Download Historical cost measurement and the use of DuPont analysis by

Historical cost measurement and the use of DuPont analysis by
market participants†
Asher Curtis
University of Washington
Melissa F. Lewis-Western
University of Utah
Sara Toynbee
University of Washington
This draft: October, 2014.
Comments Welcome.
Abstract: We investigate whether historical cost measurement of assets appears to lower the
usefulness of DuPont analysis. Specifically, we examine how variation in the age of a firm’s
assets affects the asset turnover ratio, the DuPont ratio most impacted by asset measurement. We
find that asset turnover ratios are systematically higher and more persistent for firms with older
assets. Forecast errors of asset turnover are systematically associated with the change in asset
age, and these forecast errors are positively associated with future returns. Thus, changes in asset
age provide information on asset measurement biases that investors do not appear to fully
incorporate into contemporaneous returns. Sorting firm-years by both changes in asset age and
asset turnover increases the differences in returns. Our results are consistent with investors being
unable to ex ante disentangle the effect of historical cost measurement on prior asset turnover
ratios when forecasting future asset utilization.
Keywords: Mispricing, DuPont analysis, forecasting, historical cost bias, balance sheet growth.
†
Corresponding Author: [email protected]. We gratefully acknowledge the helpful comments of an anonymous
reviewer, Christine Botosan, Patricia Dechow, Peter Demerjian (FARS discussant), Victoria Dickinson, Michael
Drake, Lucile Faurel, Mark Jackson (WAAA discussant), Christo Karuna, Sarah McVay, Scott Richardson (the
editor), Terry Shevlin, Nemit Shroff, Richard Sloan, Greg Sommers, Vicki Tang (AAA discussant), and participants
at the Fullerton CCRG-SEC Conference, AAA Annual Conference, Financial Accounting And Reporting Section
meeting, and the Western Regional AAA meeting; and workshop participants from the University of Arizona,
University of California - Berkeley, University of Michigan, Emory University, University of Utah, University of
Tennessee, and TCU. This paper was previously circulated with the title “The comparability of accounting rates of
return under historical cost accounting.” All errors remain our own responsibility.
1. Introduction
The usefulness of financial statements for investors varies with how well disclosed current
period data aids in the task of forecasting future economic outcomes. For example, equity investors
are interested in using current period data to predict future outcomes that enable them to assess the
value of equity. Investors are assumed to combine information about current period sales, current
period margins, and current period asset utilization to forecast future sales, profitability, and assets
of the firm. DuPont analysis provides a framework for forecasting future profitability using the
product of profit margin (as a measure of profitability) and asset turnover (as a measure of asset
utilization).1 Soliman (2008) identifies an apparent lag in investors’ processing of changes in asset
turnover but not of changes in profit margin. In this paper, we investigate how modified historical
cost measurement of assets affects the properties of financial ratios, whether these effects help
explain why investors appear to make forecast errors about asset utilization, and whether this links
more generally to the potential mispricing of changes in assets.
Ratios that use accounting inputs, such as the DuPont ratios, are a function of both
economic forces and accounting measurement. As a result, one possible shortcoming of DuPont
analysis, and other approaches to forecasting that use income statement data relative to assets, is
that the inputs are not measured on the same monetary basis (e.g., Konchitchki, 2011; 2013). In
particular, the income statement includes many items measured at current values, such as sales,
while assets are measured using modified historical cost. These differences in measurement lead to
a bias in reported asset-based ratios, complicating the important task of forecasting future
1
The DuPont decomposition is a well-known ratio analysis, which decomposes return on assets into profit margin and
asset turnover. It has been used since the early 1900s and began gaining popularity following Pierre DuPont’s
successful turn-around of General Motors in the 1920s using the DuPont decomposition in their managerial accounting
system. The DuPont decomposition remains a central element of ratio analysis and forecasting in current financial
statement analysis textbooks.
1
outcomes. In the case of the asset turnover ratio, because assets are measured at modified historical
cost, variation in asset turnover not only reflects economic forces, but also the effects of asset
measurement. This makes it difficult for investors to forecast future profitability based on current
period asset utilization (Konchitchki, 2011; 2013).2 We hypothesize that the bias in asset turnover
ratios induced by historical cost measurement provides a partial explanation for the documented
association between changes in asset turnover and future returns over the subsequent 12 months
(Soliman, 2008), as well as potentially contributing to broader asset growth anomalies.
We measure the effect of historical cost on reported asset values by calculating the weighted
average age of assets in years using the ratio of accumulated depreciation to depreciation expense
(e.g. Revsine, Collins, Johnson, and Mittelstaedt, 2009).3 To avoid significant industry differences
in depreciation methods, we industry-adjust this measure prior to ranking our sample firms into
asset age portfolios (hereafter, asset age). We find a significant positive relation between asset age
and asset turnover, with firms in the highest asset age group (i.e., those with relatively older assets)
having significantly higher asset turnover than firms in the lowest asset age group (i.e., those with
relatively younger assets). In contrast, we find the firms in the highest asset age group are
significantly less profitable, as measured by profit margin and return on net operating assets, than
firms in the lowest asset age group. Collectively, these results provide preliminary evidence that
2
Specifically, Konchitchki (2011, 2013) finds evidence that investors underreact to unrealized gains and losses due to
inflation, consistent with investors being unable to accurately incorporate unrecognized changes in value.
3
We assume that differences between modified historical cost and current values are more severe for firms with older
assets. Also implicit in our use of this measure is the assumption that the salvage value for all assets is zero and that all
firms employ the straight-line deprecation method. Providing some support for this assumption, Accounting Trends and
Techniques (AICPA, 2007) finds that the most common depreciation method is straight-line.
2
asset age is linked to a measurement bias, which lowers assets (and thus increases assetdenominated ratios), rather than a competitive advantage, which would be reflected in higher sales.4
We hypothesize that historical cost measurement of assets will lead to biases in the
persistence of the asset turnover ratio due to differences in the monetary basis of sales and assets.
Consistent with prior research, when we estimate persistence for each of the DuPont ratios
individually we find that asset turnover is more persistent than profit margin and return on net
operating assets (e.g., Fairfield and Yohn, 2001; Nissim and Penman, 2001; Penman and Zhang,
2002; Soliman, 2008). One explanation for the higher persistence in asset turnover relative to profit
margin is that economic rents from physical assets are harder to expropriate than knowledge assets
(i.e., Romer, 1986). We extend these results and document that the persistence of asset turnover is
significantly higher for firms with older assets than for firms with younger assets. Thus, it appears
that asset age introduces an effect that could be considered in part as an “artificial barrier to entry”.
We also explore whether asset age affects profitability forecasts by examining how changes
in asset turnover interact with sales growth. We follow the method outlined in Richardson et al.
(2006) and find that asset turnover is generally more important in forecasting future profitability
than sales growth. We also find that asset turnover and sales growth are both statistically more
important determinants of future profitability for firms with the oldest assets than firms with
younger assets. This evidence is consistent with both asset measurement (via measurement error in
asset turnover) and diminishing marginal returns (via declining sales growth) likely playing a role
in the differences in future profitability of older and younger asset firms.
4
Furthermore, we also find that the future profitability of firms in the highest and lowest quintiles of asset age is not
significantly different, thus the linkage between the asset turnover ratio and competitive advantages, at least those that
end in realized earnings, are unlikely to be correlated with asset age.
