There is a Growth Premium After All

Transcription

1 There is a Growth Premium After All Yuecheng Jia Shu Yan Haoxi Yang January 16, 2018 Abstract The conventional wisdom argues that the growth stocks are more risky to earn higher premium. However the empirical evidence points out that the value stocks, which are classified based on the Book-to-Market ratio, tend to have higher premium. To solve for this tension, this paper decompose the Book-to-Market ratio into two components, trend component and innovation component. Both economic interpretation and empirical results show the innovation component has a strong negative relation with future cross sectional stock returns even after controlling for main return predictors including Book-to-Market ratio, while the trend component is positively correlated with value premium. Therefore, consistent with conventional wisdom, our results confirm that there is growth premium captured by the innovation component of Book-to-Market ratio. We would like to thank helpful comments from Jushan Bai, Rui Chen, Dashan Huang, Fuwei Jiang, Weiping Li, Hong Liu, Linlin Niu, Guofu Zhou, and seminar participants at the Central University of Finance and Economics, Southwest Jiaotong University, IFABS 2017 Oxford Conference, Naikai University Young Scholar Forum, University of Glasgow, WISE at Xiamen University for helpful comments. All errors are our own. Jia is at Chinese Academy of Finance and Development, Central University of Finance and Economics, Changping, Beijing, China; jiayuecheng@cufe.edu.cn. Yan is at the Spears School of Business, Oklahoma State University, Stillwater, Oklahoma, USA, 74074; yanshu@okstate.edu. Yang is at School of Finance, Nankai University, Tianjin, China; haoxi.yang@outlook.com.

2 There is a Growth Premium After All Abstract The conventional wisdom argues that the growth stocks are more risky to earn higher premium. However the empirical evidence points out that the value stocks, which are classified based on the Book-to-Market ratio, tend to have higher premium. To solve for this tension, this paper decompose the Book-to-Market ratio into two components, trend component and innovation component. Both economic interpretation and empirical results show the innovation component has a strong negative relation with future cross sectional stock returns even after controlling for main return predictors including Book-to-Market ratio, while the trend component is positively correlated with value premium. Therefore, consistent with conventional wisdom, our results confirm that there is growth premium captured by the innovation component of Book-to-Market ratio. JEL Classification: G12 keyword: Book-to-Market ratio, The intensity of Book-to-Market ratio, Growth Option, Return Predictability

3 1 Introduction Conventional wisdom suggests that growth stocks, characterized by low book-to-market ratios (B/M ), should earn higher expected returns than value stocks because growth options, which are leveraged positions, are riskier than assets-in-place (e.g., Cox and Rubinstein (1985); Bernardo, Chowdhry, and Goyal (2007)). However, the empirical evidence overwhelmingly points the opposite: Value stocks with high book-to-market ratios earn higher average returns than growth stocks (e.g., Fama and French (1993); Fama and French (1998)). The value premium counter-intuitively implies that assets-in-place are more risky than growth options (e.g., Lettau and Wachter (2007); Zhang (2005)). In this paper, we reconcile the conventional wisdom and the empirical evidence by decomposing the B/M into two components, a temporary component and a persistent trend component. We use the 8-quarter backward looking moving average of the book-to-market (B/M ) ratio as the proxy for the trend component of B/M. The temporary component refers to the difference between current B/M and the persistent trend component. Our baseline results indicate that the temporary component of B/M (I (B/M) ) captures the value of real options in firms and has a strong negative relation with cross sectional stock returns even when controlling for various return predictors. The negative relation between I (B/M) and stock returns indicates a growth premium. In contrast, the trend component of B/M (BM ave ) is positively associated with stock returns. In other words, the value premium concentrates in the BM ave component while the growth premium concentrates in the I (B/M) component. Our decomposition of B/M into the trend and temporary components is motivated by the time series properties of B/M and further strengthened by the real option approach of stock valuation. Our empirical evidence finds that the B/M is both persistent and time varying. A decomposition of B/M into the trend and temporary components naturally fits the time series properties of B/M. Our decomposition is further supported by the conjectures in recent literature such as Gerakos and Linnainmaa (2017), Golubov and Konstantinidi (2016), and Rhodes-Kropf, Robinson, and Viswanathan (2005). 1

4 More importantly, the temporary and trend components are corresponding to different elements in the real option valuation models. Specifically, prior theory of real options decomposes the market equity of firms into two components: the present value of future cash flows from assets-in-place and the value of real options (e.g., Berk, Green, and Naik (1999); Bernardo, Chowdhry, and Goyal (2007); Cochrane (1991); Cochrane (1996); Gomes, Kogan, and Zhang (2003); Hillier, Grinblatt, and Titman (2011)). In the theoretical models, the sequential cash flows from the assets-in-place can be represented by a sequence of constants or a trajectory of cash flows with a fixed growth rate (e.g., Berk, Green, and Naik (1999); Bernardo, Chowdhry, and Goyal (2007)). Thus, the cash flows from assets-in-place can be represented by a drift term (or a deterministic trend) plus a random walk component, which is similar to the settings of a persistent trend component in the time series analysis. Therefore, the trend component of B/M mimics the cash flows from the assets-in-place since it captures the embedded cash flow growth path with the existing assets-in-place. The empirical evidence also supports the relation between the persistent trend component and assets-in-place. Specifically, we find a strong positive relation between the trend component and various irreversibility measures. Given the composition of market equity, we can even back out that the temporary component of B/M is related to the value of growth option. The economic intuition on the association between the value of growth options and the temporary component of B/M can be illustrated through the properties of the growth options and B/M. First, the change in B/M is largely driven by the change in the market equity (e.g., Gerakos and Linnainmaa (2017)). A step further, because the elasticity of a growth option is larger than one, the component of growth opportunities of the market equity dominates the component of assets-in-place when the book value changes. Therefore, the abnormal changes in B/M is driven by the change in the value of growth options and well captured by the temporary component of B/M. When a growth option is exercised, the book value increases but the market equity declines because the option is more valuable when it is alive than being exercised. As higher 2

