein, and Jianfeng Yu for valuable discussions and comments. We also thank Lu Zhang for sharing the investment and profitability factors returns.
a
C.T. Bauer College of Business, University of Houston, Houston, TX 77204. Email: [email protected] Rady School of Management, University of California, San Diego, La Jolla, CA 92093. Email: [email protected]
b
Innovative Capacity and the Asset Growth Anomaly
November 2011
Abstract Innovative capacity (IC) is the ability of firms to produce and commercialize a sequence of innovations. Expected returns need not fall following asset growth by high IC firms because investment can generate new growth options. Using patent intensity based IC measures we provide the first analysis of the effects of IC on financial markets' response to asset growth. We find that the well-known negative relationship between asset growth and subsequent excess returns holds only for the subset of firms with high asset growth and low IC, but in a stronger and more robust fashion than reported earlier. However, high IC firms with high asset growth rates not only do not suffer negative excess returns subsequent to asset growth, they actually earn significantly positive subsequent excess returns. Moreover, and as predicted by a model of optimal dynamic investment with sequentially arising growth options, changes in the market risk loadings of firms following asset growth episodes are positively related to their IC. Firms' innovative capacity therefore appears to play an important role in the dynamics between asset growth and returns.
Keywords: Innovative capacity; Asset growth; Excess returns; Risk dynamics; Patents JEL classification codes: G12, G32, O31
1.
Introduction The effects of capital investment and asset growth on stock returns have important
implications for both asset pricing and corporate finance. Recently, a number of empirical studies highlight a negative relationship between capital investment/asset growth and subsequent abnormal (or benchmark-adjusted) stock returns (the “asset growth anomaly”) (Titman, Wei and Xie, 2004; Anderson and Garcia-Feijoo, 2006; Cooper, Gulen and Schill, 2008).1 For example, Titman et al. (2004) argue that investors underreact to empire building by managers and show that the negative relation is stronger for firms with greater investment discretion (i.e., firms with higher cash flows and lower debt ratios), while Cooper et al. (2008) suggest an overreaction to asset growth (which is broader than over investment) and interpret the negative abnormal returns as a correction to the overreaction. On the other hand, a variety of models in the literature predict a negative equilibrium relationship between investment and future returns (see Section 2). In particular, real options models (e.g., McDonald and Siegel, 1986; Majd and Pindyck, 1987; Carlson, Fisher and Giammarino, 2006) predict a decline in systematic risk following the exercise of risky growth options. From this perspective, the observed relationship between asset growth and subsequent returns is not an anomaly, and indeed a number of recent papers present direct evidence supportive of the risk-based explanations (see Cooper and Priestly, 2011). These alternative rational and behavioral interpretations of the data have profoundly different implications. In particular, a systematic negative bias in the market's capitalization of investment (and general asset growth) should have a major impact on corporate investment and
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Additional studies on the capital investment/asset growth anomaly include Xing (2008), Li and Zhang (2010), Titman, Wei and Xie (2011), Lam and Wei (2011), and Stambaugh, Yu and Yuan (2011), among others.
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financial policies; it also suggests formulation of trading strategies to exploit this market inefficiency. In this paper, we present new evidence on the dynamics between asset growth and stock returns by building on the notion of innovative capacity (IC), which is a measure of firms' ability to generate multiple growth options --- for example, through a sequence of innovations based on their patent holdings. We motivate the role of IC by noting the potential heterogeneity in the effects of asset growth across different IC firms. Specifically, asset growth of high IC firms is more likely related to innovation activities, such as construction of long-range research facilities and purchase of machinery/materials for use on current and future R&D projects, or acquisition of patents, or development of knowledge absorption capacities. This type of asset growth tends to generate new growth options and investment opportunities because innovations are often the source of new ideas and opportunities (Schumpeter, 1942; Maclaurin, 1953). In contrast, the asset growth of low IC firms is more likely to reflect capital expenditures in traditional industries, which simply reduces growth options and lowers the likelihood of future risky investment. To fix ideas, consider a firm that has developed an innovation --- for example, a new smart-phone operating system or a new class of drugs or a more powerful resonance imaging system --- that potentially opens long run economic opportunities through multiple improvements (“new generations”) of the basic innovation and creation of new ancillary support industries. However, these new growth opportunities arise only if the firm maintains a technological lead over imitators or rival technologies, which requires an effective innovation
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generation infrastructure and additional investments over time.2 High IC firms with low asset growth may therefore obtain only the benefits of the initial innovation, but high IC firms with high asset growth will have the opportunity to generate and exploit new growth opportunities. In sum, rapid asset growth of high IC firms is more likely to be a precursor to the generation of new growth options and therefore the equilibrium market price of the firm’s risk may actually increase subsequent to asset growth as the growth options materialize. In contrast, asset growth of low IC firms mainly converts growth options to assets-in-place and thereby reduces the risk premium or expected returns. In sum, from the real options viewpoint, the predicted effects of asset growth on subsequent expected returns should differ according to firms’ IC. Specifically, if asset growth of low IC firms mainly converts growth options to asset-in-place, then it should reduce the riskpremium or expected returns. In contrast, if the asset growth of high IC firms is a precursor to the generation of future growth options, then the expected returns should not subsequently decline and may even rise. Meanwhile, unless there is a high correlation between low IC and high investment discretion firms, there is no a priori presumption of systematic differences in the mispricing of asset growth across IC groups. Examining the effects of IC on the relationship between asset growth and subsequent returns is therefore of substantial interest from both the rational and behavioral perspectives. Building on the large literature that uses patent holdings as a measure of firms’ inventive activity and available growth options (e.g., Pakes, 1986; Griliches, Hall and Pakes, 1991), we use 2
For instance, when a firm builds a laboratory or invests in technological infrastructure to enhance knowledge absorption capacities (Cohen and Levinthal, 1990), the fixed cost is capitalized and reflected as asset growth or investment; yet, the firm is not exercising a pure growth option, rather it is setting up a potential generator of future growth options.
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patent intensity based measures of IC (i.e., recent annual patents granted to a firm normalized by various measures of assets) for this study. To our knowledge, this is the first study of the effects of innovative capacity on the response of financial markets to investment and asset growth. We summarize the results of our analysis as follows. Firms’ innovative capacity plays an important role in the asset growth anomaly. While we confirm the negative correlation between asset growth and subsequent abnormal returns for the overall sample (cf. Cooper et al., 2008), we find that this anomaly holds only for the subset of firms that exhibit high asset growth and have low IC; i.e., the asset growth anomaly is essentially restricted to firms that have low innovative capacity and exhibit high asset growth. Indeed, the asset growth anomaly for the low IC firms is stronger and more robust to risk-adjustment than has been reported in the literature (e.g., Cooper et al., 2008). On the other hand, not only is there no significant effect of asset growth on subsequent abnormal returns, for high IC firms with rapid asset growth there are significantly positive abnormal returns in the fourth and fifth year after the asset growth events. These results, which are based on independent (double) sorts of IC measures and asset growth, are robust to benchmarking with the Fama and French (1992, 1993) threefactor model, the Carhart (1997) four-factor model, and the investment-based three-factor model of Chen, Novy-Marx and Zhang (2011). The positive influence of IC on the post-asset growth abnormal returns is confirmed by the Fama-MacBeth (1973) regressions. For example, in the year after investment higher patent intensity dilutes significantly the negative effects of asset growth on subsequent returns controlling for firms’ characteristics. In sum, the stylized fact of a negative relationship between asset growth and subsequent abnormal stock returns --- that we confirm for our overall sample --
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- masks considerable heterogeneity in the data, with the innovative capacity of firms playing an important role. These results are interesting from both the behavioral and rational perspectives. From the behavioral viewpoint, our analysis indicates that markets appear to have a persistent or systematic mispricing problem in evaluating high asset growth by low IC firms. But since Titman et al. (2004) argue that the asset growth anomaly is consistent with investor underreaction to empire building by managers of firms, a natural question is whether the low IC firms also tend to have high investment discretion. However, our data refute this conjecture because we find that on average the low IC firms with high asset growth have negative cash flows and their leverage is also not appreciably lower than the sample average. Furthermore, our results also do not support the hypothesis that the low IC firms are harder to arbitrage than, say, the high IC firms as detailed in Section 4.2. And, from the overreaction viewpoint of Cooper et al. (2008), our results imply that investors overreact only to low IC firms with high asset growth but not to other firms, while they underreact to the positive growth implications of asset growth by high IC firms. However, the data suggest that there is heterogeneity across IC groups in the abnormal returns following asset growth, along the lines suggested by the real options framework. In particular, the effects of asset growth on abnormal returns are increasing with the firms’ IC; moreover, asset growth by high IC firms can eventually lead to an increase in abnormal returns. If the abnormal returns following asset growth are caused by missing risk factors instead of mispricing, then the evidence is consistent with the hypothesis that effects of asset growth on firms’ systematic risk differs according to their IC. In particular, we observe significantly
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negative alphas for the high-minus-low asset growth (AG) portfolio and the high AG portfolio formed among low IC firms in the first post-sorting year and significantly positive alphas for the high AG portfolio and the hedge portfolio formed among high IC firms in the fourth and fifth post-sorting years. The delay in observing the positive abnormal returns (subsequent to the asset growth events) for the high IC firms could be due to time-to-build effects (Kydland and Prescott, 1982) on the development of new growth options. We therefore examine further the effects of innovative capacity on the firm risk premium following asset growth both theoretically and empirically. We develop this intuition by constructing a theoretical sequential real options model where the optimal dynamic investment policy of firms generates a time-varying risk premium for firms that depends on their IC. Firms initially invest to build their long run IC, and then optimally and sequentially exercise growth options that arrive at random times. Higher IC firms have both a greater likelihood of developing a sequence (“new generations”) of innovations and higher expected cash flow growth conditional on realizing the innovations.
Our model demonstrates that the post-investment drop in
equilibrium firm risk premium will be lower (or diluted) for firms with higher IC compared with low IC firms, and forms the basis of our empirical test design. Empirically, we predict that the change in the firms’ loading on the market betas (following asset growth events) will be positively associated with innovative capacity.3 We test this prediction by examining the changes in the market betas of firms subsequent to their asset growth events using independent portfolio sorts based on the IC measures and asset growth. Consistent with the prediction, when we examine the change in betas between the first 3
We emphasize that we do not restrict the sign of the post-investment change in stock returns (it may still be negative for high IC firms, for example). Rather, the prediction is that the change will be positively related to the IC.
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and the fourth year following high asset growth, we find that market betas decrease for low IC firms but increase for high IC firms. When we compare the pre- and post-asset growth betas, we find that while market betas increase after high asset growth for both the high and low IC firms, the increase in betas is significantly greater for the high IC firms. The increase in market betas (for both high and low IC firms) subsequent to asset growth appears contrary to the prediction of a variety of models where firms' systematic market risk declines subsequent to investment (see Section 2) and does not appear to have been documented in the empirical literature.4 More generally, our analysis adds to the extensive literature that identifies a variety of causes for time-varying betas (or systematic market risk of firms) --- from business cycle variables to changes in estimation risk based on firm-specific information.5 In particular, our results indicate that firms' IC is an important characteristic in explaining the timevariation in their betas that occur due to pro-cyclical asset growth. In addition, our framework may also help reconcile the negative relationship between asset growth (AG) and returns with the observed positive relationship between significant R&D growth and returns. Eberhart, Maxwell and Siddique (2004) identify positive dynamics between significant R&D growth and subsequent stock returns and offer investor under-reaction as a possible explanation. However, our results indicate that the relationship between AG and returns 4
Cooper and Priestly (2011) find that for value-weighted returns loadings of only one of the five (non-traded) Chen, Ross and Roll (1986) factors declines significantly after rapid asset growth, while the loading on unexpected inflation actually increases significantly. However, we obtain significant results on the dynamics of market beta changes, when sorted on firms’ IC, using value-weighted returns. Thus, it appears that the effects of asset growth on loadings on market risk are quite different from its effects on non-traded factors. 5
Ferson, Kandel and Stambaugh (1987), Ferson and Harvey (1991), Ferson and Schadt (1996), Jagannathan and Wang (1996), and Lettau and Ludvigson (2001), among others, relate the time-variation in betas to business cycle related variables. And Kumar, Boehme, Danielsen and Sorescu (2008) show changes in the betas following firmspecific information that affects their estimation risk component.
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of high IC firms is significantly different --- up-to a change of sign --- from the overall negative relationship. Because significant R&D growth is most likely to be associated with high IC firms, the negative (positive) relationship between AG (significant R&D growth) and returns are not inconsistent with equilibrium risk premia and correct market assessment of the implications of investment.6 There is a related literature that examines the effects of innovation activity on firms' market valuation (Griliches, Hall and Pakes, 1987, 1991; Hall, Jaffe and Trajtenberg, 2005), and typically finds a positive relationship between IC indicators and market value. In contrast, we analyze the implications of IC on the abnormal returns and market risk changes subsequent to asset growth. Our analysis indicates that patent intensities do not by themselves have a significant influence on stock returns; rather, innovative capacity influences the abnormal returns and market risk changes subsequent to asset growth. Thus, our results introduce another dimension, so to speak, in evaluating the effects of innovative activity on stock returns. We organize the paper as follows. Section 2 develops the concept of innovative capacity at the firm level and motivates the empirical measures. Section 3 describes the data and the empirical framework. Section 4 discusses the empirical results on the relationship between IC and excess returns subsequent to asset growth. Section 5 describes the empirical test design regarding the effects of IC on the changes in firms' risk factor loadings following asset growth and presents the results. Section 6 summarizes the results and concludes.
2.
The Asset Growth Anomaly and Innovative Capacity: Motivation
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For example, depreciation of innovation-related asset growth, such as building research facilities and purchase of equipment for use in current and future R&D projects, is reflected in R&D expenses and consequently R&D growth.
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2.1
The Asset Growth Anomaly The “asset growth anomaly” refers to the negative relationship between capital
investment (and more generally asset growth) and subsequent abnormal stock returns that has been uncovered by a number of recent studies. For example, Titman et al. (2004) use Carhart’s (1997) four-factor model and find negative benchmark-adjusted returns following abnormal capital investment. This effect is more pronounced for firms with greater investment discretion, i.e., firms with higher cash flows and lower leverage, and when hostile takeovers are less prevalent. They argue that their results are consistent with investors reacting slowly to overinvestment by empire building managers. And using standard models of risk-adjustment (such as, the Fama and French (1992, 1993) three-factor model and the Carhart (1997) fourfactor model), Cooper et al. (2008) document a significant negative correlation between firms’ total asset growth and subsequent abnormal returns (alphas). They then argue that investors overreact to asset growth so that the observed negative post-AG abnormal returns are a correction for the initial overreaction. On the other hand, a number of models in the literature predict a negative relationship between investment and subsequent returns.7 As we mentioned above, real options models (such as, McDonald and Siegel, 1986; Majd and Pindyck, 1987; Berk, Green, and Naik, 1999; and Carlson, Fisher and Giammarino, 2006) predict a decline in systematic risk following the exercise of risky growth options. In a related vein, Berk, Green, and Naik (2004) present a model where investment resolves uncertainty with an attendant decline in the risk premium. Similarly, optimal dynamic investment based on the neoclassical q-theory may lead to a negative 7
Cooper and Priestly (2011) provide a good summary of these models.
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relationship between investment and future returns (Liu, Whited and Zhang, 2009; Li and Zhang, 2010). From an empirical perspective, Cooper and Priestly (2011) present evidence that is consistent with the rational or risk-based explanations of the asset-growth anomaly. And complementary evidence is provided by recent papers indicating that an investment factor, i.e., the return on a portfolio of low investment stocks over the return on a portfolio of high investment stocks, can help explain cross-sectional returns (e.g., Xing, 2008; Chen, Novy-Marx and Zhang, 2011). But clearly there is substantial heterogeneity in the effects of asset growth across firms. Introspection suggests that the implications of, say, one-time additions to manufacturing capacity and acquisition of patents (both of which are examples of asset growth in accounting terms) are substantially different from the viewpoint of the generation of future growth options and investment opportunities. Consequently, there should be heterogeneity in the relationship between asset growth and subsequent risk-adjusted returns across firms based on their capacity to generate future growth options from asset growth. We now develop this intuition.
2.2
Innovative Capacity: Concept and Measures The chain of innovations and growth opportunities starts with inventions or new ideas
that, when developed for economic and commercial purposes, become innovations. Innovations not only lead to new technologies and economic opportunities through development of new markets, but are also often the source of new ideas that result in a sequence of innovations --- a process that is central to economic growth (Schumpeter, 1942; Maclaurin, 1953). Building on this, the literature on research and economic growth has developed the notion of national 10
innovative capacity, i.e., the ability of a country (or geographical region) to produce and commercialize a flow of innovative technology over the long term (Furman, Porter and Stern, 2000, and onwards). But, so defined, the concept of innovative capacity (IC) is also an important financial characteristic at the level of the firm. To fix ideas, consider the well-known decomposition of firm value into value from assets-in-place and value from growth options (Myers, 1977). Ceteris paribus, firms with higher IC should have a greater ability to generate multiple growth options and, therefore, IC should be positively associated with market value. But IC also has important dynamic implications related to capital investment and asset growth. This is because investment by higher IC firms is more likely to generate subsequent growth options and risky investment opportunities compared to low IC firms. In particular, while investment by a low IC firm may reflect exercising a non-replaceable growth option, for a high IC firm the capital investment may in fact be a precursor to the generation of new growth options and hence higher expected return. While innovative capacity, as a concept, may have interesting implications, its empirical content depends on finding appropriate proxies or measures. Since firms benefit economically from inventions only if they are protected or patented, the number of patents held by a firm (the patent count) indicates its potential to generate growth options over time through a sequence of innovations. There is a long standing literature that uses patents as measures of firms' inventive activity and growth options (Griliches, 1990; Pakes, 1986). More recently, the literature on IC at the national and geographical levels also gives prominence to patent output (Furman et al., 2000). In a related vein, Cohen and Levinthal (1990) and a large literature thereafter argue that firms
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can develop knowledge creation and absorptive capacities, i.e., their ability to recognize, assimilate, and apply new information to commercial benefit, that is reflected in higher IC. Since R&D investment is highly uncertain and mainly serves as input to innovation, while patents reflect innovation output and future growth options directly, we therefore take the patent counts as the principal building block of our measures for firm IC. In addition, we argue that for our study patent holdings are more appropriate and accessible than their citations because our interest is in the forward looking aspects of inventive activity, i.e., the expected generation of future growth options based on the invention levels achieved by the firm at any given time, whereas future citations are not fully observable to investors as it takes time for patents to be cited (Hall, Jaffe and Trajtenberg, 2005). Furthermore, patent counts are actually highly correlated with future citations as shown in Hirshleifer, Hsu, and Li (2011). Therefore, we construct IC measures based on patent counts.
3.
Data and Innovative Capacity Measures
3.1.
Data and Measures Our sample consists of firms in the intersection of Compustat, CRSP (Center for
Research in Security Prices), and the NBER patent database. We obtain accounting data from Compustat and stock returns data from CRSP. All domestic common shares trading on NYSE, AMEX, and NASDAQ with accounting and returns data available are included except financial firms, which have four-digit standard industrial classification (SIC) codes between 6000 and 6999 (finance, insurance, and real estate sectors). Following Fama and French (1993), we exclude closed-end funds, trusts, American Depository Receipts, Real Estate Investment Trusts, units of beneficial interest, and firms with negative book value of equity. To mitigate backfilling 12
bias, we require firms to be listed on Compustat for two years before including them in our sample. Patent-related data are from the updated NBER patent database originally developed by Hall, Jaffe, and Trajtenberg (2001). 8 The database contains detailed information on all U.S. patents granted by the U.S. Patent and Trademark Office (USPTO) between January 1976 and December 2006: patent assignee names, firms’ Compustat-matched identifiers, the number of citations received by each patent, the number of citations excluding self-citations received by each patent, application dates, grant dates, and other details. Patents are included in the database only if they are eventually granted by the USPTO by the end of 2006. The NBER patent database contains two time placers for each patent: its application date and grant date. To prevent any potential look-ahead bias, we choose the grant date as the effective date of each patent and measure firm i’s innovation output in year t as the number of patents granted to firm i in year t (“patent counts”). We use three proxies for innovative capacity (IC): patent counts scaled by total assets (CTA), patent counts scaled by year-end market equity (CTME), and patent counts scaled by book equity (CTBE). We construct these three IC proxies for each year from 1976 to 2006. Since we focus on the effect of IC on the asset growth anomaly, we compute asset growth for the same sample period. 3.2.
Summary Statistics At the end of June of each year t from 1977 to 2007, we sort firms independently into two
IC groups (“Low” and “High”) based on the median breakpoint of IC in calendar year t – 1 and 8
The updated NBER patent database is available at https://sites.google.com/site/patentdataproject/Home/downloads.
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asset growth deciles based on asset growth (AG) defined as percentage change in total assets (Compustat item AT) from the fiscal year ending in calendar year t – 2 to fiscal year ending in calendar year t – 1. Firms with missing IC measure are assigned to the low IC group. The intersection of these portfolios forms twenty IC-AG portfolios. For each IC-AG portfolio, Table 1 reports time-series mean of cross-sectional average for the number of firms, book-to-market equity (BTM), market equity (Size), innovative capacity, three-year average innovative capacity, asset growth, leverage (the long-term debt to assets ratio, DA) and cash flow (CF). Following Titman et al. (2004), we measure DA with the ratio of long-term debt over the sum of long-term debt plus year-end market value of equity. Cash flow, which is scaled by total assets, is operating income before depreciation minus interest expenses, taxes, preferred dividends, and common dividends. All variables are measured in the fiscal year ending in calendar year t – 1 except Size, which is market equity (in millions) at the end of June in year t. In Table 1, we measure IC with CTA, CTBE, and CTME in Panels A, B, and C, respectively. Panel A shows that the average number of firms in the low IC group is much higher than that in the high IC group. This is consistent with the inclusion of firms with missing IC in the low IC group. In general, BTM decreases with asset growth in both low and high IC groups, suggesting that high asset growth firms tend to be growth firms, while low asset growth firms tend to be value firms. Furthermore, each AG portfolio in the low IC group has higher BTM than its counterpart in the high IC group. This pattern supports our claim that IC is a proxy of growth options. The average size of low IC firms is smaller than that of high IC firms; a contributing factor here may be the high market valuations of hi-tech firms during the 1980s and the 1990s. Within each IC segment (low or high), the relationship between AG and firm size appears to be
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hump-shaped, i.e., firms in the middle AG deciles tend to be larger on average than firms in the extreme (very low and very high) AG deciles. Panel A shows that in the low IC group, the average CTA is very low and does not vary much across the AG deciles, ranging from 0.02% to 0.03%. In the high IC group, the average CTA is much higher and varies with AG in a U-shape, ranging from 16.08% for the lowest AG portfolio to 4.28% for the middle AG portfolio to 7.32% for the highest AG portfolio. In addition, the level of IC tends to be persistent as low IC firms also have low CTA averaged over the prior three years. The pattern of the variation in the three-year average CTA across AG deciles within each IC group is also similar to that in the average CTA. The spreads in asset growth across the AG deciles in both IC groups are wide and similar. Specifically, asset growth in the low IC group ranges from –0.27 (lowest AG portfolio) to 1.60 (highest AG portfolio). Similarly, asset growth in the high IC group ranges from –0.25 (lowest AG portfolio) to 1.29 (highest AG portfolio). We will comment on the leverage and cash patterns in Section 4. The summary statistics of the IC-AG portfolios based on the other two proxies of IC are very similar as reported in Panels B and C. For example, the average number of firms in each IC-AG portfolio is almost identical across the three proxies of IC. The other characteristics are also very close, such as BTM, size, and asset growth. Therefore, the three IC measures are highly correlated with each other. In addition, we find the results reported in the next two sections are also very similar across the three IC measures. Therefore, for parsimony we only report results based on CTA in the rest of the paper.9 9
The results for the other two innovative capacity proxies are available upon request.