3
We next examine the association between DuPont ratio forecast errors and changes in asset
age. We investigate two approaches to forecasting - a random walk model (i.e., the change in asset
turnover) and an out-of-sample model that estimates future asset turnover using lagged estimates of
persistence from asset age portfolios.5 We find that both of these forecasting approaches yield
forecast errors that are the most negative for the firms where asset age has declined the most and the
most positive for the firms where asset age has increased the most. One interpretation of these
results is that when firms purchase new assets at current values (decreasing the firm’s average asset
age), asset turnover falls because prior asset turnover was inflated due to unrecognized appreciation
of assets measured at their modified historical cost. Similarly, firms that do not purchase significant
new assets see an increase in asset turnover as the gap between market value and modified
historical cost widens over time. Overall, these results provide evidence that older asset firms have
temporarily inflated asset turnover ratios, which is systematically linked to forecast errors when
assets change.
Turning to whether stock market participants appear to understand the temporary inflation in
asset turnover induced by historical cost measurement, we document that asset turnover forecast
errors are positively associated with future cross-sectional stock returns, consistent with Soliman
(2008). We also find some evidence that the association between forecast errors and future stock
returns varies with changes in asset age. Specifically, across most portfolios of asset turnover
forecast errors, returns are higher for increasing asset age firms and lower for decreasing asset age
firms. As such, the link between the mispricing of asset turnover varies with changes in asset age.
5
Specifically, we assign all firms annually to five portfolios based on asset age in year t to estimate the association
between asset turnover at time t, and lagged asset turnover. We use the coefficients from this regression to estimate an
out of sample forecast of asset turnover at time t+1. We also estimate these forecasts for profit margin and return on net
operating assets.
4
That is, changes in the historical cost bias in asset values affect the extent to which asset turnover
forecasts are mispriced by investors.
In additional analyses we first provide some preliminary international evidence to generalize
our findings and to investigate the role of inflation, which, based on Konchitchki (2011, 2013),
likely increases the mispricing effects related to asset age biases. Consistent with this, we find that
future returns have a higher association with changes in asset age and changes in asset turnover in
high inflation countries relative to low inflation countries. Second, we examine whether changes in
asset age are associated with the magnitude of returns to asset growth based trading strategies
(Richardson et al., 2005; Cooper et al., 2008). We find some evidence that the return spreads and
alphas for these strategies are greater for firms in the extreme changes in asset age.
We contribute to the literature in the following ways. First, we document an important role
of accounting measurement in understanding persistence. Prior literature has generally attributed
the higher persistence of asset turnover solely to the barriers of entry associated with movements of
capital (e.g., Romer, 1986). Our results suggest another reason that asset turnover has higher
persistence. Specifically, measuring assets at historical cost but sales at current values creates the
appearance of a barrier to entry, i.e., an artificial barrier to entry. This finding is important as it
provides evidence of one consequence of differences in the measurement of accounting inputs on
the income statement and balance sheet – a lower degree of usefulness of accounting ratios to
forecast future profitability and asset utilization.
Second our findings help explain why market participants may appear to misprice
information about widely used accounting metrics; they appear to misunderstand the implications of
historical cost accounting, one of the most well-known measurement features of financial
accounting. Thus, our results should be of interest to a wide audience, following calls by Kothari
5
(2001) and others to investigate the underlying reasons that returns appear predictable based on
accounting information. Our approach is based on a practical forecasting perspective. Specifically,
our results are consistent with the practical application of DuPont ratios using unadjusted assets to
measure asset utilization. As these measures are biased upwards by historical cost, they are poor
predictors of asset utilization for the assets firms acquire in subsequent periods, and thus in these
future periods, investors revise their expectations of the firm’s ability to efficiently utilize assets to
generate sales.
2. Background and empirical predictions
2.1. Linking historical cost with asset turnover persistence
Ratios that use accounting inputs, such as the DuPont ratios are a function of both economic
forces and accounting measurement. In terms of economics, margins are considered measures of
pricing power and asset turnover measures of asset utilization. Changes in asset turnover can be
indicative of changes in the productivity of assets, and to the extent that returns on assets are not
easily imitated by competitors, these changes in productivity are likely to be persistent.6 Attributing
all of the variation in asset turnover to economic forces, however, implicitly assumes that the
financial information is measured at its current economic, or market, value. It is well understood
that historical cost lowers the book-value of net operating assets, as historical cost does not allow
for the recognition of appreciation in asset values over time. In contrast, sales are recorded at
current values. We formalize the expected effect of differences in measurement bases in this
section. We start by defining both sales (
) and net operating assets (
) in their current
dollar values as functions of reported values and unobserved appreciation:
6
Dickinson and Sommers (2012) also find that many competitive advantages do not lead to a sustainable increase in
return on net operating assets.
6
=
=
,
(1)
+
, where
≥ 0.
(2)
The superscript c refers to current dollar values, the superscript r refers to reported values (i.e.,
book value of net operating assets), and the superscript u refers to values that remain unrecognized
by the accounting system. Because accounting standards require impairments to be recognized
when asset values are lower than their reported amounts, this implies that
must be positive.
That is, the current value of assets must be at least as high as the reported value. Dividing Equation
(1) by (2) yields a measure of asset turnover (hereafter ATO) with assets measured at current
values, which is a measure of economic efficiency:
=
,
(3)
Equation (3) can be written in terms of the ATO derived from reported values and a bias
attributable to historical cost measurement:
=
1+
.
(4)
As Equation (4) illustrates, if investors calculate ATO using reported values (
they will have a biased measure of economic efficiency (
1+
) then
). The bias is given by the term
, which measures the ratio of unrecognized appreciation in assets to recognized assets.
This bias is increasing in the appreciation of NOA not captured by the accounting system (
Because of depreciation and asset appreciation,
).
will be increasing in the amount of time
since the assets were originally recorded on the balance sheet, what we term asset age. On the other
hand, when new assets are purchased (i.e.,
increases), average asset age declines and the bias
is lower. Thus, the bias in reported in ATO is higher when the average asset age is higher. This
leads to our first hypothesis, which we state in alternate form:
7
H1: Reported asset turnover is positively associated with asset age.
We will not find evidence consistent with our hypothesis, however, if the magnitude of the
bias in ATO due to asset appreciation is too small, if the variation in the asset-age bias across firms
within an industry is too small, or if the proportion of appreciable assets on the average firm’s
balance sheet is too small to have a measurable impact on reported ATO ratios.
Competition is expected to force profitability to mean-revert, or to be less persistent. Among
others Nissim and Penman (2001) provide evidence that ATO has higher persistence, or is more
slowly mean-reverting, than profit margins. Based on Equation (4), persistence in
function of the persistence in both “true” asset utilization (
cost accounting 1 +
is a
) and the bias induced by historical
. Only “true” asset utilization is expected to be mean-reverting due to
competitive forces (i.e., no firm can capture infinite sales increases without increasing assets),
whereas, absent impacting capital expenditures, competitive forces are not expected to affect the
historical cost bias in
. Consequently, because the bias term is not expected to be mean-
reverting, this dampens any mean reversion in reported ATO, making
more persistent than
.7 Thus, all else equal, the greater the bias, the more persistent reported ATO will be.
Following H1, we predict that the bias in reported ATO is increasing in asset age. This leads to our
second hypothesis, which we state in alternate form:
H2: The persistence of reported asset turnover is positively associated with asset
age.
