Heterogeneity in Intangible Risk and Cross-Section Stock Return. Abstract

Transcription

1 Heterogeneity in Intangible Risk and Cross-Section Stock Return Abstract With the rise of high technology producing companies, intangible capital becomes an important part of the capital of a modern economy. However, under current U.S. accounting standards, most of investment in intangible capital is expensed rather than capitalized, which complicates the valuation of corporate securities and the assessment of risk and return of investments. We find that it is crucial to recognize the heterogeneity in intangible capital and the risk and return differences in different types of intangible capital, and it is the key to dissect the anomalies in the stock market such as value premium and R&D anomaly. R&D expenses (developing intangible capital) to discover new technology and new products should be evaluated differently from the intangible investments to improve the existing process of production (embodied intangible capital). Embodied-intangible-capital intensive firms invest more aggressively in physical capital and have higher market value relative to book value of physical capital (lower B/M), and appear to be overvalued in an asset pricing model without intangible capital; while developing-intangible-capital intensive firms are riskier due to intensive R&D expenses are not yet embodied in the production process, appear to have weaker earnings and be undervalued in an asset pricing model with missing factor or intangible capital. Keywords: Intangible Capital, Book-to-Market Ratio, Research and Development Expenses, Factor Model.

2 I. Introduction Research and Development (R&D) is defined in the international guidelines of national accounts as creative work undertaken on a systematic basis to increase the stock of knowledge, and use of this stock of knowledge for the purpose of discovering or developing new products, including improved versions or qualities of existing products, or discovering or developing new or more efficient processes of production. However, despite the fact that expenditures for R&D have long been recognized as having the characteristics of fixed assets-defined ownership rights, long-lasting, and repeated use and benefit in the production process, most of investments in R&D is expensed rather than capitalized under current accounting standard in most countries, and becomes intangible in accounting and a missing component of capital in finance studies. With the rise of high technology producing companies, intangible capital becomes an important part of the capital of a modern economy. Both macroeconomic and microeconomic data suggest that U.S. companies own substantial amounts of intangible capital not recorded in the firm s book value or anywhere in government statistics 1. The lack of accounting information makes it complicated to evaluate stock prices and assess the risk and return of investment in intangible capital. When the productive assets are mostly physical assets, such as plant and equipment, the link between the firm s asset value and stock price is clear, and stock return should equal to investment return as demonstrated in Cochrane (1991). However, Hall (2001a) argues that if the missing information on intangible capital leads to anomalies in the valuation of corporate securities, then it would also cause anomalies in the measurement of produced capital and contaminate the assessment of risk and return of investments. McGrattan and Prescott (2010) argue that ignoring intangible capital in the neoclassical growth model is the reason behind the seemingly puzzle that the model predicts a depressed 1990s economy, when in fact it boomed. Peters and Taylor (2017) propose a new Tobin s q proxy that accounts for intangible capital and show that it helps to explain physical and intangible investments. 1 Recognizing that the asset boundary should be expanded to include innovative activities, such as R&D, one of the major changes in the 2013 comprehensive revision of the national income and product accounts (NIPAs) is the capitalization of research and development (R&D) expenditures. However, the intangible capital discussed in this paper is much more general that those R&D expenditures capitalized in the revised NIPAs.

3 Financial economists also document anomalies in the market valuation of various form of intangible capital. Ample empirical evidences based on limited accounting information suggest that market fails to incorporate intangible capital and intangible capital earns abnormal return. Hall (1993) and Hall and Hall (1993) argue that R&D intensive stocks are undervalued and have higher return adjusted for the observed risk factors in the market. Lev and Sougiannis (1996) estimate annual abnormal returns from research and development to be 4.6%, while Edmans (2011) estimates it to be 3.5% from employee satisfaction and Fornell, Morgeson, and Hult (2016) find an astounding 8.4% from customer satisfaction after controlling for risk factors such as market, size, B/M, profitability and physical investment intensity. Chan, Lakonishok and Sougiannis (2001) uses R&D expenditure reported in the income statements to proxy the investment in intangible assets, and find companies with high R&D to equity market value earn large excess returns, but they also find that R&D-to-sales ratio is not associated the average historical stock returns although it is positively associated with return volatility. Cohen, Diether and Malloy (2013) show that the market appears to under react to the information contained in R&D investments. Eisfeldt and Papanikolaou (2013) find positive relationship between link organizational capital and expected stock returns. Elsaify (2016) measure R&D intensity as R&D-to-total-investment ratio, and find that R&D-intensive firms earn abnormal risk-adjusted return. Hansen, Heaton and Li (2005) examine the return to intangible capital from another angel. They argue that in presence of intangible capital, heterogeneity in the Tobin s q or inverse of book-to-market equity ratio (B/M) is no longer simply a price signal to convey information about investment profitability, and may reflects in part different amounts of intangible capital. They show that growth firms with low book-to-market equity ratio (B/M) tend to be intangible-capital intensive firms, and suggest that the return heterogeneity of B/M portfolio may indicate importance differences between returns to the tangible and intangible component of the assets. Given the ample evidences that average stock returns are related to the book-to-market equity ratio, it seems that the low expected return of low B/M stocks implies that intangible-capital intensive firms earn lower expected return instead of higher expected return than physical capital, which contradicts the previous findings of high return of R&D intensive firms if the risk and return of intangible capital is homogeneous.

