The Tangible Risk of Intangible Capital. Abstract

Transcription

1 The Tangible Risk of Intangible Capital Nan Li Shanghai Jiao Tong University Weiqi Zhang University of Muenster, Finance Center Muenster Yanzhao Jiang Shanghai Jiao Tong University 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 assessment of risk and return of investments. We exploit the return heterogeneity of firms with different book-to-market ratio (B/M) and intensity in research and development (R&D) to study the importance of intangible capital in explaining the link between stock return and risk priced in the market. We find tangible evidences that the unobserved risk in different types of intangible capital is the key to rationalize B/M and R&D anomalies in the stock market. R&D expenses (developing intangible capital) to discover new technology and new products should be evaluated differently from the 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.

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. 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 statistics1. 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. Financial economists also document anomalies in the stock market related to the increasing importance of intangible capital. Empirical evidences based on limited accounting information suggest that intangible investment is riskier and earns abnormally higher expected return. Hall 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 (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. 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. Hansen, Heaton and Li (2005) 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. 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) argue that changes in the inferred values of intangibles 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) are among the first to study imputed risk and return to intangible capital from data on stock market value and macroeconomic variables in a neoclassical model with uncertainty, where intangible capital and physical capital are a complimentary production factors. They show that return to intangible investment provides good hedge to the long-run risk and has lower expected return.

4 Figure 1. Value of U.S. Equity and Debt Claims on Nonfarm, Nonfinancial Corporations as a Ratio to GDP, Inspired by the findings of previous literature on intangible capital, we exploit the return heterogeneity of firms with different book-to-market ratio (B/M) and intensity in research and development (R&D) to study the importance of intangible capital in explaining the link between stock return and risk. Furthermore, we propose to differentiate intangible capital as two types, developing and embodied. Developing intangible capital is associated with discovering or developing new products 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 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

5 embodied intangible capital are lower, that is, B/M ratio may serve as a noisy proxy for embodied intangible capital intensity. To understand the relationship between book-to-market ratio and embodied intangible capital intensity. we can 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) (1) 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, D t m Y * t Bt (2) In this equation, * Y Y B is total equity earnings which equal marginal product of capital t t u t minus the change in book value of intangible capital. m m m Bt Bt B t 1 is the change in total book equity, which equals to the change in book value of measured physical capital. 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) 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 expected return, expected profitability, expected investment in physical capital and intangible capital intensity. First, fixed everything in (3) except for the current stock price and book value of physical capital. Then a higher book-tomarket equity ratio implies a higher book value of physical capital and lower intangible capital

6 intensity. Next, fixed everything in (3) except for the current stock price and expected return or composite cost of capital. Then a higher book-to-market equity ratio still implies a higher expected return or cost of capital, same as the model without intangible capital. Hence, B/M ratio is a noisy proxy for embodied intangible capital intensity and expected return. 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 low 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 earn higher expected return and are R&D intensive, as developing intangible capital is associated with high risk/uncertainty, volatile/weak earnings, less aggressive investment in physical capital. 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 likely that R&D intensive firms may also own a lot of embodied intangible capital, hence without controlling for the level of embodied intangible capital, there may not be a direct link between R&D spending and expected return. This may explain the puzzling findings of Chan, Lakonishok and Sougiannis (2001) that R&D intensity is positively associated with return volatility but has no direct link to future stock returns. As data on a firm s aggregate intangible capital or each type of the intangible capital is missing, we propose two imperfect measures 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 earning help us to identify the importance of the embodied intangible capital. Hence

7 we apply the five-factor asset pricing model of Fama and French (2015) to test our model implications 2. More specifically we test the following hypothesis: 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 Hypothesis 1.a: Controlling for B/M ratio, the R/D sales is positively associated with risk-adjusted return. Hypothesis 1.b: Controlling for B/M ratio, the R/D sales is negatively associated with profitability. Hypothesis 1.c: Controlling for B/M ratio, the R/D sales is negatively associated with investment in physical capital. Hypothesis 2.a: Controlling for R/D sales, B/M is positively associated with riskadjusted return. 2 In an independent research of Hou, Xue, and Zhang (2015), they also propose to add profitability and investment intensity in physical capital in the factor asset pricing model.