5 growth opportunities imply higher risk, we posit a negative cross-sectional predictive relation between I (B/M) and future stock returns. We check the return predictability power of I (B/M) and BM ave by using both portfolio sorts and Fama MacBeth regressions approaches. When stocks are sorted on I (B/M) into decile portfolios, the equal weighted average next quarter portfolio return decreases from decile 1 to decile 10. The high minus low (H-L) spread between deciles 10 and 1 is % per quarter (an annualized spread of %) and statistically significant at the 1% level. Value weighting stock returns and adjusting returns by the conventional risk factors can even make the results stronger. The evidence is corroborated by the estimates of Fama MacBeth regressions, even in the presence of other return predictors including B/M itself. To further test the robustness of our results, we also include in our alternative sample only the non-microcap stocks and employ the value weighted least square Fama MacBeth regressions following Green, Hand, and Zhang (2017). Interestingly, in portfolios simultaneously sorted on both I (B/M) and B/M, and in cross sectional regressions of returns at the firm level, the negative I (B/M) effect on returns and positive B/M effect on returns neither drive out nor dominate each other. The growth premium of I (B/M) has important implications on the migration between value and growth stocks. Fama and French (2007a) and Fama and French (2007b) among others find that the value premium can be attributed to the convergence of value and growth stocks using B/M as the benchmark. In other words, growth value) stocks migrate to value (growth) category right after the classification of their value/growth types. However, using B/M as the benchmark cannot justify whether the increase in B/M is contributed to market value destruction or successful transformation of market value to book value. Actually, many of the value (growth) stocks with subsequent migration to the opposite portfolio are the ones with high σ B/M. In contrast, employing I (B/M) as the benchmark increases the bar for a stock with increment in B/M but high σ B/M to join the value group. Consistent with the growth premium implied by I (B/M), we find that the value and growth stocks under our I (B/M) 3

6 classification keep their value growth types instead of migration to the opposite category. In classifying value or growth type by using the I (B/M), we have designed tests to track the future dynamics of fundamentals among different I (B/M) portfolios. Specifically, stocks with high I (B/M) tend to become less profitable and grow less rapidly. On the other hand, stocks with low I (B/M) tend to be more profitable and experience even higher market valuation. In contrast, the value and growth stocks classified by B/M tend to converge after classification. Thus, our results mitigate the critiques on the convergence of value and growth stocks (e.g., Daniel and Titman (1997); Lakonishok, Shleifer, and Vishny (1994)) by showing that both value and growth stocks maintain their types without migration across value and growth portfolios in the subsequent period. Our paper contributes to the literature from at least three aspects. First, our decomposition of B/M demonstrates that growth premium and value premium co exists in the temporary component and the persistent trend component, respectively. Our decomposition adds a new dimension to the existing literature on the decomposition of B/M such as Gerakos and Linnainmaa (2017), Golubov and Konstantinidi (2016), and Rhodes-Kropf, Robinson, and Viswanathan (2005). Second, we demonstrate that to capture the migration between value and growth stocks, one need to simultaneously consider the BM ave corresponding to the value/growth convergence and the I (B/M) component corresponding to the value/growth divergence. Third, the I (B/M) is a novel and strong return predictor which has the potential to be designed for trading strategies. The remainder of the paper proceeds as follows. Section 2 defines I (B/M) and presents a simple extension of the model by Berk, Green and Naik (1999) to show the economic intuition behind I (B/M). Section 3 reports the return predictive power of I (B/M). Section 4 discusses the impact of I (B/M) on stocks migration across value and growth portfolios. Section 5 concludes. 4