7
Technically, any ratio of two nonstationary (i.e., trending variables) like sales and assets are unlikely to yield a meanreverting ratio unless they are cointegrated. Economic theory suggests that sales and assets are cointegrated as it is
difficult to increase sales over an extended period of time without increasing assets. If a ratio excludes a trending term
such as unrecognized increases in the value of an asset, then these ratios will become more like a random walk, which
increases persistence, see for example Chapter 19 of Hamilton (1994).
8
Our first two hypotheses suggest that historical cost measurement introduces a bias into the
measurement of ATO, and this bias is persistent. This persistent bias is due to how historical cost
measurement affects assets in the denominator of the ratio. However, as the proportion of newer
assets increases, the bias falls as older assets become a smaller portion of the asset base. That is, the
difference between reported asset utilization,
, and “true” asset utilization
will be
decreasing when new assets make up a higher proportion of the asset base (i.e., through purchases
of new assets at market value, and disposals of older assets) and increasing as the assets age
(naturally as a function of time and increasingly when newer assets are disposed of). Thus, changes
in the bias will affect investors’ ability to forecast
because the extent of the bias is difficult to
observe until the asset base changes and subsequent “unexpected” ratios are reported providing
information on the portion of
measurement 1 +
attributable to economic performance (
) and accounting
. Thus, our third hypothesis, stated in alternate form, is:
H3: Asset turnover forecast errors are positively associated with changes in asset
age.
2.2. Linking accounting rates of return to stock prices
Accounting rates of return are linked to stock prices as they provide information about
future cash flows. We formalize the link in this section. Finance theory describes stock returns over
the period t –1 to t, as the change in the price from t –1 to t plus dividends paid during the period t –
1 to t:
# $%&' = ( + ) − ( +, ,
(5)
9
Where # $%&' is the dollar return to an investment at the purchase price ( +, , the closing price is
( and ) is the sum of all net dividends paid over the period t –1 to t.
Edwards and Bell (1961), Peasnell (1982) and Ohlson (1995) show that clean-surplus
earnings and book values can replace dividends in a valuation model. In particular, the cleansurplus relation means that all changes in the book value of equity (- ) can be captured by net
income ( . ) and dividends, i.e., clean-surplus is the relation that - = - +, + . − ) .
Substituting the clean-surplus relation into Equation (5) yields:
# $%&' =
. + /(( − - ) − (( +, − - +, )],
(6)
Writing Equation (6) as an expected return over the period t + 1 at time t yields:
1 (# $%&'
,)
=1( .
,)
+ 1 /∆(( − - )],
(7)
Equation (7) highlights that expected returns include the change in the expected difference
between price and book value. Rearranging the price-level residual income model yields( − - =
1 ∑=
>?,
(5 6 78 + 9 ): 78;< ,
(, 9 )8
1 (# $%&'
,)
=1( .
and substituting into Equation (7) suggests that:
,)
+ 1 @∆ ∑=
>?,
(5 6 78 + 9 ): 78;< (, 9 )8
A.
(8)
Equation (8) illustrates that according to the residual income model, expected changes in
return on equity (ROE) are associated with expected returns. To isolate the role that historical cost
measurement has on accounting ratios, we decompose ROE following prior literature. Nissim and
Penman (2001) highlight that ROE is affected by capital decisions and show that it is useful to
abstract away from the effects that financial leverage has on ROE using return on net operating
assets (RNOA):
# 1 = #
+ /BC1D × (#1 ) ].
(9)
Where BC1D is financial leverage, or net financial assets, and (#1 ) is the (net) rate of return
on net financial assets. Hence, #
captures the firm’s operating profitability after removing the
10
effects of financial leverage. Fairfield and Yohn (2001) and Soliman (2008) further decompose
#
using the DuPont formula:
#
= (F ×
Where PM =
,
Operating Income
Sales
(10)
and ATO =
Sales
.
Net Operating Assets
Combined, Equations (8)-(10) illustrate that
expectations of changes in ATO are positively associated with stock returns.
Miller and Rock (1985) suggest that rational investors will price new information that
changes beliefs about future cash flows as a function of the persistence of that information. Prior
literature, however, find results consistent with investors underreacting to new information, as their
price responses do not appear to fully reflect the persistence in earnings (Kormendi and Lipe 1987;
Bernard and Thomas 1990), accruals (Sloan 1996), special items (Burgstahler et al. 2002), and asset
turnover ratios (Soliman 2008). As we argue above, changes in reported asset turnover will in part
be attributable to changes in economic performance and in part to changes in the measurement bias
in assets. We expect that both of these factors are likely to be persistent as Romer (1986) suggests
that returns to physical assets are difficult to expropriate making asset utilization persistent and as
older assets lead to a persistent bias in reported asset turnover. Although this effect on the value of
assets is well-known, Konchitchki (2011, 2013) finds evidence that unrealized gains and losses due
to inflation are underreacted to by investors, consistent with investors not being able to accurately
incorporate unrecognized changes in value. For these reasons, we conjecture that investors do not
undo the measurement bias in prior asset turnover ratios.
We also anticipate that investors may underreact to asset turnover forecast errors, leading to
predictable future returns. This is because although changes in the asset base will provide some
information about the extent of the bias in asset turnover ratios, the bias is unlikely to be completely
revealed in a single period. Therefore, as future investments are made, the persistent effects of the
11
measurement bias are likely to lead to asset turnover forecast errors in future periods. As the
measurement bias is unobservable, we expect that investors cannot disentangle the measurement
bias from changes in asset utilization completely, and we expect this will lead to an underreaction
to asset turnover forecast errors on average. This leads to our final hypothesis:
H4: Forecast errors of reported asset turnover are positively associated with future
returns.
3. Data and variable measurement
We obtain financial data from the Compustat database and stock returns from CRSP for
fiscal years from 1984-2012. We include all common shares (CRSP share codes 10 and 11) listed
on the NYSE/AMEX and NASDAQ (CRSP exchange codes 1, 2 and 3). We exclude financial
firms (with SIC codes between 6000-6999), as the DuPont ratios are not meaningful for these firms
and to maintain consistency with prior research. We also remove utilities due to the possible
regulation of capital expenditures and firms who are classified into the “Other” category in Fama
and French (1997) as it is a noisy industry grouping. Consistent with Konchitchki (2011), we delete
observations with total assets, sales, or market value of equity less than ten million dollars to avoid
problems associated with using a small denominator. We also delete firms with a closing price less
than one dollar per share at the end of fiscal year t to remove firms with poor liquidity.
We separate firm-years where a loss was reported from our main sample for three reasons.
First, accounting ratios are typically less meaningful for loss firms. Second, we are interested in
whether historical cost accounting inflates accounting based rates of return, but for loss firms,
accounting based rates of return are deflated (i.e., look less negative) when the asset base is larger.
Third, we are interested in linking persistence to historical cost and accounting based metrics and
12
loss firms tend to have lower persistence at least for earnings variables. Combined with other
sample restrictions relating to variable construction, which are discussed below, these restrictions
yield a sample of 56,300 profitable firm-year observations for our primary set of analysis.
3.1. The DuPont decomposition
Following Soliman (2008), we measure RNOA as operating income (OIADP) divided by
average net operating assets (NOA) where NOA is operating assets less operating liabilities.