8 Hypothesis 2.b: Controlling for R/D sales, B/M is negatively associated with profitability. Hypothesis 2.c: Controlling for R/D sales, B/M is negatively associated with investment in physical capital. We discuss the details of data construction in section II. Section III test hypothesis developed above using factor asset pricing models and discusses the results of empirical analysis. Section IV concludes. 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 1975 to 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 3*3 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 5*5 portfolios, but the number of firms will be substantially reduced in each portfolio, thus, we use 3*3 independent sort portfolios in our benchmark model. 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. [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 3*3 BM*RD independent sort portfolios. Consistent

9 with Fama and French (1996) and others empirical evidence, 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 consistent with 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 more intangible capital earn lower return, while high expected return of R&D intensive firms suggest that risk and return of intangible capital is higher than that of physical capital. Furthermore, the link with intangible capital and stock returns is clearer in Table 1 Panel C, when the stocks are independently sorted into the 3*3 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

10 ratios. The dispersion in R&D intensity of the BM portfolios is lower than that of the RD portfolio, whereas the dispersion in B/M of R&D portfolios is lower than that of the BM portfolio. The patterns remains and becomes slightly stronger in Panel C when the stocks are double sorted into 3*3 portfolios based on B/M and R&D intensity. 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 our model predicts that Fama and French five-factor model may fail to explain the cross-section variation of stock with different intangible-capital intensity, we find it is fruitful to use the five factor to disentangle the complexity of the risk and return due to the heterogeneity in intangible capital. In this section, we use Fama and French (2015) five-factor model to study the effect of the two types of intangible capitals on stock returns and test the implications of the model with intangible capital. While our primary objective is examine whether and how do the risk and return implied by the different types of intangible capital differ, we also test whether five factor model can correctly price the stock of firms own different amounts of embodied and developing intangible capital. [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 model, 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

11 intensity. Chan, Lakonishok and Sougiannis (2001) find similar results, and they interpret this result as the undervalue of R&D-intensive stocks due to the market pessimistic opinion about their prospects. However, as we show later, when we control for the level of B/M, the return and risk of R&D-intensity portfolios are both positively associated with R&D intensity. [Insert Table 3: Alpha and the Adjust R 2 of BM*RD portfolios] Table 3 presents the alphas of the 3*3 BM*RD double sorted portfolios. 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 and other priced factors 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 return 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 BM*RD 3*3 double sorted portfolios. This results implies that the B/M is a noisy proxy for embodied 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. We argue that this 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.

12 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 Bookto-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 Bookto-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 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. The adjusted R-squares presented in Table 3 suggest the five factor model has better explanatory power in the double sorted BM*RD 3*3 portfolios, 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 FF5 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 3*3 portfolios still suggest 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

13 in the Fama-French Five Factor Model] Table 4 shows that the RMW factor loadings decrease monotonically as R&D intensity increases, and the effect is significant across all B/M sorted groups, which is consistent with our model implication H1.b. In addition, the CMA factor loadings 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, supporting our model implication H2.c. The patterns of coefficient on RMA and CMA are consistent with our proposed separation of embodied and developing intangible capital and using book-to-market and R&D intensity to proxy for these two types of intangible capital. The RMW factor embraces the differences in risk premium of robust minus 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, and subject to huge risk and uncertainty, do not generate revenue before they are putting into production. Therefore, the profitability premium decreases as R&D intensity increases, and it partially explains the premium by firms with higher developing intangible capital. On the other hand, the embodied intangible capital has been used in the process of production. The upgraded processes, patents, branding and other improvement of the firms production process, which generates robust and sustainable profit. Since embodied intangible capital and physical capital are complimentary production factors, more investment in embodied capital has be accompanied by more aggressive physical capital investment. The negative coefficient on CMA for firms with low B/M capture the increases physical investments from firms with high embodies intangible capital. We do not find strong empirical evidence to support our model implication H1.c and H2.b. That is, 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 earn robust earning. Note that according to the current US accounting standard, investment in embodied intangible capital are deducted from the revenue as expenditure. Hence the after-expenditure profit of the firm with more embodied intangible capital may appear weak, although its actual earning is robust if intangible investment is not expensed. In addition, we do not find clear relationship between the coefficients on the physical investment (CMA factor) and R&D intensity. Since developing intangible capital does not enter into the production function as a

