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Asset Turnover and the Cross-Section of Stock Returns Rachel (Kyungyeon) Koh UMass Amherst Draft: Feb 2017 Abstract This paper documents the robustness of the asset turnover anomaly in the cross-section of stock returns. Asset turnover (ATO), measured by sales-to-net operating assets, captures the firm’s operating efficiency in asset utilization, abstracting away from the effect of financial leverage. I argue that the return predictability of ATO, a DuPont component of profitability, should be examined as a source of the profitability premium although other related studies have attributed it to irrationality and mispricing. I show that ATO and industry-adjusted ATO reduce forecasting errors in predicting future profitability, hence supporting the view that it contains incremental information about a firm’s expected earnings. Because ATO is largely a function of industry membership, industry-adjusting ATO provides completely new information that expands the investment opportunity set. Industry-adjusted ATO (ab_ATO) strengthens the future return predictability; and strategies based on ab_ATO yield significant alphas with respect to the Fama-French 3-factor and 5-factor models, have low correlation with the market and other factor-mimicking portfolios, and exhibit high Sharpe ratios. Interesingly, the ATO-based portfolio returns are potentially sources of systematic risks, rather than of sentiment-based mispricing. They are significantly linked to the GDP growth, consumption growth, industry production, inflation, term premium, and default premium, but not as associated with investor sentiments. 1 Decomposing the return on asset into asset turnover and profit margin (the Dupont decomposition) has allowed analysts to probe into a firm’s source of profitability and to estimate the firm value more accurately. Asset turnover measures a firm’s operating skill in efficiently utilizing its assets, and profit margin reflects a firm’s power over their sales and costs. A limited number of studies have documented the effect of the asset turnover for the cross-section of stock returns and have dismissed it as being subsumed by other anomalies (Fairfield and Yohn 2001, Novy-Marx 2014). In this paper, I argue in favor of the asset turnover’s robust predictability in the cross-section of stock returns. Asset turnover (ATO), measured as sales-to-net operating assets (Sale/NOA), can predict the future stock average returns, contributing unique information above that of other predictors, such as market capitalization (Size), book-to-market equity (BEME), operating profitability (OP), accrual (ACC), asset growth (dAA), net stock issues (NSI), and momentum (MOM)1. The reason for deflating sales by net operating assets (NOA) instead of total assets (TA) is motivated by Esplin, Hewitt, Plumlee, and Yohn (2014). They argue that disaggregating financial statements into operating and financial activities is essential because operating activities mainly drive firm value (Nissim and Penman 2001). For comparison, however, I also examine the role of sales-to-total assets for stock performance. In order to provide explanations for the return predictability of asset turnover, I borrow Fama and French (2006)’s intuition for the profitability premium. They state that the positive association between a firm’s profitability and expected return can be derived from the dividend 1 Plenty of studies have shown that financial ratios, firm characteristics, and accounting measures have robust predictive power on the future stock returns (Lewellen 2002, Lewellen 2014). They include the price-earnings ratio (Basu 1977), size (Banz 1981), book-to-market equity (Rosenberg et al. 1985 and Fama and French 1992), momentum (Jegadeesh and Titman 1993), accruals (Sloan 1996), profitability (Haugen and Baker 1996 and Novy-Marx 2013), net stock issues (Daniel and Titman 2006), and et cetera. 2 discount model in conjunction with clean surplus accounting. Below is the model in consideration: 𝑀𝐸𝑡 = ∑∞ 𝜏=0 𝐸𝑡 [𝑌𝑡+𝜏 −𝑑𝐵𝑡+𝜏 ] (1+𝑟)𝜏 , where 𝑀𝐸𝑡 is the market value of equity, 𝑌𝑡 is the time-t earnings, dB is the change in book equity, and r is the required rate of return on expected dividends. Holding the equity value and the change in book value constant, higher expected earnings should be followed by the higher discount rate, which is how Fama and French explains the profitability premium. Many academic studies have used current profitability to proxy for expected profitability. However, as Fama and French states, there is “a timeworn problem: we cannot tell whether the profitability effects in average stock returns are due to rational or irrational pricing.” Expectation about earnings itself can be irrationally formed by investors, so if we can come up with a better proxy or a more delicate way to evaluate a firm’s operations that can provide us insights about future profitability, then this valuation model can get us a more rational price for equity. I find that asset turnover reduces forecasting errors in predicting future profitability and that the ATO effect for stock returns is robust after controlling for profitability, suggesting that ATO contributes unique information about the expected earnings beyond that of the profitability. However, we can do better by industry-adjusting ATO. As is well known, ATO is largely a function of industry membership, so some firms naturally have high ATO or low ATO by their inherent operating structure. For example, retail and wholesale industries naturally have high asset turnover, and utility and natural gas firms naturally have low asset turnover. Each industry has a different normal level for ATO, so the cross-sectional variation in ATO can be to a large degree explained by industry membership. Comparing the ATO of a firm with another firm in a different industry to analyze profitability may be meaningless for firm valuation if we do not 3 control for their industry heterogeneity. Hence, if we adjust ATO by its industry level and extract a firm’s own skills in asset utilization, it could be more meaningful for predicting its future earnings. Indeed, Soliman (2004) documents that industry-adjusted ATO is a powerful predictor for the future return on assets. Following Soliman, industry-adjusting hereafter means subtracting the industry median from a firm’s own measure. In this paper, I find that industryadjusted ATO is a powerful, robust predictor for stock returns and for risk-adjusted returns (alphas). While the plain ATO has a zero alpha with respect to the Fama-French five-factor model, industry-adjusted ATO consistently bears significant alphas, not explained by the five factors. Another potential interpretation for the return predictability is the mispricing (behavioral) view that market participants do not act immediately on the ATO-based information, so the market forces correcting this mispricing results in consistently higher or lower future returns. In other words, finding the positive return predictability would indicate that high ATO firms are consistently undervalued by investors relative to the low ATO firms. Raife Giovinazzo (2008) considers the inverse of the asset turnover as a return predictor, and argues that firms requiring large investment for operations (asset-intensive firms have low ATO) have lower returns than asset-light firms (with high ATO). This study interprets the return predictability as an outcome of misvaluation by numerous investors, who may overlook firm differences in required investment to generate sales. My results are empirically similar to Giovinazzo, but I offer an alternative interpretation. Rather than taking ATO as a metric for asset-intensiveness, a firm’s aspect that is difficult to estimate and thus potentially lead to mispricing, I take it as a component of profitability, which can proxy for expected earnings and be used for the equity valuation. To more rigorously explore why ATO and industry-adjusted ATO persistently predict future stock returns and risk-adjusted returns, I try to link macroeconomic trends, such as GDP 4 growth, consumption growth, industrial production growth, inflation, and et cetera, to the performance of the ATO factor-mimicking portfolios. Merton’s Intertemporal CAPM (1973) dictates that state variables that proxy for sources of systematic risks should be well-motivated using macroeconomic rationale. I find that the ATO portfolio performances are significantly linked to these macroeconomic variables. I also test whether ATO performance is rather the outcome of sentiment-based mispricing, but the findings suggest that the return predictability is not due to mispricing. The paper will be organized as following: First, I introduce the data and show descriptive statistics of the variables used for this paper. Then, I will show the results from forecasting profitability using the Dupont components and the industry-adjusted ATO. The next section will lay out the sorting and regression analysis results, and factor-mimicking portfolios will be constructed to probe into the ATO-based trading performance