4 Recognizing the fact that the market value of a firm s securities measures the value of all the productive assets including both physical and intangible capital, Hall (2001a), McGrattan and Prescott (2001) and other macroeconomists exploit the information contained in the differences between aggregate stock market value and replacement costs of physical capital or book value of assets to impute the value of intangible capital. Hall (2001b) assumes that physical capital and intangible capital are perfect substitutes of each other and infers value of intangibles from the difference between aggregate stock market value and that of physical capital. He finds that changes in values of intangible capital account for a significant part of large movements of U.S. stock-market value in relation to GDP in the postwar period as shown in Figure 1. Li (2005) and An and Li (2016) measure risk and return to intangible capital from observed data on stock market value and macroeconomic variables in a neoclassical model with uncertainty and investment-specific technological change 2, where intangible capital and physical capital are a complimentary production factors 3. They show that return to intangible investment embodied in the production provides good hedge to the long-run risk and has lower expected return. Ai, Croce, and Li (2012) focus on the idea that R&D expenditures by firms can drive endogenous growth in the aggregate economy and estimate intangible capital by exploiting the cross-sectional return variation among firms with different B/M ratios. They also find that investments in (embodied) intangible capital earn lower expected return. Dyer and Gregersen (2011) measure innovation premium based on the expected cash flows and find that firms with high innovation premium have higher cash-flow growth but low expected returns over the following five years, as prices embeds investor expectations and high growth today may imply low expected return in the future. We propose to reconcile the seemingly conflicting findings in the literature is to recognize the differences in two types of the intangible capital, developing and embodied 4 intangible capital. Developing intangible capital is associated with discovering or developing new products 2 Ai, Croce, and Li (2012) and Kung and Schmid (2015) focus on the idea that R&D expenditures by firms can drive endogenous growth in the aggregate economy and estimate intangible capital by exploiting the cross-sectional return differences among firms with different B/M ratios. 3 Sakellaris and Wilson (2002) estimate the rate of embodied technological change directly from plant-level manufacturing data and find that the investment-specific technological change is a important engine of growth. 4 R&D is typically categorized in the data into product development (developing new products or services) and process development (developing new techniques or methods to produce existing offerings) and includes expenses such as research wages, patent development, and software development. However, this is different from our proposal of differentiate embodied intangible capital from developing intangible capital.

5 or new processes of production, and is yet to be used in firms production and generate revenue, for example, the R&D expenses of Apple to invent the first iphone. The uncertainty and risk associated with this type of intangible capital is substantial, and the future cash flows generated by the developing intangible capital are more volatile. Investors demand a higher risk premium to hold the stocks of developing-intangible-capital intensive firms and the value of this type of intangible capital is low. R&D expenditure reported in the income statement may be a noisy proxy for investment in this type of intangible capital. On the other hand, the embodied intangible capital is already used in the process of production as an effective complimentary factor to physical capital, for examples, the R&D expenses of Apple to upgrade iphone 1 to iphone 2. It contributes to robust future cash flows and provides a good hedge against long-run economic risk. Investors pay premium for the stocks of firms with higher embodied intangible capital. Hence the book-to-market equity ratio (B/M) of firms with more embodied intangible capital are lower, that is, B/M ratio may serve as a noisy proxy for embodied intangible capital intensity. Both types of intangible capital are missing in the book value of assets of a firm, but they have substantial difference in risk and return. Developing intangible capital is riskier than physical capital and investors demand higher return; while embodied intangible capital is less risky than physical capital and has lower expected return. Figure 1. Value of U.S. Equity and Debt Claims on Nonfarm, Nonfinancial Corporations as a Ratio to GDP, Recognizing the heterogeneity in intangible capital is the key to understand the seemingly puzzle regarding the relationship between stock return, intensity in research and development (R&D) and book-to-market ratio (B/M). If firms with low B/M hold more embodied intangible capital, while firms more intensive in R&D expenditure hold more developing intangible capital,