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4.
Innovative Capacity and the Asset Growth Anomaly In this section, we use both portfolio sorts and Fama-MacBeth (1973) cross-sectional
regressions to study the impact of innovative capacity on the asset growth anomaly documented in the literature (e.g., Cooper et. al., 2008). As discussed in the introduction, we expect a weaker AG effect among firms with higher innovative capacity since the asset growth of high IC firms may generate new investment opportunities and growth options due to the unique nature of asset growth for these firms. Total assets (Compustat item AT) used in computing asset growth includes not only tangible assets (such as property, plant and equipment) resulting from capitalization of traditional investment, but also tangible assets resulting from certain types of R&D investment and intangible assets, such as patents. In general, under current GAAP (generally accepted accounting principles), R&D investment is immediately expensed and included in R&D expenditures (Compustat item XRD) and, therefore, is excluded from total assets and asset growth. However, R&D investment that has usage for future R&D projects, such as investment in building research facilities and purchase of machinery and materials for use on current and future R&D projects, is included in total assets and asset growth. Similarly, patents acquisition costs are included in intangible assets and therefore are also a part of total assets and asset growth. 10 This type of asset growth is deemed to generate new growth options instead of reducing options.
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Since only the depreciation of this type of R&D investment is included in R&D expenses (Compustat item XRD), our results are not driven by the positive R&D-return relation documented in the literature (e.g., Chan, Lakonishok, and Sougiannis, 2001) which focuses on R&D expenses.
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However, existing studies do not disentangle different types of asset growth based on whether it is caused by traditional capital investment which tends to reduce growth options and risks or by innovation-related investment that can actually generate new options. We now examine how this differentiation sheds light on the asset growth anomaly. Although these innovation-related investments are included in total assets, they are not reported separately in Compustat. Therefore, we use firms’ innovative capacity to help differentiate these two types of asset growth. We assume asset growth of high IC firms is more related to growth in innovationrelated investment, while asset growth of low IC firms is driven by traditional capital investment. 4.1.
Portfolio Sorts
4.1.1. One-way Sort on Asset Growth We first show in Table 2 the existence of the asset growth anomaly in our sample period from July of 1977 to June of 2008, which is different from the sample period from 1968 to 2002 in Cooper et al. (2008). Following Cooper et al. (2008), we form asset growth deciles at the end of June of each year t from 1977 to 2007 based on asset growth in fiscal year ending in calendar year t – 1. We also form a high-minus-low portfolio which buys firms in the highest AG decile and sells firms in the lowest AG decile. We then hold these portfolios for the next 60 months and compute value-weighted monthly returns for each portfolio and report the time-series mean and corresponding t-statistics in parentheses of these portfolios’ returns in Panel A of Table 2. We examine value-weighted portfolio returns for two main reasons. First, because all the factors returns we use are value-weighted, using equal-weighted portfolio returns in the factor regressions will induce a bias in finding significant alphas. And, second, we want to ensure that
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our results are not driven by smaller firms that are likely to have higher patent intensity, i.e., we want to ensure that the “innovative capacity effect” is not essentially a “small firm effect”. Consistent with Cooper et al. (2008), we find a significantly negative relation between AG and returns in the first post-sorting year. The value-weighted monthly average return of the high-minus-low AG portfolio is –0.59% (t = –3.19) in the first post-sorting year. Cooper et al. (2008) finds a much higher return difference of -1.05% between the high and low AG deciles using data from 1968 to 2002. However, our finding is more consistent with Cooper and Priestley (2011), who find a return difference of 0.46% using data from 1960 to 2009. In addition, Cooper et al. (2008) find that the negative AG-return relation continues to be significant over the second and third post-sorting years. We find the relation is only significantly negative at the 10% in the second post-sorting year and insignificant over the third, fourth, and fifth post-sorting years. These differences could be attributed to the difference in the sample period. We also compute risk-adjusted returns for these portfolios over the five post-sorting years by regressing the time-series of portfolio excess returns on risk factors returns. The monthly portfolio excess return is measured by the difference between the value-weighted portfolio return and the one-month Treasury bill rate. We report the intercepts (alphas) from the Fama-French (1993) three-factor model, the Carhart (1997) four-factor model, and the investment-based threefactor model (Chen, Novy-Marx, and Zhang, 2011) in Panels B, C, and D of Table 2, respectively. The Fama-French three-factor model contains the market factor (MKT), the size factor (SMB), and the value factor (HML). The Carhart four-factor model contains the momentum factor (MOM) in addition to the Fama-French three factors. The market factor is the return on the value-weighted NYSE/AMEX/NASDAQ portfolio minus the one-month Treasury
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bill rate. The size factor and the value factor are returns on the factor-mimicking portfolios associated with the documented size effect and book-to-market effect (see, e.g., Fama and French 1992). The momentum factor is return on the factor-mimicking portfolio associated with the momentum effect (see, e.g., Jegadeesh and Titman 1993). The investment-based three-factor model contains the market factor, the investment (INV) factor, and the return on equity (ROE) factor. The INV factor is the difference between the return to a portfolio of low-investment stocks and the return to a portfolio of high-investment stocks. The ROE factor is the difference between the return to a portfolio of stocks with high ROE and the return to a portfolio of stocks with low ROE.11 Compared to Cooper et al. (2008) who focus on Fama-French alphas in the first postsorting year, we examine alphas from three different factor models over the five post-sorting year. We find some interesting patterns over time. For example, the alphas of the high AG portfolio and the high-minus-low AG portfolio become significantly positive in the fourth and/or the fifth post-sorting years. We discuss the detailed results below. Panel B of Table 2 shows a significantly negative Fama-French alpha for the high-minuslow AG portfolio in the first post-sorting year, –0.40% (t = –2.30) per month. However, it starts to weaken and turns to positive over the next four years. 12 Specifically, the monthly FamaFrench alpha for the high-minus-low AG portfolio is insignificant in the second post-sorting year (–0.13%, t = –0.71) and starts to turn positive (although insignificant) over the next three years. This pattern is driven mainly by the high AG decile. The monthly Fama-French alpha of the high 11
We obtain Carhart’s (1997) four-factor returns and the one-month Treasury bill rate from Kenneth French’s website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/.
12
Cooper et al. (2008) only reports the Fama-French alphas over the first post-sorting year.
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AG decile is significantly negative in the first post-sorting year, –0.38% (t = –3.50). It increases over the next four years to 0.22% (t = 1.81) in the fifth post-sorting year. In contrast, the FamaFrench alpha of the low AG decile is always small and insignificant over the five post-sorting years. Panel C reports the monthly Carhart alphas for the AG portfolios over the five postsorting years. It shows a negative but insignificant Carhart alpha for the high-minus-low AG portfolio in the first year (–0.25%, t = –1.39). In other words, the negative AG-return relation in the full sample can be fully explained by the Carhart four-factor model during this sample period. Furthermore, the Carhart alpha for the high-minus-low AG portfolio also increases over the next four years to 0.37% (t = 1.77) in the fifth post-sorting year. Similar to the Fama-French alphas, these patterns are also driven mainly by the high AG portfolio. For example, the Carhart alpha for the high AG portfolio is significantly negative in the first year (–0.32%, t = –2.94) but significantly positive in the fifth year (0.24%, t = 2.00). In contrast, the alphas for the low AG portfolio are always small and insignificant. In Panel D, we examine the explanatory power of the three-factor model motivated by the investment-based asset pricing and find similar patterns. The monthly alphas in the first postsorting year are negative and marginally significant for the high AG portfolio (–0.22%, t = –1.66) and significantly negative for the high-minus-low AG portfolio (–0.42%, t = –2.24). The alphas also increase over time to 0.34% (t = 2.52) for the high AG portfolio and 0.45% (t = 2.20) for the high-minus-low AG portfolio in the fifth post-sorting year. In fact, the alpha for the hedge portfolio is significantly positive as early as the fourth post-sorting year (0.44%, t = 2.10).
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Overall, these results confirm the existence of the asset growth anomaly in our sample period and illustrate some new interesting dynamics of this anomaly over the five post-sorting years. We now examine the interaction between the asset growth anomaly and the innovative capacity. For simplicity, we focus on risk-adjusted returns only. 4.1.2. Double Sorts on Innovative Capacity and Asset Growth In this subsection, we study the impact of innovative capacity on the asset growth anomaly through independent double sorts on IC and AG. Table 3 reports the value-weighted monthly alphas (in percentage) for the AG deciles across the innovative capacity groups formed in the same way as in Table 1. Specifically, at the end of June of each year t from 1977 to 2007, we sort firms independently into two innovative capacity groups (“Low” and “High”) based on the median breakpoint of innovative capacity in calendar year t – 1 and asset growth deciles based on asset growth in fiscal year ending in calendar year t – 1. Firms with missing innovative capacity measure are assigned to the low IC group. We measure IC with patent counts scaled by total assets in Table 3 since the other two measures of IC generate very similar results. The intersection of these portfolios forms twenty IC-AG portfolios. Furthermore, we create a highminus-low AG portfolio within each IC group. We then compute the monthly value-weighted portfolio returns for all these portfolios over the next 60 months and regress the time-series of portfolio excess returns on different sets of factor returns in each of the five post-sorting years. The monthly portfolio excess return is measured by the difference between the value-weighted portfolio return and the one-month Treasury bill rate. We report the intercepts (alphas) in percentage from the Fama-French model, the Carhart model, and the investment-based factor model in each of the five post-sorting years in Panels A, B, and C of Table 3, respectively.
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We find a sharp contrast in the AG anomaly across the IC groups. Panel A shows that the AG effect differs dramatically across the two IC groups. In the low IC group, the AG effect is significantly negative in the first post-sorting year. However, in the high IC group, the AG effect is insignificant in the first post-sorting year and significantly positive in the fourth and fifth postsorting years. Specifically, in the low IC group, the monthly Fama-French alpha of the highminus-low AG portfolio is significantly negative in the first post-sorting year, –0.53% (t = –2.49), but is small and insignificant over the next four years. The pattern is similar for the high AG portfolio in the low IC group. The monthly Fama-French alpha for the high AG, low IC portfolio is –0.57% (t = –3.73) and –0.29% (t = –2.25) in the first and second years, respectively, but is small and insignificant over the next three years. By contrast, in the high IC group, the monthly Fama-French alphas for the high AG portfolio and the high-minus-low AG portfolio are insignificant in the first three post-sorting years, but are significantly positive in the fourth and the fifth years. For example, the alphas for the high-minus-low AG portfolio are 0.75% (t = 2.59) and 0.81% (t = 2.27) in the fourth and the fifth years, respectively. Similarly, the alphas for the high AG portfolio are 0.58% (t = 2.82) and 0.52% (t = 2.62) in the fourth and fifth years, respectively. This striking contrast in the AG effect between the low IC group and the high IC group is robust to alternative factor models as shown in Panels B and C. For both the Carhart four-factor model and the investment-based three-factor model, we find a significantly negative alpha only for the high AG portfolio and the high-minus-low AG portfolio created in the low IC group in the first post-sorting year, but a significantly positive alpha for the high AG portfolio and the hedge portfolio created in the high IC group in the fourth and the fifth post-sorting years.
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Specifically, Panel B shows that in the low IC group, the monthly alpha estimated from the Carhart model is –0.56% (t = –3.79) for the high AG portfolio and –0.46% (t = –2.14) for the hedge portfolio in the first year, but is insignificant in the next four years. However, in the high IC group, the corresponding monthly alpha is only –0.08% (t = –0.42) for the high AG portfolio and 0.02% (t = 0.08) for the hedge portfolio in the first year, but is 0.59% (t = 2.68) and 0.59% (t = 2.97) for the high AG portfolio and 0.64 (t = 2.24) and 0.98% (t = 2.68) for the hedge portfolio in the fourth year and the fifth year, respectively. Similarly, Panel C shows that in the low IC group, the monthly alpha estimated from the investment-based three-factor model is –0.53% (t = –2.94) for the high AG portfolio and –0.74% (t = –3.34) for the hedge portfolio in the first year, but is small and insignificant in the next four years, ranging from –0.05% to 0.17%. However, in the high IC group, the corresponding monthly alpha is only 0.06% (t = 0.27) for the high AG portfolio and –0.08% (t = –0.28) for the hedge portfolio in the first year, but is 0.58% (t = 2.43) and 0.66% (t = 3.06) for the high AG portfolio and 0.82% (t = 2.50) and 1.13% (t = 3.01) for the hedge portfolio in the fourth and fifth years, respectively. Furthermore, the negative AG effect among low IC firms is stronger and more robust to risk adjustment than that in the full sample. Specifically, Table 3 shows that the monthly FamaFrench alpha, the Carhart alpha, and the investment-based alpha for the high-minus-low AG portfolio formed in the low IC group are all significantly negative: –0.53% (t = –2.49), –0.46% (t = –2.14), and –0.74% (t = –3.34), respectively. In contrast, Table 2 shows that the counterparts of these alphas for the hedge portfolio formed in the full sample are smaller and sometimes insignificant: –0.40% (t = –2.30), –0.25% (t = –1.39), and –0.42% (t = –2.24), respectively.
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This conspicuous contrast between the low IC group and the high IC group and the contrast between the low IC group and the full sample illustrated above cannot be attributed to the difference in the AG spread. Specifically, Table 1 shows that the low IC group and the high IC group have very similar average AG spread between the highest and the lowest AG deciles: 1.87 vs. 1.54. In unreported results, we find the average AG spread in the full sample is also similar at 1.82. In addition, the rank of asset growth tends to be persistent. For example, the average asset growth of the highest AG decile continues to be higher than that of the lowest AG decile over the next three (five) years for the low (high) IC group. Therefore, the positive AG effect in the high IC group in the fourth and fifth post-sorting years cannot be explained by the asset growth over the post-sorting years. These results illustrate the important role of innovative capacity in understanding the asset growth anomaly. They suggest that the negative asset growth effect documented in the literature is mainly driven by low IC firms. Among high IC firms, the asset growth effect is insignificant in the first post-sorting year and turns significantly positive in the fourth and the fifth post-sorting years. 4.2.
Fama-MacBeth Regressions In this subsection, we examine the interaction effect between innovative capacity and the
asset growth effect using Fama-MacBeth (1973) cross-sectional regressions to control for other characteristics that can predict returns and to ensure that the impact of innovative capacity on the asset growth effect documented in Section 4.1.2 is robust. The first row of Table 4 reports results from regressions with stock returns in the first post-sorting year as the dependent variable. Specifically, for each month from July of year t to 24
June of year t + 1, we regress monthly returns of individual stocks on ln(BTM), ln(Size), Momentum, asset growth (AG), patent counts scaled by total assets (CTA), and an interaction term, AG*CTA, to capture the effect of innovative capacity on the asset growth effect.13 BTM is the ratio of book equity in the fiscal year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Size is market equity at the end of June of year t. Momentum is the cumulative return over the prior six months with a one-month gap to reduce the effect of shortterm reversal. AG and CTA are measured in the fiscal year ending in calendar year t – 1. The minimum six-month lag between stock returns and BTM and AG ensures the accounting variables are fully observable. We winsorize all independent variables at the 1% and 99% levels to reduce the impact of outliers. The first row reports the time series average intercepts and slopes (in percentage) and their time-series t-statistics (in parentheses) from the series of monthly cross-sectional regressions. The slope on AG*CTA is significantly positive, 0.04% (t = 2.62). This implies a weaker AG effect in firms with high CTA, which is consistent with the findings in portfolio sorts in the first post-sorting year. Consistent with the literature, the slope on ln(BTM) is significantly positive, 0.20% (t = 3.03), and the slope on ln(Size) is significantly negative, –0.16% (t = –3.15). The slope on Momentum is positive but insignificant, 0.36% (t = 1.49). We also conduct monthly cross-sectional regressions of stock returns in the second postsorting year (July of year t + 1 to June of year t + 2) on the same set of independent variables used in the first row. We report the time series average intercepts and slopes (in percentage) and their time-series t-statistics (in parentheses) from these regressions in the second row. Similarly, 13
Similar results are obtained in Fama-MacBeth regressions with industry dummies based on Fama and French’s (1997) 48 industries.
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the dependent variables in the third to the fifth rows are stock returns in the third post-sorting year (July of year t + 2 to June of year t + 3), the fourth post-sorting year (July of year t + 3 to June of year t + 4), and the fifth post-sorting year (July of year t + 4 to June of year t + 5), respectively. The independent variables in these rows are the same as those used in the first row. The sample period for stock returns is from July 1977 to June 2008. Consistent with the results from portfolio sorts, the slope on the interaction term, AG*CTA, is significantly positive at the 10% level in the third and the fourth post-sorting years: 0.03% (t = 1.80) and 0.03% (t = 1.72), respectively. However, the slope on AG*CTA in the fifth year is insignificant. The slight difference between portfolio sorts and Fama-MacBeth (FM) regressions may be due to the fact that we impose a linear relationship in regressions and that AG and CTA could be highly correlated with the interaction term, AG*CTA.14 Overall, these FM regressions results provide evidence supporting the analysis from portfolio sorting because they indicate that the effect of asset growth on subsequent stock returns is influenced by firms’ innovative capacity in a statistically and economically significant manner, especially in the first year after the asset growth event. To summarize the results of this section, we find that firms’ innovative capacity plays a substantial role in the asset growth anomaly. The significantly negative AG effect documented in the literature exists only among low IC firms in the first post-sorting year. Furthermore, the negative AG effect among low IC firms is stronger and more robust to risk adjustment than that in the full sample. For example, the Carhart four-factor model can fully explain the negative AG 14
In order to reduce the high correlation between the interaction term and its component variables, we use decile rank of AG and a dummy variable for CTA (1 for firms above the median CTA and 0 for the other firms) in the regressions instead of the original variables. The interaction term, AG*CTA, is also constructed from the percentile rank of AG and the dummy variable for CTA.
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effect in the full sample, but not among the low IC firms. In contrast, the AG effect among high IC firms is insignificant in the first post-sorting year and turns significantly positive in the fourth and fifth post-sorting years. In addition, the Fama-MacBeth regressions also show a significant positive interaction effect between asset growth and innovative capacity on stock returns subsequent to asset growth; these results reinforce the inference from the portfolio sorts analysis that higher IC significantly weakens (and even over-turns) the asset growth anomaly. 4.3
Implications and Relation to the Literature We now relate our results to the literature on the asset growth anomaly. Specifically, we
relate the effects of firms’ IC on the relationship between asset growth and subsequent abnormal returns (described above) to some of the main mispricing explanations for the asset growth anomaly. We also develop further the implications of our results for the real options viewpoint. 4.3.1
Innovative Capacity and Investment Discretion
As we noted before, Titman et al. (2004) find that the negative relationship between high capital investment and abnormal returns is stronger for firms that have greater investment discretion, i.e., firms with higher cash flows and lower debt ratios. They then relate investment discretion to the moral hazard for managerial empire building and suggest that the anomaly may be due to investors’ slow reaction to the empire building implications of high investment. Prima facie, the fact that the asset growth anomaly appears to hold only for low IC firms may not be inconsistent with the empire building explanation of low IC firms being highly represented in the category of high investment discretion firms (e.g., cash cows). Conversely, the high IC firms are more likely to be cash constrained and their high patent intensity maybe an indicator that investment is not likely to involve “empire building.” However, returning to Table 1, we do not find support for 27
the conjecture that firms in the low IC/high asset growth (AG) group are also high investment discretion firms. In fact, this group has negative cash flows on average and their debt ratios are also not significantly lower than other groups. It is possible, of course, that the patent-based IC measures are very effective in discriminating between firms with value-destroying asset growth (i.e., the low IC firms) and potentially value-enhancing asset growth (the high IC firms), and our results may indicate slow investor reaction to the unproductive investment of the low IC firms. If this is the case, then our analysis is still of substantial interest because it would indicate that patent-intensity is a significant predictor of investment efficiency. Finally, we note that the underreaction to empire building only explains the negative effect of AG on subsequent stock returns. However, this viewpoint does not appear to be directly related to the result that there are positive abnormal returns for the high IC/high AG firms following rapid asset growth. 4.3.2
Innovative Capacity and the Limits to Arbitrage Another possible reason for the mispricing of asset growth only for the low IC firms
(following rapid asset growth) could be that these firms are harder to arbitrage compared to the high IC firms; i.e., the limits to arbitrage (Shleifer and Vishny, 1997) apply especially to our low IC/high AG group. However, in untabulated results we find that low and high IC firms have very similar average idiosyncratic volatility, a major measure of limits to arbitrage. We also note that the low IC firms are smaller than the high IC firms on average and this may be a factor that exacerbates the limits to arbitrage for this group. However, Cooper et al. (2008) show that the significantly negative AG effect is robust to size and exists in small,
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medium, and large size firms. Furthermore, the short leg of the trading strategy exploiting the AG anomaly is the high AG/low IC group. The average size of this group is $798 million, which is not very small, albeit smaller than the high AG/high IC group. In addition, we find a strong interaction effect of IC and AG on stock returns in the Fama-MacBeth regressions controlling for size in Section 4.2. Finally, our analysis also poses a challenge to the overreaction hypothesis of Cooper et al. (2008). From this perspective, our results imply that investors overreact only to low IC firms with high asset growth, but not to other firms. Furthermore, if the positive post-AG alphas for high IC/high AG firms are because of mispricing, then this suggests that investors underreact to the positive effects of high asset growth by the high IC firms (and the positive alphas reflect the correction for that underreaction). 4.3.3 Innovative Capacity and Time-Varying Firm Risk Premium Our results are potentially consistent with a framework where there is time-varying risk premium driven by investment and where the change in the risk premium is positively related to firms’ IC. From this viewpoint, asset growth of low IC firms mainly converts growth options to assets-in-place and thereby reduces the risk premium or expected returns; hence, we observe the significantly negative alphas of the high-minus-low AG portfolio and the high AG portfolio formed in the low IC group. In contrast, asset growth of high IC firms is likely related to innovation activities that can generate new growth options and therefore increase the risk premium and expected returns. And because of time-to-build effects (Kydland and Prescott, 1982), we start to observe the positive abnormal returns only in the fourth and fifth years after
29
the asset growth event; this is reflected in the significantly positive alphas of the high AG portfolio and the hedge portfolio formed in the high IC group. In sum, if the alphas following asset growth are caused by missing risk factors instead of mispricing, as would be suggested by an equilibrium asset pricing model with time-varying firm risk-premium, then our evidence is consistent with the view that high IC firms generate growth options after rapid asset growth, while the low IC firms exercise non-replaceable growth options. We turn now to explicating and testing the empirical implications of such a framework.
5. Innovative Capacity and Risk Dynamics In this section, we further examine the hypothesis that asset growth in low IC firms tends to exercise options and thereby reduce the risk premium, while asset growth in high IC firms tends to generate new growth options and increase the risk premium. In Appendix A we present a theoretical real options model where the optimal dynamic investment policy of firms generates time-varying firm risk premium that depends on the firms’ IC. Higher IC firms have both a greater likelihood of developing new growth options and higher expected cash flow growth conditional on realizing the innovations. In equilibrium, the change in the firms’ market price for risk subsequent to asset growth is positively associated with their IC (cf. Theorem 1). To test this prediction, we examine the risk dynamics of the highest AG decile formed in both IC groups. Specifically, we study the change in factor loadings between the first and the fourth post-sorting years for the high AG portfolio formed in the two IC groups. In addition, we also study the change in factor loadings before and after high asset growth across the IC groups. Our evidence supports the prediction of the equilibrium time-varying risk premium viewpoint.