relative to other asset pricing factors. Finally, the linkage to macroeconomic risks and investor sentiment is examined. Data and Descriptive Statistics Stock market data are obtained from CRSP, and the accounting data from Compustat, both provided by WRDS at UPenn. The sample includes firms listed on the NYSE, AMEX, and NASDAQ stock exchanges from 1970 through 2015 and only the common shares (with share code of 10 or 11). The omission of the 1960s is due to the lack of number of firms for many industries in the early period. I classify firms into industries based on the scheme used by Fama and French (1997). Each month, the four-digit SIC code determines its assignment in one of the 49 industries. Because I leave out financial firms (SIC Code from 6000-6999), the sample firms can be classified into 44 industries. The sample does not include firms that have missing data for accounting and financial variables (total assets, positive net operating assets, positive book 5 equity, positive market capitalization, and industry assignment.) To mitigate survivorship bias, all firms need to have existed for at least two years in Compustat. I construct four different measures for asset turnover. The main metric is sales divided by the average of the current year’s net operating assets (NOA) and the lagged NOA2, (Sales/NOA); and another is sales divided by the average of the current year’s total assets (TA) and the lagged TA (Sales/TA), which is the textbook Dupont component. Then, each is industryadjusted by the industry median (ab_Sales /NOA and ab_Sales /TA). To examine formally to what extent the industry membership explains the level of the firm characteristics including the DuPont profitability components, I run the following crosssectional regression for each variable each year (the intercept is dropped): 44 Variablet bit IndustryDummyit t i 1 The dependent variable is ATO, and the independent variables are dummy variables on the 44 industries. The focus will be on the time-series average of the adjusted R-squares obtained from each of the cross-sectional regressions. The higher the adjusted R-square, the more the industry membership is able to explain the cross-sectional variation of firm characteristics. Table 1 shows the results of the industry-membership regression. ATO has 51.77% adjusted RSquares, whereas return on net operating assets (RNOA=operating income after depreciation/NOA) and PM have much lower R-Squares (18% and 5%). ATO’s variation across firms tends to be explained by industry membership to a greater extent than PM and RNOA. Soliman (2004)’s explanation for this is that the “normal” level for ATO tends to be different across industries, whereas for RNOA and PM, the “normal” level is usually the economy-wide level. Competition and adaptation tend to drive the average RNOA to the economy-wide 2 Giovinazzo(2008) measures ATO by (Total Assets-Cash-Investments)/Sales. I also construct it this way, and find that the results are largely similar, but the main metric is more robust in sorting and regression results. 6 average, but ATO, in contrast, tend to converge to the industry averages due to permanent structural differences across industries that cannot be mimicked. Hence, it will be more meaningful if we examine a firm’s abnormal level of ATO above or below the industry level. Forecasting Profitability In this section, I establish that decomposing profitability into asset turnover and profit margin improves in forecasting the future profitability and further decomposing asset turnover into industry-adjusted component and industry-median results in even lower forecasting errors. The pooled regression in equation (1), (2), and (3) is performed on the first 20 years of the sample. (1) Profitabilityit+1 =a+b0 RNOAit +b3Log(Sizeit )+b4 Log(BEMEit )+b5dAAit +b6 Accrualit +b7 Log(OScoreit )+eit (2) Profitabilityit+1 =a+b0 RNOAit +b1ATOit +b 2 PMit +b3Log(Sizeit )+b4 Log(BEMEit )+b5dAAit +b6 Accrualit +b7 Log(OScoreit )+eit (3) Profitabilityit+1 =a+b0 RNOAit +b1a ab_ATOit +b1b med_ATOit +b 2 PM it +b3Log(Sizeit )+b 4 Log(BEME it )+ b5dAAit +b6 Accrualit +b7 Log(OScoreit )+eit Three different profitability measures are predicted: GP/TA (gross profitability profitability divided by total assets), OP/BE (operating profitability divided by book equity, and RNOA. The coefficients from the regression is used to predict each year’s profitability in the next 16 years of out-of-sample firm years. Table 2 reports the results on the sum of the errors (the absolute value of the difference between the fitted and actual value) and mean forecasting errors (the sum of the errors divided by the number of firm years). The fact that the errors are incrementally reduced for GP/TA and OP/BE suggests that decomposing profitability provide us with useful information on expected earnings. Hence, going back to the dividend discount model by Fama and French (2006), the asset turnover anomaly should be considered as a source of profitability premium, not a mere mispricing. 7 Univariate Sorting At the end of June of each year from 1970 to 2015, I sort all stocks excluding microcaps (stocks with market capitalizations below 20th NYSE market capitalization percentile) into decile portfolios according to asset turnover metrics, computed using the last available information on the formation date3. Then, monthly equal-weigted and value-weighted returns on the ten portfolios are computed from July of year t to June of the year t+1. I set the breakpoints using only the NYSE stocks. The intent of sorting is to see whether the cross-sectional average returns on the deciles exhibit a monotonic and significant spreads across the lowest and the highest deciles. The return difference between the top and bottom deciles represent returns on a trading strategy that goes long and short on the top and bottom. In Table 3, all strategies are able to generate positive, monotonic spreads across the deciles. The spread is the highest for SALES/NOA. Long-Short strategy for ab_Sales/NOA has generated 0.29% per month on average, while Sales/NOA has generated 0.37% per month. In Table 4, the decile portfolio characteristics for ab_SALES/NOA and ab_SALES/TA show that high ATO firms tend to be growth, large, and profitable firms. The return predictability of asset turnover is certainly isolated from the book-to-market and size effect. In fact, from the Fama-French’s dividend discount model in conjunction with clean surplus accounting, the inverse relation between the book-to-market ratio and asset turnover ratio is expected. If both sides of the equation are divided by the book equity, increase in the return on equity on the right-hand side is followed by the reduction on the inverse of the left-hand side, holding all else constant. No correlation with the trading volume suggests that the return predictability does not derive from illiquidity premium. The average probability of bankruptcy calculated using Ohlson’s O-Score (1980) is higher for low ATO firms. In other words, firms with low asset utilization skills 3 I also try lagging data by 4 months and rebalancing every month, which leads to larger return spreads. However, monthly rebalancing require greater trading costs, so I only report the results for annual rebalancing every June. 8 are more likely to go bankrupt, which is consistent with the finding by Giovinazzo (2006). Giovinazzo interprets this as the inherent risk of capital-intensive firms, who require heavy assets for operations. Hence, the positive default risk premium does not seem to drive the high ATO firms’ higher returns. Then, the most reasonable culprit for the source of return predictability for both industryadjusted and unadjusted ATO suggested by this table is OP/BE and OP/TA, as high ATO firms are profitable firms. Hence, it is necessary to try to control for the profitability and observe the robustness of the ATO effect. Bivariate Sorting Next, I perform bivariate sorting to see whether the ab_SALES/NOA effect is robust after controlling for size, book-to-market equity ratio, operating profitability, and default probability. First, I sort firms into three groups according to Size, BEME, OP, and O-Score, and then firms in each tercile are sorted on ab_SALES/NOA. Table 5 shows that ab_SALES/NOA is able to generate monotonic and positive spread across quintiles among low-BEME and medium-BEME (growth) firms, all size groups, low-profitability, high-profitability groups, and low and high bankruptcy groups. In the results not shown (available upon request), I sort based on unadjusted Sales/NOA after controlling for OP. SALES/NOA is similarly able to generate quite monotonic and positive spread across quintiles in BEME and Size groups, but not as much controlling for bankruptcy and OP groups. Adjusting for industry leads to more robust effect of asset turnover in bivariate sorting. The bivariate sorting demonstrates that ATO effect is robust within different subgroups of firms. Predicting Risk-Adjusted Returns 9 After sorting firms into quintiles and forming value-weighted returns over time, I run the following regressions for