6 then the low expected return of embodied intangible capital explains the low return of growth firms (with low B/M) relative to firms with high B/M, while the high expected return of developing intangible capital explain the high return of R&D intensive firms relative to firms with little R&D expenses. To further understand the relationship between book-to-market ratio and embodied intangible capital intensity, we use an extended dividend discount model with intangible capital and physical capital as complimentary production factors. The market value of a share of stock is the discounted value of expected dividends per share P t E( d ) t j j j 1 (1 r) In this equation P t is the share price at time t, which equal the market value of physical capital and intangible capital owned by the firm. E(d t+j ) is the expected dividend per share for period t+j, and r is the long-term average expected stock return or the cost of capital. If there is only one type of capital, physical capital, then r is the cost of physical capital. When there are two types of capital, physical capital and intangible capital, r is the weighted average of the costs of two types of the capital and the weights are determined by the market value of each type of capital. Use clean surplus accounting, (1) t * t D Y B m t m u t m m, t u 1 m u 1u, tlt ( ) A K K I I B (2) 1u, t 2u, t m t * In this equation, Y t is total equity earnings and equals marginal product of capital minus the investment in intangible capital, which is expensed under the current accounting standards. m m m Bt Bt Bt 1 is the change in total book equity, which equals to the investment in measured physical capital. Note that only embodied intangible capital (K 1u ) enters the production function and contribute to profit in each period. Hence the value of the firm should incorporate the value of the embodied intangible capital. On the other hand, developing intangible capital (K 2u ) is yet to be productive, and its value is yet to be incorporated in the firm value. Plug Equation (2) in equation (1) and divide both sides by time t book equity we get P B t m t j 1 E( Y * t j B m t j B t ) /(1 r) j B B t m t (3)

7 where B t is the unobservable total book value of asset, including book value of both physical and intangible capital. This is an extended version of equation (3) in Fama and French (2015). From this equation, we can extract the implication for the relations between B/M ratio, expected return, expected profitability, expected investment intensity in physical capital. First, fixed the level of developing intangible capital, then a higher market-to-book equity ratio implies a higher value of B/B m, that is, relative more embodied intangible capital(k 1u ) and investment in both embodied intangible capital(i 1u ) and physical capital( m B ), or higher earnings (Y * ), or lower expected composite return (r). Hence, B/M ratio is a noisy proxy for embodied intangible capital intensity and expected return. Next, fixed the level of embodied intangible capital and market-to-book equity ratio, then more intensive investment in developing intangible capital (I 2u ) or R&D/sales ratio implies a higher value of B/B m, that is, relative more developing intangible capital(k 2u ) or higher and more volatile earnings (Y * ), or higher expected composite return (r). In summary, fixing the level of developing intangible capital (i.e. R&D intensity), embodied-intangible-capital intensive firms earn lower expected return and have lower B/M ratio, as embodied intangible capital is associated with robust earnings, high investment in physical capital, and low long-run risk. Fixing the level embodied intangible capital (i.e. B/M), developing-intangible-capital intensive firms are more likely to be R&D intensive (high R&Dto-Sales ratio), earn higher expected return and more volatile earnings as developing intangible capital is associated with high risk/uncertainty. Low return of low B/M firms (with more embodied intangible capital) and high return of R&D intensive firms (with more developing intangible capital) can be reconciled by recognizing the differences in two types of intangible. In addition, it is very likely that the two types of intangible capital are positively correlated and, that is, firms with more developing intangible capital (high R&D-to-Sales ratio) may also own a lot of embodied intangible capital (low B/M ratio), hence without controlling for the level of embodied intangible capital, there may be hard to find a direct link between R&D expenses and expected return. This may explain the puzzling findings of Chan, Lakonishok and Sougiannis (2001) that R&D-to-Sales ratio is positively associated with return volatility but has no direct link to future stock returns. The differences in two types of the intangible capital can also help to explain the lower return of small firms that invest a lot in physical capital despite low profitability, an anomaly