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In Table 5, we form the IC-AG portfolios using the method described in Section 4.1.2. Specifically, at the end of June of each year t from 1977 to 2007, we sort firms independently into low and high innovative capacity groups based on the median breakpoint of IC in calendar year t – 1 and asset growth deciles based on asset growth in fiscal year ending in calendar year t – 1. Firms with missing IC are included in the low IC group. We measure IC with the number of patents granted (patent counts) scaled by total assets. We then compute monthly value-weighted portfolio returns for the next five years for these portfolios. As shown in Table 3, the AG effect in low IC firms is significantly negative only in the first post-sorting year, while the AG effect in high IC firms is insignificant in the first post-sorting year and turns significantly positive as early as the fourth post-sorting year. Furthermore, the AG effect is mainly driven by the highest AG decile. Therefore, we only report the factor loadings in the first and the fourth post-sorting years for the high AG and low IC portfolio (the highest AG decile formed in the low IC group) and the high AG and high IC portfolio (the highest AG decile formed in the high IC group). Table 5 reports the factor loadings along with changes in the factor loadings estimated from regressing the time series of portfolio excess returns on different sets of risk factors returns in the first (Year 1) and the fourth (Year 4) post-sorting years for the highest AG decile formed in the low IC and the high IC groups. Similar to Tables 2 and 3, we estimate the factor loadings from the Fama-French three-factor model, the investment-based three-factor model, and the Carhart four-factor model. Since the fourth post-sorting year starts from 1980, the sample period for stock returns is from July 1980 to June 2008 to ensure the same number of months for the time series of Year 1 and Year 4 returns.
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As there are still debates on whether the size (SMB), value (HML), momentum (MOM), investment (INV), and profitability (ROE) factors capture systematic risk or mispricing, we focus on the loading on the market (MKT) factor derived from general equilibrium models. Furthermore, the investment-based factor model is motivated by Q-theory and contains an investment factor based on the change in net PPE (property, plant, and equipment) plus change in inventory scaled by lagged total assets, which is a major component of asset growth. Therefore, we feel the investment-based model is the most appropriate benchmark in examining the risk dynamics related to asset growth. However, for completeness, we also report the loadings estimated from the other factor models. Consistent with our conjecture that the effect of asset growth on options and risks for low IC firms is different from that for high IC firms, we find that the market factor loading decreases from Year 1 to Year 4 for the high AG and low IC portfolio, but increases for the high AG and high IC portfolio. Specifically, for the high AG and low IC portfolio, the changes in market risk estimated from the Fama-French model, the investment-based model, and the Carhart model between Year 1 and Year 4 are negative: –0.08 (t = –1.83), –0.12 (t = –2.85), and –0.07 (t = – 1.69), respectively. In contrast, the counterparts of these changes in market risk for the high AG and high IC portfolio are positive: 0.09 (t = 1.17), 0.16 (t = 2.45), and 0.11 (t = 1.42), respectively. Following Cooper and Priestley (2011), we also examine the change in risk around investment.15 We define the pre- and post-investment portfolios in the same way as in Cooper 15
This exercise is mainly for comparison purposes only. In general, this analysis may not capture fully the risk dynamics around investment because firms assigned to the pre-investment portfolio can be very different from firms assigned to the post-investment portfolio in the same year. Furthermore, Cooper and Priestley (2011) examine loadings on non-traded factors, while we focus on traded factors.
32
and Priestley (2011). A firm is assigned to the pre-investment portfolio in year t if it is ranked in the highest asset growth decile in any one of years t + 2, t + 3, and t + 4. Following Cooper and Priestley (2011), we exclude firms in the top AG decile in year t + 1 from the pre-investment portfolio due to investment planning (e.g., Lamont, 2000) or time to build (Kydland and Prescott, 1982). A firm is assigned to the post-investment portfolio in year t if it is ranked in the highest AG decile in year t – 1. We also sort firms independently into the low and high innovative capacity (IC) groups in year t based on median IC in year t – 1. Firms with missing IC are included in the low IC group. The intersection of the two IC groups and the pre- and post-investment portfolios forms the low IC pre- and post-investment portfolios and the high IC pre- and post-investment portfolios. We measure IC with the number of patents granted (patent counts) scaled by lagged total assets.16 We then compute monthly value-weighted portfolio excess returns for these portfolios. Table 6 reports the factor loadings along with changes in the factor loadings estimated from regressions of the time series of portfolio excess returns on different sets of risk factors returns in the pre- and post-investment periods. The t-statistics are reported in parentheses. The sample period for stock returns is from July 1977 to June 2008. Similar to Table 5, we report factor loadings estimated from the Fama-French three-factor model, the investment-based threefactor model, and the Carhart four-factor model and focus on the market factor loadings. The results show that the market beta increases after high asset growth for both high IC firms and low IC firms. However, the increase in market beta for high IC firms is much larger 16
We scale patent counts by lagged total assets to avoid the confounding effect of asset growth in the same year on the IC measure.
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than that for low IC firms. Specifically, the increases in market beta estimated from the FamaFrench model, the investment-based model, and the Carhart model for the high IC firms are 0.18 (t = 3.07), 0.17 (t = 3.70), and 0.16 (t = 2.99), respectively. In contrast, the counterparts of these increases for low IC firms are only 0.08 (t = 2.08), 0.13 (t = 3.45), and 0.08 (t = 2.02), respectively. The increase in market risk after asset growth for the low IC firms may be related to the fact that firms assigned to the pre-investment portfolio can be very different from firms assigned to the post-investment portfolio based on the method in Cooper and Priestley (2011). This evidence illustrates the effect of innovative capacity on firms’ risk dynamics. In addition, it also shows that the decline in loadings on non-traded factors following high asset growth documented in Cooper and Priestley (2011) may not generalize to traded factors.
6.
Summary and Conclusions The negative relationship between asset growth and subsequent stock returns attracts
much attention because it has profound implications for both market efficiency and corporate investment policy. In particular, the observed significantly negative correlation between the firm's total asset growth and subsequent abnormal returns may indicate mispricing or biased capitalization of investment by financial markets, or it may indicate an efficient response to lower expected returns following the exercise of growth options. We motivate and document the importance of firms' innovative capacity in understanding the financial markets' response to asset growth. Theoretically, innovative capacity (IC), which is the ability of firms to produce and commercialize a sequence of innovations, should influence the evolution of equilibrium expected returns following asset growth. In particular, expected returns need not fall following asset growth by high IC firms because investment can generate 34
new growth options. More generally, we construct a sequential growth options model that predicts a positive relationship between the changes in firms' market price of risk subsequent to asset growth and their IC. Using patent intensity based IC measures, we analyze the effects of IC on financial markets' response to asset growth. We find that the well-known negative relationship between asset growth and subsequent excess returns holds only for the subset of firms with high asset growth and low IC. High IC firms with high asset growth rates not only do not suffer negative excess returns subsequent to asset growth, they actually earn significantly positive subsequent excess returns. Moreover, changes in the market risk loadings of firms following asset growth episodes are positively related to their IC. Firms' innovative capacity therefore appears to play an important role in the dynamics between asset growth and returns.
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Furman, J., M. Porter, and S. Stern, 2000, The determinants of national innovative capacity, Research Policy 31, 899-933. Griliches, Z., 1990, Patent statistics as economic indicators: A survey, Journal of Economic Literature 28, 1661-1707. Griliches, Z., B. Hall and A. Pakes, 1987, The value of patents as indicators of inventive activity. In Economic Policy and Technological Performance (P. Dasgupta and P. Stoneman, ed.), Cambridge: Cambridge University Press. Griliches, Z., B. Hall and A. Pakes, 1991, R&D, patents, and market value revisited: Is there a second (technological opportunity) factor? Economics of Innovation and New Technology, 1, 183-202. Hall, B., A. Jaffe and M. Trajtenberg, 2001, The NBER patent citation data file: Lessons, insights and methodological tools, NBER Working Paper 8498. Hall, B., A. Jaffe and M. Trajtenberg, 2005, Market value and patent citations, RAND Journal of Economics 36, 16-38. Hirshleifer, D., P. Hsu, and D. Li, 2011, Innovative efficiency and stock returns, Working Paper, University of California---San Diego. Jagannathan, R. and Z. Wang, 1996, The conditional CAPM and the cross-section of expected returns, Journal of Finance 51, 3-53. Jegadeesh, N. and S. Titman, 1993, Returns to buying winners and selling losers: Implications for stock market efficiency, Journal of Finance 56, 699-720. Kumar, P., S. Sorescu, B. Danielsen, and R. Boehme, 2008, Estimation risk and the conditional CAPM: Theory and evidence, Review of Financial Studies 21, 1045-1082. Kydland, F. and E. Prescott, 1982, Time to build and aggregate fluctuations, Econometrica 50, 1345-1370. Lamont, O., 2000, Investment plans and stock returns, Journal of Finance 55, 2719-2745. Lam, E. and J. Wei, 2011, Limits-to-arbitrage, investment frictions, and the asset growth anomaly, Journal of Financial Economics 102, 127-149 Li, D. and L. Zhang, 2010, Does Q-theory with investment frictions explain anomalies in the cross-section of returns? Journal of Financial Economics 98, 297–314. Liu, L., T. Whited and L. Zhang, 2009, Investment-based expected stock returns, Journal of Political Economy 117, 1105-1139. 37
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38
Appendix A
We model an economic environment where …rms start with a patent or intellectual property rights on an invention that is a source of potential innovations. Firms then choose to invest in innovative capacity (IC) ex ante to improve the expected returns on investment and the generation of new growth options ex post. Speci…cally, the typical …rm …rm at t = 0 chooses an investment K0 2 [0; K] that determines its IC. This project requires “time to build” (Kydland and Prescott, 1982). Time ‡ows continuously and, for simplicity, the …rm spends K0 at a constant rate to complete the project at time T0 : For t
T0 , …rms must invest to generate innovations from the patent. For simplicity,
we assume that …rms can either choose to invest in innovation development, which requires an instantaneous investment of I(t) = I at a …xed cost c, or they can choose not to develop innovations (i.e., set I(t) = 0): Conditional on investment, the arrival times for the succeeding generation of innovations are a sequence of independent exponentially distributed random variables f i gi 1 : (Here,
1
is the arrival time of the …rst generation or basic innovation and
so on.) However, if I(t) = 0; then there is zero probability of successfully developing the next generation of the innovation. Let n(t) denote the generation number of the innovation at any time t
T0 . (If the …rst
generation has not arrived at t, then n(t) = 0:) Suppose that n(t) = i; i = 0; 1; 2; ::; then we assume that: Pr( Here,
i (K0 )
i+1
t + y) = exp(
(1)
i (K0 )y)
are strictly increasing and concave functions; i.e., higher R&D infrastructure
investment increases the frequency of arrival of the new generation of innovations. However, consistent with the observed development of technologies, we allow for decreasing returns to scale or likelihood of newer generations, i.e.,
i (K0 )
>
i+1 (K0 ); i
= 0; 1; 2; :::
Successful new generations of the innovation are economically attractive; in particular, if
39
n(t) = i; i = 1; 2::; then cash ‡ows Y (t) follow a geometric Brownian motion: dY (t) = Y (t) i (K0 )
i (K0 )dt
=
(K0 ) +
+ dZ(t) n X
i
(2) (3)
i=1
Here, (K0 ) is a strictly increasing and concave function that is twice continuously di¤erentiable on (0; K): Meanwhile, f i gi
1
are a sequence of independent non-negative random
variables with the cumulative distribution F ( j K0 ) such that F ( j K00 ) strictly …rst order stochastically dominates F ( j K") if K 0 > K": In sum, higher IC investment increases both the likelihood of developing new generations of innovations and the expected growth of cash ‡ows, conditional on the successful arrival of these innovations. Turning to the risk characteristics, the cash ‡ow risk in (2) is systematic because we assume that innovations in Z(t) are positively correlated with the innovations in the pricing kernel that we will describe momentarily. However, the risk in the arrival date of the innovations is a technical risk and is therefore taken to be idiosyncratic (Berk, Green and Naik, 2006).The existence of a pricing kernel, an assumption that requires only the nonexistence of arbitrage, is described by the geometric Brownian motion where for t 2 [0; 1) : d (t) = (t)
rdt + dW (t)
(4)
Here, r is the instantaneous risk-free rate and W is a Brownian motion that has a correlation of
> 0 with Z (cf. (2)). Then using standard arguments, the market price for this risk is: (5)
!=
We can therefore represent project cash ‡ows through the risk-neutral pricing measure: If n(t) = i; i = 1; 2:::; then dY (t) = Y (t) i (K0 )
i (K0 )dt
+ ~ dQ(t)
(6)
i (K0 )
!
(7)
40
where Q is the Brownian motion under the risk-neutral measure. We let V (Y (t); n(t); K0 ) denote the equilibrium value of the …rm conditional on the cash ‡ows Y (t) and the current innovation generation n(t), while taking as given the initial IC investment K0 . (If n(t) = i, we will use the notation V (Y (t); i; K0 ):) This …rm valuation clearly depends on the optimal investment policy and is hence derived as follows. If the …rm is subject to only cash ‡ow risk, i.e., I (s) = 0, s
t, then standard arguments imply that
this valuation satis…es a continuous time version of the Gordon growth model, V (Y (t); i; K0 ) = where
i (K0 )
Y (t) ; i = 1; 2; :::; r i (K0 )
(8)
is de…ned in (7). However, if the …rm is investing for development, i.e., i.e.,
I (t) = I; then it’s value function includes the options of generating the future generation of innovations. We will denote the market price of risk for the …rm’s cash ‡ows by Rp (Y (t); n(t); K0 ) (using Rp (t; K0 ) for notational convenience). Then, conditional on continued development the value of the …rm and the risk-adjusted discount rate are determined simultaneously and recursively by:
V + (Y (t); i; K0 ) =
21 Z 4 exp ( [Rp (t; K0 )(s i (K0 )
t) +
i (K0 )s])
t
fY (s)
cI + V + (Y (s); i + 1; K0 )gds
Rp (Y (t); n(t); K0 ) =
V1+ (Y (t); n(t); K0 )Y (t) V + (Y (t); n(t); K0 )
(9)
(10)
!
And thus V (Y (t); n(t); K0 ) = max(V (Y (t); n(t); K0 ); V + (Y (t); n(t); K0 )
cI)
(11)
Note that by construction Rp (t; K0 ) > ! as long as I (t) = I: To characterize the equilibrium evolution of risk-premia, we …rst characterize the …rm’s optimal innovation investment policy. The next result shows that, under the assumption of strictly increasing wait times for innovations, …rms optimally cease to invest in innovation development beyond some threshold
41
innovation generation, and this threshold level is conditional on Y (t) and K0 : Proposition 1 Conditional on (Y (t); K0 ), there exists i (Y (t); K0 ) such that the optimal investment policy for developing new generations of the innovation is I (t) = I if n(t) i (Y (t); K0 ) but I (t) = 0 otherwise. Moreover,i ( ; K0 ) is increasing in the IC investment K0 : Proof: Because f i (K0 )g is a strictly decreasing sequence, it follows that for every " > 0 there exists i" (K0 ) such that
j (K0 )
< " for every j > i" (K0 ). Therefore, the
expected arrival time for a successful innovation, namely, 1= i (K0 ) exceeds 1=" for every j > i" (K0 ), for any given " > 0:Now take any t with (Y (t); n(t)): Given that Rp > ! and c > 0; it follows immediately from a comparison of (8) and (9) that there exists some (Y (t); K0 ) such that V (Y (t); n(t); K0 ) = V + (Y (t); n(t); K0 ) if V (Y (t); n(t); K0 ) > () (Y (t); K0 ): Hence, (12)
< (Y (t); K0 )) i (K0 )
is strictly increasing for all i and
V + (Y (t); n(t); K0 ) is also strictly increasing in K0 in light of the assumption on
i (K0 )
(cf.
(3)). It therefore follows from Proposition 1 that the evolution of the risk-premium satis…es:
p
R (t; K0 ) =
8
i (Y (t); K0 )
Hence, the change in the risk-premium subsequent to asset growth is: p
8
i (Y (t); K0 )
Note that the change in risk-premium is negative if n(t) = i (Y (t); K0 ) for in this case I (t) = I but E[ I (s) = 0 j s > t]: Furthermore, Proposition 1 implies that: Theorem 1 For each t and any given (Y (t); n(t)), 42
Rp (t;K00 ) I
Rp (t;K"0 ) I
t if K00 > K0" :
Table 1. Summary statistics of innovative capacity-asset growth portfolios At the end of June of each year t from 1977 to 2007, we sort firms independently into two innovative capacity (IC) groups based on the median breakpoint of IC in calendar year t – 1 and asset growth deciles based on asset growth (AG) defined as percentage change in total assets (Compustat item AT) from the fiscal year ending in calendar year t – 2 to fiscal year ending in calendar year t – 1. We measure IC with the number of patents granted (patent counts) scaled by total assets (CTA), patent counts scaled by book equity (CTBE), and patent counts scaled by year-end market equity (CTME) in Panels A, B, and C, respectively. The intersection of these portfolios forms twenty IC-AG portfolios. For each IC-AG portfolio, this table reports time-series mean of cross-sectional average for each variable measured in the fiscal year ending in calendar year t – 1 except Size, which is market equity (in $mn) at the end of June in year t. BTM denotes book-to-market equity. DA is the long term debt to assets ratio. CF is cash flows scaled by assets.