each quintile: 𝑋𝑟𝑒𝑡𝑖𝑡 = 𝛼𝑖 + 𝛽𝑖 ∗ 𝐹𝑎𝑚𝑎𝐹𝑟𝑒𝑛𝑐ℎ 𝐹𝑎𝑐𝑡𝑜𝑟𝑠𝑡 + 𝜀𝑖𝑡 Table 6 reports the intercepts and their T-statistics. With respect to the three-factor model, both ab_ATO and Sales/NOA are all able to generate monotonically increasing alphas and generate significantly positive alpha on the long-short portfolio. With respect to the five-factor model, ab_Sales/NOA is still able to generate monotonically increasing alphas and significantly positive alpha on the long-short. The returns on other strategies are subsumed by the Fama-French factors. Fama-Macbeth Regression Next, I examine the predictive power of asset turnover after controlling for other firm characteristics, such as size, book-to-market ratio, momentum, net stock issues, asset growth, and accrual. The regression analysis illustrates the marginal effect of each variable on returns controlling for other factors, while the univariate sorting does not control for other factors. The Fama-Macbeth slopes on regressors can be interpreted returns on characteristic-based portfolios (Fama 1976) and the R-squares reflect how much ex-post volatility these portfolios explain (Lewellen 2014). Following standard empirical analysis, I perform monthly FamaMacbeth regressions of monthly excess returns (in %) on the lagged variables. The annual variables are lagged at least 6 months to ensure that stock market participants have the accounting data available at the time of portfolio formation. The monthly variables are lagged one month. The standard errors are corrected for correlation over time, and the number of lags used is 12 months assuming that the effect of a particular month can spread as far as one year. I exclude all microcap stocks. 10 Although not shown, RNOA and PM are insignificant in the univariate regression, consistent with Soliman (2008)’s finding. In Table 7, Sales/NOA has a significantly positive coefficient in (5) and (7), controlling for either OP/BE or OP/TA. ATO may be proxying for some risks in stocks, or the market may be consistently underpricing high-ATO stocks at the time that information is available. Industry-adjusting results in higher magnitude and higher T-stats in equation (1). Unadjusted ATO weakens in significance with all other controls included, but industry-adjusted ATO is significant including other controls. My result complies with the view that industry-adjusting and thereby extracting a firm’s own skills in its asset utilization should be informative but tend to be underappreciated by the market participants. DuPont components are largely ignored in the asset pricing literature, but the analysis reveals that they may contain valuable information that investors can utilize. The asset turnover metrics that robustly survive in effects after controlling for other factors are ab_SALES/NOA and SALES/NOA. Deflated by total assets, the asset turnover loses its power once I use OP/TA (operating profitability deflated by total assets) as control. However, ab_SALES/NOA and SALES/NOA add incremental information on top of the profitability measured by either OP/BE or OP/TA. As can be seen by the median_ATO variable, the industry-level ATO has no effect on the stock returns. To address the concern for high within-industry dispersion of ATO driving the results, I normalize the industry-adjusted ATO variables by the range of the absolute value of the ab_ATO within each industry so that all ab_ATO lie between -1 and 1. The results (not reported) robustly confirm the previous FM regressions. Within-Industry Regressions 11 Industry-adjusting was motivated because ATO is largely a function of industrial structure of firms and because I wanted to test for the ATO’s return predictability independently of its industry structure. Another way to explore this issue is to perform within-industry regressions, that is, to run Fama-Macbeth regressions only among firms in the same industry. I drop the industries with inadequate number of firm observations (less than 15 firms in more than half the sample period), which leads to 30 industries from 44. Out of the 30 industries, I count the number of industries with significant Fama-Macbeth estimates on the regressors, which is reported in Table 8. For ATO, 15 of the 30 qualifying industries (including Business Services, Measuring and Control Eq, Wholesale, Restaurants, etc) have significant predictability for future stock returns. OP, Size, Accrual, and dAA are significantly predictive in less than 15 industries. NSI is only significantly negative for 3 of the industries. This suggests that controlling for industry, some anomalies do fade in predictability. For BEME, all except 2 industries (Books and Construction) have significant BEME contribution to stock returns within industry. Within-industry regression analysis confirms that the ATO effect is robust controlling for industry heterogeneity although ATO itself is largely driven by industry membership. Change in asset turnover Several studies (Fairfield and Yohn 2001 and Soliman 2004) have documented that the change in asset turnover and change in profit margin predict stock returns in the future, instead of the levels. I perform regressions to see their incremental contribution to stock returns after controlling for all other factors. In unreported results (available upon request), I find that the change in ATO and change in ab_ATO are not significant predictors once adding asset growth, net stock issues, momentum, and accrual. Hence, I find that it is not the change in ATO, but the level that has greater effect on the stock returns. 12 Factor-Mimicking Portfolios Next, I construct factor-mimicking portfolios following Fama and French. I reconstruct all the factors, rather than downloading the Fama-French’s factors from their online library, as my sample differs from theirs. 1. Market factor (MKTRF): MKTRF is the value-weighted excess return including dividends of all stocks in my sample. 2. Small minus Big (SMB): SMB is constructed first by intersecting three-by-three sort on size and book-to-market (BEME). The breakpoints are the 30th and 70th NYSE percentiles. After value-weighting the nine intersected portfolios, I create SMB portfolios as follows: SMB=(1/3)*(Small Value+Small Medium+Small Growth)-(1/3)*(Big Value+Big Medium+Big Growth) 3. Value/Growth (BEME): The portfolios are the intersections of three portfolios formed on size and three portfolios formed on BEME. The breakpoints are 30th and 70th NYSE percentiles. BEME=1/3(Small Value+Medium Value+Big Value)-1/3(Small Growth+Medium Growth +Big Growth). 4. Profitability (OP): The portfolios are the intersections of three portfolios formed on size and three portfolios formed on OP. The breakpoints are 30th and 70th NYSE percentiles. OP=1/3(Small Profitable+Medium Profitable +Big Profitable)-1/3(Small Unprofitable+Medium Unprofitable +Big Unprofitable). 5. Investment (dAA): The portfolios are the intersections of three portfolios formed on size and three portfolios formed on dAA. Low dAA firms are conservative firms with low investment, and 13 high dAA firms are aggressive firms with high investment. The breakpoints are 30th and 70th NYSE percentiles. dAA=1/3(Small Conservative+Medium Conservative +Big Conservative)-1/3(Small Aggressive+Medium Aggressive +Big Aggressive). 6. Efficiency (ATO): Firms with high ATO are efficient firms in asset utilization (measured by Sales/NOA or Sales/TA), while firms with low ATO are less efficient firms. The portfolios are the intersections of 3 portfolios formed on size and 3 portfolios formed on ATO. ATO=1/3(Small Efficient+Medium Efficient +Big Efficient)-1/3(Small Inefficient+Medium Inefficient +Big Inefficient). 7. Adjusted Efficiency (ab_ATO): Measured by ab_Sales/NOA or ab_Sales/TA. Firms with high ab_ATO are more efficient firms within their industry. The portfolios are the intersections of 3 portfolios formed on size and 3 portfolios formed on ab_ATO. Table 9 reports the correlation matrix of the factors. As can be seen, adjusted and unadjusted ATO variables lead to completely different return factors. Ab_Sales/NOA is negatively correlated with the market and size factor, moderately negatively correlated with the BEME factor, moderately positively correlated with the OP factor, and not much correlated with dAA and ACC factors. However, the unadjusted Sales/NOA is positively correlated with the market and size factor, highly negatively correlated with BEME, ACC, and dAA, and highly positively correlated with OP. Adjusting for industry clearly reduces the correlation with other factors overall. To examine whether the ATO-based factors can be spanned by the other factors, I regress each ATO factor on the Fama-French three and five factors. Table 10 reports that only the ab_Sales/NOA portfolio cannot be spanned by the five factors. The three factors can completely 14 span the Sales/TA, but not other portfolios. It is now evident why the asset turnover has been dismissed in asset pricing literatures. Trailing Sharpe Ratios Table 11 shows that the factor-mimicking portfolios generate positive average returns and annualized Sharpe ratios. The strategy constructed