8 cannot be explained by Fama and French (2015) five-factor model. Since these small firms are more likely to be the firms with lots of embodied intangible capital, so they invest aggressively in physical capital to accompany the investment in embodied intangible capital, and their earnings appear to be weak because investment in embodied intangible capital is large and is deducted from the profits as expenses. The stock returns of these firms are low because of the low expected return of embodied intangible capital. As data on a firm s aggregate intangible capital or each type of the intangible capital is missing, we propose two measures, albeit imperfect, to proxy for the two types of intangible capital. Specifically, we proxy firms with low B/M for embodied-intangible-capital intensive firms and R&D intensive firms for firms with more developing intangible capital. In Figure 2, we illustrate the implication of differentiating two types of the capital on the risk, earning and investment in physical capital. We form portfolios by allocating firms into independently sorted groups based on the two proxies of intangible capital, the book-to-market ratio and R&D intensity. As we illustrated above, the association of expected return with investment intensity in physical capital as well as earnings help us to identify the importance of the embodied intangible capital. Hence we apply the five-factor asset pricing model of Fama and French (2015) and Q- factor model of Hou, Xue, and Zhang (2015) to test our model implications 5. We find that controlling for B/M ratio, a firm s R/D to sales ratio is positively associated with risk-adjusted return and negatively associated with profitability; while controlling for R/D to sales ratio, firm s B/M is positively associated with risk-adjusted return and negatively associated with investment in physical capital. These results are consistent with the predictions associated with differentiating two types of intangible capital and help to explain the puzzling findings of Chan, Lakonishok and Sougiannis (2001) that firms with high R&D-to-sales ratio do not earn high return and that of Fama and French (2015) that small firms that invest a lot in physical capital earn lower return despite low profitability. This paper closely relates to the structural asset pricing papers by Li (2005) and An and Li (2015), who estimate the value and risk of embodied intangible capital as a complimentary 5 Through independent research, both Fama and French (2015) and Hou, Xue, and Zhang (2015) find that risk factors that capture profitability and investment intensity in physical capital help to explain the cross sectional expected return variation.

9 production factor to the physical capital in a two-sector model with capital adjustment costs and investment specific technological changes. This paper finds empirical evidence supporting the implications of their structural model that embodied intangible capital is positively associated with future cash flows and earns lower expected return than physical capital. A recent study by Elsaify (2016) proposes a production-based asset pricing model that incorporates product market competition to explain the positive relationship between expected return and R&D-to-investment ratio, while our paper focuses on the heterogeneity of intangible capital and its implication in explaining the relationship between expected returns and the R&D-to-sales as well as B/M ratios. We discuss the details of data construction in section II. Section III presents and discusses the empirical results. Section IV concludes. Figure 2 Segmentation of Firms According to R&D and B/M Indicators Low B/M Embedded IC: high Developing IC: low Risk: low Earning: robust Physical investment: aggressive Embedded IC: high Developing IC: high Risk: medium Earning: ambiguous Physical investment: aggressive Low R&D High R&D Embedded IC: low Developing IC: low Risk: medium Earning: ambiguous Physical investment: conservative Embedded IC: low Developing IC: high Risk: high Earning: weak Physical investment: conservative High B/M II. Data Construction Our sample is based non-financial and non-utility ordinary shares (share code 10 and 11) listed on NYSE, AMEX and NASDAQ from January 1975 to December The sample is

10 from 1975 since the accounting treatment of R&D expense reporting was standardized in 1975 (Financial Accounting Standards Board Statement No. 2). Financial Statement data are obtained from COMPUSTAT, merged with stock returns from Center for Research in Security Prices (CRSP). To ensure full incorporation of accounting data in stock returns, we follow Fama and French (1992) to merge the accounting data for fiscal year end in calendar year t-1 with stock returns data from July of year t to June of year t+1. Firm s book-to-market ratio is calculated using a firms market equity at the end of December and firm s size is measured using its market equity in June of the following year. We delete firms with negative or missing book value. We use R&D expenditure divided by Sales as the primary measures of firm s R&D intensity. At the end of June in each year, each stock is allocated to one of the 3x3 independently sorted, equally sized portfolios based on the firm s R&D intensity and Book-to-Market ratio at the end of the fiscal year ending in year t-1. Qualitatively similar results are obtained if we sort stocks into 5x5 portfolios, but the number of firms will be substantially reduced in each portfolio, thus, we use 3x3 independent sort portfolios in our benchmark model. Our sample only includes firmyear combinations with positive R&D expenditure. The sample includes 69,417 firm years with 1,735 firms each year on average. We keep stocks with missing R&D expenditure and zero R&D expenditures in a separate portfolio and calculate the value weighted and equal weighted portfolio returns for each portfolio on a monthly basis (untabulated). [Insert Table 1: Summary Statistics] Table 1 presents the summary statistics of the five Book-to-Market sorted portfolios, the five R&D intensity sorted portfolios and the 3x3 BM*RD independent double-sorted portfolios. Consistent with the empirical findings of Fama and French (1996) and others, stocks with higher book-to-market ratio have higher returns. In addition, consistent with Hansen, Heaton and Li (2005) s findings, firms with lower book-to-market are associated with higher R&D intensity. However, in the portfolios sorted on R&D intensity, stock returns increase with R&D intensity except for the portfolio with the highest R&D, which is same as the findings of Chan, Lakonishok and Sougiannis (2001). These summary statistics implies that the heterogeneity in the intangible capital, otherwise the low expected return of low B/M portfolio suggest firms with