Panel A. IC = CTA 3-year avg. No. IC AG of CTA CTA Rank Rank Firms BTM Size (%) (%) AG DA Low Low
Panel B. IC = CTBE 3-year avg. No. of CTBE CTBE CF Firms BTM Size (%) (%) AG DA
CF
276
1.12 206 0.02 0.51 -0.27 0.21 -0.10
276
1.13 192 0.05
1.08 -0.27 0.21 -0.11 277 1.12
242
0.02
0.83 -0.27 0.21 -0.11
2
268
1.27 496 0.03 0.37 -0.08 0.26 0.00
268
1.27 485 0.05
0.76 -0.08 0.26 0.00
268 1.27
511
0.02
0.60 -0.08 0.26 0.00
3
261
1.19 700 0.03 0.29 -0.02 0.28 0.04
261
1.19 688 0.05
0.77 -0.02 0.28 0.04
260 1.19
752
0.01
0.46 -0.02 0.28 0.04
4
262
1.11 1005 0.02 0.27 0.03 0.27 0.05
262
1.11 990 0.05
0.53
0.03 0.27 0.05
261 1.11 1028
0.02
0.43 0.03 0.27 0.05
5
256
1.00 1177 0.02 0.26 0.06 0.26 0.06
256
1.00 1190 0.05
0.77
0.06 0.26 0.06
256 0.99 1218
0.02
0.41 0.06 0.26 0.06
6
260
0.92 1255 0.03 0.27 0.10 0.23 0.07
260
0.92 1220 0.05
0.49
0.10 0.23 0.07
259 0.91 1264
0.02
0.36 0.10 0.23 0.07
7
262
0.83 1366 0.03 0.35 0.15 0.22 0.08
261
0.83 1324 0.04
0.82
0.15 0.22 0.08
262 0.83 1398
0.02
0.36 0.15 0.22 0.08
8
266
0.74 939 0.03 0.32 0.23 0.19 0.09
267
0.74 917 0.05
0.66
0.23 0.19 0.09
267 0.74 1063
0.02
0.31 0.23 0.19 0.09
9
274
0.64 793 0.03 0.44 0.38 0.18 0.09
274
0.64 791 0.06
0.97
0.38 0.18 0.09
275 0.64
827
0.02
0.40 0.38 0.18 0.09
High 282
0.57 798 0.03 0.63 1.60 0.20 -0.01
282
0.57 827 0.06
1.34
1.60 0.20 -0.01 283 0.57
824
0.02
0.43 1.60 0.20 -0.01
76
0.93 604 16.08 9.86 -0.25 0.19 -0.13
75
0.93 637 51.76 27.68 -0.25 0.19 -0.13
75
0.93
533
19.54 15.36 -0.25 0.19 -0.13
2
84
1.00 1384 7.53 5.61 -0.08 0.22 -0.01
84
1.00 1433 17.38 13.16 -0.08 0.22 0.00
85
1.01 1339 13.84 9.12 -0.08 0.22 0.00
3
91
0.97 2733 4.67 3.76 -0.02 0.22 0.04
91
0.98 2797 9.25
7.55 -0.02 0.22 0.04
92
0.99 2384
7.69
6.09 -0.02 0.22 0.04
4
90
0.89 3441 4.51 3.80 0.03 0.20 0.06
91
0.89 3532 9.75 10.11 0.03 0.20 0.06
91
0.91 3364
6.69
6.61 0.03 0.21 0.06
5
96
0.83 3581 4.28 3.72 0.06 0.18 0.07
96
0.83 3546 8.35
7.12
0.06 0.18 0.07
97
0.84 3456
5.54
4.77 0.06 0.18 0.07
6
93
0.77 3484 3.89 3.47 0.10 0.16 0.08
93
0.76 3682 7.24
6.50
0.10 0.16 0.08
93
0.77 3482
5.11
4.53 0.10 0.16 0.08
7
91
0.63 3804 4.63 4.03 0.15 0.14 0.08
91
0.63 3968 9.07
6.99
0.15 0.14 0.08
90
0.65 3630
4.66
4.01 0.15 0.14 0.08
8
86
0.57 3298 5.01 4.51 0.22 0.13 0.10
86
0.57 3411 44.71 8.41
0.23 0.13 0.10
85
0.58 2789
4.46
4.18 0.22 0.14 0.10
9
78
0.51 3249 6.03 6.01 0.38 0.13 0.08
78
0.51 3262 11.42 12.92 0.38 0.14 0.08
77
0.52 3138
5.12
5.39 0.38 0.14 0.08
High
70
0.46 1717 7.32 8.35 1.29 0.14 -0.02
70
0.46 1650 17.32 17.70 1.29 0.14 -0.02
69
0.47 1642
5.29
5.08 1.28 0.14 -0.03
High Low
43
Panel C. IC = CTME 3-year avg. No. of CTME CTME CF Firms BTM Size (%) (%) AG DA
Table 2. Returns and alphas of asset growth deciles At the end of June of each year t from 1977 to 2007, we sort firms into asset growth deciles based on asset growth (AG) in fiscal year ending in calendar year t – 1. We also form a high-minus-low asset growth portfolio. We then compute monthly value-weighted portfolio returns for the next 60 months for these portfolios. The table reports the average portfolio returns (in Panel A) and intercepts (alphas) from regressions of the time series of portfolio excess returns on different sets of risk factors returns in each of the five postsorting years. The portfolio excess returns are the difference between monthly portfolio returns and the one month Treasury bill rate. Panels B, C, and D report monthly alphas (in percentage) from the Fama-French (1993) three-factor model, the Carhart (1996) fourfactor model, and the investment-based three-factor model (Chen, Novy-Marx, and Zhang, 2011), respectively. Panel A. Monthly Returns of AG Deciles Post-Sorting Year 1 2 3 4 5
1(Low) 1.25 (4.13) 1.17 (3.90) 1.21 (4.14) 0.92 (3.19) 1.08 (3.66)
2 1.16 (4.57) 1.13 (4.52) 1.18 (4.84) 0.98 (3.97) 1.23 (4.95)
3 1.20 (5.36) 1.22 (5.47) 1.14 (5.33) 1.04 (4.73) 1.07 (4.67)
4 1.05 (5.32) 1.01 (4.85) 1.04 (5.02) 0.99 (4.76) 1.12 (5.29)
5 1.08 (5.15) 1.03 (4.89) 0.81 (4.03) 1.04 (4.98) 0.99 (4.71)
6 1.02 (4.70) 1.02 (4.85) 1.07 (5.07) 0.91 (4.34) 0.90 (4.45)
7 1.06 (4.70) 1.10 (4.95) 0.99 (4.20) 1.04 (4.45) 0.96 (4.19)
8 1.08 (3.96) 1.07 (3.82) 0.94 (3.36) 1.00 (3.71) 0.97 (3.68)
9 10(High) High-Low 0.94 0.66 -0.59 (3.11) (2.00) (-3.19) 1.02 0.87 -0.30 (3.44) (2.70) (-1.67) 1.09 1.13 -0.08 (3.75) (3.68) (-0.45) 1.21 1.13 0.21 (4.24) (3.45) (1.10) 1.14 1.16 0.08 (4.06) (3.75) (0.42)
5 0.10 (1.40) 0.14 (1.71) -0.09 (-1.03) 0.13 (1.41) 0.03 (0.39)
6 0.11 (1.24) 0.13 (1.74) 0.17 (2.57) 0.04 (0.51) 0.01 (0.13)
7 0.17 (2.33) 0.19 (2.40) 0.13 (1.67) 0.12 (1.41) 0.05 (0.62)
8 0.17 (1.81) 0.20 (1.81) 0.00 (-0.04) 0.06 (0.60) 0.06 (0.59)
9 10(High) High-Low 0.05 -0.38 -0.40 (0.47) (-3.50) (-2.30) 0.07 -0.12 -0.13 (0.65) (-1.02) (-0.71) 0.20 0.13 0.10 (1.88) (1.08) (0.58) 0.30 0.14 0.31 (2.74) (1.18) (1.68) 0.22 0.22 0.27 (2.09) (1.81) (1.34)
5 0.08 (1.14) 0.12 (1.35) -0.08 (-0.94) 0.16 (1.70) 0.02 (0.17)
6 0.05 (0.57) 0.13 (1.74) 0.14 (2.02) 0.02 (0.27) 0.02 (0.19)
7 0.15 (1.93) 0.16 (2.02) 0.14 (1.72) 0.11 (1.30) 0.04 (0.54)
8 0.13 (1.40) 0.15 (1.50) 0.01 (0.07) 0.13 (1.28) 0.13 (1.18)
9 10(High) High-Low 0.06 -0.32 -0.25 (0.55) (-2.94) (-1.39) 0.16 -0.06 -0.05 (1.53) (-0.48) (-0.27) 0.26 0.11 0.13 (2.50) (0.90) (0.74) 0.31 0.19 0.31 (2.75) (1.39) (1.67) 0.25 0.24 0.37 (2.42) (2.00) (1.77)
6 -0.06 (-0.65) -0.01 (-0.14) 0.03 (0.40) -0.14 (-1.56) -0.18 (-2.06)
7 0.02 (0.27) 0.17 (1.63) 0.01 (0.06) 0.10 (1.04) 0.00 (-0.03)
8 0.23 (1.71) 0.21 (1.47) 0.07 (0.64) 0.11 (0.98) 0.09 (0.79)
9 10(High) High-Low 0.12 -0.22 -0.42 (0.87) (-1.66) (-2.24) 0.23 0.03 -0.09 (2.03) (0.20) (-0.45) 0.28 0.20 0.06 (2.08) (1.46) (0.29) 0.35 0.29 0.44 (2.33) (1.88) (2.10) 0.31 0.34 0.45 (2.43) (2.52) (2.20)
Panel B. Fama-French Monthly Alphas of AG Deciles Post-Sorting Year 1 2 3 4 5
1(Low) 0.02 (0.14) 0.01 (0.07) 0.03 (0.20) -0.17 (-1.12) -0.06 (-0.34)
2 0.04 (0.33) 0.01 (0.10) 0.11 (0.98) -0.11 (-0.89) 0.19 (1.48)
3 0.11 (1.31) 0.18 (1.77) 0.14 (1.44) 0.03 (0.27) 0.03 (0.33)
4 0.11 (1.44) 0.03 (0.40) 0.06 (0.71) 0.00 (0.02) 0.12 (1.36)
Panel C. Carhart Monthly Alphas of AG Deciles Post-Sorting Year 1 2 3 4 5
1(Low) -0.07 (-0.48) -0.01 (-0.06) -0.02 (-0.14) -0.13 (-0.82) -0.13 (-0.76)
2 0.06 (0.50) -0.07 (-0.56) 0.12 (1.04) -0.13 (-1.04) 0.14 (1.00)
3 0.11 (1.19) 0.12 (1.20) 0.11 (1.12) 0.00 (0.03) 0.04 (0.40)
4 0.11 (1.31) 0.02 (0.30) 0.02 (0.24) -0.05 (-0.55) 0.08 (0.80)
Panel D. Investment-Based Monthly Alphas of AG Deciles Post-Sorting Year 1 2 3 4 5
1(Low) 0.20 (1.09) 0.12 (0.76) 0.14 (0.93) -0.15 (-0.92) -0.11 (-0.66)
2 0.03 (0.25) -0.04 (-0.29) 0.08 (0.61) -0.12 (-0.93) 0.18 (1.34)
3 0.09 (0.87) 0.03 (0.26) 0.01 (0.14) -0.07 (-0.62) -0.03 (-0.26)
4 0.00 (-0.01) -0.07 (-0.71) -0.07 (-0.75) -0.15 (-1.50) -0.03 (-0.29)
5 0.06 (0.88) -0.04 (-0.41) -0.18 (-2.19) -0.03 (-0.26) -0.16 (-1.62)
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Table 3. Monthly alphas of innovative capacity-asset growth portfolios from different factor models At the end of June of each year t from 1977 to 2007, we sort firms independently into two innovative capacity (IC) groups based on the median breakpoint of IC in calendar year t – 1 and asset growth deciles based on asset growth (AG) defined as percentage change in total assets from the fiscal year ending in calendar year t – 2 to fiscal year ending in calendar year t – 1. We measure IC with the number of patents granted (patent counts) scaled by total assets (CTA). The intersection of these portfolios forms twenty CTA-AG portfolios. We also form a high-minus-low asset growth portfolio within each IC group. We then compute monthly value-weighted portfolio returns for the next 60 months for these portfolios. The table reports the intercepts (alphas) in percentage from regressions of the time series of portfolio excess returns on different sets of risk factors returns in each of the five post-sorting years. The portfolio excess returns are the difference between monthly portfolio returns and the one month Treasury bill rate. Panels A, B, and C report monthly alphas from the Fama-French (1993) three-factor model, the Carhart (1996) fourfactor model, and the investment-based three-factor model (Chen, Novy-Marx, and Zhang, 2011). The sample period for stock returns is from July 1977 to June 2008.
Panel A. Value-Weighted Portfolio Fama-French Monthly Alphas by Innovative Capacity Groups Asset Growth Deciles Rank of CTA Year 1(Low) 2 Low CTA 1 -0.04 -0.21 (-0.25) (-1.70) 2 -0.30 -0.21 (-1.96) (-1.60) 3 -0.24 0.10 (-1.61) (0.77) 4 -0.28 -0.20 (-1.75) (-1.51) 5 -0.07 -0.14 (-0.39) (-1.07) High CTA 1 -0.01 0.10 (-0.05) (0.59) 2 0.20 0.02 (0.92) (0.11) 3 -0.03 0.11 (-0.14) (0.71) 4 -0.17 -0.04 (-0.74) (-0.26) 5 -0.29 0.39 (-1.08) (2.09)
3 -0.01 (-0.10) 0.02 (0.16) 0.01 (0.04) -0.06 (-0.46) -0.01 (-0.06) 0.07 (0.53) 0.18 (1.35) 0.11 (0.85) -0.01 (-0.06) 0.03 (0.24)
4 0.09 (0.90) 0.09 (0.84) 0.06 (0.46) -0.03 (-0.25) 0.22 (1.79) -0.01 (-0.07) -0.04 (-0.35) 0.05 (0.39) -0.07 (-0.58) 0.12 (1.10)
5 0.07 (0.65) 0.12 (1.05) -0.10 (-1.00) 0.12 (1.09) 0.00 (-0.04) 0.07 (0.65) -0.01 (-0.09) -0.21 (-1.96) 0.03 (0.21) 0.05 (0.42)
45
6 -0.01 (-0.13) 0.07 (0.71) 0.20 (1.95) 0.00 (-0.04) 0.00 (0.02) 0.10 (0.75) 0.16 (1.40) 0.08 (0.70) -0.09 (-0.73) -0.02 (-0.19)
7 0.01 (0.13) -0.02 (-0.18) -0.01 (-0.11) 0.09 (0.82) -0.01 (-0.08) 0.28 (2.08) 0.25 (1.78) 0.26 (1.99) 0.12 (0.80) -0.08 (-0.47)
8 0.09 (0.81) 0.19 (1.42) 0.07 (0.56) 0.00 (0.01) -0.04 (-0.27) 0.24 (1.48) 0.22 (1.32) 0.04 (0.29) 0.21 (1.35) 0.09 (0.53)
9 10(High) -0.11 -0.57 (-0.90) (-3.73) -0.07 -0.29 (-0.66) (-2.25) 0.02 -0.18 (0.15) (-1.29) 0.08 -0.17 (0.57) (-1.25) 0.40 -0.14 (2.59) (-0.88) -0.10 -0.23 (-0.60) (-1.16) 0.15 -0.08 (0.91) (-0.44) 0.29 0.30 (1.60) (1.59) 0.50 0.58 (2.56) (2.82) 0.04 0.52 (0.24) (2.62)
High-Low (10-1) -0.53 (-2.49) 0.01 (0.06) 0.06 (0.34) 0.11 (0.53) -0.07 (-0.28) -0.22 (-0.82) -0.28 (-1.00) 0.33 (1.26) 0.75 (2.59) 0.81 (2.27)
Panel B. Value-Weighted Portfolio Carhart Monthly Alphas by Innovative Capacity Groups Asset Growth Deciles High-Low Rank of CTA Year 1(Low) 2 3 4 5 6 7 8 9 10(High) (10-1) Low CTA 1 2 3 4 5 High CTA 1 2 3 4 5
-0.10 -0.24 0.07 0.05 0.08 -0.03 -0.04 -0.01 -0.10 (-0.57) (-1.69) (0.62) (0.45) (0.77) (-0.31) (-0.43) (-0.05) (-0.86) -0.30 -0.33 -0.04 0.05 0.04 0.06 -0.03 0.11 -0.04 (-1.92) (-2.52) (-0.31) (0.44) (0.38) (0.59) (-0.36) (0.89) (-0.37) -0.25 0.09 -0.03 -0.02 -0.09 0.16 -0.04 0.03 0.04 (-1.65) (0.56) (-0.25) (-0.17) (-0.85) (1.61) (-0.42) (0.27) (0.31) -0.35 -0.21 -0.11 -0.09 0.08 0.02 0.10 0.05 0.12 (-2.22) (-1.52) (-0.88) (-0.85) (0.75) (0.21) (0.88) (0.38) (0.85) -0.24 -0.11 -0.05 0.11 -0.01 0.00 -0.01 0.04 0.39 (-1.38) (-0.75) (-0.32) (0.84) (-0.11) (-0.03) (-0.12) (0.31) (2.57) -0.11 0.19 0.07 0.05 0.03 0.05 0.28 0.23 -0.07 (-0.52) (1.15) (0.55) (0.41) (0.28) (0.37) (1.94) (1.45) (-0.38) 0.16 0.00 0.12 -0.01 0.05 0.18 0.23 0.21 0.26 (0.72) (0.02) (0.95) (-0.12) (0.40) (1.47) (1.67) (1.33) (1.55) -0.07 0.19 0.08 0.06 -0.13 0.06 0.31 0.12 0.40 (-0.33) (1.16) (0.64) (0.44) (-1.17) (0.54) (2.30) (0.77) (2.19) -0.05 -0.08 0.03 -0.12 0.15 -0.07 0.13 0.31 0.50 (-0.22) (-0.42) (0.24) (-0.96) (1.19) (-0.56) (0.83) (1.89) (2.55) -0.39 0.32 0.10 0.10 0.01 0.04 -0.03 0.27 0.10 (-1.40) (1.68) (0.77) (0.85) (0.08) (0.31) (-0.17) (1.56) (0.58)
-0.56 (-3.79) -0.18 (-1.46) -0.18 (-1.33) -0.10 (-0.74) -0.04 (-0.26) -0.08 (-0.42) 0.11 (0.49) 0.32 (1.61) 0.59 (2.68) 0.59 (2.97)
-0.46 (-2.14) 0.12 (0.64) 0.06 (0.34) 0.25 (1.13) 0.20 (0.85) 0.02 (0.08) -0.06 (-0.18) 0.39 (1.44) 0.64 (2.24) 0.98 (2.68)
Panel C. Value-Weighted Portfolio Investment-Based Monthly Alphas by Innovative Capacity Groups Asset Growth Deciles High-Low Rank of CTA Year 1(Low) 2 3 4 5 6 7 8 9 10(High) (10-1) Low CTA 1 2 3 4 5 High CTA 1 2 3 4 5
0.21 -0.11 0.16 0.03 0.06 -0.03 -0.02 0.09 0.01 (1.03) (-0.75) (1.20) (0.28) (0.56) (-0.29) (-0.19) (0.69) (0.04) -0.10 -0.13 0.01 -0.04 -0.02 0.05 0.02 0.12 0.13 (-0.48) (-0.71) (0.04) (-0.37) (-0.15) (0.48) (0.21) (0.82) (0.89) -0.05 0.21 -0.03 0.01 -0.19 0.09 0.03 0.17 0.05 (-0.30) (1.15) (-0.18) (0.10) (-1.62) (0.86) (0.35) (1.29) (0.45) -0.13 -0.03 -0.07 -0.14 0.10 -0.02 0.07 0.04 0.13 (-0.67) (-0.21) (-0.46) (-1.18) (0.78) (-0.15) (0.59) (0.27) (0.87) 0.10 -0.03 0.01 0.07 -0.02 -0.09 0.07 -0.02 0.60 (0.37) (-0.21) (0.03) (0.51) (-0.14) (-0.76) (0.62) (-0.14) (2.92) 0.14 0.01 0.01 -0.08 -0.04 -0.09 0.07 0.36 -0.08 (0.52) (0.08) (0.07) (-0.60) (-0.33) (-0.67) (0.47) (1.68) (-0.39) 0.14 -0.02 0.02 -0.11 -0.16 -0.07 0.22 0.30 0.30 (0.63) (-0.09) (0.14) (-0.81) (-1.27) (-0.58) (1.27) (1.36) (1.69) 0.09 0.04 -0.04 -0.10 -0.22 -0.07 0.06 0.12 0.38 (0.37) (0.25) (-0.31) (-0.72) (-1.88) (-0.57) (0.43) (0.70) (1.74) -0.23 -0.13 -0.05 -0.22 -0.10 -0.25 0.17 0.23 0.57 (-0.97) (-0.70) (-0.35) (-1.64) (-0.65) (-1.74) (1.02) (1.30) (2.31) -0.47 0.33 0.02 -0.03 -0.26 -0.21 -0.14 0.22 0.12 (-1.65) (1.66) (0.13) (-0.26) (-1.86) (-1.51) (-0.74) (1.22) (0.61)
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-0.53 (-2.94) -0.01 (-0.07) -0.01 (-0.08) 0.04 (0.28) 0.04 (0.25) 0.06 (0.27) 0.11 (0.48) 0.31 (1.58) 0.58 (2.43) 0.66 (3.06)
-0.74 (-3.34) 0.08 (0.42) 0.04 (0.21) 0.17 (0.79) -0.05 (-0.18) -0.08 (-0.28) -0.03 (-0.10) 0.23 (0.76) 0.82 (2.50) 1.13 (3.01)
Table 4. Fama-MacBeth regressions of stock returns on asset growth, innovative capacity and other variables This table reports the time-series average slopes and intercepts in percentage and their time series t-statistics in parentheses from monthly Fama and MacBeth (1973) cross-sectional regressions of individual stocks’ returns on ln(BTM), ln(Size), Momentum, asset growth (AG), patent counts scaled by total assets (CTA), and an interaction term, AG*CTA. BTM is the ratio of book equity in the fiscal year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Size is market equity at the end of June of year t. Momentum is the cumulative return over the prior six months with a one-month gap. AG and CTA are measured in the fiscal year ending in calendar year t – 1. The dependent variable in the first row is stock returns from July of year t to June of year t + 1. The dependent variable in the second row is stock returns from July of year t + 1 to June of year t + 2. The dependent variable in the third row is stock returns from July of year t + 2 to June of year t + 3. The dependent variable in the fourth row is stock returns from July of year t + 3 to June of year t + 4. The dependent variable in the fifth row is stock returns from July of year t + 4 to June of year t + 5. All rows share the same set of independent variables. The sample period for stock returns is from July 1977 to June 2008.
Dependent variable Next-year return Second-year-ahead return Third-year-ahead return Fourth-year-ahead return Fifth-year-ahead return
Intercept 2.47 (6.20) 1.95 (4.99) 2.00 (5.35) 1.99 (5.25) 1.64 (4.39)
ln(BTM) 0.20 (3.03) 0.17 (2.65) 0.12 (1.94) 0.08 (1.36) 0.09 (1.61)
ln(size) -0.16 (-3.15) -0.17 (-3.25) -0.16 (-3.12) -0.17 (-3.40) -0.16 (-3.07)
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Momentum 0.36 (1.49) 0.45 (1.84) 0.48 (1.92) 0.44 (1.73) 0.45 (1.72)
AG -0.14 (-5.68) -0.03 (-1.45) -0.04 (-2.03) -0.05 (-2.17) 0.02 (0.83)
CTA 0.13 (1.19) 0.29 (2.57) 0.13 (1.25) 0.19 (1.76) 0.35 (3.04)
AG*CTA 0.04 (2.62) 0.01 (0.49) 0.03 (1.80) 0.03 (1.72) -0.02 (-1.27)
Table 5. Risk dynamics after investment At the end of June of each year t from 1977 to 2007, we sort firms independently into low and high innovative capacity (IC) groups based on the median breakpoint of IC in calendar year t – 1 and asset growth deciles based on asset growth (AG) defined as percentage change in total assets from the fiscal year ending in calendar year t – 2 to fiscal year ending in calendar year t – 1. Firms with missing IC are included in the low IC group. We measure IC with the number of patents granted (patent counts) scaled by total assets (CTA). We then compute monthly value-weighted portfolio returns for the next 5 years for these portfolios. This table reports the factor loadings estimated from regressing the time series of portfolio excess returns on different sets of risk factors returns in the first (Year 1) and the fourth (Year 4) post-sorting years for the highest AG decile in the low IC and the high IC groups. The t-statistics are reported in parentheses. The portfolio excess returns are the difference between monthly portfolio returns and the one month Treasury bill rate. The Fama-French (1993) three-factor model includes the market (MKT), size (SMB), and value (HML) factors. The investment-based three-factor model (Chen, Novy-Marx, and Zhang, 2011) includes the market, investment (INV), and return-on-equity (ROE) factors. The Carhart (1996) four-factor model includes the Fama-French three factors and the momentum (MOM) factor. The sample period for stock returns is from July 1980 to June 2008.
Fama-French Model MKT SMB HML Low IC, High AG, Year 1 1.18 0.30 -0.37 (24.76) (2.91) (-4.47) Low IC, High AG, Year 4 1.10 0.31 -0.18 (28.70) (5.90) (-2.90) High IC, High AG, Year 1 1.15 0.14 -0.50 (21.34) (1.97) (-5.48) High IC, High AG, Year 4 1.24 -0.08 -0.58 (20.68) (-0.87) (-5.38) 0.01 0.19 Low IC, High AG, Year 4 – Year 1 -0.08 (-1.83) (0.12) (2.30) -0.22 -0.08 High IC, High AG, Year 4 – Year 1 0.09 (1.17) (-1.84) (-0.54)
Investment-based Model MKT INV ROE 1.29 -0.45 -0.05 (28.63) (-4.04) (-0.91) 1.17 -0.27 -0.06 (28.97) (-2.63) (-1.07) 1.21 -0.78 -0.20 (24.05) (-5.71) (-2.90) 1.37 -0.25 -0.21 (25.71) (-1.43) (-2.53) -0.12 0.18 -0.01 (-2.85) (2.09) (-0.11) 0.16 0.54 -0.01 (2.45) (2.26) (-0.10)
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MKT 1.17 (25.72) 1.10 (28.36) 1.13 (21.87) 1.24 (19.52) -0.07 (-1.69) 0.11 (1.42)
Carhart Model SMB HML 0.30 -0.39 (3.10) (-4.99) 0.31 -0.18 (5.83) (-2.79) 0.15 -0.54 (2.08) (-5.97) -0.08 -0.58 (-0.85) (-5.20) 0.01 0.20 (0.09) (2.76) -0.23 -0.05 (-1.90) (-0.31)
MOM -0.05 (-1.01) -0.01 (-0.14) -0.13 (-2.17) -0.02 (-0.29) 0.05 (0.89) 0.11 (1.06)
Table 6. Risk dynamics around investment A firm is assigned to the pre-investment portfolio in year t if it is ranked in the highest asset growth (AG) decile in any one of years t + 2, t + 3, and t + 4. A firm is assigned to the post-investment portfolio in year t if it is ranked in the highest AG decile in year t – 1. We also sort firms independently into low and high innovative capacity (IC) groups in year t based on median IC in year t – 1. Firms with missing IC are included in the low IC group. The intersection of the two IC groups and the pre- and post-investment portfolios forms the low IC pre- and post-investment portfolios and the high IC pre- and post-investment portfolios. We measure IC with the number of patents granted (patent counts) scaled by lagged total assets. We then compute monthly value-weighted portfolio excess returns for these portfolios. This table reports the factor loadings estimated from regressions of the time series of portfolio excess returns on different sets of risk factors returns for these portfolios. The t-statistics are reported in parentheses. The portfolio excess returns are the difference between monthly portfolio returns and the one month Treasury bill rate. The Fama-French (1993) three-factor model includes the market (MKT), size (SMB), and value (HML) factors. The investmentbased three-factor model (Chen, Novy-Marx, and Zhang, 2011) includes the market, investment (INV), and return-on-equity (ROE) factors. The Carhart (1996) four-factor model includes the Fama-French three factors and the momentum (MOM) factor. The sample period for stock returns is from July 1977 to June 2008.