based on ab_SALES/NOA generates the highest Sharpe ratio of 0.61, exhibiting unusually low standard deviation. It seems just fit for investors seeking low risk investments. It outperforms all other strategies, including those blending two different factors. Mixing ab_SALES/NOA with BEME certainly improves upon the plain BEME strategy in Sharpe ratio, but not so much over ab_SALES/NOA. However, investors desiring higher target for returns than the return offered by ab_SALES/NOA can choose to blend with BEME. Mixing ab_ATO with OP does not improve either returns or risk on ab_SALES/NOA. For ab_SALES/TA, mixing with BEME and OP is certainly more profitable than plain strategies. Figure 1 shows the five-year trailing Sharpe ratios on ab_ATO, ATO, BEME, OP/BE, and 50/50 mixed strategies of ab_ATO with BEME and OP. Clearly, ab_ATO strategy outperforms either BEME and OP/BE for the majority of time over the 1970-2015 period. Mixing ab_ATO with BEME almost immune investors from negative Sharpe ratios at all, but OP&ab_ATO 50/50 does not seem to offer any additional benefits above that of ab_ATO. Returns on Factor-Mimicking Portfolios as State Variables Merton’s ICAPM suggests that economic state variables should be related to equity returns if equity prices reflect investor rationality. This section is an attempt toward determining any potential link between the economic trends and the returns on ATO-based portfolios before dismissing them as the outcome of mispricing. 15 i) GDP Growth as a State Variable In this section, I test whether the persistent profitability of the factor-mimicking portfolios based on the asset turnover can be linked to future Gross Domestic Product (GDP) growth. Liew and Vassalou (2000) supported a risk-based explanation for the book-to-market equity and size factors due to their significant linkage to future growth in the real economy. Such evidence supports the hypothesis of Fama and French (1998) and Merton’s intertemporal capital asset pricing model (1973) that they reflect macroeconomic signals to some extent. The U.S. macroeconomic variables, the seasonally-adjusted GDP growth and Industrial Production (IDP) quarterly series, are obtained from Organization for Economic Co-operation and Development (OECD) Main Indicators and the National Government Series. The growth is calculated from the previous year’s same quarter. The monthly factor returns from the factormimicking portfolios are compounded over the previous 12 months at the end of every quarter. After matching the data frequency of the return and OECD series, I first associate the GDP growth contemporaneously with annual returns, and then associate the next year’s growth in GDP with past year’s annual return. In other words, the following two regression equations are estimated: GDPgrowth𝑡−4,𝑡 = 𝑏0 + 𝑏1 𝐹𝑎𝑐𝑡𝑜𝑟𝑡−4,𝑡 + 𝑏2 𝐼𝐷𝑃𝑡−4,4 + 𝑏3 𝑀𝐾𝑇𝑅𝐹𝑡−4,4 + 𝜀𝑡 GDPgrowth𝑡,𝑡+4 = 𝑏0 + 𝑏1 𝐹𝑎𝑐𝑡𝑜𝑟𝑡−4,𝑡 + 𝑏2 𝐼𝐷𝑃𝑡−4,4 + 𝑏3 𝑀𝐾𝑇𝑅𝐹𝑡−4,4 + 𝜀𝑡 The coefficient ‘𝑏1 ’ captures the extent of the linkage between each of the factors and the GDP growth. The GDP growth is modestly autocorrelated (0.43) but very highly correlated with IDP growth (0.87). The lagged annual market returns and GDP growth are correlated at 0.45. The correlation matrix of quarterly returns on the ATO-based factors and the GDP growth is shown in Table 12. The rab_Sale/NOA represents ab_Sale/NOA orthogonalized to returns on 16 OP (the residuals after regressing ab_Sale/NOA on OP and compounding last 12 observations every quarter) because ab_Sale/NOA exhibited considerable correlation with OP. The rab_Sale/NOA series is significantly positively correlated with all of contemporaneous, lagged, and lead GDP. Ab_Sale/NOA is positively correlated with future and past GDP; interestingly, the unadjusted Sale/NOA is positively correlated with the future GDP growth but negatively correlated with past GDP growth. Table 13A reports the regression results for the contemporaneous regression, and Table 13B the predictive regression. The T-statistics are adjusted for autocorrelation and heteroskedasticity up to three lags, using the Newey-West (1987) estimator. In 13A, Sales/NOA, ab_Sales/NOA, and rab_Sales/NOA are the only ones that are significantly associated with the GDP growth after controlling for the market. For instance, a 10% higher annual return on the ab_Sales/NOA portfolio is associated with 0.5% higher GDP growth over the same period. All other Fama-French factors do not have significant associations. In Table 13B, consistently with the findings of Fama (1981) and Liew and Vassalou, the market factor returns are significantly related to the future economic growth. If ‘𝑏1 ’ is significantly positive, it would mean that a firm having a higher BEME, smaller size, slower investment growth, higher asset turnover, and higher profitability are better off when periods of high economic growth are expected. In almost all specifications, MKTRF is significantly positive. However, in contrast to Liew and Vassalou’s finding, I do not find that size factor is significantly linked to either the past or future GDP growth. The main interesting finding is the persistently positive linkage between each of all (for predictive) ATO-related factors and the GDP growth. The R-squared is the highest when Sales/NOA and ab_Sales/NOA are added. The orthogonalized ab_Sales/NOA factor is also significantly linked to GDP. To examine the economic significance, the annual return of 10% on the High-Low portfolio constructed on 17 industry-adjusted Sales/NOA is associated with 1.2% higher GDP growth over the next year, which is larger than twice the magnitude for the contemporaneous regression. All other factors except for the profitability factor become insignificant. The efficiency factor seems to be correlated with future economic prospects, potentially qualifying itself as a state variable. When the economy is likely to grow in the future, firms with high asset efficiency perform well. ii) Consumption Growth as a State Variable Next, I consider the possibility that these factors correlate with investors’ consumption risk. The consumption-based asset pricing model (CCAPM) developed by Rubinstein (1976), Lucas (1978), and Breeden (1979) states that assets that are positively correlated with the consumption growth should command higher expected returns because investors want insurance against shocks to their consumption. If the factor-mimicking portfolio returns have a positive relation to consumption growth, then the asset pricing capability of the portfolios we saw in the previous section may be substantiated by the CCAPM. Following Jagannathan and Wang (2007), I use the quarterly seasonally adjusted aggregate nominal consumption expenditure on nondurables and services for the period 19702015 from National Income and Product Accounts (NIPA) Table 2.3.5. To convert the nominal series to real series adjusted for inflation, I obtain quarterly price deflator series from NIPA Tables 2.3.4. To construct per capital real consumption series, I use the population numbers from NIPA Table 2.1. I calculate the annual consumption growth over the same previous quarter as ct ( ct 1) 100% . Table 12 shows the correlation of ATO-based quarterly returns and ct 1 consumption growth. Both ab_Sale/NOA and rab_Sale/NOA (orthogonalized to OP) are positively correlated with the contemporaneous, future, and past consumption growth, but the orthogonalized one exhibits stronger correlation. The market return and Sale/NOA have similar 18 correlation patterns with the future (positive correlation) and past consumption (negative correlation). The following two regression models will be estimated: ct b0 b1Factort b2 MKTRFt b3ct 1 t ct 1 b0 b1Factort b2 MKTRFt b3ct t The T-values are adjusted for autocorrelation and heteroskedasticity up to three lags, using the Newey-West (1987) estimator. In both the contemporaneous (Table 14A) and predictive regressions (Table 14B), the market returns almost always enter significantly. In 14A, all of Size, BEME, OP, and dAA are insignificant, so I only report the results for ATO-based factors. Interestingly enough, only the Sales/NOA, adjusted Sales/NOA, and residuals of the ab_Sales/NOA are significant in the regressions. The ab_Sales/NOA that is orthogonal to profitability is the most significant with the highest R-squared. For economic significance, the 10% annual return on High-Low of adjusted Sales/NOA is associated with 0.6% higher consumption growth contemporaneously. In 14B, the Size factor is significant, so is included in all regressions. The Sales/NOA, Sales/AT, and ab_Sales/NOA are significantly associated with the consumption growth increase over the next year. iii) Chen, Roll, and Ross (1986) macroeconomic variables as state variables and possibility of mispricing The previous section with the quarterly returns seemed to suggest that ATO potentially proxy for sources of systematic risks, exhibiting a significant linkage to the risks related to the GDP and aggregate consumption. Now, I perform additional tests using the monthly returns and investigate whether the asset turnover is correlated