Operating assets (OA) is total assets (AT) less financial assets (FA).8 FA is cash and short-term
investments (CHE) plus investments and advances (IVOA). Operating liabilities is calculated as
total liabilities (TL) less the current and long-term portion of long-term debt (DLC+DLTT). Asset
turnover (ATO) is sales (SALE) divided by average NOA, profit margin (PM) is operating income
(OIADP) divided by sales (SALE). We restrict our analysis to firms with non-missing operating
income, total assets, common equity, net operating assets, and gross and net property, plant and
equipment and positive sales. All other variables are set to zero when missing. Because we require
these variables in both levels and changes, we require that the ratios can be computed for year t and
year t - 1 for the observation to enter the sample.
3.2. Asset age
We measure asset age as the ratio of accumulated depreciation to depreciation expense. This
is a simple estimate of the age of a firm’s assets that is advocated by financial analyses texts (e.g.,
Revsine, Collins, Johnson, Mittelstaedt 2011).9 We measure accumulated depreciation as the
difference between gross property plant and equipment and net property plant and equipment
8
Note that total assets reported by Compustat aggregates net property, plant and equipment.
Although we anticipate that more precise measures, for example by the method of Konchitchki (2011), would increase
the power of our tests, we do not expect any systematic bias resulting from using our simple measure.
9
13
(PPEGT – PPENT). In order to isolate depreciation expense, we calculate the difference between
depreciation, depletion and amortization (DP) and amortization (AM), where missing values of
amortization are set to zero. We identify and remove observations where asset age appears to be a
data error. Specifically, we eliminate observations where: (i) asset age is negative, (ii) asset age is
greater than the age of the firm, and the (iii) accumulated depreciation is greater than gross property
plant and equipment. Finally, we industry-adjust our asset age variable based on the Fama-French
48 industry classifications. We report the unadjusted means for each industry in Appendix A, as
expected, average asset age varies significantly by industry, highlighting the need for industry
adjustments to this variable.
3.3. Concurrent and future returns
We calculate average buy-and-hold size-adjusted abnormal returns for each portfolio over
holding periods of 12, 24, and 36 months beginning five months after the end of the fiscal year.
Buy-and-hold returns for firms that delist during our sample period are adjusted for delisting returns
following Beaver et al. (2007). We also calculate concurrent returns using returns for the 12 months
ending four months after the end of fiscal year t (Ret).
4. Empirical results
4.1. Descriptive statistics
In Table 1, we provide mean values for the variables used in our study, both for the full
sample, for loss firm-years separately, and by quintiles of asset age (excluding loss firms). We
report differences between the mean characteristics of firms with the oldest asset age and the mean
characteristics of firms with the youngest asset age in the final column. All financial ratios are
14
winsorized at the 1st and 99th percentile to reduce the impact of outliers on the means. The average
return on net operating assets is 0.153. Average asset age is 6.103, the average asset turnover ratio
is 2.676, and the average profit margin is 0.060, similar to Soliman (2008). The average firm in our
sample has a market value of equity of 2,586 million, consistent with these companies being larger
and reflects our removal of smaller firms in our sample screens.
Asset turnover is significantly higher for the portfolio of firms with the highest asset age.
Specifically, asset turnover is 2.503 for firms with the youngest assets (in Q1) and 2.837 for firms
with the oldest age (in Q5). The difference of 0.334 is statistically significant at the 1% level.10
Thus, we find evidence consistent with H1, which predicts a positive association between ATO and
asset age.11 We also report the average values of other accounting ratios and performance
indicators. We find significant differences in profit margin (PM) and return on net operating assets
(RNOA) between the oldest and youngest asset firms. However, we find that firms with the
youngest assets have significantly higher PM and RNOA than those firms with the oldest assets. To
the extent that RNOA is driven more by PM than ATO (Amir et al., 2011), these results suggest
that relation between asset age and ATO is not driven by asset age reflecting factors correlated with
economic performance, as we would find similar relations between asset age and both RNOA and
PM.12 Rather, these results suggest that asset measurement impacts reported ATO ratios, with olderasset firms reporting more upwardly biased ATO ratios.13
10
We estimate the statistical significance of the difference in the mean values between the extreme quintiles after
accounting for both cross-sectional and time-series correlation.
11
We confirm the robustness of this result to several controls for determinants of economic performance. We discuss
this analysis further in section 5.2.
12
Related to this observation, Konchitchki and Patatoukas (2014) find that the relation between ∆RNOA and future real
GDP growth is driven by ∆PM, not by ∆ATO.
13
Throughout our analyses, we industry-adjust asset age and changes in asset age due to significant variation across
industries in this measure, which could be attributable to differences in depreciation methods across industries. In
untabulated analyses, we also confirm the robustness of our results to industry-adjusting the accounting ratios.
Inferences are unchanged with these adjustments (not tabulated).
15
We also provide evidence that our measure of asset age captures changes in the asset base.
Specifically, we use a broad measure of investment following Richardson (2006) and compare
investment as a proportion of total assets for firms in each asset age quintile. Specifically, we
measure total investment as the sum of capital expenditures, research and development
expenditures, and acquisitions, less the sale of property, plant and equipment, plus amortization and
depreciation (CAPX + XRD + AQC – SPPE + DPC). The results illustrate that firms with the
youngest assets invest significantly more than firms with the oldest assets. Older asset age firms are
also typically value firms with higher book-to-market ratios and are on average significantly older
than firms with the youngest assets.14 Similarly, we also find that firms with the youngest assets
have significantly higher sales growth and accruals (∆NOA) than firms with the oldest assets. As
asset turnover is lower for these firms with higher sales growth our results are consistent with
conservatism and growth being substitutes (Rajan et al., 2007). Finally, consistent with asset age
capturing accounting measurement effects as opposed to economic forces, we find no significant
differences in the change in future profits over the period t to t+3 between the highest and lowest
asset age quintiles.
4.2. The association between the persistence of the DuPont ratios and asset age
Hypothesis 2 predicts a positive association between the persistence of asset turnover and
asset age. To test this hypothesis, we estimate the following persistence regressions for each of the
five portfolios ranked by asset age:
#
>
>
14
=
K
+
= LK + L,
,#
> +,
> +,
+
(11)
+
,
(12)
Note however, that the market value of equity suggests that the extreme asset age firms are smaller on average.
16
(F> = MK + M, (F>
+,
+
(13)
The regressions in Equations (11) – (13) are standard in the accounting literature and
measure the average persistence for equally-weighted portfolios. Sorting on asset age allows us to
test whether the average persistence of RNOA, ATO, PM is higher for firms with older assets. We
predict that asset age will increase the persistence of asset turnover but we do not make any ex-ante
predictions regarding the persistence of PM or RNOA. Specifically, hypothesis 2 predicts L, will be
higher for firms with older assets.
We estimate Equations (11) – (13) by asset age quintiles and present the results of the
pooled estimates that correct for cross-sectional and time-series correlation in Table 2 (Petersen,
2009).15 We also present results separately for the full sample (including loss firms) and for loss
firm-years separately. In Panel A, we provide the estimates of the RNOA. The persistence of
RNOA in our sample varies across the asset age groups, but is not significantly different between
the oldest and youngest asset firms.
In Panel B, we report the persistence of asset turnover. In this case, consistent with
hypothesis 2, we see a clear increase in the persistence of asset turnover as asset age increases.
Specifically, the persistence of asset turnover for firms with the youngest assets is equal to 0.715,
whereas the persistence of asset turnover for firms with the oldest assets is 0.836, where the
difference is significant at the 1% level.16 Thus variation in asset age appears to make asset turnover
less comparable, as it biases the asset turnover of older asset firms upwards. This comparability
concern will be persistent until the bias in the asset base is removed, either by disposals of older
assets or purchasing newer assets.