Low IC, Pre-investment Low IC, Post-investment High IC, Pre-investment High IC, Post-investment Low IC, Post-minus-Pre High IC, Post-minus-Pre
Fama-French Model MKT SMB HML 1.11 0.31 -0.19 (34.55) (5.73) (-3.15) 1.19 0.35 -0.33 (25.54) (3.55) (-3.94) 1.02 -0.12 -0.34 (31.95) (-2.26) (-6.09) 1.19 0.15 -0.47 (25.54) (2.25) (-5.70) 0.08 0.05 -0.14 (2.08) (0.59) (-1.66) 0.18 0.26 -0.13 (3.07) (3.11) (-1.44)
Investment-based Model MKT INV ROE 1.19 -0.28 -0.06 (34.87) (-3.89) (-1.24) 1.31 -0.46 0.01 (29.92) (-4.11) (0.11) 1.10 -0.07 0.00 (35.02) (-0.67) (-0.01) 1.28 -0.63 -0.21 (27.97) (-4.80) (-3.13) 0.13 -0.18 0.07 (3.45) (-1.73) (1.15) 0.17 -0.56 -0.21 (3.70) (-3.76) (-2.77)
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MKT 1.11 (35.33) 1.19 (26.39) 1.02 (32.79) 1.18 (25.97) 0.08 (2.02) 0.16 (2.99)
Carhart Model SMB HML 0.30 -0.18 (5.50) (-2.88) 0.35 -0.33 (3.62) (-4.10) -0.12 -0.34 (-2.38) (-6.22) 0.17 -0.50 (2.45) (-6.12) 0.05 -0.15 (0.70) (-1.79) 0.29 -0.17 (3.37) (-1.90)
MOM 0.05 (1.55) 0.01 (0.14) 0.03 (0.87) -0.14 (-2.58) -0.04 (-0.68) -0.17 (-2.97)
Dongmei Lib
November 2011
Abstract Innovative capacity (IC) is the ability of firms to produce and commercialize a sequence of innovations. Expected returns need not fall following asset growth by high IC firms because investment can generate new growth options. Using patent intensity based IC measures we provide the first analysis of the effects of IC on financial markets' response to asset growth. We find that the well-known negative relationship between asset growth and subsequent excess returns holds only for the subset of firms with high asset growth and low IC, but in a stronger and more robust fashion than reported earlier. However, high IC firms with high asset growth rates not only do not suffer negative excess returns subsequent to asset growth, they actually earn significantly positive subsequent excess returns. Moreover, and as predicted by a model of optimal dynamic investment with sequentially arising growth options, changes in the market risk loadings of firms following asset growth episodes are positively related to their IC. Firms' innovative capacity therefore appears to play an important role in the dynamics between asset growth and returns. Keywords: Innovative capacity; Asset growth; Excess returns; Risk dynamics; Patents JEL classification codes: G12, G32, O31 *
We thank Jonathan Berk, Wayne Ferson, Michael Fishman, Paolo Fulghieri, Robert Goldstein, Joao Gomes, Richard Green, David Hirshleifer, Kewei Hou, Po-Hsuan (Paul) Hsu, Nisan Langberg, Robert Stambaugh, Jeremy Stein, and Jianfeng Yu for valuable discussions and comments. We also thank Lu Zhang for sharing the investment and profitability factors returns.
a
C.T. Bauer College of Business, University of Houston, Houston, TX 77204. Email: [email protected] Rady School of Management, University of California, San Diego, La Jolla, CA 92093. Email: [email protected]
b
Innovative Capacity and the Asset Growth Anomaly
November 2011
Abstract Innovative capacity (IC) is the ability of firms to produce and commercialize a sequence of innovations. Expected returns need not fall following asset growth by high IC firms because investment can generate new growth options. Using patent intensity based IC measures we provide the first analysis of the effects of IC on financial markets' response to asset growth. We find that the well-known negative relationship between asset growth and subsequent excess returns holds only for the subset of firms with high asset growth and low IC, but in a stronger and more robust fashion than reported earlier. However, high IC firms with high asset growth rates not only do not suffer negative excess returns subsequent to asset growth, they actually earn significantly positive subsequent excess returns. Moreover, and as predicted by a model of optimal dynamic investment with sequentially arising growth options, changes in the market risk loadings of firms following asset growth episodes are positively related to their IC. Firms' innovative capacity therefore appears to play an important role in the dynamics between asset growth and returns.
Keywords: Innovative capacity; Asset growth; Excess returns; Risk dynamics; Patents JEL classification codes: G12, G32, O31
1.
Introduction The effects of capital investment and asset growth on stock returns have important
implications for both asset pricing and corporate finance. Recently, a number of empirical studies highlight a negative relationship between capital investment/asset growth and subsequent abnormal (or benchmark-adjusted) stock returns (the “asset growth anomaly”) (Titman, Wei and Xie, 2004; Anderson and Garcia-Feijoo, 2006; Cooper, Gulen and Schill, 2008).1 For example, Titman et al. (2004) argue that investors underreact to empire building by managers and show that the negative relation is stronger for firms with greater investment discretion (i.e., firms with higher cash flows and lower debt ratios), while Cooper et al. (2008) suggest an overreaction to asset growth (which is broader than over investment) and interpret the negative abnormal returns as a correction to the overreaction. On the other hand, a variety of models in the literature predict a negative equilibrium relationship between investment and future returns (see Section 2). In particular, real options models (e.g., McDonald and Siegel, 1986; Majd and Pindyck, 1987; Carlson, Fisher and Giammarino, 2006) predict a decline in systematic risk following the exercise of risky growth options. From this perspective, the observed relationship between asset growth and subsequent returns is not an anomaly, and indeed a number of recent papers present direct evidence supportive of the risk-based explanations (see Cooper and Priestly, 2011). These alternative rational and behavioral interpretations of the data have profoundly different implications. In particular, a systematic negative bias in the market's capitalization of investment (and general asset growth) should have a major impact on corporate investment and
1
Additional studies on the capital investment/asset growth anomaly include Xing (2008), Li and Zhang (2010), Titman, Wei and Xie (2011), Lam and Wei (2011), and Stambaugh, Yu and Yuan (2011), among others.
1
financial policies; it also suggests formulation of trading strategies to exploit this market inefficiency. In this paper, we present new evidence on the dynamics between asset growth and stock returns by building on the notion of innovative capacity (IC), which is a measure of firms' ability to generate multiple growth options --- for example, through a sequence of innovations based on their patent holdings. We motivate the role of IC by noting the potential heterogeneity in the effects of asset growth across different IC firms. Specifically, asset growth of high IC firms is more likely related to innovation activities, such as construction of long-range research facilities and purchase of machinery/materials for use on current and future R&D projects, or acquisition of patents, or development of knowledge absorption capacities. This type of asset growth tends to generate new growth options and investment opportunities because innovations are often the source of new ideas and opportunities (Schumpeter, 1942; Maclaurin, 1953). In contrast, the asset growth of low IC firms is more likely to reflect capital expenditures in traditional industries, which simply reduces growth options and lowers the likelihood of future risky investment. To fix ideas, consider a firm that has developed an innovation --- for example, a new smart-phone operating system or a new class of drugs or a more powerful resonance imaging system --- that potentially opens long run economic opportunities through multiple improvements (“new generations”) of the basic innovation and creation of new ancillary support industries. However, these new growth opportunities arise only if the firm maintains a technological lead over imitators or rival technologies, which requires an effective innovation
2
generation infrastructure and additional investments over time.2 High IC firms with low asset growth may therefore obtain only the benefits of the initial innovation, but high IC firms with high asset growth will have the opportunity to generate and exploit new growth opportunities. In sum, rapid asset growth of high IC firms is more likely to be a precursor to the generation of new growth options and therefore the equilibrium market price of the firm’s risk may actually increase subsequent to asset growth as the growth options materialize. In contrast, asset growth of low IC firms mainly converts growth options to assets-in-place and thereby reduces the risk premium or expected returns. In sum, from the real options viewpoint, the predicted effects of asset growth on subsequent expected returns should differ according to firms’ IC. Specifically, if asset growth of low IC firms mainly converts growth options to asset-in-place, then it should reduce the riskpremium or expected returns. In contrast, if the asset growth of high IC firms is a precursor to the generation of future growth options, then the expected returns should not subsequently decline and may even rise. Meanwhile, unless there is a high correlation between low IC and high investment discretion firms, there is no a priori presumption of systematic differences in the mispricing of asset growth across IC groups. Examining the effects of IC on the relationship between asset growth and subsequent returns is therefore of substantial interest from both the rational and behavioral perspectives. Building on the large literature that uses patent holdings as a measure of firms’ inventive activity and available growth options (e.g., Pakes, 1986; Griliches, Hall and Pakes, 1991), we use 2
For instance, when a firm builds a laboratory or invests in technological infrastructure to enhance knowledge absorption capacities (Cohen and Levinthal, 1990), the fixed cost is capitalized and reflected as asset growth or investment; yet, the firm is not exercising a pure growth option, rather it is setting up a potential generator of future growth options.
3
patent intensity based measures of IC (i.e., recent annual patents granted to a firm normalized by various measures of assets) for this study. To our knowledge, this is the first study of the effects of innovative capacity on the response of financial markets to investment and asset growth. We summarize the results of our analysis as follows. Firms’ innovative capacity plays an important role in the asset growth anomaly. While we confirm the negative correlation between asset growth and subsequent abnormal returns for the overall sample (cf. Cooper et al., 2008), we find that this anomaly holds only for the subset of firms that exhibit high asset growth and have low IC; i.e., the asset growth anomaly is essentially restricted to firms that have low innovative capacity and exhibit high asset growth. Indeed, the asset growth anomaly for the low IC firms is stronger and more robust to risk-adjustment than has been reported in the literature (e.g., Cooper et al., 2008). On the other hand, not only is there no significant effect of asset growth on subsequent abnormal returns, for high IC firms with rapid asset growth there are significantly positive abnormal returns in the fourth and fifth year after the asset growth events. These results, which are based on independent (double) sorts of IC measures and asset growth, are robust to benchmarking with the Fama and French (1992, 1993) threefactor model, the Carhart (1997) four-factor model, and the investment-based three-factor model of Chen, Novy-Marx and Zhang (2011). The positive influence of IC on the post-asset growth abnormal returns is confirmed by the Fama-MacBeth (1973) regressions. For example, in the year after investment higher patent intensity dilutes significantly the negative effects of asset growth on subsequent returns controlling for firms’ characteristics. In sum, the stylized fact of a negative relationship between asset growth and subsequent abnormal stock returns --- that we confirm for our overall sample --
4
- masks considerable heterogeneity in the data, with the innovative capacity of firms playing an important role. These results are interesting from both the behavioral and rational perspectives. From the behavioral viewpoint, our analysis indicates that markets appear to have a persistent or systematic mispricing problem in evaluating high asset growth by low IC firms. But since Titman et al. (2004) argue that the asset growth anomaly is consistent with investor underreaction to empire building by managers of firms, a natural question is whether the low IC firms also tend to have high investment discretion. However, our data refute this conjecture because we find that on average the low IC firms with high asset growth have negative cash flows and their leverage is also not appreciably lower than the sample average. Furthermore, our results also do not support the hypothesis that the low IC firms are harder to arbitrage than, say, the high IC firms as detailed in Section 4.2. And, from the overreaction viewpoint of Cooper et al. (2008), our results imply that investors overreact only to low IC firms with high asset growth but not to other firms, while they underreact to the positive growth implications of asset growth by high IC firms. However, the data suggest that there is heterogeneity across IC groups in the abnormal returns following asset growth, along the lines suggested by the real options framework. In particular, the effects of asset growth on abnormal returns are increasing with the firms’ IC; moreover, asset growth by high IC firms can eventually lead to an increase in abnormal returns. If the abnormal returns following asset growth are caused by missing risk factors instead of mispricing, then the evidence is consistent with the hypothesis that effects of asset growth on firms’ systematic risk differs according to their IC. In particular, we observe significantly
5
negative alphas for the high-minus-low asset growth (AG) portfolio and the high AG portfolio formed among low IC firms in the first post-sorting year and significantly positive alphas for the high AG portfolio and the hedge portfolio formed among high IC firms in the fourth and fifth post-sorting years. The delay in observing the positive abnormal returns (subsequent to the asset growth events) for the high IC firms could be due to time-to-build effects (Kydland and Prescott, 1982) on the development of new growth options. We therefore examine further the effects of innovative capacity on the firm risk premium following asset growth both theoretically and empirically. We develop this intuition by constructing a theoretical sequential real options model where the optimal dynamic investment policy of firms generates a time-varying risk premium for firms that depends on their IC. Firms initially invest to build their long run IC, and then optimally and sequentially exercise growth options that arrive at random times. Higher IC firms have both a greater likelihood of developing a sequence (“new generations”) of innovations and higher expected cash flow growth conditional on realizing the innovations.
Our model demonstrates that the post-investment drop in
equilibrium firm risk premium will be lower (or diluted) for firms with higher IC compared with low IC firms, and forms the basis of our empirical test design. Empirically, we predict that the change in the firms’ loading on the market betas (following asset growth events) will be positively associated with innovative capacity.3 We test this prediction by examining the changes in the market betas of firms subsequent to their asset growth events using independent portfolio sorts based on the IC measures and asset growth. Consistent with the prediction, when we examine the change in betas between the first 3
We emphasize that we do not restrict the sign of the post-investment change in stock returns (it may still be negative for high IC firms, for example). Rather, the prediction is that the change will be positively related to the IC.
6
and the fourth year following high asset growth, we find that market betas decrease for low IC firms but increase for high IC firms. When we compare the pre- and post-asset growth betas, we find that while market betas increase after high asset growth for both the high and low IC firms, the increase in betas is significantly greater for the high IC firms. The increase in market betas (for both high and low IC firms) subsequent to asset growth appears contrary to the prediction of a variety of models where firms' systematic market risk declines subsequent to investment (see Section 2) and does not appear to have been documented in the empirical literature.4 More generally, our analysis adds to the extensive literature that identifies a variety of causes for time-varying betas (or systematic market risk of firms) --- from business cycle variables to changes in estimation risk based on firm-specific information.5 In particular, our results indicate that firms' IC is an important characteristic in explaining the timevariation in their betas that occur due to pro-cyclical asset growth. In addition, our framework may also help reconcile the negative relationship between asset growth (AG) and returns with the observed positive relationship between significant R&D growth and returns. Eberhart, Maxwell and Siddique (2004) identify positive dynamics between significant R&D growth and subsequent stock returns and offer investor under-reaction as a possible explanation. However, our results indicate that the relationship between AG and returns 4
Cooper and Priestly (2011) find that for value-weighted returns loadings of only one of the five (non-traded) Chen, Ross and Roll (1986) factors declines significantly after rapid asset growth, while the loading on unexpected inflation actually increases significantly. However, we obtain significant results on the dynamics of market beta changes, when sorted on firms’ IC, using value-weighted returns. Thus, it appears that the effects of asset growth on loadings on market risk are quite different from its effects on non-traded factors. 5
Ferson, Kandel and Stambaugh (1987), Ferson and Harvey (1991), Ferson and Schadt (1996), Jagannathan and Wang (1996), and Lettau and Ludvigson (2001), among others, relate the time-variation in betas to business cycle related variables. And Kumar, Boehme, Danielsen and Sorescu (2008) show changes in the betas following firmspecific information that affects their estimation risk component.
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of high IC firms is significantly different --- up-to a change of sign --- from the overall negative relationship. Because significant R&D growth is most likely to be associated with high IC firms, the negative (positive) relationship between AG (significant R&D growth) and returns are not inconsistent with equilibrium risk premia and correct market assessment of the implications of investment.6 There is a related literature that examines the effects of innovation activity on firms' market valuation (Griliches, Hall and Pakes, 1987, 1991; Hall, Jaffe and Trajtenberg, 2005), and typically finds a positive relationship between IC indicators and market value. In contrast, we analyze the implications of IC on the abnormal returns and market risk changes subsequent to asset growth. Our analysis indicates that patent intensities do not by themselves have a significant influence on stock returns; rather, innovative capacity influences the abnormal returns and market risk changes subsequent to asset growth. Thus, our results introduce another dimension, so to speak, in evaluating the effects of innovative activity on stock returns. We organize the paper as follows. Section 2 develops the concept of innovative capacity at the firm level and motivates the empirical measures. Section 3 describes the data and the empirical framework. Section 4 discusses the empirical results on the relationship between IC and excess returns subsequent to asset growth. Section 5 describes the empirical test design regarding the effects of IC on the changes in firms' risk factor loadings following asset growth and presents the results. Section 6 summarizes the results and concludes.
2.
The Asset Growth Anomaly and Innovative Capacity: Motivation
6
For example, depreciation of innovation-related asset growth, such as building research facilities and purchase of equipment for use in current and future R&D projects, is reflected in R&D expenses and consequently R&D growth.
8
2.1
The Asset Growth Anomaly The “asset growth anomaly” refers to the negative relationship between capital
investment (and more generally asset growth) and subsequent abnormal stock returns that has been uncovered by a number of recent studies. For example, Titman et al. (2004) use Carhart’s (1997) four-factor model and find negative benchmark-adjusted returns following abnormal capital investment. This effect is more pronounced for firms with greater investment discretion, i.e., firms with higher cash flows and lower leverage, and when hostile takeovers are less prevalent. They argue that their results are consistent with investors reacting slowly to overinvestment by empire building managers. And using standard models of risk-adjustment (such as, the Fama and French (1992, 1993) three-factor model and the Carhart (1997) fourfactor model), Cooper et al. (2008) document a significant negative correlation between firms’ total asset growth and subsequent abnormal returns (alphas). They then argue that investors overreact to asset growth so that the observed negative post-AG abnormal returns are a correction for the initial overreaction. On the other hand, a number of models in the literature predict a negative relationship between investment and subsequent returns.7 As we mentioned above, real options models (such as, McDonald and Siegel, 1986; Majd and Pindyck, 1987; Berk, Green, and Naik, 1999; and Carlson, Fisher and Giammarino, 2006) predict a decline in systematic risk following the exercise of risky growth options. In a related vein, Berk, Green, and Naik (2004) present a model where investment resolves uncertainty with an attendant decline in the risk premium. Similarly, optimal dynamic investment based on the neoclassical q-theory may lead to a negative 7
Cooper and Priestly (2011) provide a good summary of these models.
9
relationship between investment and future returns (Liu, Whited and Zhang, 2009; Li and Zhang, 2010). From an empirical perspective, Cooper and Priestly (2011) present evidence that is consistent with the rational or risk-based explanations of the asset-growth anomaly. And complementary evidence is provided by recent papers indicating that an investment factor, i.e., the return on a portfolio of low investment stocks over the return on a portfolio of high investment stocks, can help explain cross-sectional returns (e.g., Xing, 2008; Chen, Novy-Marx and Zhang, 2011). But clearly there is substantial heterogeneity in the effects of asset growth across firms. Introspection suggests that the implications of, say, one-time additions to manufacturing capacity and acquisition of patents (both of which are examples of asset growth in accounting terms) are substantially different from the viewpoint of the generation of future growth options and investment opportunities. Consequently, there should be heterogeneity in the relationship between asset growth and subsequent risk-adjusted returns across firms based on their capacity to generate future growth options from asset growth. We now develop this intuition.
2.2
Innovative Capacity: Concept and Measures The chain of innovations and growth opportunities starts with inventions or new ideas
that, when developed for economic and commercial purposes, become innovations. Innovations not only lead to new technologies and economic opportunities through development of new markets, but are also often the source of new ideas that result in a sequence of innovations --- a process that is central to economic growth (Schumpeter, 1942; Maclaurin, 1953). Building on this, the literature on research and economic growth has developed the notion of national 10
innovative capacity, i.e., the ability of a country (or geographical region) to produce and commercialize a flow of innovative technology over the long term (Furman, Porter and Stern, 2000, and onwards). But, so defined, the concept of innovative capacity (IC) is also an important financial characteristic at the level of the firm. To fix ideas, consider the well-known decomposition of firm value into value from assets-in-place and value from growth options (Myers, 1977). Ceteris paribus, firms with higher IC should have a greater ability to generate multiple growth options and, therefore, IC should be positively associated with market value. But IC also has important dynamic implications related to capital investment and asset growth. This is because investment by higher IC firms is more likely to generate subsequent growth options and risky investment opportunities compared to low IC firms. In particular, while investment by a low IC firm may reflect exercising a non-replaceable growth option, for a high IC firm the capital investment may in fact be a precursor to the generation of new growth options and hence higher expected return. While innovative capacity, as a concept, may have interesting implications, its empirical content depends on finding appropriate proxies or measures. Since firms benefit economically from inventions only if they are protected or patented, the number of patents held by a firm (the patent count) indicates its potential to generate growth options over time through a sequence of innovations. There is a long standing literature that uses patents as measures of firms' inventive activity and growth options (Griliches, 1990; Pakes, 1986). More recently, the literature on IC at the national and geographical levels also gives prominence to patent output (Furman et al., 2000). In a related vein, Cohen and Levinthal (1990) and a large literature thereafter argue that firms
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can develop knowledge creation and absorptive capacities, i.e., their ability to recognize, assimilate, and apply new information to commercial benefit, that is reflected in higher IC. Since R&D investment is highly uncertain and mainly serves as input to innovation, while patents reflect innovation output and future growth options directly, we therefore take the patent counts as the principal building block of our measures for firm IC. In addition, we argue that for our study patent holdings are more appropriate and accessible than their citations because our interest is in the forward looking aspects of inventive activity, i.e., the expected generation of future growth options based on the invention levels achieved by the firm at any given time, whereas future citations are not fully observable to investors as it takes time for patents to be cited (Hall, Jaffe and Trajtenberg, 2005). Furthermore, patent counts are actually highly correlated with future citations as shown in Hirshleifer, Hsu, and Li (2011). Therefore, we construct IC measures based on patent counts.
3.
Data and Innovative Capacity Measures
3.1.
Data and Measures Our sample consists of firms in the intersection of Compustat, CRSP (Center for
Research in Security Prices), and the NBER patent database. We obtain accounting data from Compustat and stock returns data from CRSP. All domestic common shares trading on NYSE, AMEX, and NASDAQ with accounting and returns data available are included except financial firms, which have four-digit standard industrial classification (SIC) codes between 6000 and 6999 (finance, insurance, and real estate sectors). Following Fama and French (1993), we exclude closed-end funds, trusts, American Depository Receipts, Real Estate Investment Trusts, units of beneficial interest, and firms with negative book value of equity. To mitigate backfilling 12
bias, we require firms to be listed on Compustat for two years before including them in our sample. Patent-related data are from the updated NBER patent database originally developed by Hall, Jaffe, and Trajtenberg (2001). 8 The database contains detailed information on all U.S. patents granted by the U.S. Patent and Trademark Office (USPTO) between January 1976 and December 2006: patent assignee names, firms’ Compustat-matched identifiers, the number of citations received by each patent, the number of citations excluding self-citations received by each patent, application dates, grant dates, and other details. Patents are included in the database only if they are eventually granted by the USPTO by the end of 2006. The NBER patent database contains two time placers for each patent: its application date and grant date. To prevent any potential look-ahead bias, we choose the grant date as the effective date of each patent and measure firm i’s innovation output in year t as the number of patents granted to firm i in year t (“patent counts”). We use three proxies for innovative capacity (IC): patent counts scaled by total assets (CTA), patent counts scaled by year-end market equity (CTME), and patent counts scaled by book equity (CTBE). We construct these three IC proxies for each year from 1976 to 2006. Since we focus on the effect of IC on the asset growth anomaly, we compute asset growth for the same sample period. 3.2.
Summary Statistics At the end of June of each year t from 1977 to 2007, we sort firms independently into two
IC groups (“Low” and “High”) based on the median breakpoint of IC in calendar year t – 1 and 8
The updated NBER patent database is available at https://sites.google.com/site/patentdataproject/Home/downloads.