14 complimentary factor to the physical capital, increases in developing intangible capital does not have to be accompanied by the increase in physical-capital investment. 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 more risks, so that they should carry higher betas. As the developing intangible capital carries higher market risk premium and higher alpha, it would be more suitable for investors pursing for high risk and high return. The loadings on the SMB and HML factors indicate firms with higher R&D intensity are tend to be smaller firms with lower B/M ratio. 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 loading for higher R&D firms indicates that the SMB factor also partially explains the premium carried by the developing intangible capital. Moreover, as neither B/M nor R&D are perfect measures of the two types of intangible capital, and both of them correlate to firms intangible capital, it is nature to expect the negative relationship between B/M and R&D, which explains the 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 (with HML removed)] 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 3*3 portfolios, we first sort all companies into three equal

15 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 3*3 portfolios, 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] IV. Conclusion With the rise of the importance 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 assessment of risk and return of investments. We exploit the return heterogeneity of firms with different book-to-market ratio (B/M) and research and development (R&D) expenses to study the nature of intangible capital and find tangible evidences that there exist heterogeneity in the intangible capital in term of their in the process of production and risk. 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 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.

16 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. 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, hence they invest aggressively in physical capital to accompany the investment in embodied intangible capital, and their profit appears to be weak because investment in embodied intangible capital is large and is deducted from the profit 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 risk in the unobserved different types of intangible capital is the key to rationalize the B/M and R&D anomalies in the stock market. To better evaluate a company or assess the risk of a stock, investors should pay attention to not only the accounting information, but also the different roles of research and development expenses play in production process. References: An, Sungbae and Li, Nan, Measuring Intangible Capital with Uncertainty, working paper. Hall, Bronwyn H The Stock Market s Valuation of R&D Investment during the 1980 s, American Economic Review 83,

17 Hall, Bronwyn H. and Hall, Robert E., The Value and Performance of U.S. Corporations, Bookings Papers on Economic Activity 1, Hall, Robert E., 2001a. The Stock Market and Capital Accumulation. American Economic Review, 91(5): Hall, Robert E b. "Struggling to Understand the Stock Market." American Economic Review, 91(2): Chan, L. K. C., Lakonishok, J. and Sougiannis, T. (1998), The Risk and Return From Factors, Journal of Financial and Quantitative Analysis 33, 1998, Chan, L. K. C., Lakonishok, J. and Sougiannis, T. (2001), The Stock Market Valuation of Research and Development Expenditures. Journal of Finance 56, Cochrane, J. H. (1991), Production-Based Asset Pricing and the Link Between Stock Returns and Economic Fluctuations. Journal of Finance 46, Daniel, K., Titman, S., Market Reactions to Tangible and Intangible Information. Journal of Finance 61, Fama, E., French, K.,1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, Fama, E., French, K., Size and book-to-market factors in earnings and returns. Journal of Finance 50, Fama, E., French, K., Profitability, investment, and average returns. Journal of Financial Economics 82, Fama, E. F., and K. R. French A Five-Factor Asset Pricing Model. Journal of Financial Economics 116, Fama, E., French, K., Dissecting Anomalies with a Five-Factor Model. Review of Financial Studies 29,