with the trends in a broader set of macroeconomic variables and examine whether the rational pricing view is supported here as 19 well. Then, I also test the mispricing hypothesis by investigating whether the asset turnover premium is related to the investor sentiments. If the asset turnover premium represents compensation for systematic risks, then it should be correlated with macroeconomic state variables. I use five state variables used by Chen, Roll, and Ross (1986) (CRR). Also, I use investor sentiment index that was made orthogonal to the macroeconomic factors, provided by Baker and Wurgler (2006). If the premium is the result of overpricing during high sentiment periods, then the investor sentiment factor should be able to explain a significant portion of the returns on asset turnover. The test construction closely follows the procedures in Lam, Wang, and Wei (2016) who find that the profitability premium is largely driven by investor sentiments and only a small percentage of the premium is explained by the state variables. I perform the following predictive regression for the asset turnover premium: ATOt 1 a b1Sentt b2 MPt b3UIt b4 DEIt b5UTSt b6UPRt et 1 I obtain the five CRR variables following Liu and Zhang (2008). The data and the descriptions are provided on Liu’s website. MP is defined as the growth rate of industry production; UI and DEI represent unexpected dinflation and the change in expected inflation, respectively; UTS is defined as the yield spread between long-term and 1-year T-bonds; and UPR is the yield spread between Moody’s Baa and Aaa corporate bonds. Sent represents the investor sentiment index provided on Wurgler’s website, constructed as the first principal component of six stock-marketbased sentiment proxies, orthogonalized to macroeconomic trends. Table 15 shows the correlation matrix of the return-based factors, the CRR macroeconomic variables, and the investor sentiment index. All ATO-based factors and OP factor have modest positive correlations with Sent, with OP having the highest correlation. The 20 ATO factors have modest correlations with some of concurrent and past macro variables, including UTS, lagged MP, and lagged UTS. Table 16 reports the regression results. The dependent variables are the monthly returns on portfolios constructed on ab_Sales/NOA, ab_Sales/TA, Sales/NOA, and Sales/TA. Because asset turnover premium exhibits a modest positive correlation with the profitability premium, we extract the asset turnover residuals orthogonal to the profitability premium by regressing the returns on asset turnover High-Low on the profitability premium. The T-statistics are NeweyWest adjusted with lag of 12. Consistently with Lam et al’s finding, wefind that the profitability premium is significantly associated with the sentiment index but has no correlation with macro variables (Column 7). Hence, the profitability premium seems to be largely driven by the investor sentiments related to firm profitability, devoid of macroeconomic content. The regression results indicate that ATO-based returns are significantly related to both the sentiment index and some of the macro state variables. The ATO factors not adjusted for industry (Sales/NOA and Sales/TA) are more strongly linked to investor sentiments than others and are not linked to either industrial production or inflation but to term structure and default spread. The magnitude of the ‘lag_Sent’ slope for ab_Sales/NOA is half the magnitude for OP in column (7). A one-unit increase in the sentiment index is associated with 0.22% higher returns for ab_ATO and with 0.50% higher returns for OP. Higher industry production (MP) is associated with higher returns on ab_Sales/NOA over the next period, higher unexpected increase in price level (UI) with lower returns, and higher expected inflation (DEI) with higher returns. 21 The orthogonalized ab_ATO premium loses the significant positive association with lagged investor sentiment while the link with the state variables are strengthened. The results indicate that ATO premium is macroeconomically linked and is not the result of mispricing driven by sentiments. In sum, the asset turnover portfolio return is higher following high sentiment periods, growing industrial production, higher expected inflation, lower unexpected inflation, and lower credit-risk period, potentially qualifying itself as a state variable. ATO-based Factor-Mimicking Portfolio as the Sixth Risk Factor In the previous section, the factor-mimicking portfolio contructed on industry-adjusted ATO had positive risk-adjusted returns relative to the Fama-French 5-factor model, and exhibited close links to macroeconomic trends and were not merely driven by investor sentiments. If ATO indeed represents a source of systematic risk, then it should provide incremental explanatory power in stock pricing cross-sectionally. The low correlation of ab_ATO factor with all other Fama-French factors motivates adding it as another factor in the asset pricing model and examining whether it helps to price stock returns. The test results of asset pricing models are often sensitive to how the test assets are formed. The first requirement for the test portfolios is that the portfolios need to exhibit sufficiently large cross-sectional spreads in average returns, and also the pattern in average returns across the portfolios is fairly monotonic. It is known that using test portfolios sorted on variables that are also used for creating risk factors can produce results biased in favor of the factors. Hence, it is important to test on various groups of test assets. To minimize the bias, weinclude portfolios formed on industry (49 portfolios), investment (10 portfolios), profitability (10 portfolios), size and book-to-market (25 intersected portfolios), earnings/price ratio (10 portfolios), and net stock issues (10 portfolios). All these portfolios are available from Ken French’s data library. 22 The time-series testing will be conducted on all test portfolios. Table 17 reports the average alphas and the t-statistics. In addition, to evaluate the factor model’s capability to explain the returns on the test assets, the GRS test-statistic is constructed for a joint test for the null hypothesis that all the pricing errors are jointly zero. In short, the mean-variance efficiency of the risk factors is tested. The following is the time-series regression equation that will be estimated for all test portfolio, p: Rpt R ft p p1F1t ... pK FKt pt p p' Ft pt , where R pt is the return on the test portfolio p (p=1, 2, …N) at time t (t=1, 2, …T), R ft is the risk-free return, Fkt is the return on the k-th risk factor at time t, pk is the factor loading on the k-th factor, and pt is the residual. If the asset pricing model is well-specified, then the following should hold: E[ Rpt R ft ] p' E[ Ft ] , implying that the intercept should be close to zero. Table shows the average alpha and t-statistic in parentheses. I start the testing with the Fama-French three- and five-factor model, and then add the ATO factor (measured with Sales/NOA): Rpt R ft p p1MKTRF p 2 Size p3 BEME p 4 dAA p5OP p 6 ATO pt I replace ATO with Sales/NOA and ab_Sales/NOA one after another. The results in Table 17 shows that adding ab_Sales/NOA as an additional factor significantly reduces average alphas and T-statistics (in parentheses) for the majority of test assets while adding Sales/AT does not. I also report the GRS F-statistic for a joint test for the null hypothesis in Table 18. Assuming that the errors are i.i.d. normally distributed with mean zero, the statistic can be 23 computed as following: T N K ˆ 1 ˆ ˆ 1E ( f ))1ˆ ' (1 ET ( f ) ' T N FN ,T N k , where N= number ˆ 1 T ˆ ˆ ' . ˆ 1 T [ f E ( f )][ f E ( f )]', of test assets, K= number of risk factors, and tt T t T t 1 t T T t 1 Adding ab_ATO has an influential effect on the test of the null. For instance, GRS fails to reject the null for industry portfolios after adding ab_ATO after five factors, and the significance of the rejection is reduced from 1% to 2.5% for the EP portfolios. Just adding ab_ATO on top of the FF 3 factors reduces the F-stats lower than or close to FF 5 factors. The conservativeness of the GRS testing is well-known, more prone to rejection than non-rejection, but the magnitude of the F-statistics itself is meaningful in that it represents the distance of the factor return away from the ex-post mean-variance efficient frontier (Cochrane 2009). For all portfolios, the magnitudes of the test statistics get noticeably reduced. To address the possibility that just adding more factors leads to a lower GRS statistic, wetry adding the ATO factor, instead of the ab_ATO. The GRS statistics for the industry and Size-BEME portfolios increase (from 1.59 to 2.05 and from 13.19 to 14.80, respectively). For other test assets, adding ATO has a negligent effect on the GRS statistic. Conclusion This paper is a comprehensive analysis of the informativeness of the asset turnover (ATO) for the future stock performance. To test whether the asset turnover forecasts future stock returns, I perform regression and sorting analysis. Although the exact source that drives the predictability cannot be identified yet, I interpret the results as ATO’s informativeness about the expected profitability, which drives the expected return higher according to the equity valuation model. 