7 2 Decomposition of Book-to-Market Ratio 2.1 The definition of I (B/M) and BM ave Before approaching to the decomposition results, we first define the quarterly B/M following Hou, Xue, and Zhang (2015): B/M : Book to market ratio is the ratio of quarterly book equity to quarter end market capitalization. Quarterly book equity is constructed by following Hou, Xue, and Zhang (2015) (footnote 9), which is basically a quarterly version of book equity of Davis, Fama, and French (2000). We consider all NYSE, AMEX, and NASDAQ firms in the CRSP monthly stock return files up to December, In this study, stock return and accounting data are obtained from the CRSP and COMPUSTAT, except financial stocks (four digit SIC codes between 6000 and 6999) and stocks with end of quarter share price less than $1. We further require a firm to have at least 16 quarters of B/M during to be included in the sample. t is the year quarter indicator such as January 1996 and t 1 indicates December Cohen, Polk, and Vuolteenaho (2003) relate today s book-to-market to historical quantities and the changes in the market and book values of equity. Gerakos and Linnainmaa (2017) and Daniel and Titman (2006) use a returns-based book-to-market decomposition and show that the change in market value component is largely responsible for predicting future returns. Golubov and Konstantinidi (2016) show multiples-based market-to-book decomposition interprets value premium. Inspired by their studies and the time-varying properties of B/M presented in Appendix I, we presume that there exists a decomposition of a firm s book-to-market at time t into a persistent trend and a temporary component of the type: B t M t = 1 s s i=1 B t i M t i + ( B t M t 1 s s i=1 B t i M t i ) (1) The trend component is s-period backward looking moving-average of { B }, and the tempo- M 5

8 rary component is the difference between current Bt M t and the trend component. Persistent trend presents the accumulated historical quantities of the book-to-market, i.e. the past information. Temporary component presents the innovation of today s book-to-market to its time-varying historical mean, i.e. the news of firm s future performance. In our empirical test, we define the corresponding persistent trend component and the temporary component of B/M as follows. BM ave = 1 s s i=1 ( B t i M t i ) (2) I (B/M) = B t M t BM ave (3) The persistent trend component is measured by BM ave, which is the previous 8-quarter rolling window moving average of the book-to-market ratio. The temporary component is defined in Equation (3) as the difference between the current book-to-market ratio and the BM ave. High book-to-market today may due to either a high level trend of Bt M t or a large positive innovation at time t. Hence, if a firm is classified as a value firm according to its today s book-to-market, there are two different scenarios. In one scenario, it is a value type of firm from the past and still a value firm at today. In the other scenario, it was a growth type of firm based on firm s past performance, but there is a positive innovation at time t to rise current book-to-market. Today s innovation, I (B/M), is temporary, and would not affect trend component, BM ave, since the increments vanish rapidly. However, if today s innovation is permanent, it would raise the level of the trend from now onwards and the firm tends to be a value firm permanently. Existing empirical studies points out that the value stocks, which are classified based on B/M earn higher premium, which is named as value premium (Fama and French (1993), Fama and French (1998)). Recent studies by Gerakos and Linnainmaa (2017) shows that 6

9 this evidence mistakes an increase in today s book-to-market for the value premium since strong factor structure deliver low pricing errors as the results of luck (Lewellen, Nagel, and Shanken (2010)). Consistent with Gerakos and Linnainmaa (2017) and Gerakos and Linnainmaa (2017), our decomposition results reveals that high book-to-market is not necessarily connected with value premium. Value premium is mainly caused by the trend component of book-to-market, BM ave. High level trend of book-to-market earns higher future returns. Furthermore, we are the first study to show there is also a growth premium, which connect with the innovation of book-to-market, i.e. the temporary component I (B/M). To understand the sources of both value and growth premium, we provide economic intuition and theoretical interpretation in the following. 2.2 Understanding the B/M As the benchmark case, we consider an all-equity firm with book value B t and market value M t at time t. It can be easily extended to the more general case of a levered firm. We rewrite the market value M t into two terms: M t = V (B t ) + C(B t, Z t ), (4) where V (B t ) is the present value of cash flows generated by assets-in-place, and C(B t, Z t ) is the value of growth opportunities, which depends on some state variables Z t in addition to B t. The book-to-market ratio is therefore: B t M t = B t V (B t ) + C(B t, Z t ). (5) The above equation illustrates the shortcomings of applying B/M as a proxy of growth opportunities. Fixing the book value, a high value of B/M can be caused not only by a high value of growth options but also a low value of V (B t ). In the simple Gordon growth model, V (B t ) = B t /(r g), where r and g are the average discount rate and growth rate of the cash 7

10 flows generated by the assets-in-place. 1 While the growth rate can be estimated using past book values, finding a good proxy of the discount rate is difficult. Because different stocks are likely to have different discount rates on their assets-in-place, B/M does not provide a clean measure of growth opportunities across stocks. 2.3 Understanding the Trend of B/M We use the cumulated historical quantities of the book-to-market as the proxy of the trend component of B/M. It refers to the past performance of the firm. Substituting equation (2) with specification (5), the trend component of B/M can be expressed as BM ave = 1 s s i=1 B t i V (B t i ) + C(B t i, Z t i ). (6) where V (B t i ) is the present value of cash flows generated by assets-in-place at time t i, and C(B t, Z t ) is the value of growth opportunities at time t i. Suppose there is a new growth opportunity at time t i. If the opportunity is temporary and fail to convert into a successful investing projects, then it vanishes rapidly in the next period. This temporary change of C(B t, Z t ) would not affect the quantity of BM ave. However, if this growth opportunity succeeds to convert into the asset-in-place, then level of trend would be changed permanently. High BM ave relates with a value type of firm, which continuously allocates within the category of value firm. Trend component would not be determined by any temporary shock to B/M. For instance, a growth type of firm, because of a temporary shock, reach a high book-to-market at time t i, i < s, and becomes a value type of firm at t i based on B t i M t i. However, since the shock is temporary, the increments of B/M vanish rapidly in the following period. Therefore, it would be still a growth type of firm at t. Hence, the persistent trend component smooths the temporary shock to B/M and reveal 1 More generally, the discount rate and growth rate can be time-varying, adding another layer of complexity to inferring the growth opportunities. 8