18 Fama, E., and MacBeth, J., Risk, Return and Equilibrium: Empirical Tests, Journal of Political Economy, 1973, Hansen, Lars Peter, Heaton, John C. and Li, Nan, Intangible Risk?, Measuring Capital in the New Economy, edited by Carol Corrado, John Haltiwanger and Dan Sichel, Chicago, University of Chicago Press, Hansen, Lars Peter, Heaton, John C. and Li, Nan, Consumption Strikes Back? Measuring Long-Run Risk, Journal of Political Economy 116, Hirshleifer, David, Hsu, PoHsuan and Li, Dongmei, Innovative Efficiency and Stock Returns, Journal of Financial Economics 107, Haugen, R., Baker, N., 1996, Commonality in the determinants of expected stock returns. Journal of Financial Economics 41, Harvey, C.,Y. Liu, and H. Zhu and the cross-section of expected returns. Review of Financial Studies 29, 5-68 Hou, K., Xue, C., Zhang, L., Digesting Anomalies: An Investment Approach. Review of Financial Studies 28, Li, Nan, Intangible Capital and Stock Market, Ph.D. thesis, Department of Economics, The University of Chicago. Lintner, J., The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics 47, Loughran, T., Book-to-market across firm size, exchange, and seasonality: Is there an effect? Journal of Financial and Quantitative Analysis 32, McGrattan, Ellen R. and Edward C. Prescott Is the Stock Market Overvalued? NBER Working Paper McGrattan, Ellen R. and Edward C. Prescott Unmeasured Investment and the Puzzling US Boom in the 1990s. American Economic Journal: Macroeconomics, 2(4):

19 Merton, R., An Intertemporal Capital Asset Pricing Model. Econometrica 41, Miller, M., Modigliani, F., Dividend policy, growth, and the valuation of shares. Journal of Business 34, Novy-Marx, R., The other side of value: The gross profitability premium. Journal of Financial Economics 108, Titman, S., Wei, K., Xie, F., Capital investments and stock returns. Journal of Financial and Quantitative Analysis 39,

20 Table 1: Summary Statistics Sample period: July 1976 December At the end of each June, stocks are allocated to equally sized portfolios base on their characteristics. B/M is book value of equity at the end of the fiscal year ending in year t-1 divided by market value of the firm at the end of December of year t-1. R&D intensity is measured using R&D expenses divided by sales at the end of the fiscal year ending in year t-1. Panel A presents the summary statistics (average and standard deviation of equally-weighted monthly returns, average number of firms, average firm size in logs, average B/M, average R&D intensity) for the 5 Book-to-Market sorted portfolios (1 to 5 - low to high). Panel B presents the summary statistics for the 5 R&D intensity sorted portfolios, Panel C presents the summary statistics of the 3*3 independent sorted portfolios based on B/M and R&D intensity. BM1 BM2 BM3 Panel A: BM Portfolios BM1 BM2 BM3 BM4 BM5 Average Return(%) Return Std. Dev.(%) Sample size Firm Size (in logs) B/M R&D Intensity Panel B: RD Portfolios RD1 RD2 RD3 RD4 RD5 Average Return(%) Std(Ret) Sample size Firm Size (in logs) B/M R&D Intensity Panel C: BM*RD portfolio RD1 RD2 RD3 Average Return(%) Std(Ret) Sample size Firm Size (in logs) B/M R&D Intensity Average Return(%) Std(Ret) Sample size Firm Size (in logs) B/M R&D Intensity Average Return(%) Std(Ret) Sample size Firm Size (in logs) B/M R&D Intensity

21 Table 2: Alpha and the Adjust R 2 of R&D Portfolios Sample period: July 1976 December At the end of each June, stocks are allocated to equally sized portfolios base on R&D intensity, where R&D intensity is measured using R&D expense divided by sales at the end of the fiscal year ending in year t-1. We regress the monthly portfolio returns on the Fama-French three-factor and fivefactor model respectively. Panel A presents the alphas (in percentage) and adjusted R 2 for the three factor model and Panel B presents the alphas and adjusted R 2 for the five factor model. The factors are obtained from Kenneth French website. Panel A: Fama French Three Factor Model RD1 RD2 RD3 RD4 RD5 Alpha(%) *** 0.57*** 0.32 t-statistic Adjusted R Panel B: Fama French Five Factor Model Alpha(%) *** 0.90*** 0.79*** t-statistic Adjusted R