11 more intangible capital earn lower return, while the high expected return of R&D intensive firms suggest that the return of intangible capital is higher than that of physical capital. The contradictory relationship between intangible capital and returns suggests that there exists a fundamental difference in the intangible capital measured by B/M and R&D intensity. Furthermore, the link with intangible capital and stock returns is clearer in Table 1 Panel C, when the stocks are independently sorted into the 3x3 portfolios based on B/M and R&D intensity. Within each R&D intensity sorted group, stocks with higher book-to-market ratio have higher returns. More importantly, within each B/M sorted group, stock return increases monotonically with R&D intensity, which suggests it is important to control for the level of B/M to disentangle the relationship between stock returns and R&D intensity. The raw return pattern presented in Table 1 is consistent with our arguments about the heterogeneity of intangible capital in term of risk and return. Firms with low book-to-market ratio and high R&D intensity carry more intangible capital while their stock return patterns are different. Firms with low Book-to-Market ratio carry more embodied intangible capitals, which is already embodied and used in the process of production and stably contribute to future cash flows, therefore the market value of the firm is relatively high compared with firms with same level of book value of physical capital but low level of embodied intangible capital. Whereby firms with high R&D intensity own more developing intangible capital, which are riskier and yet to be used in firms production, and investors demand higher risk premium. Table 1 also shows that B/M and R&D are not perfect proxies for the two types of the intangible capital, although B/M firms are more likely to have more embodied intangible capital and R&D intensive firms are more likely to have more developing intangible capital. As the two types of intangible capital are closely related to each other, firms with low B/M or high R&D intensive may own more of both types of intangible capital. In Panel A, firms with low B/M ratios have high R&D intensity, while in Panel B, firms with high R&D intensity have low B/M ratios. The dispersion in R&D intensity of the B/M portfolios is lower than that of the R&D portfolio, whereas the dispersion in B/M of R&D portfolios is lower than that of the B/M portfolio. The patterns remains and becomes slightly stronger in Panel C when the stocks are double sorted into 3x3 portfolios based on B/M and R&D intensity.

12 III. Empirical Results Fama and French (2016) argue that with introduction of factors capture profitability and investment intensity in physical capital, their five-factor model help to explain the cross-section variation of stock returns, especially the low average stock returns associated with high market risk, large share issues, and highly volatile returns. We illustrate in the extended dividend discount model with intangible capital that, the presence of intangible capital complicates the association between expected return and B/M, profitability, and investment intensity in physical capital. Although Fama and French (2015) five-factor model ignores the intangible risk, we find it is still a useful model to disentangle the complexity of the risk and return due to the heterogeneity in intangible capital, as the difference in two types of intangible capital implies different relationship between physical-capital-investment intensity, profitability and stock returns, which can be captured by the differences in the factor loadings in the Fama and French (2015) five-factor model. As Fama (1991) points out, any asset pricing test is a joint test about the market efficiency and the asset pricing model used in the test, the primary objective of our empirical investigation is neither to test the market efficiency nor to test the five-factor model, but to study whether and how do the risk and return implied by the different types of intangible capital differ. That is, the underlying assumption of our empirical analysis is that market is efficient, and the abnormal returns of B/M-R&D-intensity portfolio are the tangible evidences for the missing intangible risk in the asset pricing model. [Insert Table 2: Alpha and the Adjusted R 2 of R&D Portfolios] Table 2 presents the alphas of the portfolios sorted on R&D intensity in the regression of equally-weighted portfolio returns on the Fama-French three and five-factor models. Panel A reports the alphas and adjusted R-square for the Fama-French five-factor model and Panel B reports the alphas and R-square for the Fama-French three-factor model for comparison. In both models, the alphas of R&D portfolios are not positively associated with the R&D intensity. In particular, stocks in the highest R&D intensity quintile do not earn significantly higher return than the stocks in the other quintiles, although the volatility of the return increases with R&D intensity. Chan, Lakonishok and Sougiannis (2001) find similar results, and they interpret this result as the undervaluation of R&D-intensive stocks due to the market pessimistic opinion about