11 the real type of the firm based on a rolling-window past information. A persistent value firm owns high trend component of B/M, while a persistent growth firm owns low trend component of B/M. 2.4 Understanding Innovation of B/M Equation (5) shows that B/M is time-varying even when B t and V t are constants because the growth options change with other state variables. Hence, growth options are another driver for migrations between growth and value stocks (e.g., Fama and French (2007b)). Although the level of B/M does not measure growth opportunities cleanly, we may draw inference about growth opportunities by exploiting the time variation of B/M. We examine the dynamics of B/M by considering three basic types of change of B/M. Any change of B/M is a combination of the three base cases. In the first case, we assume that both B t and V (B t ) are unchanged from t 1 but C(B t, Z t ) changes as a result of changes in the state variables Z t. B/M increases(decreases) if the growth options become less valuable. Therefore, I (B/M) is negatively associated with the change of growth opportunities. Second, we let the state variables Z t remain unchanged from t 1 but B t change. The change of B/M is determined by the changes of V (B t ) and C(B t, Z t ) relative to that of B t. We need to make some assumptions about the functional forms of V (B t ) and C(B t, Z t ). In light of the Gordon s growth model, it is plausible to assume that V (B t ) is linear in B t so that the change of V (B t ) is proportional to that of B t. On the other hand, C(B t, Z t ), which consists of call options, should be non-linear in B t. A well-known result in option pricing theory is that the elasticity of call option is greater than 1 (e.g., Cox and Rubinstein (1985)). 2 Applying this result, it is easy to show that when B t increases(decreases), B/M decreases(increases) because the call option values increase more in proportion. For this case, I (B/M) is again negatively associated with the change of growth opportunities. In the third case, B t and Z t remain unchanged but an growth opportunity is taken. 2 The elasticity of an option is the ratio of percentage change of the option value to that of the underlying. 9

12 Let I denote the investment cost of the opportunity, W be the present value of the cash flows of the growth opportunity, and C 0 be the option value of the opportunity of the last period t 1. The growth option can be regarded as a European option with expiration at t. After the growth opportunity being taken, the book value becomes B t 1 + I, the value of growth opportunities is reduced to C(B t 1, Z t 1 ) C 0, and the market value becomes V (B t 1 ) + W I + C(B t 1, Z t 1 ) C 0. Using the fact that C 0 W I from the option pricing theory, it is straight forward to show that Bt M t opposite direction of growth opportunities. > 0. Once again, Bt M t changes in the In practice, B t and Z t move simultaneously while options are exercised. The analysis will become more complex but the intuition of the three base cases carries through. Taken together, we postulate a negative relation between I (B/M) and firm s growth opportunities. One caveat about our argument is that we have assumed the valuation of existing assetsin-place V (B t ) to be driven by B t only. If V (B t ) is affected by other variables such as time-varying discount rate and growth rate, then a change of B/M may not be replicated by a combinations of the three basic changes listed above. Nonetheless, the variation of V (B t ) should be much lower than that of C(B t, Z t ) because growth options are levered positions. Relatively speaking, the variation in change of B/M is mostly driven by the change of growth options. 2.5 Distinguish Value and Growth Premium Existing empirical studies points out that high book-to-market firms earn the value premium (Fama and French (1993), Fama and French (1998)) which is opposite with the argument raised by the conventional wisdom. To solve for this tension, we decompose the B/M into a persistent trend component and a cyclical innovation component. BM ave, captures the persistent past performance of the firm and mainly related with the value of cash flow of asset-in-place. Therefore, high BM ave yields to high premium. Meanwhile, the innovation component, I (B/M) negatively related with the growth opportunities. 10

13 Since growth opportunities brings high premium, the innovation component moves opposite direction with future returns. Our decomposition succeeds in isolated growth premium from the classical value premium. High BM ave causes high premium, as value premium, while I (B/M) causes growth premium. Moreover, migrating from growth to value category, the innovation of B/M must be permanent to affect the trend of B/M. Otherwise, a firm would still stay as a growth firm. Therefore, directly using Bt M t to interpret value premium would raise two type of errors. Type I: Value premium is under estimated when I (B/M) > 0. Type II:Value premium is over estimated when I (B/M) < 0. Type I error consistent with the results shown in Gerakos and Linnainmaa (2017). Type II error reveals the reason of why growth stocks are more risky but earn lower premium by only using Bt M t to predict portfolio returns. Both of types of error indicates that after all there is growth premium. We will provide more detailed empirical analysis in the next sections. 3 The Information Contents of I (B/M) and BM ave To justify the needs for the decomposition of B/M into I (B/M) and BM ave, we first explore the time series properties of B/M, specifically the persistence and the time variation of B/M. We use the transition matrix for the two different quarters to detect the persistence of B/M. Specifically, in each quarter t and t+n, we sort the stocks based on B/M into deciles. The elements in the transition matrix forb/m count the time-series average percentage of stocks in the given quarter t B/M decile fallen in the quarter t + n B/M decile. Panel A in Table 1 presents the transition matrix for forward eight quarter. The results indicate that B/M is highly persistent. To gauge the degree of persistency, we look at the diagonal of 11

