Download Asset Turnover and the Cross-Section of Stock

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.
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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
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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.
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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
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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
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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
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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.
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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.
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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.
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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
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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.
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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
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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.
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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
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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.
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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  b3ct 1   t
ct 1  b0  b1Factort  b2 MKTRFt  b3ct   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 ))1ˆ ' 
(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
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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