24 However, the mispricing view that high ATO firms are consistently undervalued by investors is not completely invalidated until I perform further tests. ATO alone may not be informative about a firm’s future earnings as ATO is largely determined by the inherent industry operating structure. Industry-adjusting (subtracting the industry median from the firm variables) allows us to focus on a firm’s relative position within its industry. Industries have their own “normal” levels for the ATO, and comparing with a firm’s own peers instead of with all other firms in the economy may be more relevant for stock analysis. Indeed, I find that industry-adjusting ATO is more powerful predictor, and survives robustly after the effects of other anomalies, such as the book-to-market equity, size, momentum, accrual, and asset growth. The trading strategy formed based on the adjusted ATO has the highest Sharpe ratio among all strategies based on the anomalies. This paper adds to the body of literature on market anomalies, the cross-section of stock returns, and also a smaller group of studies that look at industry effects for stock returns. Also, I believe this work contributes to a small group of studies that have focused on analyzing the profitability premium alone. I argue that more consideration should be given to the role of ATO in determining the a firm’s risk exposure. Firms distinguishing themselves from the average peers in their skills in asset utilization systematically have higher or lower future returns than the peers. The finding that the asset turnover effect is significantly correlated with the macroeconomic variables, such as GDP growth, consumption growth and others, leads us to posit on the possibility of ATO as a source of systematic risk. While the profitability premium seems to be mainly driven by investor sentiments, the ATO premium is not. 25 Appendix: Variable Description All variables are winsorized at the 1% and 99% levels every month. The item numbers from Compustat are shown in parentheses. NOA: Net Operating Assets=Operating Assets – Operating Liabilities, where Operating Asset=Total Assets (#6) – Cash and Short-term Investments (#1 and #32), Operating Liabilities=Total Assets-Total Debt (#9 and #34) – book value of total common and preferred equity (#60 and #130) – minority interest (#38). PM: Profit Margin=Operating Income (#178)/Total Sales (#12). ATO: Asset Turnover=Sales/Average of NOA t and NOA t-1 . RNOA: Return on NOA=PM x ATO. Leverage: Leverage=total assets(#6)/total stockholders’ equity(#60). ACC: Operating Accruals=[(∆Current Assets(#4)-∆Cash and short-term investments)-(∆Current Liabilities(#5)-∆Debt in Current Liabilities(#34)-∆Taxes Payable(#71))-Depreciation and Amortization Expense(#14)]/Average Total Assets. BEME: Book equity as defined by Fama and French (2008)/Size OP/TA: Novy-Marx Profitability=(Sales-Cost of goods sold (#41))/Average total asset. OP/BE: Fama-French Operating Profitability=(Sales-Cost of goods sold (#41)Selling&Administrative Expenses+Research and Development Expenses)/Average book equity. MOM: Momentum=Cumulative return from t-12 to t-2. dAA: Asset Growth=%∆Total Assets. Size: Firm size=Price x Shares outstanding. NSI: Net stock issue=log(%∆(Shares outstanding x Factor to adjust shares)), where factor to adjust shares is the item ‘cfacshr’ from CRSP. ‘ab_’: This prefix means the variable is demeaned by the industry median. The winsorized variables were used to get the industry-adjusted variables. 26 References Baker, Malcolm, and Jeffrey Wurgler. "Investor sentiment and the cross‐section of stock returns." Journal of Finance 61.4 (2006): pp.1645-1680. Banz, Rolf W. “The relationship between return and market value of common stocks.” Journal of Financial Economics, 9 (1981), pp.3-18. 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Sloan, Richard G. “Do Stock Prices Fully Reflect Information in Accruals and Cash Flows about Future Earnings?” Accounting Review,71 (1996), pp.289-315. Soliman, Mark T. “Using Industry-Adjusted DuPont Analysis to Predict Future Profitability.” Working Paper, University of Southern California (2004) Soliman, Mark. “The Use of DuPont Analysis by Market Participants.” Accounting Review, 83 (2008), pp.823-853. 29 Trailing Sharpe Ratios Five-year rolling Sharpe ratios on the factor-mimicking portfolios are plotted. Table 1: Industry Membership Explaining the Asset Turnover Table 1 reports average adjusted R-squares from running the following regressions for each of the variables: 44 X V ariablet = bit IndustryDummyit + εt i=1 For dependent variables, sales-to-net operating assets (ATO), return on net operating assets (RNOA), and profit margin (PM) are used. See the variable descriptions in the appendix for detailed explanations for the variables used. Std.Dev. is the standard deviation of the 44 R-Squares. Variable ATO RNOA PM Avg. Rsq. 51.77% 18.43% 5.51% Std. Dev. 18.46% 23.59% 14.04% Table 2: Forecasting Profitability Table 2 reports the forecasting errors from predicting the future profitability measures (gross profitability divided by total assets (GP/TA), operating profitability divided by book equity (OP/BE), and return on net operating assets(RNOA)). First, the three equations below are estimated using pooled regression on the first 20 years of data; then the coefficients are used to forecast next 16 years of out-of-sample profitability. The error is the absolute value of the actual and the fitted values of RNOA. Three measures of prediction accuracy are given: mean forecasting errors (MFE), mean absolute deviation (MAD), and mean absolute percentage error (MAPE). The controls in the estimated equations are Log(Sizeit ), Log(BEM Eit ), dAA, Accrual, Log(OScoreit ) (1)P rof itit+1 = a + b0 RN OAit + Controls + eit (2)P rof itit+1 = a + b0 RN OAit + b1 AT Oit + b2 P Mit + Controls + eit (3)P rof itit+1 = a + b0 RN OAit + b1a ab AT Oit + b1b med AT Oit + b2 P Mit + Controls + eit Eq Sum(Error) Sum(Abs Error) MFE*100 MAD*100 MAPE GP/TA (1) (2) (3) 413.56 489.46 351.62 3344.24 3181.05 2899.84 1.91 2.26 1.62 15.435 14.682 13.384 143.86 100.98 99.72 OP/BE (1) (2) (3) 1171.38 1158.76 1127.11 4673.78 4665.76 4665.34 5.41 5.35 5.20 21.571 21.534 21.532 165.40 157.66 155.80 RNOA (1) (2) (3) -62.97 -75.67 -78.05 2319.66 2325.47 2326.57 -0.29 -0.35 -0.36 10.706 10.733 10.738 144.15 149.44 149.34 Table 3: Average Monthly Return on Long-Short Stocks are sorted into deciles based on unadjusted and industry-adjusted variables every June, and next 12-month returns are matched to form value-weighted and equal-weighted portfolio returns. The table displays the average monthly returns on the Long-Short strategy of going long the highest decile and short the lowest (LS); the T-statistics showing whether the average is statistically greater than zero. The breakpoints for grouping use all NYSE non-financial stocks with a share code of 10 or 11. Sorting Variable Portfolio 1 2 3 4 5 6 7 8 9 10 10-1 Portfolio 1 2 3 4 5 6 7 8 9 10 10-1 ab Sales/NOA VW EW 0.85 (3.64) 0.98 (4.13) 0.88 (4.25) 1.03 (5.33) 0.99 (5.42) 1.02 (5.28) 1.14 (5.71) 1.11 (5.55) 1.01 (4.94) 1.14 (4.87) 0.29 (2.05) 1.06 (3.86) 1.13 (4.31) 1.19 (4.9) 1.18 (5.09) 1.11 (5.28) 1.11 (5.24) 1.21 (5.28) 1.28 (5.32) 1.23 (4.96) 1.24 (4.74) 0.18 (2.32) Sales/NOA VW EW 0.73 (3.21) 0.95 (4.88) 0.95 (4.71) 1 (4.91) 0.97 (4.95) 1.11 (5.35) 1.06 (4.94) 1.1 (5.18) 1.08 (5.07) 1.1 (4.41) 0.37 (1.94) 0.77 (3.18) 1.11 (5.16) 1.2 (5.17) 1.15 (4.82) 1.21 (4.94) 1.25 (5.02) 1.23 (4.98) 1.22 (4.84) 1.23 (4.74) 1.26 (4.7) 0.49 (2.82) ab Sales/TA VW EW 0.86 (3.75) 0.94 (3.9) 1.03 (4.43) 0.95 (4.61) 1.02 (5.47) 1.03 (5.14) 1.03 (5.12) 1.21 (5.98) 0.93 (4.51) 1.1 (5.26) 0.25 (1.66) 1.02 (3.71) 1.12 (4.19) 1.25 (4.95) 1.19 (5.13) 1.1 (5.01) 1.23 (5.54) 1.21 (5.27) 1.25 (5.28) 1.22 (5.04) 1.21 (4.95) 0.19 (2.00) Sales/TA VW EW 0.75 (3.43) 1 (4.99) 1.04 (5.11) 1.07 (4.75) 0.97 (4.59) 0.99 (4.71) 1.13 (5.36) 1.04 (4.72) 1.03 (4.77) 1.18 (5.31) 0.43 (2.27) 0.78 (3.18) 1.14 (5.2) 1.24 (5.17) 1.28 (5.02) 1.16 (4.63) 1.24 (4.99) 1.28 (5.11) 1.2 (4.78) 1.2 (4.76) 1.26 (4.99) 0.48 (2.81) Table 4: Decile Characteristics The table reports the value-weighted average characteristics of firms in each asset turnover decile (excluding microcaps): the number of firms, book-to-market equity (BEME), Market Cap (Size), Operating Profitability deflated by book equity and total asset (OP/BE, OP/TA), Asset Growth (dAA), Trading volume (Vol), O-Score, ATO and ab ATO. ab Sales/NOA Rank 1 2 3 4 5 6 7 8 9 10 #Firms 143 140 138 129 126 131 134 143 151 172 BEME 0.67 0.61 0.70 0.76 0.74 0.68 0.55 0.56 0.65 0.53 Size OP/BE 21,327,177 0.40 20,982,956 0.45 22,857,565 0.45 29,811,436 0.43 24,228,574 0.43 28,117,604 0.49 32,770,406 0.55 34,581,677 0.57 42,702,825 0.57 57,215,338 0.64 OP/TA 0.34 0.36 0.37 0.33 0.32 0.39 0.46 0.47 0.45 0.53 dAA 0.18 0.14 0.14 0.14 0.13 0.12 0.14 0.14 