13 their prospects. However, as we show later, the return and risk of R&D-intensity portfolios are both positively associated with R&D intensity as long as the level of B/M is controlled. [Insert Table 3: Alpha and the Adjust R 2 of BM*RD portfolios] Table 3 presents the alphas of the 3x3 double sorted portfolios based on B/M and R&D intensity. Panel A reports the alphas and adjusted R-square for the Fama-French five-factor model and Panel B reports the alphas and R-square for the Fama-French three-factor model for comparison. In the five-factor model, controlling for B/M, firms with higher R&D intensity have higher alphas; controlling for R&D intensity, low Book-to-Market value firms have lower alphas. This result is consistent with our model implication H1.a and H2.a. Note that value premium is robust in both five-factor and three-factor models, with or without controlling for R&D. However, controlling for B/M is the key to identify the positive association of R&D intensity and average return. In particularly, for firms with both higher value of embodied and developing intangible capital, the opposite effect on returns of the two types of intangible capital makes the relationship between return and R&D ambiguous. This explains the pattern we find in Table 1 that the return of portfolio with highest R&D intensity is actually low, and in the three-factor model, the returns of portfolios in lowest B/M group are not significantly positively associated with R&D intensity. Although the three-factor and the five-factor models have explicitly used the HML as a risk factor, we still find significantly higher alphas for firms with higher B/M in the double sorted portfolios. This result implies that the B/M is a noisy proxy for embodied intangible capital. Prior studies have proposed various explanations on the higher return for high Book-to-Market firms. For example, Fama and French (1992, 1996) propose that firms with high Book-to-Market ratio are likely to be relatively distressed and irrational pricing causes the high premium. Zhang (2005) proposed a theoretical model to justify that the assets in place are riskier than growth options, therefore contribute to the risk premium of the value premium. We explain the value premium from the perspective of intangible capital. In general, firms with lower Book-to- Market ratio are believed to have higher embodied intangible capitals, but since return to embodied intangible capital provides a good hedge against firms risk associated to long-run economic activities as showed in An and Li (2016), these firms pay lower cost of capital or

14 investors demand lower risk premium. On the other hand, the developing intangible capital is not yet used in firms production and associated with substantial uncertainty and risk, hence investors ask for higher risk premium. The higher return and alphas from portfolios with high R&D intensity potentially suggest that the intangible capital held by R&D intensive firms are more likely to be associated with the developing intangible capital. Fama and French (2015) find that their five-factor model fails to capture the low average returns on small stocks whose returns behave like those of firms that invest a lot despite low profitability. This result is actually consistent with our arguments that small firms that invest a lot despite low profitability are more likely to be the firms with lots of embodied intangible capital and the stock return is low due the low expected return of embodied intangible capital. The adjusted R-squares presented in Table 3 suggest the five-factor model has a better explanatory power in the double sorted portfolios based on B/M and R&D intensity, especially for the portfolios with high R&D intensity. The Fama-French three-factor model for the highest B/M and highest R&D intensity portfolio is only 51%, as compared to 78% in the five-factor model. The results indicate that the additional two factors in the five-factor model provide additional explanatory power to explain the return heterogeneity of portfolios sorted based on the proxies of intangible capital. Note that the significant alphas in the 3x3 portfolios still suggest that neither the three nor five-factor models can fully capture the cross-section return variation due to differences in intangible-capital intensity. We examine furthermore how the two additional factors in the five-factor model help to disentangle the risk and risk premium of different types of intangible capital. The two additional factors are the RMW (Robust minus Weak operating profitability) and CMA (Conservative minus Aggressive investment). Table 4 presents the regression coefficients of the regression of the portfolios returns on Fama French five-factor models. [Insert Table 4: Factor Loadings of the BM*RD Portfolios in the Fama-French Five-Factor Model] Table 4 Panel D shows that the RMW factor loadings decrease monotonically as R&D intensity increases, and the effect is significant across all B/M sorted groups. However, the five-