15
Our inferences are unchanged when estimating Equations (11)-(13) by year and asset age quintiles and obtaining the
t-statistics based on the distribution of the parameter estimates (untabulated).
16
Results are robust to estimating persistence by quintiles of the average asset age in t and t-1 (untabulated).
17
In Panel C, we report the persistence coefficients for PM. The results are similar to those of
the RNOA where we find evidence of an inverted U-shape in the persistence of PM across the asset
age quintiles. Furthermore, the bottom and top quintiles of asset age do not differ significantly in
the persistence of PM. Thus, asset age does not have a systematic effect on the persistence of the
PM, which provides further support that asset age captures an accounting measurement effect rather
than differences in economic forces across the firms in the different quintiles. Given the lower
persistence of loss firm-years, we exclude these firm-years in our remaining analyses, unless stated
otherwise.
4.3. Forecasting RNOA using additional decompositions
Because forecasting financial statement elements is typically undertaken jointly, we also
investigate two decompositions of RNOA, which highlight how asset turnover contributes to
forecasting RNOA. We present the results of these decompositions in Table 3. In Panel A, we
examine the DuPont decomposition and find a marginal increase in the association between lagged
asset turnover and RNOA for firms with older assets. However, the difference in the coefficients
between Q5 and Q1 is not significant at conventional levels. Consistent with Amir et al. (2011), we
also find that PM appears to have stronger predictive power for forecasting future RNOA than ATO
even though ATO is individually more persistent. This result also provides some descriptive
evidence as to why the persistence of RNOA is more similar to PM than ATO in Table 2.
In Panel B, we use a decomposition of RNOA based on long-term accruals provided by
Richardson et al. (2006). This decomposition illustrates that long-term accruals can be decomposed
into sales growth, the change in asset turnover, and the interaction of the two terms. We estimate
the model in Richardson et al. (2006) for the full sample, loss firm-years and by quintiles of asset
18
age separately. Our results illustrate that both the change asset turnover and sales growth are
significantly more negatively associated with future RNOA for older asset firms than for younger
assets firms. These results suggest that the historical cost bias in asset measurement creates
accounting distortions, which contribute to the lower persistence of accruals (e.g., Richardson et al.,
2006). Additionally, the difference in the effect of sales growth on future RNOA by asset age
quintiles suggests a significant role of diminishing marginal returns, as sales growth has a lower
effect on persistence for firm-years with older assets. Finally, we also present the F-statistic
comparing the coefficients for sales growth and the change in asset turnover in Panel B. Except for
the highest quintile of asset age, we find a significant difference in the coefficients for each
subsample examined. Overall, the results in Panel B suggest that both asset measurement and
diminishing marginal returns likely play a role in the differences in forecasting RNOA for older and
younger asset firms.
4.4. Correlation between asset turnover forecast errors and changes in asset age
Hypothesis 3 predicts that forecast errors of asset-based ratios are positively associated with
changes in asset age. We calculate forecast errors for each DuPont ratio based on two different
forecasting models. First, we forecast each ratio as a random walk, where the forecast error is
simply the change in the ratio from year t-1 to year t. Second, we calculate forecast errors based on
the AR(1) models described in Equations (11) - (13). Specifically, we subtract from the actual
realizations of each DuPont ratio the predicted value, where the predicted values are calculated
using parameter estimates from the asset age portfolio that the firm belonged to in the prior year.17
17
Thus, the AR(1) forecast errors are out of sample forecast errors and are estimated from 1985-2012.
19
We present the average value of these forecast errors as well as additional variables for
quintiles sorted on the basis of the industry-adjusted change in asset age in Table 4. Consistent with
expectations, in Panel A, we find the mean random walk forecast error for firms in quintile 1 is 0.139 and the mean forecast error for firms in quintile 5 is 0.128. The difference between these
mean forecast errors is 0.268 and is significant at the 1% level. The AR(1) forecast errors are
presented in Panel B and although the forecast errors are smaller than the random walk forecast
errors, we continue to observe a similar pattern in the forecast errors and document a similarly
significant difference in the AR(1) forecast errors between the highest and lowest change in asset
age quintiles. These results suggest that when firms make more investments in assets or dispose of
older assets, thus reducing the average age of their assets, forecasts of ATO overestimate the
persistence of the ratio. In contrast, when firms asset base increases in average age, forecasts of
ATO underestimate the persistence of the ratio. Thus, consistent with hypothesis 3, we find
evidence of a positive relationship between ATO forecast errors and changes in asset age. We also
find evidence of significant differences in the random walk forecast errors for PM and RNOA for
firms in the highest and lowest quintiles of changes in asset age, suggesting that asset age effects
may also be correlated with future profit margins. Overall, Table 4 provides evidence consistent
with the notion that changes in asset age are systematically associated with ATO forecast errors,
consistent with our third hypothesis.
We present additional descriptive statistics for quintiles sorted on the basis of the industryadjusted change in asset age in Panel C. First, we illustrate that firms whose average asset age has
declined the most (i.e., Q1) made significantly greater investments (TI/TA) and experienced
significantly greater sales growth during the year than firms whose average asset age has increased
20
the most (i.e., Q5), and this difference is significant at the 1% level.18 This provides additional
support for our asset age variable. As changes in asset age provide information about the removal of
a bias in asset measurement, we expect these changes to be associated with poor stock price
performance. Consistent with this prediction, we find that both contemporaneous and future returns
are significantly greater for firms with the largest increases in asset age (Q5) relative to firms with
the greatest declines in asset age (Q1). As we see similar patterns in future returns over longer
horizons, suggesting that investors do not immediately impound the information in changes in asset
age.
4.5. The correlation between stock returns, asset turnover forecast errors, and changes in asset age
Our fourth hypothesis predicts that asset turnover forecast errors are positively associated
with concurrent and future returns. In Table 5, we report the mean buy-and-hold returns for various
portfolios over several horizons. Specifically, we measure concurrent returns (Ret) as buy-and-hold
returns for 12 months ending four months after the end of fiscal year t. Future size-adjusted buyand-hold abnormal returns are held at 12, 24 and 36 month, beginning five months after the end of
the fiscal year t. We report statistical significance of the hedge returns to the extreme portfolios
after adjusting for cross-sectional and time-series correlation (Petersen, 2009; Gow et al., 2010).
In Panel A, we report the raw returns to portfolios formed on the basis of the random walk
forecast errors for ATO (i.e., changes in ATO). In the year over which ATO is realized and
reported, returns are increasing across quintiles. However, consistent with Soliman (2008), we find
evidence that investors fail to fully incorporate the effect of changes in asset turnover ratios, as the
returns subsequent to the realization of the asset turnover are significantly greater for the firms with
18
We also find consistent results when examining only capital expenditures as a measure of investment (untabulated).
21
positive changes in asset turnover relative to the firms with the lowest changes in asset turnover.
We also report returns over longer horizons and find that the returns are increasing over the holding
period, suggesting that the incorporation of forecast errors into stock prices occurs over a relatively
long horizon. Nonetheless, the majority of the future returns are realized within the first year after
portfolio formation. This is consistent with market participants calibrating their estimates of the
magnitude of the bias over time as subsequent ATO ratios are reported.