14 the matrix. For instance, the results in Table A.1 show that more than 76% of the stocks with B/M classified within decile 1 in quarter t are still in decile 1 in quarter t + 1. Even in a much longer horizon such as two years time period, the B/M can still be classified as persistent. Specifically, the results in Table 1 indicate that 46% of the stocks with B/M classified within decile 1 in quarter t are still in decile 1 after eight quarters evolution. Even though highly persistent, the B/M still exhibits some degrees of time variation. In two years time period, 54% (1-46%) of the stocks classified within the decile with lowest B/M migrates to other deciles. The time variation of B/M is further confirmed in the Appendix 1 using the variance ratio test. In contrast to the B/M, the results in the Panel B of Table 1 reveal that the I (B/M) is not persistent, confirming that I (B/M) captures the temporary component of B/M. Specifically, Panel B of Table 1 indicates that only around 10% of the stocks classified in a certain I (B/M) decile remains in the same decile in eight quarters. To better understand the information content of I (B/M) and BM ave, we use correlation matrix to detect the interaction of I (B/M), BM ave and other control variables. Firm characteristics in our analysis include size (Size), the book to market ratio (B/M ), momentum (MOM), return reversal (REV), gross profitability (GP), and standardized unexpected earnings surprises. All the variables are constructed following convention in the literature and are described as follows: Size: The logarithm of market capitalization at the end of each quarter. Market capitalization is the end of quarter share outstanding multiplied by the stock price. B/M: Book to market ratio is the ratio of quarterly book equity to quarter end market capitalization. Quarterly book equity is constructed by following Hou, Xue, and Zhang (2015) (footnote 9), which is basically a quarterly version of book equity of Davis, Fama, and French (2000). MOM: Momentum for month t is defined as the cumulative return between month 12

15 t 12 and month t 1. We following the convention in the literature by skipping month t when momentum is used to predict returns in month t + 1. We have also use the cumulative return between month t 6 and t 1 and obtained similar results. REV : The return reversal in quarter t is the monthly return of the last month within the quarter. GP : Following Novy-Marx (2013), gross profitability is defined as quarterly revenue minus quarterly cost of goods sold scaled by quarterly asset total. SUE 1 : SUE stands for the standardized unexpected earnings. SUE at time t is the quarter t end price scaled difference between realized earnings in quarter t and the earnings in quarter t 1. SUE 2 : SUE stands for the standardized unexpected earnings. SUE at time t is the quarter t end price scaled difference between realized earnings in quarter t and the median of analyst earnings forecast. SUE 3 : SUE stands for the standardized unexpected earnings. SUE at time t is the quarter t end price scaled difference between realized earnings in quarter t and the mean of analyst earnings forecast. Table 2 reports the summary statistics and the correlation matrix for I (B/M) and other control variables. Many interesting patterns show up. First, we find that our I (B/M) measure has low correlations with both B/M and BM ave. Specifically, the correlation between I (B/M) and B/M is only Even though I (B/M) is a transformation of B/M, the low correlation indicates that they have different information contents. Additionally, the correlation between I (B/M) and BM ave is significantly negative at The correlation, on one hand, indicates that the temporary component and persistent trend component share different information contents. On the other hand, we demonstrate in the previous sections that the persistent trend component captures the cash flows from 13

16 assets-in-place and the temporary component gauges the change in the value of growth options. The negative correlation between I (B/M) and BM ave justifies our decomposition since the correlation indicates that the firms deriving more values from assets-in-place tend to be not the ones deriving their values from growth options. Second, Table 2 indicates that the correlation between I (B/M) and past cumulative returns is high (-0.198). The high correlation is not surprising: if we take a second look at I (B/M), we can find it captures the unexpected increase in B/M. The strongly negative correlation is straightforward given the connection between fundamentals and momentum (Liu and Zhang (2014); Novy-Marx (2015)). Last, the correlations of I (B/M) and other control variables are also consistent with our argument. For instance, the negative correlation between I (B/M) and gross profitability indicates that value firms are less profitable than growth firms. 4 The Return Predictability To detect the return predictive power of I (B/M) and BM ave, we rely mostly on the portfolio sorts and cross sectional regressions of Fama and Macbeth (1973) for our empirical investigation. For single portfolio sorts, we rank stocks on I (B/M) into decile portfolios and then consider both equal weighted and value weighted portfolio returns. If I (B/M) is negatively related to stock returns, we expect a decreasing pattern of portfolio returns from decile 1 to decile 10. For double portfolio sorts, we first rank stocks into quintiles by a control variable such as size and then further sort stocks within each portfolio into quintiles by I (B/M). If the control variable can explain the predictability of I (B/M), we expect the increasing pattern of returns in I (B/M) to be much less significant in each quintile of the control variable. To compute t statistics of average portfolio returns, we use the Newey and West (1987) adjusted standard 14