22 Table 3: Alpha and Adjusted R 2 of BM*RD Portfolios From July 1976 to December 2015, at the end of each June, stocks are allocated to 3*3 independent sorted BM and RD portfolios. B is book equity at the end of the fiscal year ending in year t-1 and M is market cap at the end of December of year t-1. R&D intensity is measured using R&D expense divided by sales at the end of the fiscal year ending in year t-1. We regress the monthly portfolio returns on the Fama-French three-factor and five-factor model respectively. Panel A presents the alphas (in percentage) and adjusted R 2 for the three factor model and Panel B presents the alphas and adjusted R 2 for the five factor model. The factors are obtained from Kenneth French website. Panel C presents the statistical significance of the portfolio returns for the highest and lowest BM and RD portfolios, respectively. Panel A: Fama-French Five Factor Model Alpha(%) RD1 RD2 RD3 RD3-RD1 BM t(alpha) BM t(alpha) BM t(alpha) BM3-BM t(alpha) Adjusted R 2 RD1 RD2 RD3 BM BM BM Panel B: Fama-French Three Factor Model alpha(%) RD1 RD2 RD3 BM t(alpha) BM t(alpha) BM t(alpha) Adjusted R 2 RD1 RD2 RD3 BM BM BM

23 Table 4: Factor Loadings of BM*RD Portfolios in Fama-French Five Factor Model From July 1976 to December 2015, at the end of each June, stocks are allocated to 3*3 independent sorted BM and RD portfolios. B is book equity at the end of the fiscal year ending in year t-1 and M is market cap at the end of December of year t-1. R&D intensity is measured using R&D expense divided by sales at the end of the fiscal year ending in year t-1. We regress the monthly portfolio returns on the Fama-French five-factor model. This table presents the factor loadings from the regression. Rm-RF is the value-weight return on the market portfolio minus the one-month Treasury bill rate; SMB (small minus big) is the size factor; HML (high minus low B/M) is the value factor; RMW (robust minus weak OP) is the profitability factor; and CMA (conservative minus aggressive Inv) is the investment factor. RD1 RD2 RD3 RD1 RD2 RD3 β (Rm-Rf) r (RMW) BM t-stat BM t-stat BM t-stat s (SMB) c (CMA) BM t-stat BM t-stat BM t-stat h (HML) BM t-stat BM t-stat BM t-stat

24 Table 5: Alphas and Adjusted R 2 of RD*BM Portfolios in the Four-Factor Model (remove HML) From July 1976 to December 2015, at the end of each June, stocks are allocated to 3*3 independent sorted BM and RD portfolios. B is book equity at the end of the fiscal year ending in year t-1 and M is market cap at the end of December of year t-1. R&D intensity is measured using R&D expense divided by sales at the end of the fiscal year ending in year t-1. We regress the monthly portfolio returns on a four factor model (Fama-French five-factor model without the HML factor). This table presents the Alphas and R-squares of the four factor model regressions. Alpha RD1 RD2 RD3 BM1 REMOVE HML t-stat BM2 REMOVE HML t-stat BM3 REMOVE HML t-stat Adjusted R 2 RD1 RD2 RD3 BM1 KEEP HML REMOVE HML BM2 KEEP HML REMOVE HML BM3 KEEP HML REMOVE HML

25 Table 6: Alphas and Adjusted R 2 of RD-then-BM and BM-then-RD Sorted Portfolios From July 1976 to December 2015, at the end of each June, stocks are allocated to 3*3 BM then RD sorted or RD then BM sorted portfolios. For the BM then RD sorted portfolios, stocks are allocated to three equally sized portfolios based on B/M first, and then within each of these three portfolios, stocks are further allocated to three equally sized portfolios based on their R&D intensity. For the RD then BM sorted portfolios, stocks are allocated to three equally sized portfolios based on RD intensity first, and then within each of these three portfolios, stocks are further allocated to three equally sized portfolios based on their B/M. B is book equity at the end of the fiscal year ending in year t-1 and M is market cap at the end of December of year t-1. R&D intensity is measured using R&D expense divided by sales at the end of the fiscal year ending in year t-1. We regress the monthly portfolio returns on the Fama-French five-factor model. This table presents the alphas (in percentage), t-statistics and adjusted R 2 for the regressions. BM then RD RD then BM alpha(%) RD1 RD2 RD3 RD1 RD2 RD3 BM t(alpha) BM t(alpha) BM t(alpha) Adjusted R 2 RD1 RD2 RD3 RD1 RD2 RD3 BM BM BM