In Panel B, we report returns to portfolios sorted on the forecast errors generated from the
AR(1) forecast model in which firm-years are assigned based on membership in the asset age
portfolio in year t-1, and the forecast errors being the difference between time t asset turnover and
the predicted value of the ratio. This method generates slightly greater hedge returns than the
random walk specification. Specifically, the raw hedge return is 0.076 or 7.6% spread over the 24
months after portfolio formation, is approximately 2.2% higher than the random walk model.19
In Panels C and D, we report the average value of one-year ahead size-adjusted buy-andhold abnormal returns to portfolios formed by independent double sorts on the basis of the change
in asset age and ATO forecast errors. Here we examine whether the returns associated with asset
age vary by the change in asset age. We expect that the returns will be lower for firms in the lowest
asset age quintile within each change in asset turnover quintile. In Panel C, we find some evidence
consistent with this expectation, as in each column the returns appear higher in the highest change
in asset age (Q5) portfolio than in the lowest change in asset age (Q1) portfolio. Other than in Q3 of
the change in asset age, however, the results are typically not statistically significant. When we
19
In untabulated analyses, we estimate the hedge returns to portfolios formed on the basis of AR(1) forecast errors in
PM and RNOA. As expected, we find that the concurrent hedge returns are significantly positive, suggesting that firms
with higher than predicted PM and RNOA have significantly higher future returns than firms with lower than predicted
PM and RNOA. However, in contrast to the results in Table 5, future returns to a hedge portfolio based on AR(1)
forecast errors of PM (RNOA) are significantly (insignificantly) negative.
22
examine the two most extreme portfolios in Panel C (i.e., firm-years in the lowest quintiles for both
the change in asset age and forecast errors and those in the highest quintiles for both the change in
asset age and forecast errors), we see a significantly positive return spread (0.055), which we
confirm is statistically significant and robust to controlling for various proxies for risk. We find
similar results in Panel D, although these results are statistically significant in the predicted
direction within four of the five quintiles of the change in asset turnover.
Overall, the evidence in Table 5 provides evidence in support of hypothesis 4. In addition,
the out-of-sample forecast errors based on prior levels of persistence have a greater association with
future returns and have a greater ability to sort future returns within each portfolio, which is
consistent with investors being unable to disentangle changes in asset measurement effects from the
change in asset turnover.
4.6. Multivariate analysis of future returns
In Table 6 we examine the association between one-year ahead size-adjusted buy-and-hold
returns, changes in asset age, and asset turnover ratio forecast errors, controlling for known sources
of variation in returns. We follow the methodology of Doyle et al. (2003) and rank the independent
variables into quintiles ranging from 0 to 4 and divide the rank by 4. We also include controls for
sales growth and the change in net operating assets, as well as the ratio of total investment to total
assets from Richardson (2006). We also calculate a number of variables that aim to control for firmcharacteristics and risk in our tests. Specifically, for each firm we calculate market capitalization
(MVE) at the end of the fiscal year as the product of shares outstanding and the closing price
(CSHO*PRCC_F), the book-to-market ratio (BM) as common equity divided by MVE (CEQ /
23
MVE), lagged annual beta from the market-model using the CRSP value-weighted index (beta),
lagged annual idiosyncratic risk using the variance of the market model residuals (Sigma).
We report these results in Table 6. In column (1) we report results using the random walk
forecast errors. After controlling for various firm and risk characteristics, we find a positive
association between these forecast errors of asset turnover and future returns, although this
association is not significant at conventional levels. Untabulated analyses reveal that including the
change in net operating assets in the model subsumes the predictive power of the change in asset
turnover. Furthermore, we find no evidence of an association between changes in asset age and
future returns. In column (2) we investigate the forecast errors generated by the AR(1) model, and
find evidence of a positive and significant association between asset turnover forecast errors and
future returns (p<0.01). These results suggest that the future market prices are predictably related to
the errors resulting from forecasts using biased prior asset turnover.
We next examine whether there are differences in the apparent mispricing of asset turnover
between firms with the largest and smallest changes in asset age. Specifically, we examine the
model in column (2) of Table 6 for the bottom and top quintiles of the change in asset age
separately and report results in columns (3) and (4) of Table 6 respectively. We find no evidence of
mispricing for asset turnover for firms whose average asset age has declined the most (Q1) but we
continue to document a significant positive association between the asset turnover forecast errors
and future returns for firms whose average asset age has increased the most (Q5). Despite visual
evidence of an economically greater coefficient, we find that this difference is not statistically
significant at conventional levels (two-sided p-value = 0.183; untabulated).
5. Additional Analyses
24
5.1.
International evidence
In this section we report some preliminary international evidence to examine whether asset
age and DuPont ratios are associated with future returns in an international sample. In addition to
expanding the generalizability of our results, the international setting allows us to examine variation
in the inflation of assets, which we expect to exacerbate the effects of asset age on asset values
(Konchitchki 2011, 2013). Thus, we sort each country into one of three inflation portfolios, low,
middle, or high, based on their historical inflation rates according to the average inflation rate for
each country on the World Bank’s country level database. We collect accounting and return data for
Australia, Canada, Brazil, Switzerland, Chile, China, Germany, Denmark, Egypt, France, UK,
Greece, Hong Kong, Indonesia, Israel, India, Italy, Japan, Korea, Cayman Islands, Mexico,
Malaysia, Netherlands, Norway, Pakistan, Sweden, Singapore, Thailand, Taiwan, Vietnam,
Bermuda, and South Africa, from Bureau van Dijk’s Osiris database.
We are able to examine the period 2001-2012, limited mainly by the availability of return
data on Osiris. We measure the change in asset age as the change in the ratio of accumulated
depreciation over depreciation expense, which we industry-adjust using 1-digit SICs within each
country, and then rank within each country to form quintile portfolios of the change in asset age.
We measure the change in asset turnover (∆ATO) as sales divided by NOA and the change in
profit margin (∆PM) as net sales divided by operating income after tax. We also calculate market
value and book-to-market ratios using the closing price at the time of the fiscal year end. We rank
each of these variables annually within each country to assign firms to quintile portfolios for each
variable.
We report estimates of the association between future returns, asset age, and the DuPont
variables by inflation groups in Table 7. Each regression includes country fixed effects and we
25
cluster standard errors by firm. In columns (1) - (3) we report the association between future returns
and the change in asset age. In each case, the coefficient is positive and significant, which is
consistent with the univariate results we report in Table 5 Panel A for the US sample. In contrast to
the US sample the change in asset age is not subsumed by the inclusion of the change in asset
turnover in columns (4) - (6). In addition, the association appears to be higher among high-inflation
countries, but the difference between the high and low inflation countries is not statistically
significant. Consistent with the US sample, we also find international evidence of future returns
being associated with changes in the asset turnover ratio in columns (4) - (6). In this case, the
association is statistically stronger in the high-inflation countries relative to the low-inflation
countries. We find inconsistent results for the change in the profit margin driven primarily by the
negative association between future returns and changes in profit margin for the low inflation
countries.
Taken together we provide some preliminary international evidence that is consistent with
evidence in the US sample where we see evidence of a positive association between changes in
asset age and asset turnover with future returns. Further the results extend the generalizability of our
US evidence as the asset related associations are stronger in countries with higher levels of
inflation. This analysis has to be interpreted with the important caveat that although we use country
fixed effects in this analysis, it is difficult to rule out differences in market structure as many high
inflation countries are also developing countries.