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asset growth deciles based on asset growth (AG) defined as percentage change in total assets (Compustat item AT) from the fiscal year ending in calendar year t – 2 to fiscal year ending in calendar year t – 1. Firms with missing IC measure are assigned to the low IC group. The intersection of these portfolios forms twenty IC-AG portfolios. For each IC-AG portfolio, Table 1 reports time-series mean of cross-sectional average for the number of firms, book-to-market equity (BTM), market equity (Size), innovative capacity, three-year average innovative capacity, asset growth, leverage (the long-term debt to assets ratio, DA) and cash flow (CF). Following Titman et al. (2004), we measure DA with the ratio of long-term debt over the sum of long-term debt plus year-end market value of equity. Cash flow, which is scaled by total assets, is operating income before depreciation minus interest expenses, taxes, preferred dividends, and common dividends. All variables are measured in the fiscal year ending in calendar year t – 1 except Size, which is market equity (in millions) at the end of June in year t. In Table 1, we measure IC with CTA, CTBE, and CTME in Panels A, B, and C, respectively. Panel A shows that the average number of firms in the low IC group is much higher than that in the high IC group. This is consistent with the inclusion of firms with missing IC in the low IC group. In general, BTM decreases with asset growth in both low and high IC groups, suggesting that high asset growth firms tend to be growth firms, while low asset growth firms tend to be value firms. Furthermore, each AG portfolio in the low IC group has higher BTM than its counterpart in the high IC group. This pattern supports our claim that IC is a proxy of growth options. The average size of low IC firms is smaller than that of high IC firms; a contributing factor here may be the high market valuations of hi-tech firms during the 1980s and the 1990s. Within each IC segment (low or high), the relationship between AG and firm size appears to be
14
hump-shaped, i.e., firms in the middle AG deciles tend to be larger on average than firms in the extreme (very low and very high) AG deciles. Panel A shows that in the low IC group, the average CTA is very low and does not vary much across the AG deciles, ranging from 0.02% to 0.03%. In the high IC group, the average CTA is much higher and varies with AG in a U-shape, ranging from 16.08% for the lowest AG portfolio to 4.28% for the middle AG portfolio to 7.32% for the highest AG portfolio. In addition, the level of IC tends to be persistent as low IC firms also have low CTA averaged over the prior three years. The pattern of the variation in the three-year average CTA across AG deciles within each IC group is also similar to that in the average CTA. The spreads in asset growth across the AG deciles in both IC groups are wide and similar. Specifically, asset growth in the low IC group ranges from –0.27 (lowest AG portfolio) to 1.60 (highest AG portfolio). Similarly, asset growth in the high IC group ranges from –0.25 (lowest AG portfolio) to 1.29 (highest AG portfolio). We will comment on the leverage and cash patterns in Section 4. The summary statistics of the IC-AG portfolios based on the other two proxies of IC are very similar as reported in Panels B and C. For example, the average number of firms in each IC-AG portfolio is almost identical across the three proxies of IC. The other characteristics are also very close, such as BTM, size, and asset growth. Therefore, the three IC measures are highly correlated with each other. In addition, we find the results reported in the next two sections are also very similar across the three IC measures. Therefore, for parsimony we only report results based on CTA in the rest of the paper.9 9
The results for the other two innovative capacity proxies are available upon request.
15
4.
Innovative Capacity and the Asset Growth Anomaly In this section, we use both portfolio sorts and Fama-MacBeth (1973) cross-sectional
regressions to study the impact of innovative capacity on the asset growth anomaly documented in the literature (e.g., Cooper et. al., 2008). As discussed in the introduction, we expect a weaker AG effect among firms with higher innovative capacity since the asset growth of high IC firms may generate new investment opportunities and growth options due to the unique nature of asset growth for these firms. Total assets (Compustat item AT) used in computing asset growth includes not only tangible assets (such as property, plant and equipment) resulting from capitalization of traditional investment, but also tangible assets resulting from certain types of R&D investment and intangible assets, such as patents. In general, under current GAAP (generally accepted accounting principles), R&D investment is immediately expensed and included in R&D expenditures (Compustat item XRD) and, therefore, is excluded from total assets and asset growth. However, R&D investment that has usage for future R&D projects, such as investment in building research facilities and purchase of machinery and materials for use on current and future R&D projects, is included in total assets and asset growth. Similarly, patents acquisition costs are included in intangible assets and therefore are also a part of total assets and asset growth. 10 This type of asset growth is deemed to generate new growth options instead of reducing options.
10
Since only the depreciation of this type of R&D investment is included in R&D expenses (Compustat item XRD), our results are not driven by the positive R&D-return relation documented in the literature (e.g., Chan, Lakonishok, and Sougiannis, 2001) which focuses on R&D expenses.
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However, existing studies do not disentangle different types of asset growth based on whether it is caused by traditional capital investment which tends to reduce growth options and risks or by innovation-related investment that can actually generate new options. We now examine how this differentiation sheds light on the asset growth anomaly. Although these innovation-related investments are included in total assets, they are not reported separately in Compustat. Therefore, we use firms’ innovative capacity to help differentiate these two types of asset growth. We assume asset growth of high IC firms is more related to growth in innovationrelated investment, while asset growth of low IC firms is driven by traditional capital investment. 4.1.
Portfolio Sorts
4.1.1. One-way Sort on Asset Growth We first show in Table 2 the existence of the asset growth anomaly in our sample period from July of 1977 to June of 2008, which is different from the sample period from 1968 to 2002 in Cooper et al. (2008). Following Cooper et al. (2008), we form asset growth deciles at the end of June of each year t from 1977 to 2007 based on asset growth in fiscal year ending in calendar year t – 1. We also form a high-minus-low portfolio which buys firms in the highest AG decile and sells firms in the lowest AG decile. We then hold these portfolios for the next 60 months and compute value-weighted monthly returns for each portfolio and report the time-series mean and corresponding t-statistics in parentheses of these portfolios’ returns in Panel A of Table 2. We examine value-weighted portfolio returns for two main reasons. First, because all the factors returns we use are value-weighted, using equal-weighted portfolio returns in the factor regressions will induce a bias in finding significant alphas. And, second, we want to ensure that
17
our results are not driven by smaller firms that are likely to have higher patent intensity, i.e., we want to ensure that the “innovative capacity effect” is not essentially a “small firm effect”. Consistent with Cooper et al. (2008), we find a significantly negative relation between AG and returns in the first post-sorting year. The value-weighted monthly average return of the high-minus-low AG portfolio is –0.59% (t = –3.19) in the first post-sorting year. Cooper et al. (2008) finds a much higher return difference of -1.05% between the high and low AG deciles using data from 1968 to 2002. However, our finding is more consistent with Cooper and Priestley (2011), who find a return difference of 0.46% using data from 1960 to 2009. In addition, Cooper et al. (2008) find that the negative AG-return relation continues to be significant over the second and third post-sorting years. We find the relation is only significantly negative at the 10% in the second post-sorting year and insignificant over the third, fourth, and fifth post-sorting years. These differences could be attributed to the difference in the sample period. We also compute risk-adjusted returns for these portfolios over the five post-sorting years by regressing the time-series of portfolio excess returns on risk factors returns. The monthly portfolio excess return is measured by the difference between the value-weighted portfolio return and the one-month Treasury bill rate. We report the intercepts (alphas) from the Fama-French (1993) three-factor model, the Carhart (1997) four-factor model, and the investment-based threefactor model (Chen, Novy-Marx, and Zhang, 2011) in Panels B, C, and D of Table 2, respectively. The Fama-French three-factor model contains the market factor (MKT), the size factor (SMB), and the value factor (HML). The Carhart four-factor model contains the momentum factor (MOM) in addition to the Fama-French three factors. The market factor is the return on the value-weighted NYSE/AMEX/NASDAQ portfolio minus the one-month Treasury
18
bill rate. The size factor and the value factor are returns on the factor-mimicking portfolios associated with the documented size effect and book-to-market effect (see, e.g., Fama and French 1992). The momentum factor is return on the factor-mimicking portfolio associated with the momentum effect (see, e.g., Jegadeesh and Titman 1993). The investment-based three-factor model contains the market factor, the investment (INV) factor, and the return on equity (ROE) factor. The INV factor is the difference between the return to a portfolio of low-investment stocks and the return to a portfolio of high-investment stocks. The ROE factor is the difference between the return to a portfolio of stocks with high ROE and the return to a portfolio of stocks with low ROE.11 Compared to Cooper et al. (2008) who focus on Fama-French alphas in the first postsorting year, we examine alphas from three different factor models over the five post-sorting year. We find some interesting patterns over time. For example, the alphas of the high AG portfolio and the high-minus-low AG portfolio become significantly positive in the fourth and/or the fifth post-sorting years. We discuss the detailed results below. Panel B of Table 2 shows a significantly negative Fama-French alpha for the high-minuslow AG portfolio in the first post-sorting year, –0.40% (t = –2.30) per month. However, it starts to weaken and turns to positive over the next four years. 12 Specifically, the monthly FamaFrench alpha for the high-minus-low AG portfolio is insignificant in the second post-sorting year (–0.13%, t = –0.71) and starts to turn positive (although insignificant) over the next three years. This pattern is driven mainly by the high AG decile. The monthly Fama-French alpha of the high 11
We obtain Carhart’s (1997) four-factor returns and the one-month Treasury bill rate from Kenneth French’s website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/.
12
Cooper et al. (2008) only reports the Fama-French alphas over the first post-sorting year.
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AG decile is significantly negative in the first post-sorting year, –0.38% (t = –3.50). It increases over the next four years to 0.22% (t = 1.81) in the fifth post-sorting year. In contrast, the FamaFrench alpha of the low AG decile is always small and insignificant over the five post-sorting years. Panel C reports the monthly Carhart alphas for the AG portfolios over the five postsorting years. It shows a negative but insignificant Carhart alpha for the high-minus-low AG portfolio in the first year (–0.25%, t = –1.39). In other words, the negative AG-return relation in the full sample can be fully explained by the Carhart four-factor model during this sample period. Furthermore, the Carhart alpha for the high-minus-low AG portfolio also increases over the next four years to 0.37% (t = 1.77) in the fifth post-sorting year. Similar to the Fama-French alphas, these patterns are also driven mainly by the high AG portfolio. For example, the Carhart alpha for the high AG portfolio is significantly negative in the first year (–0.32%, t = –2.94) but significantly positive in the fifth year (0.24%, t = 2.00). In contrast, the alphas for the low AG portfolio are always small and insignificant. In Panel D, we examine the explanatory power of the three-factor model motivated by the investment-based asset pricing and find similar patterns. The monthly alphas in the first postsorting year are negative and marginally significant for the high AG portfolio (–0.22%, t = –1.66) and significantly negative for the high-minus-low AG portfolio (–0.42%, t = –2.24). The alphas also increase over time to 0.34% (t = 2.52) for the high AG portfolio and 0.45% (t = 2.20) for the high-minus-low AG portfolio in the fifth post-sorting year. In fact, the alpha for the hedge portfolio is significantly positive as early as the fourth post-sorting year (0.44%, t = 2.10).
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Overall, these results confirm the existence of the asset growth anomaly in our sample period and illustrate some new interesting dynamics of this anomaly over the five post-sorting years. We now examine the interaction between the asset growth anomaly and the innovative capacity. For simplicity, we focus on risk-adjusted returns only. 4.1.2. Double Sorts on Innovative Capacity and Asset Growth In this subsection, we study the impact of innovative capacity on the asset growth anomaly through independent double sorts on IC and AG. Table 3 reports the value-weighted monthly alphas (in percentage) for the AG deciles across the innovative capacity groups formed in the same way as in Table 1. Specifically, at the end of June of each year t from 1977 to 2007, we sort firms independently into two innovative capacity groups (“Low” and “High”) based on the median breakpoint of innovative capacity in calendar year t – 1 and asset growth deciles based on asset growth in fiscal year ending in calendar year t – 1. Firms with missing innovative capacity measure are assigned to the low IC group. We measure IC with patent counts scaled by total assets in Table 3 since the other two measures of IC generate very similar results. The intersection of these portfolios forms twenty IC-AG portfolios. Furthermore, we create a highminus-low AG portfolio within each IC group. We then compute the monthly value-weighted portfolio returns for all these portfolios over the next 60 months and regress the time-series of portfolio excess returns on different sets of factor returns in each of the five post-sorting years. The monthly portfolio excess return is measured by the difference between the value-weighted portfolio return and the one-month Treasury bill rate. We report the intercepts (alphas) in percentage from the Fama-French model, the Carhart model, and the investment-based factor model in each of the five post-sorting years in Panels A, B, and C of Table 3, respectively.
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We find a sharp contrast in the AG anomaly across the IC groups. Panel A shows that the AG effect differs dramatically across the two IC groups. In the low IC group, the AG effect is significantly negative in the first post-sorting year. However, in the high IC group, the AG effect is insignificant in the first post-sorting year and significantly positive in the fourth and fifth postsorting years. Specifically, in the low IC group, the monthly Fama-French alpha of the highminus-low AG portfolio is significantly negative in the first post-sorting year, –0.53% (t = –2.49), but is small and insignificant over the next four years. The pattern is similar for the high AG portfolio in the low IC group. The monthly Fama-French alpha for the high AG, low IC portfolio is –0.57% (t = –3.73) and –0.29% (t = –2.25) in the first and second years, respectively, but is small and insignificant over the next three years. By contrast, in the high IC group, the monthly Fama-French alphas for the high AG portfolio and the high-minus-low AG portfolio are insignificant in the first three post-sorting years, but are significantly positive in the fourth and the fifth years. For example, the alphas for the high-minus-low AG portfolio are 0.75% (t = 2.59) and 0.81% (t = 2.27) in the fourth and the fifth years, respectively. Similarly, the alphas for the high AG portfolio are 0.58% (t = 2.82) and 0.52% (t = 2.62) in the fourth and fifth years, respectively. This striking contrast in the AG effect between the low IC group and the high IC group is robust to alternative factor models as shown in Panels B and C. For both the Carhart four-factor model and the investment-based three-factor model, we find a significantly negative alpha only for the high AG portfolio and the high-minus-low AG portfolio created in the low IC group in the first post-sorting year, but a significantly positive alpha for the high AG portfolio and the hedge portfolio created in the high IC group in the fourth and the fifth post-sorting years.
22
Specifically, Panel B shows that in the low IC group, the monthly alpha estimated from the Carhart model is –0.56% (t = –3.79) for the high AG portfolio and –0.46% (t = –2.14) for the hedge portfolio in the first year, but is insignificant in the next four years. However, in the high IC group, the corresponding monthly alpha is only –0.08% (t = –0.42) for the high AG portfolio and 0.02% (t = 0.08) for the hedge portfolio in the first year, but is 0.59% (t = 2.68) and 0.59% (t = 2.97) for the high AG portfolio and 0.64 (t = 2.24) and 0.98% (t = 2.68) for the hedge portfolio in the fourth year and the fifth year, respectively. Similarly, Panel C shows that in the low IC group, the monthly alpha estimated from the investment-based three-factor model is –0.53% (t = –2.94) for the high AG portfolio and –0.74% (t = –3.34) for the hedge portfolio in the first year, but is small and insignificant in the next four years, ranging from –0.05% to 0.17%. However, in the high IC group, the corresponding monthly alpha is only 0.06% (t = 0.27) for the high AG portfolio and –0.08% (t = –0.28) for the hedge portfolio in the first year, but is 0.58% (t = 2.43) and 0.66% (t = 3.06) for the high AG portfolio and 0.82% (t = 2.50) and 1.13% (t = 3.01) for the hedge portfolio in the fourth and fifth years, respectively. Furthermore, the negative AG effect among low IC firms is stronger and more robust to risk adjustment than that in the full sample. Specifically, Table 3 shows that the monthly FamaFrench alpha, the Carhart alpha, and the investment-based alpha for the high-minus-low AG portfolio formed in the low IC group are all significantly negative: –0.53% (t = –2.49), –0.46% (t = –2.14), and –0.74% (t = –3.34), respectively. In contrast, Table 2 shows that the counterparts of these alphas for the hedge portfolio formed in the full sample are smaller and sometimes insignificant: –0.40% (t = –2.30), –0.25% (t = –1.39), and –0.42% (t = –2.24), respectively.
23
This conspicuous contrast between the low IC group and the high IC group and the contrast between the low IC group and the full sample illustrated above cannot be attributed to the difference in the AG spread. Specifically, Table 1 shows that the low IC group and the high IC group have very similar average AG spread between the highest and the lowest AG deciles: 1.87 vs. 1.54. In unreported results, we find the average AG spread in the full sample is also similar at 1.82. In addition, the rank of asset growth tends to be persistent. For example, the average asset growth of the highest AG decile continues to be higher than that of the lowest AG decile over the next three (five) years for the low (high) IC group. Therefore, the positive AG effect in the high IC group in the fourth and fifth post-sorting years cannot be explained by the asset growth over the post-sorting years. These results illustrate the important role of innovative capacity in understanding the asset growth anomaly. They suggest that the negative asset growth effect documented in the literature is mainly driven by low IC firms. Among high IC firms, the asset growth effect is insignificant in the first post-sorting year and turns significantly positive in the fourth and the fifth post-sorting years. 4.2.
Fama-MacBeth Regressions In this subsection, we examine the interaction effect between innovative capacity and the
asset growth effect using Fama-MacBeth (1973) cross-sectional regressions to control for other characteristics that can predict returns and to ensure that the impact of innovative capacity on the asset growth effect documented in Section 4.1.2 is robust. The first row of Table 4 reports results from regressions with stock returns in the first post-sorting year as the dependent variable. Specifically, for each month from July of year t to 24
June of year t + 1, we regress monthly returns of individual stocks on ln(BTM), ln(Size), Momentum, asset growth (AG), patent counts scaled by total assets (CTA), and an interaction term, AG*CTA, to capture the effect of innovative capacity on the asset growth effect.13 BTM is the ratio of book equity in the fiscal year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Size is market equity at the end of June of year t. Momentum is the cumulative return over the prior six months with a one-month gap to reduce the effect of shortterm reversal. AG and CTA are measured in the fiscal year ending in calendar year t – 1. The minimum six-month lag between stock returns and BTM and AG ensures the accounting variables are fully observable. We winsorize all independent variables at the 1% and 99% levels to reduce the impact of outliers. The first row reports the time series average intercepts and slopes (in percentage) and their time-series t-statistics (in parentheses) from the series of monthly cross-sectional regressions. The slope on AG*CTA is significantly positive, 0.04% (t = 2.62). This implies a weaker AG effect in firms with high CTA, which is consistent with the findings in portfolio sorts in the first post-sorting year. Consistent with the literature, the slope on ln(BTM) is significantly positive, 0.20% (t = 3.03), and the slope on ln(Size) is significantly negative, –0.16% (t = –3.15). The slope on Momentum is positive but insignificant, 0.36% (t = 1.49). We also conduct monthly cross-sectional regressions of stock returns in the second postsorting year (July of year t + 1 to June of year t + 2) on the same set of independent variables used in the first row. We report the time series average intercepts and slopes (in percentage) and their time-series t-statistics (in parentheses) from these regressions in the second row. Similarly, 13
Similar results are obtained in Fama-MacBeth regressions with industry dummies based on Fama and French’s (1997) 48 industries.
25
the dependent variables in the third to the fifth rows are stock returns in the third post-sorting year (July of year t + 2 to June of year t + 3), the fourth post-sorting year (July of year t + 3 to June of year t + 4), and the fifth post-sorting year (July of year t + 4 to June of year t + 5), respectively. The independent variables in these rows are the same as those used in the first row. The sample period for stock returns is from July 1977 to June 2008. Consistent with the results from portfolio sorts, the slope on the interaction term, AG*CTA, is significantly positive at the 10% level in the third and the fourth post-sorting years: 0.03% (t = 1.80) and 0.03% (t = 1.72), respectively. However, the slope on AG*CTA in the fifth year is insignificant. The slight difference between portfolio sorts and Fama-MacBeth (FM) regressions may be due to the fact that we impose a linear relationship in regressions and that AG and CTA could be highly correlated with the interaction term, AG*CTA.14 Overall, these FM regressions results provide evidence supporting the analysis from portfolio sorting because they indicate that the effect of asset growth on subsequent stock returns is influenced by firms’ innovative capacity in a statistically and economically significant manner, especially in the first year after the asset growth event. To summarize the results of this section, we find that firms’ innovative capacity plays a substantial role in the asset growth anomaly. The significantly negative AG effect documented in the literature exists only among low IC firms in the first post-sorting year. Furthermore, the negative AG effect among low IC firms is stronger and more robust to risk adjustment than that in the full sample. For example, the Carhart four-factor model can fully explain the negative AG 14
In order to reduce the high correlation between the interaction term and its component variables, we use decile rank of AG and a dummy variable for CTA (1 for firms above the median CTA and 0 for the other firms) in the regressions instead of the original variables. The interaction term, AG*CTA, is also constructed from the percentile rank of AG and the dummy variable for CTA.
26
effect in the full sample, but not among the low IC firms. In contrast, the AG effect among high IC firms is insignificant in the first post-sorting year and turns significantly positive in the fourth and fifth post-sorting years. In addition, the Fama-MacBeth regressions also show a significant positive interaction effect between asset growth and innovative capacity on stock returns subsequent to asset growth; these results reinforce the inference from the portfolio sorts analysis that higher IC significantly weakens (and even over-turns) the asset growth anomaly. 4.3
Implications and Relation to the Literature We now relate our results to the literature on the asset growth anomaly. Specifically, we
relate the effects of firms’ IC on the relationship between asset growth and subsequent abnormal returns (described above) to some of the main mispricing explanations for the asset growth anomaly. We also develop further the implications of our results for the real options viewpoint. 4.3.1
Innovative Capacity and Investment Discretion
As we noted before, Titman et al. (2004) find that the negative relationship between high capital investment and abnormal returns is stronger for firms that have greater investment discretion, i.e., firms with higher cash flows and lower debt ratios. They then relate investment discretion to the moral hazard for managerial empire building and suggest that the anomaly may be due to investors’ slow reaction to the empire building implications of high investment. Prima facie, the fact that the asset growth anomaly appears to hold only for low IC firms may not be inconsistent with the empire building explanation of low IC firms being highly represented in the category of high investment discretion firms (e.g., cash cows). Conversely, the high IC firms are more likely to be cash constrained and their high patent intensity maybe an indicator that investment is not likely to involve “empire building.” However, returning to Table 1, we do not find support for 27
the conjecture that firms in the low IC/high asset growth (AG) group are also high investment discretion firms. In fact, this group has negative cash flows on average and their debt ratios are also not significantly lower than other groups. It is possible, of course, that the patent-based IC measures are very effective in discriminating between firms with value-destroying asset growth (i.e., the low IC firms) and potentially value-enhancing asset growth (the high IC firms), and our results may indicate slow investor reaction to the unproductive investment of the low IC firms. If this is the case, then our analysis is still of substantial interest because it would indicate that patent-intensity is a significant predictor of investment efficiency. Finally, we note that the underreaction to empire building only explains the negative effect of AG on subsequent stock returns. However, this viewpoint does not appear to be directly related to the result that there are positive abnormal returns for the high IC/high AG firms following rapid asset growth. 4.3.2
Innovative Capacity and the Limits to Arbitrage Another possible reason for the mispricing of asset growth only for the low IC firms
(following rapid asset growth) could be that these firms are harder to arbitrage compared to the high IC firms; i.e., the limits to arbitrage (Shleifer and Vishny, 1997) apply especially to our low IC/high AG group. However, in untabulated results we find that low and high IC firms have very similar average idiosyncratic volatility, a major measure of limits to arbitrage. We also note that the low IC firms are smaller than the high IC firms on average and this may be a factor that exacerbates the limits to arbitrage for this group. However, Cooper et al. (2008) show that the significantly negative AG effect is robust to size and exists in small,
28
medium, and large size firms. Furthermore, the short leg of the trading strategy exploiting the AG anomaly is the high AG/low IC group. The average size of this group is $798 million, which is not very small, albeit smaller than the high AG/high IC group. In addition, we find a strong interaction effect of IC and AG on stock returns in the Fama-MacBeth regressions controlling for size in Section 4.2. Finally, our analysis also poses a challenge to the overreaction hypothesis of Cooper et al. (2008). From this perspective, our results imply that investors overreact only to low IC firms with high asset growth, but not to other firms. Furthermore, if the positive post-AG alphas for high IC/high AG firms are because of mispricing, then this suggests that investors underreact to the positive effects of high asset growth by the high IC firms (and the positive alphas reflect the correction for that underreaction). 4.3.3 Innovative Capacity and Time-Varying Firm Risk Premium Our results are potentially consistent with a framework where there is time-varying risk premium driven by investment and where the change in the risk premium is positively related to firms’ IC. From this viewpoint, asset growth of low IC firms mainly converts growth options to assets-in-place and thereby reduces the risk premium or expected returns; hence, we observe the significantly negative alphas of the high-minus-low AG portfolio and the high AG portfolio formed in the low IC group. In contrast, asset growth of high IC firms is likely related to innovation activities that can generate new growth options and therefore increase the risk premium and expected returns. And because of time-to-build effects (Kydland and Prescott, 1982), we start to observe the positive abnormal returns only in the fourth and fifth years after
29
the asset growth event; this is reflected in the significantly positive alphas of the high AG portfolio and the hedge portfolio formed in the high IC group. In sum, if the alphas following asset growth are caused by missing risk factors instead of mispricing, as would be suggested by an equilibrium asset pricing model with time-varying firm risk-premium, then our evidence is consistent with the view that high IC firms generate growth options after rapid asset growth, while the low IC firms exercise non-replaceable growth options. We turn now to explicating and testing the empirical implications of such a framework.