15 factor exposure to RMW does not decreases nor increases with B/M, within each R&D intensity group. These patterns of coefficients on RMA are consistent with our model implication. The profitability factor (RMW) embraces the differences in risk premium of robust and weak profitability firms. Firms with more developing intangible capital (measured by higher R&D/Sale) spend more on innovation and idea generating process, research and development, which are incurred as costs, subject to huge risk and uncertainty, and do not generate stable revenue before they are put into production. Therefore, the earnings of R&D intensive firms appear to be weaker due to high expensed investment in developing intangible capital and high risk. Controlling for the level of B/M, the five-factor exposures to RMW decreases from positive to negative with R&D intensity as shown in Table 4 Panel D, that is, firms with high R&D-to- Sales appear to be less profitable firms. On the other hand, the coefficients on the profitability (RMW factor) are not associated with B/M ratio, which implies that firms with more embodied intangible capital do not necessarily appear to be more profitability. The embodied intangible capital has been used in the process of production, such as the upgraded processes, patents, branding and other improvement of the firms production process. It does generate robust and sustainable profits, but the investment in embodied intangible capital is expensed, deducted from the earnings. Hence firms with more embodied intangible capital (low B/M ratio) do not necessarily appear to more profitable or less profitable, even controlling for the level of R&D intensity. Table 4 Panel E shows the five-factor exposure to CMA change from negative to positive from the lowest B/M group to the highest B/M group, and the effect prevails across all R&D sorted groups; while association of R&D intensity and the factor loadings on CMA is not clear within each B/M group. These patterns of coefficients on CMA are again consistent with our model implication. The (physical-capital) investment factor (CMA) embraces the differences in risk premium of conservative and aggressive investment firms. Since embodied intangible capital and physical capital are complimentary production factors, more investment in embodied intangible capital must be accompanied by more aggressive physical capital investment. Hence firms with more embodied intangible capital (lower B/M) are firms invest more in physical capital, that is, a more negative five-factor exposure to CMA. On the other hand, we do not find clear relationship between the coefficients on the physical investment (CMA factor) and R&D intensity. Since developing intangible capital is yet to enter the production function as a

16 complimentary factor to the physical capital, intensive investment in developing intangible capital does not have to be accompanied by the aggressive investment in physical capital, and there is not a clear link between the R&D intensity and investment intensity in physical capital. The three traditional risk factor loadings (β, s, h) of the double sorted portfolios are also reported in Table 4. The coefficient on market risk (β) is higher for firms with more R&D intensity. It is consistent with our argument that firms with more developing intangible capital are subject to more risks, so that they carry higher betas. The positive loadings on the SMB and negative loadings HML factors indicate firms with higher R&D intensity tend to be smaller firms with lower B/M ratios. Firms with more developing intangible capital that are yet to be used in productions are usually in their early stage of life cycles. These firms are expected to have smaller size and carry higher risks. The higher loadings for higher R&D firms indicate that the SMB factor also partially explains the premium carried by the developing intangible capital. Moreover, as neither B/M nor R&D intensity are perfect measures of the two types of intangible capital which are likely to be positively correlated. That is, firms with more embodied intangible capital are likely to have more developing intangible capital, hence firms with high R&D intensity may have lower B/M, which means a more negative loading on HML for firms with higher R&D intensity. Fama and French (2015) find that the value factor HML become redundant after adding the profitability (RMW) and investment (CMA) factors. Table 5 presents the Alphas and adjusted R- squares for the double sorted portfolios. Consistent with the findings of Fama and French (2015), removing the HML factor does not have material impact on the alphas and explanatory power (R-squares) of our double sorted portfolios based on R&D intensity and B/M. [Insert Table 5: Alphas and Adjusted R 2 of BM*RD Portfolio in Four Factor Model] Since neither B/M nor R&D intensity is a perfect measure for the two types of intangible capital, their correlations might have introduced noises in our tests. To examine the robustness of our results, instead of conducting independent sorting, we repeat our tests in two controlled double sorting. In the first controlled 3x3 portfolios, we first sort all companies into three equal sized portfolios by their book-to-market ratio, and then sort the companies in each of the previously sorted three portfolios by their R&D intensity. In the second controlled 3x3 portfolios,