5.2. Is asset age associated with the returns to asset-growth trading strategies?
In this section we provide investigate whether asset age helps explain cross-sectional asset
pricing anomalies that are based on the change in assets. Richardson et al. (2006) highlight that
26
asset growth measures can be decomposed into functions of growth measures, changes in efficiency
measures, and the interaction of growth and efficiency. We find that asset age affects the
persistence and forecast errors of asset turnover which is an asset-denominated efficiency measure.
It is possible that asset growth anomalies will share a common mispricing of asset utilization. To
investigate this we follow prior literature in asset pricing and form decile portfolios based on two
broad asset growth based anomalies, the change in net operating assets (Richardson et al., 2005),
and the change in total assets (Cooper et. al., 2008).20
In Panel A of Table 8 we report the average monthly returns for each of the decile portfolios
ranked on the two measures of asset growth, along with the average monthly return spread between
portfolio 10 and portfolio 1. For ∆NOA the spread returns (P10 - P1) are significant and negative in
all asset age portfolios. Comparing columns (1) and (2) the return spreads (P10-P1) are weakly
statistically more negative for firms with declining asset age, (p = 0.093, untabulated), but the
difference between Q1 and Q5 of the change in asset age is not statistically significant. In terms of
the magnitude of the return spread, the 90 basis points reported in column (1) (P10-P1) is
approximately equal to 10.8% on an annualized basis. The lower returns than those reported by
Richardson et al. (2006) are most likely due to lower hedge returns in more recent years. We find
similar results for the declining asset age firms for the change in total assets strategy (column 4),
with visual differences between the portfolios but no statistical evidence of difference between the
portfolios.
In Panel B, we report the monthly abnormal return spread for each portfolio and the spread
portfolio, controlling for the monthly factor returns related to market returns, size, book-to-market,
20
The differences between these two strategies relates to how they treat financial leverage. That is, Richardson et al.
(2006) examine the effect of changes in operating assets, while Cooper et al. (2008) combine this effect with changes in
financial leverage.
27
and momentum. The results are similar to the raw returns in Panel A, with the exception that we
find a weak statistical difference between the return spreads (P10-P1) between the change in asset
age Q1 and Q5 portfolios. The main reason for the differences across age quintiles is that the lowest
change in asset age portfolio (Q1) has much lower returns, especially for the short-side of the
strategy (for example, both P9 and P10 have statistically negative alphas). This result is consistent
with our conjecture that declines in asset age provide information on asset biases that affect future
profitability. Taken together, there is some weak evidence that changes in asset age aid in
explaining broader asset based anomalies, with these effects concentrated in the short-side of the
strategy.
5.3.
Gross-profitability-to-total assets
Novy-Marx (2013) finds evidence of a link between the gross-profit-to-assets ratio and
future stock returns, where gross-profit is the difference between sales and cost of goods sold. Due
to the similarity between gross profit and the asset turnover, we provide estimates of the persistence
of gross-profit to assets by asset age quintile. We report these results in Table 9 and find that the
results are very similar to those for the asset turnover ratio. The gross-profit to assets ratio,
however, is even more persistent than the asset turnover ratio, which is likely due to the strong
persistence in the difference between sales and COGS due to relatively stable pricing power and
sticky costs. In Panel B, we replicate the forecast errors relating to the changes in asset age by asset
age quintile. Unlike the results for asset turnover, we do not find consistent evidence of differences
in changes in gross-profit-to-assets ratios across asset age quintiles. In part this appears to be due to
the changes being very small. We do find that the forecast errors based on the prior persistence of
gross-profit-to-assets differ by change in asset age quintile, consistent with the asset turnover ratio.
28
We report the association between future returns and the gross-profit-to-assets ratio in Panel C of
Table 9. In untabulated results, however, we find that there is no evidence of an association
between future returns and the gross-profit-to-assets ratio for any of the change in asset quintile
portfolios.21
5.4.
Robustness tests
We conduct several additional untabulated robustness analyses on our key findings. First,
we confirm that the positive relation between asset age and ATO ratios is robust to controlling for
economic determinants of performance such as size, book-to-market, beta, sigma, firm age, lagged
operating performance, and future performance. Second, we also estimate the persistence of the
DuPont ratios by quintiles formed on the basis of firm age. Although we find a positive monotonic
relation between the persistence of both PM and RNOA across firm age quintiles, the persistence of
ATO is virtually identical in the top three quintiles of firm age (i.e., amongst the oldest 60% of
firm-year observations). Thus, our results are more consistent with asset measurement effects
driving the associations we find rather than firm life-cycle effects. Third, we consider the possibility
that firms with high levels of analyst coverage will mitigate the apparent mispricing of changes in
asset turnover. Specifically, we investigate whether the association between future returns and
changes in asset turnover are systematically different for firms which have the highest level of
analyst following on I/B/E/S. We do not find any evidence consistent with this prediction when
measuring high analyst following as firms in the top quintile of annual analyst coverage.
21
In these untabulated results, whereas the results are not significant at conventional levels, all of the gross-profit to
asset portfolios exhibit lower returns to the lowest change in asset age portfolios, similar to the results for asset
turnover. These results can be reconciled to Novy-Marx (2013) as our change in asset age quintiles exclude loss firms,
whereas the univariate evidence, which is consistent with Novy-Marx (2013), includes loss firms.
29
6. Conclusion
One of the well-known implications of historical cost accounting is that reported asset
values can be biased downward, as appreciation in these assets cannot be recognized on the
financial statements. This feature of historical cost accounting has implications for the level and
persistence of accounting rates of return when the numerator and denominator have different
measurement bases. We find that firms with older assets have significantly higher and more
persistent asset turnover ratios, consistent with historical cost accounting inducing a bias in the
reported ratio. Consistent with the age of the asset base leading to biased asset turnover persistence
measures, we also find that changes in the average asset age of a firm (i.e., changes in the bias in
asset turnover ratios) are positively associated with asset turnover forecast errors. Finally, we
provide evidence that these forecast errors are significantly associated with future returns,
suggesting that investors update their expectations about the economic forces driving reported asset
turnover as the asset base changes and the bias induced by historical cost is revealed in future
periods.
Our results highlight a practical shortcoming in the application of DuPont ratios, and more
broadly, efficiency ratios that use information that is not measured on a consistent monetary basis.
This finding is important as it provides evidence of one consequence of the broad problem of
measurement differences of accounting inputs on the income statement and balance sheet – a lower
degree of usefulness of accounting ratios commonly used to forecast future profitability. In
addition, our findings contribute to the understanding of why market participants may misprice
information about widely used accounting metrics that aid in understanding future profitability as
current disclosures make it difficult to estimate the extent of the bias in the measurement of assets
until the asset base changes and subsequent financial ratios are realized.
30
References
AICPA, 2007. Accounting Trends and Techniques. American Institute of Certified Public
Accountants: New York.
Amir, Eli, Itay Kama, and Joshua Livnat, 2011. Conditional versus unconditional persistence of
RNOA components: implications for valuation. Review of Accounting Studies 16 (2): 302-327.
Beaver, W. H., M. McNichols, and R. Price. 2007. Delisting returns and their effect on accountingbased market anomalies. Journal of Accounting and Economics, 43: 341-368.
Bernard, V. L., and J. K. Thomas. 1990. Evidence that stock prices do not fully reflect the
implications of current earnings for future earnings. Journal of Accounting and Economics,
13(4): 305-340.