17 errors because of the persistence in the portfolio compositions 3. For the Fama and MacBeth regression, we expected the average estimated coefficient of I (B/M) to be negative and significant. The cross sectional regressions allow us to examine the marginal effect of the I (B/M) when controlling for other variables known to predict stock returns. In the most general specification, we include all control variables in the regression. If I (B/M) captures information about expected stock returns beyond that in other variables, the coefficient of the I (B/M) should be significant even in the presence of all control variables. We show the results of portfolio sorts first and then the estimates of Fama and MacBeth regressions. After confirming the return predictive power of I (B/M), we turn to more specific tests for the real effect of I (B/M). 4.1 Single Portfolio Sorts Panel A of Table 3 reports the average returns and characteristics of the decile portfolios formed by sorting stocks on I (B/M) for the full sample. When sorted on I (B/M), the average equal weighted quarterly return decreases from decile 1 (4.91%) to decile 10 (2.76%). The average high minus low (H-L) spread is % per quarter (or % per year) and highly significant (t=-4.56). To make sure the significant H-L spread is not driven by higher stock risk, we estimate the risk-adjusted α using the Fama and French (2016) five factor model. The risk-adjusted H-L spread is even larger at %. The value weighted H-L spreads are very similar to but slightly smaller than the equal weighted H-L spreads, indicating that the results are not dominated by small stocks. Next, we look at the characteristics of the equal weighted decile portfolios. Low I (B/M) stocks have lower B/M, higher past cumulative returns, and lower return reversal. To make sure that the return predictive power of I (B/M) is not driven by the firm characteristics, we will reexamine the return predictability by double portfolio sorts and Fama MacBeth regressions. 3 We use six lags to adjust the standard error. Using more lags does not change the results. 15

18 We then examine the return predictability of BM ave. In untabulated results, we find that the difference between quarterly high BM ave minus low decile portfolio returns is 1.824% and highly significant with a t statistics of The positive association between BM ave and returns indicates that the value premium is largely driven by the persistent trend component in the B/M. Overall, we find a negative relation between the I (B/M) and future stock returns. The results are robust regardless whether the returns are equal weighted or value weighted, and unadjusted or risk adjusted. We also find a positive relation between BM ave and future stock returns. The above results indicate that the value premium is corresponding to the persistent trend component and the growth premium is corresponding to the temporary component. We then explore the marginal return predictive power of I (B/M) by using double portfolio sorts. 4.2 Double Portfolio Sorts We now investigate whether the predictability of I (B/M) are caused by firm characteristics. We use the double portfolio sort approach by first sorting stocks on firm characteristics and then sorting on I B/M). Table 4 reports the average value weighted returns and value weighted adjusted returns for the characteristics reported in Table 2. We have also examined a number of other control variables and those results are available upon requests. Since the return predictive power of B/M is more concentrated in firms with small market capitalization, we first consider the impact of market capitalization on the return predictive power of I (B/M). When stocks are initially ranked by firm size, the H-L spreads of I (B/M) quintiles show a hump shaped pattern (in magnitude) from size quintile 1 ( %) to size quintile 3 (-3.318%) and then to size quintile 5 (-1.022%), suggesting the return predictive power of I (B/M) is stronger for medium to large stocks. Even though the return predictive power of I (B/M) is modest within the quintile portfolio of the smallest stocks, I (B/M) has a strong negative relation with stock returns in portfolios of medium size to largest size. The 16

19 results indicate that the return predictive power of I (B/M) is not a phenomenon for small capitalization stocks but works for stocks with medium to large stocks. The phenomenon that the return predictive power of I (B/M) is more pronounced in medium size firms indicates that medium size firms are the ones with more frequent migration across value and growth portfolios. One may still concern the incremental explanatory of I (B/M) against B/M since I (B/M) is a simple transformation of B/M. We mitigate the concern by first sorting on book to market ratio and then on I (B/M). Table 4 shows that the H-L spreads of I (B/M) quintiles show an increasing pattern (in magnitude) from B/M quintile 1 to B/M quintile 5. The results indicate that the impact of I (B/M) is stronger for value stocks. The H-L spreads across five B/M quintiles are all significant positive, suggesting that the return- predictive power of I (B/M) is strong in all B/M quintiles. In other words, the B/M effect and I (B/M) effect are different. We also control for the effect of past return measures. Even though the correlation between I (B/M) and past cumulative returns are extremely high, the return predictive power of I (B/M) is robust to both past cumulative returns and return reversal. The return predictive power of I (B/M) is more pronounced in the portfolios of past winner stocks. On the other hand, the return reversal has nonlinear impact on I (B/M) s predictive power. The return predictive power of I (B/M) are more pronounced in high and low return reversal portfolios. Given the concern that historical information of B/M is already incorporated in firms current gross profitability, we control the effect of gross profitability. We find I (B/M) has return predictive power in all gross profitability portfolios. Beyond that, the return predictive power of I (B/M) is stronger in the highest and lowest gross profitability portfolios. This nonlinear effect of gross profitability on the return predictive power of I (B/M) indicates that firms with extreme gross profit tend to change in type between value and growth. Ang, Hodrick, Xing, and Zhang (2006) document a negative relation between IVOL and stock returns. To make sure the negative relation between I (B/M) and returns is not absorbed 17