5. Innovative Capacity and Risk Dynamics In this section, we further examine the hypothesis that asset growth in low IC firms tends to exercise options and thereby reduce the risk premium, while asset growth in high IC firms tends to generate new growth options and increase the risk premium. In Appendix A we present a theoretical real options model where the optimal dynamic investment policy of firms generates time-varying firm risk premium that depends on the firms’ IC. Higher IC firms have both a greater likelihood of developing new growth options and higher expected cash flow growth conditional on realizing the innovations. In equilibrium, the change in the firms’ market price for risk subsequent to asset growth is positively associated with their IC (cf. Theorem 1). To test this prediction, we examine the risk dynamics of the highest AG decile formed in both IC groups. Specifically, we study the change in factor loadings between the first and the fourth post-sorting years for the high AG portfolio formed in the two IC groups. In addition, we also study the change in factor loadings before and after high asset growth across the IC groups. Our evidence supports the prediction of the equilibrium time-varying risk premium viewpoint.
30
In Table 5, we form the IC-AG portfolios using the method described in Section 4.1.2. Specifically, at the end of June of each year t from 1977 to 2007, we sort firms independently into low and high innovative capacity groups based on the median breakpoint of IC in calendar year t – 1 and asset growth deciles based on asset growth in fiscal year ending in calendar year t – 1. Firms with missing IC are included in the low IC group. We measure IC with the number of patents granted (patent counts) scaled by total assets. We then compute monthly value-weighted portfolio returns for the next five years for these portfolios. As shown in Table 3, the AG effect in low IC firms is significantly negative only in the first post-sorting year, while the AG effect in high IC firms is insignificant in the first post-sorting year and turns significantly positive as early as the fourth post-sorting year. Furthermore, the AG effect is mainly driven by the highest AG decile. Therefore, we only report the factor loadings in the first and the fourth post-sorting years for the high AG and low IC portfolio (the highest AG decile formed in the low IC group) and the high AG and high IC portfolio (the highest AG decile formed in the high IC group). Table 5 reports the factor loadings along with changes in the factor loadings estimated from regressing the time series of portfolio excess returns on different sets of risk factors returns in the first (Year 1) and the fourth (Year 4) post-sorting years for the highest AG decile formed in the low IC and the high IC groups. Similar to Tables 2 and 3, we estimate the factor loadings from the Fama-French three-factor model, the investment-based three-factor model, and the Carhart four-factor model. Since the fourth post-sorting year starts from 1980, the sample period for stock returns is from July 1980 to June 2008 to ensure the same number of months for the time series of Year 1 and Year 4 returns.
31
As there are still debates on whether the size (SMB), value (HML), momentum (MOM), investment (INV), and profitability (ROE) factors capture systematic risk or mispricing, we focus on the loading on the market (MKT) factor derived from general equilibrium models. Furthermore, the investment-based factor model is motivated by Q-theory and contains an investment factor based on the change in net PPE (property, plant, and equipment) plus change in inventory scaled by lagged total assets, which is a major component of asset growth. Therefore, we feel the investment-based model is the most appropriate benchmark in examining the risk dynamics related to asset growth. However, for completeness, we also report the loadings estimated from the other factor models. Consistent with our conjecture that the effect of asset growth on options and risks for low IC firms is different from that for high IC firms, we find that the market factor loading decreases from Year 1 to Year 4 for the high AG and low IC portfolio, but increases for the high AG and high IC portfolio. Specifically, for the high AG and low IC portfolio, the changes in market risk estimated from the Fama-French model, the investment-based model, and the Carhart model between Year 1 and Year 4 are negative: –0.08 (t = –1.83), –0.12 (t = –2.85), and –0.07 (t = – 1.69), respectively. In contrast, the counterparts of these changes in market risk for the high AG and high IC portfolio are positive: 0.09 (t = 1.17), 0.16 (t = 2.45), and 0.11 (t = 1.42), respectively. Following Cooper and Priestley (2011), we also examine the change in risk around investment.15 We define the pre- and post-investment portfolios in the same way as in Cooper 15
This exercise is mainly for comparison purposes only. In general, this analysis may not capture fully the risk dynamics around investment because firms assigned to the pre-investment portfolio can be very different from firms assigned to the post-investment portfolio in the same year. Furthermore, Cooper and Priestley (2011) examine loadings on non-traded factors, while we focus on traded factors.
32
and Priestley (2011). A firm is assigned to the pre-investment portfolio in year t if it is ranked in the highest asset growth decile in any one of years t + 2, t + 3, and t + 4. Following Cooper and Priestley (2011), we exclude firms in the top AG decile in year t + 1 from the pre-investment portfolio due to investment planning (e.g., Lamont, 2000) or time to build (Kydland and Prescott, 1982). A firm is assigned to the post-investment portfolio in year t if it is ranked in the highest AG decile in year t – 1. We also sort firms independently into the low and high innovative capacity (IC) groups in year t based on median IC in year t – 1. Firms with missing IC are included in the low IC group. The intersection of the two IC groups and the pre- and post-investment portfolios forms the low IC pre- and post-investment portfolios and the high IC pre- and post-investment portfolios. We measure IC with the number of patents granted (patent counts) scaled by lagged total assets.16 We then compute monthly value-weighted portfolio excess returns for these portfolios. Table 6 reports the factor loadings along with changes in the factor loadings estimated from regressions of the time series of portfolio excess returns on different sets of risk factors returns in the pre- and post-investment periods. The t-statistics are reported in parentheses. The sample period for stock returns is from July 1977 to June 2008. Similar to Table 5, we report factor loadings estimated from the Fama-French three-factor model, the investment-based threefactor model, and the Carhart four-factor model and focus on the market factor loadings. The results show that the market beta increases after high asset growth for both high IC firms and low IC firms. However, the increase in market beta for high IC firms is much larger 16
We scale patent counts by lagged total assets to avoid the confounding effect of asset growth in the same year on the IC measure.
33
than that for low IC firms. Specifically, the increases in market beta estimated from the FamaFrench model, the investment-based model, and the Carhart model for the high IC firms are 0.18 (t = 3.07), 0.17 (t = 3.70), and 0.16 (t = 2.99), respectively. In contrast, the counterparts of these increases for low IC firms are only 0.08 (t = 2.08), 0.13 (t = 3.45), and 0.08 (t = 2.02), respectively. The increase in market risk after asset growth for the low IC firms may be related to the fact that firms assigned to the pre-investment portfolio can be very different from firms assigned to the post-investment portfolio based on the method in Cooper and Priestley (2011). This evidence illustrates the effect of innovative capacity on firms’ risk dynamics. In addition, it also shows that the decline in loadings on non-traded factors following high asset growth documented in Cooper and Priestley (2011) may not generalize to traded factors.
6.
Summary and Conclusions The negative relationship between asset growth and subsequent stock returns attracts
much attention because it has profound implications for both market efficiency and corporate investment policy. In particular, the observed significantly negative correlation between the firm's total asset growth and subsequent abnormal returns may indicate mispricing or biased capitalization of investment by financial markets, or it may indicate an efficient response to lower expected returns following the exercise of growth options. We motivate and document the importance of firms' innovative capacity in understanding the financial markets' response to asset growth. Theoretically, innovative capacity (IC), which is the ability of firms to produce and commercialize a sequence of innovations, should influence the evolution of equilibrium expected returns following asset growth. In particular, expected returns need not fall following asset growth by high IC firms because investment can generate 34
new growth options. More generally, we construct a sequential growth options model that predicts a positive relationship between the changes in firms' market price of risk subsequent to asset growth and their IC. Using patent intensity based IC measures, we analyze the effects of IC on financial markets' response to asset growth. We find that the well-known negative relationship between asset growth and subsequent excess returns holds only for the subset of firms with high asset growth and low IC. High IC firms with high asset growth rates not only do not suffer negative excess returns subsequent to asset growth, they actually earn significantly positive subsequent excess returns. Moreover, changes in the market risk loadings of firms following asset growth episodes are positively related to their IC. Firms' innovative capacity therefore appears to play an important role in the dynamics between asset growth and returns.
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Appendix A
We model an economic environment where …rms start with a patent or intellectual property rights on an invention that is a source of potential innovations. Firms then choose to invest in innovative capacity (IC) ex ante to improve the expected returns on investment and the generation of new growth options ex post. Speci…cally, the typical …rm …rm at t = 0 chooses an investment K0 2 [0; K] that determines its IC. This project requires “time to build” (Kydland and Prescott, 1982). Time ‡ows continuously and, for simplicity, the …rm spends K0 at a constant rate to complete the project at time T0 : For t
T0 , …rms must invest to generate innovations from the patent. For simplicity,
we assume that …rms can either choose to invest in innovation development, which requires an instantaneous investment of I(t) = I at a …xed cost c, or they can choose not to develop innovations (i.e., set I(t) = 0): Conditional on investment, the arrival times for the succeeding generation of innovations are a sequence of independent exponentially distributed random variables f i gi 1 : (Here,
1
is the arrival time of the …rst generation or basic innovation and
so on.) However, if I(t) = 0; then there is zero probability of successfully developing the next generation of the innovation. Let n(t) denote the generation number of the innovation at any time t
T0 . (If the …rst
generation has not arrived at t, then n(t) = 0:) Suppose that n(t) = i; i = 0; 1; 2; ::; then we assume that: Pr( Here,
i (K0 )
i+1
t + y) = exp(
(1)
i (K0 )y)
are strictly increasing and concave functions; i.e., higher R&D infrastructure
investment increases the frequency of arrival of the new generation of innovations. However, consistent with the observed development of technologies, we allow for decreasing returns to scale or likelihood of newer generations, i.e.,
i (K0 )
>
i+1 (K0 ); i
= 0; 1; 2; :::
Successful new generations of the innovation are economically attractive; in particular, if
39
n(t) = i; i = 1; 2::; then cash ‡ows Y (t) follow a geometric Brownian motion: dY (t) = Y (t) i (K0 )
i (K0 )dt
=
(K0 ) +
+ dZ(t) n X
i
(2) (3)
i=1
Here, (K0 ) is a strictly increasing and concave function that is twice continuously di¤erentiable on (0; K): Meanwhile, f i gi
1
are a sequence of independent non-negative random
variables with the cumulative distribution F ( j K0 ) such that F ( j K00 ) strictly …rst order stochastically dominates F ( j K") if K 0 > K": In sum, higher IC investment increases both the likelihood of developing new generations of innovations and the expected growth of cash ‡ows, conditional on the successful arrival of these innovations. Turning to the risk characteristics, the cash ‡ow risk in (2) is systematic because we assume that innovations in Z(t) are positively correlated with the innovations in the pricing kernel that we will describe momentarily. However, the risk in the arrival date of the innovations is a technical risk and is therefore taken to be idiosyncratic (Berk, Green and Naik, 2006).The existence of a pricing kernel, an assumption that requires only the nonexistence of arbitrage, is described by the geometric Brownian motion where for t 2 [0; 1) : d (t) = (t)
rdt + dW (t)
(4)
Here, r is the instantaneous risk-free rate and W is a Brownian motion that has a correlation of
> 0 with Z (cf. (2)). Then using standard arguments, the market price for this risk is: (5)
!=
We can therefore represent project cash ‡ows through the risk-neutral pricing measure: If n(t) = i; i = 1; 2:::; then dY (t) = Y (t) i (K0 )
i (K0 )dt
+ ~ dQ(t)
(6)
i (K0 )
!
(7)
40
where Q is the Brownian motion under the risk-neutral measure. We let V (Y (t); n(t); K0 ) denote the equilibrium value of the …rm conditional on the cash ‡ows Y (t) and the current innovation generation n(t), while taking as given the initial IC investment K0 . (If n(t) = i, we will use the notation V (Y (t); i; K0 ):) This …rm valuation clearly depends on the optimal investment policy and is hence derived as follows. If the …rm is subject to only cash ‡ow risk, i.e., I (s) = 0, s
t, then standard arguments imply that
this valuation satis…es a continuous time version of the Gordon growth model, V (Y (t); i; K0 ) = where
i (K0 )
Y (t) ; i = 1; 2; :::; r i (K0 )
(8)
is de…ned in (7). However, if the …rm is investing for development, i.e., i.e.,
I (t) = I; then it’s value function includes the options of generating the future generation of innovations. We will denote the market price of risk for the …rm’s cash ‡ows by Rp (Y (t); n(t); K0 ) (using Rp (t; K0 ) for notational convenience). Then, conditional on continued development the value of the …rm and the risk-adjusted discount rate are determined simultaneously and recursively by:
V + (Y (t); i; K0 ) =
21 Z 4 exp ( [Rp (t; K0 )(s i (K0 )
t) +
i (K0 )s])
t
fY (s)
cI + V + (Y (s); i + 1; K0 )gds
Rp (Y (t); n(t); K0 ) =
V1+ (Y (t); n(t); K0 )Y (t) V + (Y (t); n(t); K0 )
(9)
(10)
!
And thus V (Y (t); n(t); K0 ) = max(V (Y (t); n(t); K0 ); V + (Y (t); n(t); K0 )
cI)
(11)
Note that by construction Rp (t; K0 ) > ! as long as I (t) = I: To characterize the equilibrium evolution of risk-premia, we …rst characterize the …rm’s optimal innovation investment policy. The next result shows that, under the assumption of strictly increasing wait times for innovations, …rms optimally cease to invest in innovation development beyond some threshold
41
innovation generation, and this threshold level is conditional on Y (t) and K0 : Proposition 1 Conditional on (Y (t); K0 ), there exists i (Y (t); K0 ) such that the optimal investment policy for developing new generations of the innovation is I (t) = I if n(t) i (Y (t); K0 ) but I (t) = 0 otherwise. Moreover,i ( ; K0 ) is increasing in the IC investment K0 : Proof: Because f i (K0 )g is a strictly decreasing sequence, it follows that for every " > 0 there exists i" (K0 ) such that
j (K0 )
< " for every j > i" (K0 ). Therefore, the
expected arrival time for a successful innovation, namely, 1= i (K0 ) exceeds 1=" for every j > i" (K0 ), for any given " > 0:Now take any t with (Y (t); n(t)): Given that Rp > ! and c > 0; it follows immediately from a comparison of (8) and (9) that there exists some (Y (t); K0 ) such that V (Y (t); n(t); K0 ) = V + (Y (t); n(t); K0 ) if V (Y (t); n(t); K0 ) > () (Y (t); K0 ): Hence, (12)
< (Y (t); K0 )) i (K0 )
is strictly increasing for all i and
V + (Y (t); n(t); K0 ) is also strictly increasing in K0 in light of the assumption on
i (K0 )
(cf.
(3)). It therefore follows from Proposition 1 that the evolution of the risk-premium satis…es:
p
R (t; K0 ) =
8
i (Y (t); K0 )
Hence, the change in the risk-premium subsequent to asset growth is: p
8
i (Y (t); K0 )
Note that the change in risk-premium is negative if n(t) = i (Y (t); K0 ) for in this case I (t) = I but E[ I (s) = 0 j s > t]: Furthermore, Proposition 1 implies that: Theorem 1 For each t and any given (Y (t); n(t)), 42
Rp (t;K00 ) I
Rp (t;K"0 ) I
t if K00 > K0" :
Table 1. Summary statistics of innovative capacity-asset growth portfolios At the end of June of each year t from 1977 to 2007, we sort firms independently into two innovative capacity (IC) groups based on the median breakpoint of IC in calendar year t – 1 and asset growth deciles based on asset growth (AG) defined as percentage change in total assets (Compustat item AT) from the fiscal year ending in calendar year t – 2 to fiscal year ending in calendar year t – 1. We measure IC with the number of patents granted (patent counts) scaled by total assets (CTA), patent counts scaled by book equity (CTBE), and patent counts scaled by year-end market equity (CTME) in Panels A, B, and C, respectively. The intersection of these portfolios forms twenty IC-AG portfolios. For each IC-AG portfolio, this table reports time-series mean of cross-sectional average for each variable measured in the fiscal year ending in calendar year t – 1 except Size, which is market equity (in $mn) at the end of June in year t. BTM denotes book-to-market equity. DA is the long term debt to assets ratio. CF is cash flows scaled by assets.
Panel A. IC = CTA 3-year avg. No. IC AG of CTA CTA Rank Rank Firms BTM Size (%) (%) AG DA Low Low
Panel B. IC = CTBE 3-year avg. No. of CTBE CTBE CF Firms BTM Size (%) (%) AG DA
CF
276
1.12 206 0.02 0.51 -0.27 0.21 -0.10
276
1.13 192 0.05
1.08 -0.27 0.21 -0.11 277 1.12
242
0.02
0.83 -0.27 0.21 -0.11
2
268
1.27 496 0.03 0.37 -0.08 0.26 0.00
268
1.27 485 0.05
0.76 -0.08 0.26 0.00
268 1.27
511
0.02
0.60 -0.08 0.26 0.00
3
261
1.19 700 0.03 0.29 -0.02 0.28 0.04
261
1.19 688 0.05
0.77 -0.02 0.28 0.04
260 1.19
752
0.01
0.46 -0.02 0.28 0.04
4
262
1.11 1005 0.02 0.27 0.03 0.27 0.05
262
1.11 990 0.05
0.53
0.03 0.27 0.05
261 1.11 1028
0.02
0.43 0.03 0.27 0.05
5
256
1.00 1177 0.02 0.26 0.06 0.26 0.06
256
1.00 1190 0.05
0.77
0.06 0.26 0.06
256 0.99 1218
0.02
0.41 0.06 0.26 0.06
6
260
0.92 1255 0.03 0.27 0.10 0.23 0.07
260
0.92 1220 0.05
0.49
0.10 0.23 0.07
259 0.91 1264
0.02
0.36 0.10 0.23 0.07
7
262
0.83 1366 0.03 0.35 0.15 0.22 0.08
261
0.83 1324 0.04
0.82
0.15 0.22 0.08
262 0.83 1398
0.02
0.36 0.15 0.22 0.08
8
266
0.74 939 0.03 0.32 0.23 0.19 0.09
267
0.74 917 0.05
0.66
0.23 0.19 0.09
267 0.74 1063
0.02
0.31 0.23 0.19 0.09
9
274
0.64 793 0.03 0.44 0.38 0.18 0.09
274
0.64 791 0.06
0.97
0.38 0.18 0.09
275 0.64
827
0.02
0.40 0.38 0.18 0.09
High 282
0.57 798 0.03 0.63 1.60 0.20 -0.01
282
0.57 827 0.06
1.34
1.60 0.20 -0.01 283 0.57
824
0.02
0.43 1.60 0.20 -0.01
76
0.93 604 16.08 9.86 -0.25 0.19 -0.13
75
0.93 637 51.76 27.68 -0.25 0.19 -0.13
75
0.93
533
19.54 15.36 -0.25 0.19 -0.13
2
84
1.00 1384 7.53 5.61 -0.08 0.22 -0.01
84
1.00 1433 17.38 13.16 -0.08 0.22 0.00
85
1.01 1339 13.84 9.12 -0.08 0.22 0.00
3
91
0.97 2733 4.67 3.76 -0.02 0.22 0.04
91
0.98 2797 9.25
7.55 -0.02 0.22 0.04
92
0.99 2384
7.69
6.09 -0.02 0.22 0.04
4
90
0.89 3441 4.51 3.80 0.03 0.20 0.06
91
0.89 3532 9.75 10.11 0.03 0.20 0.06
91
0.91 3364
6.69
6.61 0.03 0.21 0.06
5
96
0.83 3581 4.28 3.72 0.06 0.18 0.07
96
0.83 3546 8.35
7.12
0.06 0.18 0.07
97
0.84 3456
5.54
4.77 0.06 0.18 0.07
6
93
0.77 3484 3.89 3.47 0.10 0.16 0.08
93
0.76 3682 7.24
6.50
0.10 0.16 0.08
93
0.77 3482
5.11
4.53 0.10 0.16 0.08
7
91
0.63 3804 4.63 4.03 0.15 0.14 0.08
91
0.63 3968 9.07
6.99
0.15 0.14 0.08
90
0.65 3630
4.66
4.01 0.15 0.14 0.08
8
86
0.57 3298 5.01 4.51 0.22 0.13 0.10
86
0.57 3411 44.71 8.41
0.23 0.13 0.10
85
0.58 2789
4.46
4.18 0.22 0.14 0.10
9
78
0.51 3249 6.03 6.01 0.38 0.13 0.08
78
0.51 3262 11.42 12.92 0.38 0.14 0.08
77
0.52 3138
5.12
5.39 0.38 0.14 0.08
High
70
0.46 1717 7.32 8.35 1.29 0.14 -0.02
70
0.46 1650 17.32 17.70 1.29 0.14 -0.02
69
0.47 1642
5.29
5.08 1.28 0.14 -0.03
High Low
43
Panel C. IC = CTME 3-year avg. No. of CTME CTME CF Firms BTM Size (%) (%) AG DA
Table 2. Returns and alphas of asset growth deciles At the end of June of each year t from 1977 to 2007, we sort firms into asset growth deciles based on asset growth (AG) in fiscal year ending in calendar year t – 1. We also form a high-minus-low asset growth portfolio. We then compute monthly value-weighted portfolio returns for the next 60 months for these portfolios. The table reports the average portfolio returns (in Panel A) and intercepts (alphas) from regressions of the time series of portfolio excess returns on different sets of risk factors returns in each of the five postsorting years. The portfolio excess returns are the difference between monthly portfolio returns and the one month Treasury bill rate. Panels B, C, and D report monthly alphas (in percentage) from the Fama-French (1993) three-factor model, the Carhart (1996) fourfactor model, and the investment-based three-factor model (Chen, Novy-Marx, and Zhang, 2011), respectively. Panel A. Monthly Returns of AG Deciles Post-Sorting Year 1 2 3 4 5
1(Low) 1.25 (4.13) 1.17 (3.90) 1.21 (4.14) 0.92 (3.19) 1.08 (3.66)
2 1.16 (4.57) 1.13 (4.52) 1.18 (4.84) 0.98 (3.97) 1.23 (4.95)
3 1.20 (5.36) 1.22 (5.47) 1.14 (5.33) 1.04 (4.73) 1.07 (4.67)
4 1.05 (5.32) 1.01 (4.85) 1.04 (5.02) 0.99 (4.76) 1.12 (5.29)
5 1.08 (5.15) 1.03 (4.89) 0.81 (4.03) 1.04 (4.98) 0.99 (4.71)
6 1.02 (4.70) 1.02 (4.85) 1.07 (5.07) 0.91 (4.34) 0.90 (4.45)
7 1.06 (4.70) 1.10 (4.95) 0.99 (4.20) 1.04 (4.45) 0.96 (4.19)
8 1.08 (3.96) 1.07 (3.82) 0.94 (3.36) 1.00 (3.71) 0.97 (3.68)
9 10(High) High-Low 0.94 0.66 -0.59 (3.11) (2.00) (-3.19) 1.02 0.87 -0.30 (3.44) (2.70) (-1.67) 1.09 1.13 -0.08 (3.75) (3.68) (-0.45) 1.21 1.13 0.21 (4.24) (3.45) (1.10) 1.14 1.16 0.08 (4.06) (3.75) (0.42)
5 0.10 (1.40) 0.14 (1.71) -0.09 (-1.03) 0.13 (1.41) 0.03 (0.39)
6 0.11 (1.24) 0.13 (1.74) 0.17 (2.57) 0.04 (0.51) 0.01 (0.13)
7 0.17 (2.33) 0.19 (2.40) 0.13 (1.67) 0.12 (1.41) 0.05 (0.62)
8 0.17 (1.81) 0.20 (1.81) 0.00 (-0.04) 0.06 (0.60) 0.06 (0.59)
9 10(High) High-Low 0.05 -0.38 -0.40 (0.47) (-3.50) (-2.30) 0.07 -0.12 -0.13 (0.65) (-1.02) (-0.71) 0.20 0.13 0.10 (1.88) (1.08) (0.58) 0.30 0.14 0.31 (2.74) (1.18) (1.68) 0.22 0.22 0.27 (2.09) (1.81) (1.34)
5 0.08 (1.14) 0.12 (1.35) -0.08 (-0.94) 0.16 (1.70) 0.02 (0.17)
6 0.05 (0.57) 0.13 (1.74) 0.14 (2.02) 0.02 (0.27) 0.02 (0.19)
7 0.15 (1.93) 0.16 (2.02) 0.14 (1.72) 0.11 (1.30) 0.04 (0.54)
8 0.13 (1.40) 0.15 (1.50) 0.01 (0.07) 0.13 (1.28) 0.13 (1.18)
9 10(High) High-Low 0.06 -0.32 -0.25 (0.55) (-2.94) (-1.39) 0.16 -0.06 -0.05 (1.53) (-0.48) (-0.27) 0.26 0.11 0.13 (2.50) (0.90) (0.74) 0.31 0.19 0.31 (2.75) (1.39) (1.67) 0.25 0.24 0.37 (2.42) (2.00) (1.77)
6 -0.06 (-0.65) -0.01 (-0.14) 0.03 (0.40) -0.14 (-1.56) -0.18 (-2.06)
7 0.02 (0.27) 0.17 (1.63) 0.01 (0.06) 0.10 (1.04) 0.00 (-0.03)
8 0.23 (1.71) 0.21 (1.47) 0.07 (0.64) 0.11 (0.98) 0.09 (0.79)
9 10(High) High-Low 0.12 -0.22 -0.42 (0.87) (-1.66) (-2.24) 0.23 0.03 -0.09 (2.03) (0.20) (-0.45) 0.28 0.20 0.06 (2.08) (1.46) (0.29) 0.35 0.29 0.44 (2.33) (1.88) (2.10) 0.31 0.34 0.45 (2.43) (2.52) (2.20)
Panel B. Fama-French Monthly Alphas of AG Deciles Post-Sorting Year 1 2 3 4 5
1(Low) 0.02 (0.14) 0.01 (0.07) 0.03 (0.20) -0.17 (-1.12) -0.06 (-0.34)
2 0.04 (0.33) 0.01 (0.10) 0.11 (0.98) -0.11 (-0.89) 0.19 (1.48)
3 0.11 (1.31) 0.18 (1.77) 0.14 (1.44) 0.03 (0.27) 0.03 (0.33)
4 0.11 (1.44) 0.03 (0.40) 0.06 (0.71) 0.00 (0.02) 0.12 (1.36)
Panel C. Carhart Monthly Alphas of AG Deciles Post-Sorting Year 1 2 3 4 5
1(Low) -0.07 (-0.48) -0.01 (-0.06) -0.02 (-0.14) -0.13 (-0.82) -0.13 (-0.76)
2 0.06 (0.50) -0.07 (-0.56) 0.12 (1.04) -0.13 (-1.04) 0.14 (1.00)
3 0.11 (1.19) 0.12 (1.20) 0.11 (1.12) 0.00 (0.03) 0.04 (0.40)
4 0.11 (1.31) 0.02 (0.30) 0.02 (0.24) -0.05 (-0.55) 0.08 (0.80)
Panel D. Investment-Based Monthly Alphas of AG Deciles Post-Sorting Year 1 2 3 4 5
1(Low) 0.20 (1.09) 0.12 (0.76) 0.14 (0.93) -0.15 (-0.92) -0.11 (-0.66)
2 0.03 (0.25) -0.04 (-0.29) 0.08 (0.61) -0.12 (-0.93) 0.18 (1.34)
3 0.09 (0.87) 0.03 (0.26) 0.01 (0.14) -0.07 (-0.62) -0.03 (-0.26)
4 0.00 (-0.01) -0.07 (-0.71) -0.07 (-0.75) -0.15 (-1.50) -0.03 (-0.29)
5 0.06 (0.88) -0.04 (-0.41) -0.18 (-2.19) -0.03 (-0.26) -0.16 (-1.62)
44
Table 3. Monthly alphas of innovative capacity-asset growth portfolios from different factor models At the end of June of each year t from 1977 to 2007, we sort firms independently into two innovative capacity (IC) groups based on the median breakpoint of IC in calendar year t – 1 and asset growth deciles based on asset growth (AG) defined as percentage change in total assets from the fiscal year ending in calendar year t – 2 to fiscal year ending in calendar year t – 1. We measure IC with the number of patents granted (patent counts) scaled by total assets (CTA). The intersection of these portfolios forms twenty CTA-AG portfolios. We also form a high-minus-low asset growth portfolio within each IC group. We then compute monthly value-weighted portfolio returns for the next 60 months for these portfolios. The table reports the intercepts (alphas) in percentage from regressions of the time series of portfolio excess returns on different sets of risk factors returns in each of the five post-sorting years. The portfolio excess returns are the difference between monthly portfolio returns and the one month Treasury bill rate. Panels A, B, and C report monthly alphas from the Fama-French (1993) three-factor model, the Carhart (1996) fourfactor model, and the investment-based three-factor model (Chen, Novy-Marx, and Zhang, 2011). The sample period for stock returns is from July 1977 to June 2008.