0.14 0.20 Vol Oscore 1.01 0.23 0.99 0.21 0.92 0.20 0.89 0.20 0.88 0.22 0.81 0.22 0.85 0.18 0.88 0.18 0.90 0.16 1.11 0.18 ab ATO -1.48 -0.75 -0.46 -0.25 -0.10 0.05 0.26 0.60 1.27 4.01 ATO 1.31 1.38 1.44 1.28 1.25 1.61 2.00 2.30 2.85 5.94 BEME 1.05 0.92 0.77 0.63 0.58 0.56 0.59 0.54 0.52 0.42 Size OP/BE 16,149,049 0.30 17,284,201 0.35 25,802,262 0.41 26,728,586 0.46 31,428,896 0.52 28,776,743 0.55 37,076,058 0.56 44,555,530 0.58 40,623,329 0.59 38,440,943 0.65 OP/TA 0.14 0.19 0.27 0.36 0.42 0.45 0.48 0.49 0.53 0.63 dAA 0.21 0.13 0.13 0.13 0.13 0.12 0.12 0.13 0.17 0.23 Vol Oscore 1.01 0.30 0.85 0.28 0.83 0.23 0.87 0.18 0.85 0.17 0.87 0.17 0.89 0.16 0.86 0.16 1.00 0.17 1.22 0.20 ab ATO -0.40 -0.39 -0.38 -0.37 -0.13 0.09 0.29 0.65 1.00 4.04 ATO 0.39 0.68 1.02 1.32 1.58 1.86 2.19 2.64 3.44 6.86 Sales/NOA Rank 1 2 3 4 5 6 7 8 9 10 #Firms 128 122 127 133 135 137 145 148 155 177 Table 5: Bivariate Sorting Stocks are first sorted into terciles based on book-to-market equity (BEME), Market Cap (Size), Operating Profitability (OP), and Ohlson (1980)’s O-Score; then firms within each tercile are sorted into quintiles based on ab Sales/NOA every June. The next 12-month returns are matched to form value-weighted portfolio returns. The table displays the average monthly returns on the Long-Short strategy of going long the highest quintile and short the lowest (LS); the T-statistics showing whether the average is statistically greater than zero. The breakpoints for grouping use all NYSE non-financial stocks with a share code of 10 or 11. ab ATO LS Log BEME Low Medium High ab ATO LS 1 2 3 4 5 0.40 0.46 0.57 0.63 0.66 0.50 0.62 0.60 0.79 0.76 0.89 0.83 0.78 0.90 1.00 1 2 3 4 5 0.26 2.06 0.26 1.75 0.12 0.58 Small Size Medium Large 0.66 0.87 0.97 1.01 1.00 0.70 0.80 0.72 0.84 0.84 0.34 3.99 0.14 1.78 5-1 ab ATO LS 1 2 3 4 5 5-1 Low OP Medium High 0.34 0.50 0.51 0.49 0.71 0.54 0.62 0.65 0.74 0.65 0.51 0.60 0.61 0.73 0.78 0.36 2.20 0.11 0.85 0.28 1.78 ab ATO LS Low O-Score Medium High 0.44 0.47 0.59 0.61 0.66 1 2 3 4 5 0.22 0.45 0.57 0.56 0.65 0.64 0.60 0.63 0.67 0.73 0.61 0.55 0.60 0.73 0.86 0.22 1.75 5-1 0.43 2.66 0.09 0.81 0.25 1.77 5-1 Table 6: Risk-Adjusted Returns Table 6 reports the intercepts from the time-series regression of the returns on each ATO quintile and high-low long-short (5-1) strategy on the Fama-French factors. The t-statistics are in the parenthesis. Three Factor Alphas VW Portfolio ab Sale/NOA Sorting Variable ab Sale/TA Sale/NOA 1 2 3 4 5 5-1 -0.14 (-1.7) -0.03 (-0.54) 0.08 (1.22) 0.20 (3.26) 0.15 (2.27) 0.29 (2.67) -0.13 (-1.69) 0.03 (0.4) 0.12 (1.99) 0.18 (3.35) 0.11 (1.42) 0.25 (2.00) Five Factor Alphas VW Portfolio ab Sale/NOA Sorting Variable ab Sale/TA Sale/NOA 1 2 3 4 5 5-1 -0.09 (-1.02) -0.05 (-0.74) 0.05 (0.75) 0.11 (1.84) 0.16 (2.42) 0.25 (2.23) -0.06 (-0.78) 0.12 (1.55) 0.13 (2.04) 0.11 (1.95) 0 (-0.01) 0.06 (0.50) -0.14 (-1.31) 0.02 (0.33) 0.06 (0.9) 0.08 (1.34) 0.18 (2.54) 0.32 (2.40) 0.12 (1.22) -0.08 (-1.1) -0.12 (-1.76) 0.01 (0.23) 0.21 (2.99) 0.1 (0.75) Sale/TA -0.08 (-0.74) 0.12 (1.71) 0.03 (0.46) 0.09 (1.48) 0.13 (1.51) 0.21 (1.39) Sale/TA 0.19 (2.02) 0.12 (1.62) -0.04 (-0.61) 0.03 (0.56) 0 (0) -0.19 (-1.51) Table 7: Monthly Fama-Macbeth Regression The following regression equations are estimated for all firms in the sample. (1)-(4)Xretit+1 = interceptt + c1t (Xit − XIt ) + c2t XIt + controlsit + εit (5)-(8)Xretit+1 = interceptt + c1t Xit + controlsit + εit Xret is the monthly excess return over the risk-free, Xit represents an unadjusted ATO, Xit − XIt is an industry-adjusted ATO, and XIt is an industry-median ATO. Industry classification follows Fama and French’s 49 industry portfolios. Controls include all the other unadjusted variables but X. (1) ab Sale/NOA (2) 0.034 3.49 ab Sale/TA (3) (4) (5) 0.07 1.92 0.04 3.00 NSI MOM dAA Size BEME OP/BE 0.06 0.53 -0.59 -1.52 -1.21 -5.37 0.78 3.15 -0.25 -2.61 -0.07 -1.84 0.36 4.02 0.38 4.82 OP/TA Adj-RSQ 0.02 1.77 0.07 1.31 0.22 1.24 -0.69 -1.80 -1.15 -5.22 0.80 3.23 -0.26 -2.63 -0.06 -1.65 0.38 4.21 0.38 4.69 0.07 (8) 0.01 0.19 Sale/TA ACC (7) 0.02 2.31 Sale/NOA med ATO (6) 0.07 -0.02 -0.42 -0.73 -1.85 -1.03 -4.64 0.82 3.31 -0.13 -1.29 -0.06 -1.65 0.40 4.59 -0.12 -1.11 -0.73 -1.85 -1.03 -4.64 0.81 3.29 -0.13 -1.35 -0.06 -1.72 0.40 4.68 0.80 4.96 0.07 0.80 4.96 0.07 -0.58 -1.42 -1.23 -5.08 0.78 3.14 -0.26 -2.54 -0.07 -1.76 0.38 4.27 0.38 4.74 0.06 -0.60 -1.51 -1.23 -5.14 0.76 3.07 -0.25 -2.52 -0.07 -1.83 0.36 4.01 0.38 4.87 0.06 -0.03 -0.48 -0.80 -1.97 -1.02 -4.43 0.80 3.25 -0.12 -1.19 -0.06 -1.60 0.40 4.54 -0.79 -1.97 -1.01 -4.40 0.79 3.23 -0.12 -1.20 -0.06 -1.70 0.39 4.58 0.62 3.71 0.06 0.74 4.37 0.06 Table 8: Within-Industry Fama-Macbeth Regressions Within each industry, next-period stock returns are regressed on accrual (ACC), sales-to-net operating assets (ATO), momentum (MOM), natural log book-to-market equity (Ln(BEME)), log market capitalization (Ln(Size)), net stock issue (NSI), asset growth (dAA), and operating profitability-to-book equity (OP/BE). Industry classification follows Fama French 49 industry portfolios, and industries with less than 15 firms during more than half the sample period are dropped. This leads to having 30 industries, and out of the 30, the number of industries with statistically significant estimates is counted and reported in the table. #significant industry ACC ATO NSI MOM dAA ln(Size) ln(BEME) OP/BE 13 15 3 21 12 12 27 17 Table 9: Correlations among Factor-Mimicking Portfolios Table 9 reports the correlation matrix of the factors. I construct the factors as detailed on page 13-14. MKTRF SMB BEME OP dAA ACC ab Sales/NOA ab Sales/TA Sales/NOA Sales/TA MKTRF SMB BEME OP dAA ACC 1 0.306 -0.337 0.261 -0.394 -0.119 -0.204 -0.369 0.285 0.077 0.306 1 -0.279 0.087 -0.185 -0.111 -0.266 -0.502 0.37 0.05 -0.337 -0.279 1 -0.524 0.656 0.268 -0.15 0.275 -0.467 -0.042 0.261 0.087 -0.524 1 -0.628 -0.521 0.211 0.15 0.532 0.507 -0.394 -0.185 0.656 -0.628 1 0.4 -0.091 0.212 -0.4 -0.14 -0.119 -0.111 0.268 -0.521 0.4 1 0.109 -0.028 -0.438 -0.48 ab Sales /NOA -0.204 -0.266 -0.15 0.211 -0.091 0.109 1 0.582 0.166 0.133 ab Sales /TA -0.369 -0.502 0.275 0.15 0.212 -0.028 0.582 1 -0.152 0.351 Sales /NOA 0.285 0.37 -0.467 0.532 -0.4 -0.438 0.166 -0.152 1 0.72 Sales /TA 0.077 0.05 -0.042 0.507 -0.14 -0.48 0.133 0.351 0.72 1 Table 10: Spanning Asset-Turnover Factor-Mimicking Portfolios Table 10 reports the intercept, the slopes, and the adjusted R-squares after regressing ATO-based factors on the Fama-French factors. Sales/NOA Sales/TA ab Sales/NOA ab Sales/TA Sales/NOA Sales/TA ab Sales/NOA ab Sales/TA Intercept MKTRF BEME SMB 0.26*** 3.06 0.15 1.35 0.29*** 6.36 0.25*** 3.81 0.09 1.13 -0.18 -1.90 0.25*** 5.33 0.07 1.20 0.04 2.20 0.04 1.39 -0.06 -5.10 -0.08 -5.46 0.03 1.35 0.01 0.36 -0.06 -5.36 -0.09 -6.18 -0.26 -9.45 -0.01 -0.26 -0.11 -7.12 0.05 2.28 -0.13 -4.14 0.20 5.39 -0.08 -4.18 0.11 4.50 0.13 6.19 0.02 0.59 -0.08 -6.75 -0.17 -10.80 0.15 7.80 0.05 2.33 -0.07 -6.41 -0.16 -11.00 dAA OP Adjusted r-squared 0.28 0.00 0.16 0.31 0.09 1.44 0.23 3.36 0.03 0.74 0.22 4.78 0.57 10.16 1.04 16.25 0.13 4.04 0.49 11.68 0.41 0.34 0.18 0.44 Table 11: Average Returns, Standard Deviations, and Sharpe Ratios on Long-Short Strategies Table 11 shows average returns(%), standard deviations, and annualized Sharpe Ratios of Long-Short portfolios based on book-to-market equity (BEME), operating profitability-to-book equity (OP), asset turnover (Sales/NOA and Sales/TA), industry-adjusted asset turnover (ab Sales/NOA and ab Sales/TA) and the mix of the Long-Short Portfolios from July 1970 to Dec 2015 excluding microcaps. BEME OP ab Sales/NOA ab Sales/TA dAA ACC Sales/NOA Sales/TA BEME&ab Sales/NOA BEME&ab Sales/TA OP&ab Sales/NOA OP&ab Sales/TA Mean Stdev Sharpe 0.33 0.19 0.20 0.15 0.28 0.21 0.24 0.17 0.26 0.24 0.19 0.17 3.28 1.77 1.14 1.76 1.89 1.51 2.28 2.49 1.65 2.06 1.15 1.34 0.349 0.372 0.608 0.295 0.513 0.482 0.365 0.237 0.546 0.404 0.572 0.439 Table 12: Correlation Matrix: ATO-based Factors, GDP Growth, and Consumption Growth The correlation matrix of the annual returns on the ATO-based factors and the annual GDP growth at a quarterly frequency is shown in Table 12. The seasonally-adjusted GDP growth and Industrial Production (IDP) quarterly series, are obtained from Organization for Economic Co-operation and Development (OECD) Main Indicators and the National Government Series. The growth is calculated from the previous year’s same quarter. For consumption growth, the quarterly seasonally adjusted aggregate nominal consumption expenditure on nondurables and services for the period 1970-2015 are obtained from National Income and Product Accounts (NIPA) Table 2.3.5. The nominal series are converted to real series adjusted for inflation using the quarterly price deflator series from NIPA Tables 2.3.4. Using the population numbers from NIPA Table 2.1, per-capital real consumption series are constructed. The annual consumption growth over the same previous quarter is calculated as ct − 1) ∗ 100. The monthly ATO-based factor returns are compounded over the previous 12 ∆ct = ( ct−1 months at the end of every quarter. The rab Sale/NOA represents ab