20 by the IVOL effect, we perform the sequential portfolio sort first on IVOL and then on I (B/M). The I (B/M) effect is still robust even after controlling for IVOL. Standardized unexpected earnings are similar to our I (B/M) measure. The reason is that SUE is the unexpected component of earnings while our I (B/M) measure is the unexpected component of B/M. One may concern that I (B/M) only captures the post-earnings announcement drift. We perform sequential portfolio sorts first on various SUE measures and then on I (B/M). We find that the association between I (B/M) and stock returns is still robust under different SUE measures. To sum up, the results of double portfolio sorts indicate that the return predictive power of I (B/M) is robust to different return predictors and is not restricted to small stocks. 4.3 Fama MacBeth Regressions We now examine the return predictability of I (B/M) with the Fama MacBeth regressions, which allow us to control for multiple return predictors simultaneously. We perform the Fama MacBeth regression for both full sample and the reduce sample. The corresponding results are reported in Table 5. Panel A is for the normal Fama MacBeth regressions and Panel B is for the Fama MacBeth regressions using value weighted least square estimation. We estimate four regression models. The first one uses I (B/M) as the only explanatory variable. Model (2) examines the return predictive power of I (B/M) when controlling for the market capitalization and the B/M. Model (3) simultaneously control for I (B/M), B/M and other control variables. Models (4) and (5) add in the two different SUE measures. Models (6) to (8) run regressions of returns on BM a ve. Models (9) to (12) include I (B/M) and B/M simultaneously. From Model (1), the average coefficient of I (B/M) is negative and significant at the 1% level ( and t=-5.33). In Model (2), we include the market capitalization and B/M. The inclusion of B/M does not influence the return-predictive power of I (B/M). When we include other control variables in Model (4) and (5), the return predictive power of both 18

21 I (B/M) and B/M is not influenced. In sum, the incremental return predictive power of I (B/M) is stronger even after controlling for various return predictors. Models (6) through (8) indicate that BM ave is a robust return predictor even after controlling for major control variables. The pattern becomes more interesting when we include simultaneously the I (B/M) and B/M ave in Models (9) through (12). In Model (9) when we include only I (B/M) and B/M ave in the regression, the average coefficients of I (B/M) and B/M are both significant at 1% level, indicating that the I (B/M) effect and BM ave effect on returns cannot dominate or absorb each other. Thus, the growth premium from I (B/M) and the value premium from BM ave co exist. The coefficients of I (B/M) effect and BM ave are both significant at the level of 1% even after controlling for various control variables. Since positive and negative innovations in fundamentals can have different asset pricing implications (e.g., Segal, Shaliastovich, and Yaron (2015); Patton and Sheppard (2015)), we create corresponding positive and negative innovations in I (B/M), I (B/M), and I (B/M),+ as follows: I (B/M),+ = I (B/M), = I (B/M) I (B/M) B t M t BM ave > 0 0 B t M t BM ave 0 B t M t BM ave 0 0 B t M t BM ave > 0 Specifically, I (B/M),+ is equal to zero when innovation in B/M ( Bt M t BM ave ) is smaller than zero and equal to I (B/M) when B/M innovation is larger than zero. I (B/M), is the opposite of I (B/M),+, being equal to zero when innovation in B/M is larger than zero and equal to I (B/M) when B/M innovation is smaller than zero. Table 6 presents the average coefficients of the Fama MacBeth regression of returns on I (B/M),+, I (B/M),, and control variables. Models (1) and (2) in Table 6 shows that in univariate regressions of returns, I (B/M),+ and I (B/M), have similar return predictive power. As 19

22 Models (3) and (4) indicate, the return predictive power of I (B/M),+ outperforms that of I (B/M), in multivariate regressions controlling for B/M. As we add in more control variables, the return predictive power of I (B/M),+ is weaken and that of I (B/M), is uninfluenced. Specifically, in Model (7), the average coefficient of I (B/M), is more than twice as large as that of I (B/M),+ (0.009 vs 0.004). The unequal return predictive power of I (B/M),+ and I (B/M), reveals that the return predictability is more pronounced in growth stocks with low I (B/M). This finding is further confirmed by our exploration on the relation between I (B/M) and firms future fundamentals in Section 5. 5 I (B/M) and the Firms Future Fundamentals To detect the real effect of I (B/M), we examine its predictability of firms future fundamentals. Regarding firm fundamentals, we focus on gross profitability and B/M which are used to identify whether a stock belongs to value or growth stock. Prior research such as Fama and French (2007b) and Daniel and Titman (1997) use B/M as the indicator to identify value and growth stocks. They find that value and growth stocks tend to move to the other extreme after their identification. In other words, these studies state that growth (value) stocks with low (high) B/M tend to become value stocks by losing (gaining) profit and gaining (losing) increase in B/M. The value premium comes from the opposite migration between value and growth stocks (Fama and French (2007b)). Since our I (B/M) measure indicates a growth premium, we expect a different pattern than the one in Fama and French (2007b) if we use I (B/M) to classify value and growth stocks. To identify the migration of stocks across value and growth types, we explore whether I (B/M) has predictive power on firms future gross profitability and B/M. If I (B/M) has a negative relation with B/M and positive relation with gross profitability, I (B/M) implies the convergence of value and growth stocks after value/growth type identification. If I (B/M) has a negative relation with gross profitability but positive relation with future B/M, it indicates 20