Panel A. Value-Weighted Portfolio Fama-French Monthly Alphas by Innovative Capacity Groups Asset Growth Deciles Rank of CTA Year 1(Low) 2 Low CTA 1 -0.04 -0.21 (-0.25) (-1.70) 2 -0.30 -0.21 (-1.96) (-1.60) 3 -0.24 0.10 (-1.61) (0.77) 4 -0.28 -0.20 (-1.75) (-1.51) 5 -0.07 -0.14 (-0.39) (-1.07) High CTA 1 -0.01 0.10 (-0.05) (0.59) 2 0.20 0.02 (0.92) (0.11) 3 -0.03 0.11 (-0.14) (0.71) 4 -0.17 -0.04 (-0.74) (-0.26) 5 -0.29 0.39 (-1.08) (2.09)
3 -0.01 (-0.10) 0.02 (0.16) 0.01 (0.04) -0.06 (-0.46) -0.01 (-0.06) 0.07 (0.53) 0.18 (1.35) 0.11 (0.85) -0.01 (-0.06) 0.03 (0.24)
4 0.09 (0.90) 0.09 (0.84) 0.06 (0.46) -0.03 (-0.25) 0.22 (1.79) -0.01 (-0.07) -0.04 (-0.35) 0.05 (0.39) -0.07 (-0.58) 0.12 (1.10)
5 0.07 (0.65) 0.12 (1.05) -0.10 (-1.00) 0.12 (1.09) 0.00 (-0.04) 0.07 (0.65) -0.01 (-0.09) -0.21 (-1.96) 0.03 (0.21) 0.05 (0.42)
45
6 -0.01 (-0.13) 0.07 (0.71) 0.20 (1.95) 0.00 (-0.04) 0.00 (0.02) 0.10 (0.75) 0.16 (1.40) 0.08 (0.70) -0.09 (-0.73) -0.02 (-0.19)
7 0.01 (0.13) -0.02 (-0.18) -0.01 (-0.11) 0.09 (0.82) -0.01 (-0.08) 0.28 (2.08) 0.25 (1.78) 0.26 (1.99) 0.12 (0.80) -0.08 (-0.47)
8 0.09 (0.81) 0.19 (1.42) 0.07 (0.56) 0.00 (0.01) -0.04 (-0.27) 0.24 (1.48) 0.22 (1.32) 0.04 (0.29) 0.21 (1.35) 0.09 (0.53)
9 10(High) -0.11 -0.57 (-0.90) (-3.73) -0.07 -0.29 (-0.66) (-2.25) 0.02 -0.18 (0.15) (-1.29) 0.08 -0.17 (0.57) (-1.25) 0.40 -0.14 (2.59) (-0.88) -0.10 -0.23 (-0.60) (-1.16) 0.15 -0.08 (0.91) (-0.44) 0.29 0.30 (1.60) (1.59) 0.50 0.58 (2.56) (2.82) 0.04 0.52 (0.24) (2.62)
High-Low (10-1) -0.53 (-2.49) 0.01 (0.06) 0.06 (0.34) 0.11 (0.53) -0.07 (-0.28) -0.22 (-0.82) -0.28 (-1.00) 0.33 (1.26) 0.75 (2.59) 0.81 (2.27)
Panel B. Value-Weighted Portfolio Carhart Monthly Alphas by Innovative Capacity Groups Asset Growth Deciles High-Low Rank of CTA Year 1(Low) 2 3 4 5 6 7 8 9 10(High) (10-1) Low CTA 1 2 3 4 5 High CTA 1 2 3 4 5
-0.10 -0.24 0.07 0.05 0.08 -0.03 -0.04 -0.01 -0.10 (-0.57) (-1.69) (0.62) (0.45) (0.77) (-0.31) (-0.43) (-0.05) (-0.86) -0.30 -0.33 -0.04 0.05 0.04 0.06 -0.03 0.11 -0.04 (-1.92) (-2.52) (-0.31) (0.44) (0.38) (0.59) (-0.36) (0.89) (-0.37) -0.25 0.09 -0.03 -0.02 -0.09 0.16 -0.04 0.03 0.04 (-1.65) (0.56) (-0.25) (-0.17) (-0.85) (1.61) (-0.42) (0.27) (0.31) -0.35 -0.21 -0.11 -0.09 0.08 0.02 0.10 0.05 0.12 (-2.22) (-1.52) (-0.88) (-0.85) (0.75) (0.21) (0.88) (0.38) (0.85) -0.24 -0.11 -0.05 0.11 -0.01 0.00 -0.01 0.04 0.39 (-1.38) (-0.75) (-0.32) (0.84) (-0.11) (-0.03) (-0.12) (0.31) (2.57) -0.11 0.19 0.07 0.05 0.03 0.05 0.28 0.23 -0.07 (-0.52) (1.15) (0.55) (0.41) (0.28) (0.37) (1.94) (1.45) (-0.38) 0.16 0.00 0.12 -0.01 0.05 0.18 0.23 0.21 0.26 (0.72) (0.02) (0.95) (-0.12) (0.40) (1.47) (1.67) (1.33) (1.55) -0.07 0.19 0.08 0.06 -0.13 0.06 0.31 0.12 0.40 (-0.33) (1.16) (0.64) (0.44) (-1.17) (0.54) (2.30) (0.77) (2.19) -0.05 -0.08 0.03 -0.12 0.15 -0.07 0.13 0.31 0.50 (-0.22) (-0.42) (0.24) (-0.96) (1.19) (-0.56) (0.83) (1.89) (2.55) -0.39 0.32 0.10 0.10 0.01 0.04 -0.03 0.27 0.10 (-1.40) (1.68) (0.77) (0.85) (0.08) (0.31) (-0.17) (1.56) (0.58)
-0.56 (-3.79) -0.18 (-1.46) -0.18 (-1.33) -0.10 (-0.74) -0.04 (-0.26) -0.08 (-0.42) 0.11 (0.49) 0.32 (1.61) 0.59 (2.68) 0.59 (2.97)
-0.46 (-2.14) 0.12 (0.64) 0.06 (0.34) 0.25 (1.13) 0.20 (0.85) 0.02 (0.08) -0.06 (-0.18) 0.39 (1.44) 0.64 (2.24) 0.98 (2.68)
Panel C. Value-Weighted Portfolio Investment-Based Monthly Alphas by Innovative Capacity Groups Asset Growth Deciles High-Low Rank of CTA Year 1(Low) 2 3 4 5 6 7 8 9 10(High) (10-1) Low CTA 1 2 3 4 5 High CTA 1 2 3 4 5
0.21 -0.11 0.16 0.03 0.06 -0.03 -0.02 0.09 0.01 (1.03) (-0.75) (1.20) (0.28) (0.56) (-0.29) (-0.19) (0.69) (0.04) -0.10 -0.13 0.01 -0.04 -0.02 0.05 0.02 0.12 0.13 (-0.48) (-0.71) (0.04) (-0.37) (-0.15) (0.48) (0.21) (0.82) (0.89) -0.05 0.21 -0.03 0.01 -0.19 0.09 0.03 0.17 0.05 (-0.30) (1.15) (-0.18) (0.10) (-1.62) (0.86) (0.35) (1.29) (0.45) -0.13 -0.03 -0.07 -0.14 0.10 -0.02 0.07 0.04 0.13 (-0.67) (-0.21) (-0.46) (-1.18) (0.78) (-0.15) (0.59) (0.27) (0.87) 0.10 -0.03 0.01 0.07 -0.02 -0.09 0.07 -0.02 0.60 (0.37) (-0.21) (0.03) (0.51) (-0.14) (-0.76) (0.62) (-0.14) (2.92) 0.14 0.01 0.01 -0.08 -0.04 -0.09 0.07 0.36 -0.08 (0.52) (0.08) (0.07) (-0.60) (-0.33) (-0.67) (0.47) (1.68) (-0.39) 0.14 -0.02 0.02 -0.11 -0.16 -0.07 0.22 0.30 0.30 (0.63) (-0.09) (0.14) (-0.81) (-1.27) (-0.58) (1.27) (1.36) (1.69) 0.09 0.04 -0.04 -0.10 -0.22 -0.07 0.06 0.12 0.38 (0.37) (0.25) (-0.31) (-0.72) (-1.88) (-0.57) (0.43) (0.70) (1.74) -0.23 -0.13 -0.05 -0.22 -0.10 -0.25 0.17 0.23 0.57 (-0.97) (-0.70) (-0.35) (-1.64) (-0.65) (-1.74) (1.02) (1.30) (2.31) -0.47 0.33 0.02 -0.03 -0.26 -0.21 -0.14 0.22 0.12 (-1.65) (1.66) (0.13) (-0.26) (-1.86) (-1.51) (-0.74) (1.22) (0.61)
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-0.53 (-2.94) -0.01 (-0.07) -0.01 (-0.08) 0.04 (0.28) 0.04 (0.25) 0.06 (0.27) 0.11 (0.48) 0.31 (1.58) 0.58 (2.43) 0.66 (3.06)
-0.74 (-3.34) 0.08 (0.42) 0.04 (0.21) 0.17 (0.79) -0.05 (-0.18) -0.08 (-0.28) -0.03 (-0.10) 0.23 (0.76) 0.82 (2.50) 1.13 (3.01)
Table 4. Fama-MacBeth regressions of stock returns on asset growth, innovative capacity and other variables This table reports the time-series average slopes and intercepts in percentage and their time series t-statistics in parentheses from monthly Fama and MacBeth (1973) cross-sectional regressions of individual stocks’ returns on ln(BTM), ln(Size), Momentum, asset growth (AG), patent counts scaled by total assets (CTA), and an interaction term, AG*CTA. BTM is the ratio of book equity in the fiscal year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Size is market equity at the end of June of year t. Momentum is the cumulative return over the prior six months with a one-month gap. AG and CTA are measured in the fiscal year ending in calendar year t – 1. The dependent variable in the first row is stock returns from July of year t to June of year t + 1. The dependent variable in the second row is stock returns from July of year t + 1 to June of year t + 2. The dependent variable in the third row is stock returns from July of year t + 2 to June of year t + 3. The dependent variable in the fourth row is stock returns from July of year t + 3 to June of year t + 4. The dependent variable in the fifth row is stock returns from July of year t + 4 to June of year t + 5. All rows share the same set of independent variables. The sample period for stock returns is from July 1977 to June 2008.
Dependent variable Next-year return Second-year-ahead return Third-year-ahead return Fourth-year-ahead return Fifth-year-ahead return
Intercept 2.47 (6.20) 1.95 (4.99) 2.00 (5.35) 1.99 (5.25) 1.64 (4.39)
ln(BTM) 0.20 (3.03) 0.17 (2.65) 0.12 (1.94) 0.08 (1.36) 0.09 (1.61)
ln(size) -0.16 (-3.15) -0.17 (-3.25) -0.16 (-3.12) -0.17 (-3.40) -0.16 (-3.07)
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Momentum 0.36 (1.49) 0.45 (1.84) 0.48 (1.92) 0.44 (1.73) 0.45 (1.72)
AG -0.14 (-5.68) -0.03 (-1.45) -0.04 (-2.03) -0.05 (-2.17) 0.02 (0.83)
CTA 0.13 (1.19) 0.29 (2.57) 0.13 (1.25) 0.19 (1.76) 0.35 (3.04)
AG*CTA 0.04 (2.62) 0.01 (0.49) 0.03 (1.80) 0.03 (1.72) -0.02 (-1.27)
Table 5. Risk dynamics after investment At the end of June of each year t from 1977 to 2007, we sort firms independently into low and high innovative capacity (IC) groups based on the median breakpoint of IC in calendar year t – 1 and asset growth deciles based on asset growth (AG) defined as percentage change in total assets from the fiscal year ending in calendar year t – 2 to fiscal year ending in calendar year t – 1. Firms with missing IC are included in the low IC group. We measure IC with the number of patents granted (patent counts) scaled by total assets (CTA). We then compute monthly value-weighted portfolio returns for the next 5 years for these portfolios. This table reports the factor loadings estimated from regressing the time series of portfolio excess returns on different sets of risk factors returns in the first (Year 1) and the fourth (Year 4) post-sorting years for the highest AG decile in the low IC and the high IC groups. The t-statistics are reported in parentheses. The portfolio excess returns are the difference between monthly portfolio returns and the one month Treasury bill rate. The Fama-French (1993) three-factor model includes the market (MKT), size (SMB), and value (HML) factors. The investment-based three-factor model (Chen, Novy-Marx, and Zhang, 2011) includes the market, investment (INV), and return-on-equity (ROE) factors. The Carhart (1996) four-factor model includes the Fama-French three factors and the momentum (MOM) factor. The sample period for stock returns is from July 1980 to June 2008.
Fama-French Model MKT SMB HML Low IC, High AG, Year 1 1.18 0.30 -0.37 (24.76) (2.91) (-4.47) Low IC, High AG, Year 4 1.10 0.31 -0.18 (28.70) (5.90) (-2.90) High IC, High AG, Year 1 1.15 0.14 -0.50 (21.34) (1.97) (-5.48) High IC, High AG, Year 4 1.24 -0.08 -0.58 (20.68) (-0.87) (-5.38) 0.01 0.19 Low IC, High AG, Year 4 – Year 1 -0.08 (-1.83) (0.12) (2.30) -0.22 -0.08 High IC, High AG, Year 4 – Year 1 0.09 (1.17) (-1.84) (-0.54)
Investment-based Model MKT INV ROE 1.29 -0.45 -0.05 (28.63) (-4.04) (-0.91) 1.17 -0.27 -0.06 (28.97) (-2.63) (-1.07) 1.21 -0.78 -0.20 (24.05) (-5.71) (-2.90) 1.37 -0.25 -0.21 (25.71) (-1.43) (-2.53) -0.12 0.18 -0.01 (-2.85) (2.09) (-0.11) 0.16 0.54 -0.01 (2.45) (2.26) (-0.10)
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MKT 1.17 (25.72) 1.10 (28.36) 1.13 (21.87) 1.24 (19.52) -0.07 (-1.69) 0.11 (1.42)
Carhart Model SMB HML 0.30 -0.39 (3.10) (-4.99) 0.31 -0.18 (5.83) (-2.79) 0.15 -0.54 (2.08) (-5.97) -0.08 -0.58 (-0.85) (-5.20) 0.01 0.20 (0.09) (2.76) -0.23 -0.05 (-1.90) (-0.31)
MOM -0.05 (-1.01) -0.01 (-0.14) -0.13 (-2.17) -0.02 (-0.29) 0.05 (0.89) 0.11 (1.06)
Table 6. Risk dynamics around investment A firm is assigned to the pre-investment portfolio in year t if it is ranked in the highest asset growth (AG) decile in any one of years t + 2, t + 3, and t + 4. A firm is assigned to the post-investment portfolio in year t if it is ranked in the highest AG decile in year t – 1. We also sort firms independently into low and high innovative capacity (IC) groups in year t based on median IC in year t – 1. Firms with missing IC are included in the low IC group. The intersection of the two IC groups and the pre- and post-investment portfolios forms the low IC pre- and post-investment portfolios and the high IC pre- and post-investment portfolios. We measure IC with the number of patents granted (patent counts) scaled by lagged total assets. We then compute monthly value-weighted portfolio excess returns for these portfolios. This table reports the factor loadings estimated from regressions of the time series of portfolio excess returns on different sets of risk factors returns for these portfolios. The t-statistics are reported in parentheses. The portfolio excess returns are the difference between monthly portfolio returns and the one month Treasury bill rate. The Fama-French (1993) three-factor model includes the market (MKT), size (SMB), and value (HML) factors. The investmentbased three-factor model (Chen, Novy-Marx, and Zhang, 2011) includes the market, investment (INV), and return-on-equity (ROE) factors. The Carhart (1996) four-factor model includes the Fama-French three factors and the momentum (MOM) factor. The sample period for stock returns is from July 1977 to June 2008.
Low IC, Pre-investment Low IC, Post-investment High IC, Pre-investment High IC, Post-investment Low IC, Post-minus-Pre High IC, Post-minus-Pre
Fama-French Model MKT SMB HML 1.11 0.31 -0.19 (34.55) (5.73) (-3.15) 1.19 0.35 -0.33 (25.54) (3.55) (-3.94) 1.02 -0.12 -0.34 (31.95) (-2.26) (-6.09) 1.19 0.15 -0.47 (25.54) (2.25) (-5.70) 0.08 0.05 -0.14 (2.08) (0.59) (-1.66) 0.18 0.26 -0.13 (3.07) (3.11) (-1.44)
Investment-based Model MKT INV ROE 1.19 -0.28 -0.06 (34.87) (-3.89) (-1.24) 1.31 -0.46 0.01 (29.92) (-4.11) (0.11) 1.10 -0.07 0.00 (35.02) (-0.67) (-0.01) 1.28 -0.63 -0.21 (27.97) (-4.80) (-3.13) 0.13 -0.18 0.07 (3.45) (-1.73) (1.15) 0.17 -0.56 -0.21 (3.70) (-3.76) (-2.77)
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MKT 1.11 (35.33) 1.19 (26.39) 1.02 (32.79) 1.18 (25.97) 0.08 (2.02) 0.16 (2.99)
Carhart Model SMB HML 0.30 -0.18 (5.50) (-2.88) 0.35 -0.33 (3.62) (-4.10) -0.12 -0.34 (-2.38) (-6.22) 0.17 -0.50 (2.45) (-6.12) 0.05 -0.15 (0.70) (-1.79) 0.29 -0.17 (3.37) (-1.90)
MOM 0.05 (1.55) 0.01 (0.14) 0.03 (0.87) -0.14 (-2.58) -0.04 (-0.68) -0.17 (-2.97)