Sale/NOA orthogonalized to returns on OP (the residuals after regressing ab Sale/NOA monthly returns on the OP returns and compounding last 12 observations every quarter). * denotes the significance of at least 5%. (1) (2) (1) MKTRF 1 (2) Sale/NOA 0.123 1 (3) ab Sale/NOA -0.253* 0.351* (4) rab Sale/NOA -0.15* 0.181 (5) OP -0.233* 0.368* GDP 0.283* -0.064 CG 0.28* 0.059 IDP 0.19* -0.21* lead GDP 0.487* 0.298* lead CG 0.342* 0.374* lag GDP -0.194* -0.271* lag CG -0.148* -0.175* (3) 1 0.823* 0.566* 0.078 0.26* 0.01 0.142* 0.221* 0.201* 0.268* (4) (5) 1 -0.001 1 0.146* -0.076 0.384* -0.093 0.078 -0.1 0.168* 0.003 0.294* -0.035 0.258* -0.018 0.337* -0.01 Table 13A: Contemporaneous Regressions with GDP Growth The following regression is performed: GDP growtht−4,t = b0 + b1 F actort−4,t + b2 IDPt−4,4 + b3 M KT RFt−4,4 + εt The dependent variable is the seasonally-adjusted GDP growth obtained from Organization for Economic Co-operation and Development (OECD) Main Indicators. The growth is calculated from the previous year’s same quarter. The monthly factor returns from the factor-mimicking portfolios are compounded over the previous 12 months at the end of every quarter. The T-values are adjusted for autocorrelation and heteroskedasticity up to three lags, using the Newey-West (1987) estimator. In place of F actort is each of the ATO-based factors or a Fama-French factor for which 12-month returns are compounded every quarter. The rab Sale/NOA represents ab Sale/NOA orthogonalized to returns on OP (the residuals after regressing ab Sale/NOA on OP and compounding last 12 observations every quarter). Table 13B: Predictive Regressions with GDP Growth The following regression is performed: GDP growtht,t+4 = b0 + b1 F actort−4,t + b2 IDPt−4,4 + b3 M KT RFt−4,4 + εt The dependent variable is the seasonally-adjusted GDP growth obtained from Organization for Economic Co-operation and Development (OECD) Main Indicators. The growth is calculated from the previous year’s same quarter. The monthly factor returns from the factor-mimicking portfolios are compounded over the previous 12 months at the end of every quarter. The t-statistics are adjusted for autocorrelation and heteroskedasticity up to three lags, using the Newey-West (1987) estimator. In place of is each ATO-based factor and Fama-French factor for which 12-month returns are compounded every quarter. The rab Sale/NOA represents ab Sale/NOA orthogonalized to returns on OP (the residuals after regressing ab Sale/NOA on OP and compounding last 12 observations every quarter). Table 14A: Contemporaneous Regressions with Consumption Growth The following regression is performed: ∆ct = b0 + b1 F actort + b2 M KT RFt + b3 ∆ct−1 + εt The T-values are adjusted for autocorrelation and heteroskedasticity up to three lags, using the Newey-West (1987) estimator. In place of F actort is each of the ATO-based factors. The rab Sale/NOA represents ab Sale/NOA orthogonalized to returns on OP (the residuals after regressing ab Sale/NOA on OP and compounding last 12 observations every quarter). Following Jagannathan and Wang (2007), I use the quarterly seasonally adjusted aggregate nominal consumption expenditure on nondurables and services for the period 1970-2015 from National Income and Product Accounts (NIPA) Table 2.3.5. The nominal series are converted to real series adjusted for inflation using the quarterly price deflator series from NIPA Tables 2.3.4. Using the population numbers from NIPA Table 2.1, per-capital real consumption series are constructed. The annual consumption growth over the same previous quarter is ct − 1) ∗ 100. calculated as ∆ct = ( ct−1 Table 14B: Predictive Regressions with Consumption Growth The following regression is performed: ∆ct+1 = b0 + b1 F actort + b2 M KT RFt + b3 ∆ct−1 + εt The t-statistics are adjusted for autocorrelation and heteroskedasticity up to three lags, using the Newey-West (1987) estimator. In place of F actort is each of the ATO-based factors or a Fama-French factor. The rab Sale/NOA represents ab Sale/NOA orthogonalized to returns on OP (the residuals after regressing ab Sale/NOA on OP and compounding last 12 observations every quarter). Following Jagannathan and Wang (2007), I use the quarterly seasonally adjusted aggregate nominal consumption expenditure on nondurables and services for the period 1970-2015 from National Income and Product Accounts (NIPA) Table 2.3.5. The nominal series are converted to real series adjusted for inflation using the quarterly price deflator series from NIPA Tables 2.3.4. Using the population numbers from NIPA Table 2.1, per-capital real consumption series are constructed. The annual consumption growth over the − 1) ∗ 100. same previous quarter is calculated as ∆ct+1 = ( ct+1 ct Table 15: Correlation Matrix: ATO-based Factors, Macroeconomic Variables, and Investor Sentiments Table 15 shows the correlation matrix of the factor-mimicking portfolios’ monthly returns, the Chen, Roll, and Ross (CRR 1986) macroeconomic variables, and the investor sentiment index. I obtain the five CRR variables following Liu and Zhang (2008). The data and the descriptions are provided on Liu’s website. MP is defined as the growth rate of industry production; UI and DEI represent unexpected dinflation and the change in expected inflation, respectively; UTS is defined as the yield spread between long-term and 1-year T-bonds; and UPR is the yield spread between Moody’s Baa and Aaa corporate bonds. Sent represents the investor sentiment index provided by Baker and Wurgler (2006), constructed as the first principal component of six stock-market-based sentiment proxies, orthogonalized to macroeconomic trends. * denotes statistical significance at at least 5%. (1) (2) (3) (4) (5) (1) MKTRF 1 (2) Sale/NOA 0.209* 1 (3)ab Sale/NOA -0.375* 0.088* 1 (4) rab Sale/NOA -0.337* -0.037 0.884* 1 (5) OP -0.166* 0.256* 0.468* 0 1 MP -0.021 -0.053 0.06 0.064 0.008 UI -0.04 -0.148* -0.011 0.041 -0.1* DEI 0.002 -0.056 0.056 0.07 -0.013 UTS 0.105 0.078* -0.072* -0.087* 0.01 UPR 0.042 0.113* -0.037 -0.043 0.003 SENT -0.042 0.159* 0.156* 0.08* 0.181* lag MP 0.045 -0.084* 0.091* 0.107* -0.008 lag UI -0.009 -0.035 -0.032 -0.044 0.014 lag DEI -0.111* -0.056 0.037 0.047 -0.01 lag UTS 0.097* 0.089* -0.049 -0.074* 0.034 lag UPR 0.056 0.114* -0.056 -0.063 -0.001 lag Sent -0.025 0.171* 0.158* 0.083* 0.18* Table 16: Investor Sentiment, Macroeconomic Factors, and ATOs The dependent variables are the monthly returns on long-short portfolios constructed on ab Sales/NOA, ab Sales/TA, Sales/NOA, and Sales/TA. ⊥(1) indicates residuals after regressing the returns of Column 1 on the OP (operating profitability) long-short returns. The independent variables are lagged values of the Chen, Roll, and Ross (CRR 1986) macroeconomic variables, and the investor sentiment index. I obtain the five CRR variables following Liu and Zhang (2008) and from Lui’s website. MP is defined as the growth rate of industry production; UI and DEI represent unexpected dinflation and the change in expected inflation, respectively; UTS is defined as the yield spread between long-term and 1-year T-bonds; and UPR is the yield spread between Moody’s Baa and Aaa corporate bonds. ’Sent’ represents the investor sentiment index provided by Baker and Wurgler (2006), constructed as the first principal component of six stock-market-based sentiment proxies, orthogonalized to macroeconomic trends. The T-statistics in parentheses are Newey-West adjusted with lag of 12. Table 17: Asset Pricing Tests: Alpha Horserace with ATO-based Factor Table 17 reports the average alphas and the average t-statistics after regressing each test portfolio’s excess returns on Fama-French factors and either ATO or ab ATO factor. ATO is measured as Sales/NOA. Test Assets 49 Industry 10 EP 10 NSI 10 INV 10 OP 25 Size-BEME 3-Factor 0.304 0.109 0.13 0.098 0.097 0.133 (1.645) (1.305) (1.46) (1.413) (1.341) (1.555) Test Assets 5-Factor 49 Industry 10 EP 10 NSI 10 INV 10 OP 25 Size-BEME 0.222 (1.2) 0.046 (0.563) 0.147 (1.649) 0.076 (1.023) 0.163 (2.109) 0.108 (1.268) 3 Factor+ATO 3 Factor+ab ATO 0.31 (1.714) 0.104 (1.248) 0.127 (1.426) 0.093 (1.345) 0.093 (1.29) 0.125 (1.475) 0.246 (1.295) 0.083 (0.949) 0.129 (1.418) 0.07 (1.018) 0.071 (1.004) 0.112 (1.321) 5-Factor+ATO 5-Factor+ab ATO 0.255 0.043 0.142 0.084 0.133 0.096 (1.423) (0.528) (1.589) (1.111) (1.727) (1.116) 0.218 (1.118) 0.051 (0.607) 0.142 (1.538) 0.091 (1.182) 0.111 (1.43) 0.099 (1.167) Table 18: Asset Pricing Tests: GRS F-Statistic Horserace with ATO-based Factor Table 18 reports the Gibbons, Ross, and Shanken (1989) F-statistic for a joint test for the null hypothesis that all the pricing errors are jointly zero. The critical values and p-values are shown below. GRS Test Assets 3-Factor +ab ATO +ATO 5-Factor +ab ATO +ATO 49 Industry 10 E/P 10 INV 10 OP 10 NSI 25 Size-BEME 4.73 7.84 12.09 16.48 16.89 41.16 1.85 2.27 4.05 5.61 7.24 15.06 5.56 6.03 7.93 10.46 11.27 30.82 1.59 3.47 6.63 6.65 3.47 13.19 1.11 2.06 4.62 4.35 4.69 8.78 2.05 3.50 6.35 6.26 5.29 14.80 F(49,inf) F(10, inf) F(25,Inf) At p<0.05 1.36 1.84 1.52 At p<0.025 1.45 2.06 1.64 At p<0.001 1.77 2.99 2.14