23 a divergence of value and growth stocks. Table 7 reports the average coefficients from Fama MacBeth regressions of gross profitability in quarter t + 1 on I (B/M) and other control variables in quarter t under different econometric specifications. The average coefficients show that I (B/M) has a strong negative relation with firm s future gross profitability even after controlling for gross profitability itself in quarter t. Moreover, I (B/M),+ and I (B/M), have similar explanatory power on future gross profitability. We then perform the Fama MacBeth regressions of future B/M on current I (B/M) and other control variables. Table 8 reports the corresponding average coefficients. Models (1) through (3) demonstrate that all of the three measures, I (B/M), I (B/M),+, and I (B/M), have strong positive explanatory power of future B/M in the univariate regressions. However, their explanatory power differs in the multivariate regressions when controlling for other variables. I (B/M) and I (B/M),+ cannot predict future B/M in the multivariate regressions. The signs of their coefficients even switch to negative. In contrast, the average coefficients of I (B/M), in multivariate regressions are still significantly positive. The significant negative relation between I (B/M), and future B/M is consistent with the more pronounced return predictive power of I (B/M),. The predictive power of I (B/M) on future gross profitability and B/M not only concentrate in the short future but also continues in even more than two years. To explore the impact of I (B/M) on firm s fundamentals in the long run, we sort the stocks in quarter t based on I (B/M) into decile portfolios and look at the portfolio average gross profitability and B/M in quarter t+1 to t+8. Table 9 presents the corresponding results. Consistent with the Fama MacBeth regressions, I (B/M) has a significant negative relation with the gross profitability and a significant positive relation with the B/M in the immediate one quarter. Table 9 shows that the positive (negative) relation between B/M (gross profitability) continues in the future two years. For instance, even in quarter t+8, the gross profitability (B/M ) spread between highest and lowest deciles is -0.4% (0.30) which is significant at 1% level. Table 9 21

24 indicates that the value and growth stocks classified by I (B/M) maintain their types for even more than two years. Combining the predictive power of I (B/M) on future gross profitability and B/M, we can conclude that firms with high I (B/M) tend to become even less profitable and has lower book to price ratio. In other words, after being classified as value and growth stocks by I (B/M), the stocks keep their type into the next period. The above finding has important implications. Fama and French (2007a) and Fama and French (2007b) among others find that the value premium comes from the convergence of value and growth stocks after their value-vs-growth type identification. Employing I (B/M) to classify value and growth stocks, value and growth stocks tend to keep their types, implying a growth premium. In sum, our empirical exploration of I (B/M) implies that growth stocks are more risky. 6 Conclusions The empirical evidence has shown that the value stocks, which are classified based on the B/M ratio, tend to have higher premium than the growth stocks. This phenomenon conflicts the conventional wisdom, which argues that the growth stocks is more risky to earn higher premium. In this paper, we reconcile the conventional wisdom and the empirical evidence by decomposing the B/M into two components, a temporary component and a persistent trend component. Our baseline results indicate that the temporary component of B/M (I (B/M) ) captures the value of real options in firms and has a strong negative relation with cross sectional stock returns even when controlling for various return predictors. The negative relation between I (B/M) and stock returns indicates a growth premium. In contrast, the trend component of B/M (BM ave ) is positively associated with stock returns. In other words, the value premium concentrates in the BM ave component while the growth premium concentrates in the I (B/M) component. 22

25 The empirical evidence also supports the relation between the persistent trend component and assets-in-place. Specifically, we find a strong positive relation between the trend component and various irreversibility measures. We check the return predictability power of I (B/M) and BM ave by using both portfolio sorts and Fama MacBeth regressions approaches. Interestingly, in portfolios simultaneously sorted on both I (B/M) and B/M, and in cross sectional regressions of returns at the firm level, the negative I (B/M) effect on returns and positive B/M effect on returns neither drive out nor dominate each other. We have designed tests to track the future dynamics of fundamentals among different I (B/M) portfolios, to classify the value or growth type of individual stocks. Stocks with high I (B/M) tend to become less profitable and grow less rapidly. On the other hand, stocks with low I (B/M) tend to be more profitable and experience even higher market valuation. Our results show that both value and growth stocks maintain their types without migration across value and growth portfolios in the subsequent period ((e.g., Daniel and Titman (1997); Lakonishok, Shleifer, and Vishny (1994))). We apply both portfolio sorts and Fama MacBeth regressions approach to check the return predictability power of I (B/M). We then turn to check return predictability power of I (B/M) by using both portfolio sorts and Fama MacBeth regressions approach. Both approaches show that I (B/M) has a strong negative relation with future cross sectional stock returns even after controlling for main return predictors including B/M. It confirms our hypothesis, such that growth stocks tend to earn higher expected premium and growth stocks are more risky than value stocks. 23