17 we first sort all companies into three portfolios by their R&D intensity, and then sort the companies in each of the previously sorted three portfolios by their book-to-market ratio. The alphas and R-squares for the tests are reported in Table 6. Table 6 indicates our prior results are robust to the correlation between B/M and RD intensity. [Insert Table 6: Alphas and Adjusted R 2 for RD-then-BM and BM-then-RD Sorted Portfolios] In an independent research, Hou, Xue and Zhang (2015) also find that factors that proxy for profitability and investment intensity help to explain the cross-section return variations and propose a Q-factor asset pricing model. In Table 7, we report the alphas and the adjusted R- squares of regressing R&D and B/M double sorted portfolio returns on the four factors of Hou, Xue and Zhang (2015) 6. We still find that controlling for B/M, firms with higher R&D intensity have higher alphas, and controlling for R&D intensity, low Book-to-Market value firms have lower alphas, same as what we find in Table 3 using Fama-French five factor model. [Insert Table 7: Alpha and the Adjust R 2 of BM*RD portfolios (Q-factor model)] Firms with high investment low profitability are the ones with more embodied intangible capital, hence they should have the lowest B/M. While the difference between B/M of low and high investment represents the importance of embodied intangible capital, the difference should be higher for firms with lower profitability. Using the portfolios sorted by size, investment and profitability (i.e. Fama-French Size_INV_OP 2*4*4), Figure 3 presents the difference between low and high investment firms in the high profit portfolio (OPHigh) and low profit portfolio (OPLow). The differences are statistically significant in both small and big firms, and particularly in small firms (t = 8.15). Figure 3 further support our argument of using B/M as a noisy proxy for embodied intangible capital. IV. Conclusion Intangible investments include not only risky research and development (R&D) expenses to discover or invent new products or technology, but also investments to implement the feasible technology progress or improve the existing technology. These two types of intangible capital 6 We thank Zhang Lu for kindly providing us the data on Q-factors.

18 differ substantially in term of risk and return. Firms with relatively more embodied intangible capital have lower book-to-market ratio and earn lower expected return, while R&D-intensive firms tend to earn higher expected return. We find that the link between B/M and intangible capital is the key to decipher the intangible risk. Furthermore, recognizing the difference in the two types of intangible capital is essential to understand the coexistence of value premium and excess return of R&D-intensive stocks. The developing intangible capital accumulated through research and development expenses is much more risky than that of the investment in the physical capital, hence the investors demand for higher risk premium; the embodied intangible capital helps the firm to improve the productivity and earn robust profit, and the investors bid up the price of firm s stock and require less expected return. Figure 3 B/M Difference between Low-Investment and High-Investment Firms in High-Profitability and Low-Profitability portfolios BMDiff(Low INV - High INV)_OPLow BMDiff(Low INV - High INV)_OPHigh Recognizing the difference in the two types of intangible capital also helps us to better understand the anomalies of asset pricing models. Fama and French (2015) find that their fivefactor model fails to capture the low average returns on small stocks whose returns behave like those of firms that invest a lot despite low profitability. We argue that this actually consistent with our model implication that small firms that invest a lot in physical capital despite low profitability are more likely to be the firms with lots of embodied intangible capital, and they

19 invest aggressively in physical capital to accompany the investment in embodied intangible capital, and their earnings appear to be weak because investment in embodied intangible capital is large and is deducted from the profits as expenses. The stock returns of these firms are low because of the low expected return of embodied intangible capital. The findings of Chan, Lakonishok and Sougiannis (2001) that R&D to sales ratio not associated with the average historical stock returns can be rationalized in our framework as well. The high level of spending on R&D may be associated with high level of investment in embodied intangible capital, which implies that we may not find direct link between R&D spending and future stock returns. After controlling for the level of embodied intangible capital by controlling for the B/M, we find R&D intensive firms earn significantly higher return than firms with low R&D spending. The lack of accounting information on intangible capital makes it complicated to evaluate stock prices and assess the risk and return of stocks and investment. However, it is possible to impute the unobserved intangible capital from observed data and disentangle anomalies in the stock market with the help of reasonable economic models. Furthermore, the controlling the long-run risk of the embodied intangible capital through B/M ratio is the key to rationalize the B/M and R&D anomalies in the stock market and potentially other anomalies related to various forms of intangible capital, such as customer satisfaction (Fornell, Morgeson, and Hult 2016), employee satisfaction (Edmans 2011), advertising (Chan, Lakonishok, and Sougiannis,2001), patent citation (Deng, Lev, and Narin,1999), software development (Aboody and Lev,1998). To better evaluate a company or assess the risk of a stock, investors should pay attention to not only the accounting information and proxies for intangible capital, but also the different roles of research and development expenses play in the production process. The empirical findings in this paper suggest that it is crucial to recognize the heterogeneity in capital in asset pricing studies. The seeming anomalies in the stock market might be mistakenly characterized as evidences for behaviour bias or market inefficiency, if the importance differences in risk and return of different types of intangible capital are ignored.

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