Burgstahler D., J. Jiambalvo, and T. Shevlin. 2002. Do Stock Prices Fully Reflect the Implications
of Special Items for Future Earnings? Journal of Accounting Research, 40(3): 585-612.
Dickinson, V., and Sommers, G. A. 2012. Which Competitive Efforts Lead to Future Abnormal
Economic Rents? Using Accounting Ratios to Assess Competitive Advantage. Journal of
Business Finance & Accounting, 39(3‐4), 360-398.
Doyle, J. T., R. J. Lundholm, R. J., M. T. and Soliman. 2003. The predictive value of expenses
excluded from pro forma earnings. Review of Accounting Studies, 8(2-3): 145-174.
Edwards E. O. and P. W. Bell, 1961. The Theory and Measurement of Business Income. University
of California Press: Berkley, CA.
Fairfield, P., and T. Yohn. 2001. Using asset turnover and profit margin to forecast changes in
profitability. Review of Accounting Studies 6: 371-385.
Fairfield, P., J. S. Whisenant, and T. Yohn. 2003. Accrued earnings and growth: Implications for
future profitability and market mispricing. The Accounting Review, 78: 353-371.
Fama, and K. R. French, 1997. Industry costs of equity. Journal of Financial Economics, 43:153193.
Frankel, R., and C. Lee. 1998. Accounting valuation, market expectation, and cross-sectional stock
returns. Journal of Accounting and Economics, 25(3): 283-319.
Gow, I. D., G. Ormazabal, and D. Taylor. 2010. Correcting for cross-sectional and time-series
dependence in accounting research. The Accounting Review, 85(2): 483-512.
Hamilton, J. 1994. Times series analysis. 1st Ed., NJ: Princeton University Press.
Konchitchki, Y. 2011. Inflation and nominal financial reporting. Implications for performance and
stock prices. The Accounting Review, 86 (3): 1,045-1,085.
Konchitchki, Y. 2013. Accounting and the macroeconomy: The case of aggregate price-level effects
on individual stocks. Financial Analysts Journal, 69 (6): 40-54.
Konchitchki, Y. and P. Patatoukas. 2014. Taking the pulse of the real economy using financial
statement analysis: Implications for macro forecasting and stock valuation. The Accounting
Review, 89(2): 669-694.
Kormendi, R., and R. Lipe. 1987. Earnings innovations, earnings persistence, and stock returns.
Journal of Business: 323-345.
Miller, M. H., and K. Rock. 1985. Dividend policy under asymmetric information. The Journal of
Finance, 40(4): 1031-1051.
Nissim, D., and S. H. Penman, 2001. Ratio analysis and equity valuation: From research to practice.
Review of Accounting Studies, 6: 109-154.
Novy-Marx, R. 2013. The other side of value: The gross profitability premium. Journal of
Financial Economics, 108(1), 1-28.
31
Ohlson, J. A. 1995. Earnings, book values, and dividends in equity valuation. Contemporary
Accounting Research, 11(2): 661-687.
Peasnell, K. V. 1982. Some formal connections between economic values and yields and
accounting numbers. Journal of Business Finance & Accounting, 9(3): 361-381.
Penman S. H. and X. J. Zhang, 2002. Accounting conservatism, the quality of earnings, and stock
returns. The Accounting Review, 77 (2): 237-264.
Petersen, M. A. (2009). Estimating standard errors in finance panel data sets: Comparing
approaches. Review of Financial Studies, 22(1), 435-480.
Rajan, M. V., Reichelstein, S., & Soliman, M. T. (2007). Conservatism, growth, and return on
investment. Review of Accounting Studies, 12(2-3), 325-370.
Richardson, S. (2006). Over-investment of free cash flow. Review of Accounting Studies, 11(2-3),
159-189.
Richardson, S. A., Sloan, R. G., Soliman, M. T., & Tuna, I. (2005). Accrual reliability, earnings
persistence and stock prices. Journal of Accounting and Economics, 39(3), 437-485.
Richardson, S. A., Sloan, R. G., Soliman, M. T., & Tuna, I. (2006). The implications of accounting
distortions and growth for accruals and profitability. The Accounting Review, 81(3), 713-743.
Revsine, L., D. Collins, B. Johnson, F. Mittelstaedt. 2009. Financial Reporting and Analysis.
McGraw Hill. ISBN 978-0-07-811086-3.
Romer, P. M. 1986. Increasing returns and long-run growth. The Journal of Political Economy,
1002-1037.
Sloan, R. 1996. Do stock prices fully reflect information in accruals and cash flows about future
earnings? The Accounting Review, 289-315.
Soliman, M. T., 2008. The use of DuPont analysis by market participants. The Accounting Review,
83 (3): 823-853.
32
Figure 1: Persistence of Accounting Ratios
The persistence coefficients are calculated as:
#
=
K
+
,#
= LK + L,
+,
+,
+
+
(F = MK + M, (F +, +
Asset age is the ratio of accumulated depreciation to depreciation expense. RNOA is return on net operating assets,
ATO is asset turnover, and PM is profit margin. All variables are winsorized at the 1% and 99% levels. Asset age
portfolios are assigned annually based on industry adjusted asset age. Industry is defined following Fama and French
(1997).
33
Table 1: Average Descriptive Statistics
Loss
firms
Variable
Asset aget
RNOAt
ATOt
PMt
ΒΜt
MVEt
Firm aget
TI/TAt
∆Future profitt,t+3
Sales growtht
∆NOAt
GP/TAt
Rett, t+12
Rett, t+24
Rett, t+36
N
66,010
66,010
66,010
66,010
66,010
66,010
65,673
65,348
49,829
66,010
66,010
66,010
62,897
62,897
62,897
All firms
6.103
0.153
2.676
0.060
0.595
2586.144
24.954
0.171
0.433
0.147
0.188
0.404
0.056
0.107
0.148
5.653
-0.336
2.532
-0.227
0.716
579.257
18.549
0.223
-0.344
0.100
0.101
0.304
0.105
0.170
0.209
Q1
(Young)
3.094
0.239
2.503
0.116
0.574
2189.458
18.943
0.182
-0.763
0.273
0.341
0.397
0.052
0.111
0.159
Q2
4.281
0.251
2.740
0.114
0.541
2869.767
23.299
0.174
-0.042
0.189
0.248
0.437
0.051
0.116
0.183
Q3
5.531
0.242
2.716
0.110
0.551
3260.125
26.843
0.162
0.356
0.133
0.176
0.437
0.059
0.105
0.137
Q4
7.065
0.230
2.710
0.107
0.570
3594.869
30.021
0.153
2.879
0.100
0.137
0.432
0.042
0.086
0.125
Q5
(Old)
10.931
0.222
2.837
0.100
0.633
2745.686
31.185
0.137
0.275
0.080
0.113
0.404
0.032
0.065
0.084
Differenc
e (Q5 –
Q1)
7.838***
-0.017**
0.334***
-0.017***
0.059***
556.228
12.242***
-0.045***
1.038
-0.193***
-0.228***
0.007
-0.020
-0.046**
-0.075**
Table 1 presents descriptive statistics for the period 1984-2012. We present average statistics for the full sample (including loss firm-years), loss firm-years, and
by industry-adjusted asset age quintiles (which exclude loss firm-years) separately. Asset age is the ratio of accumulated depreciation over depreciation expense,
and industry adjusted using the Fama-French 48 Industry Classification. Asset age quintiles are sorted annually. RNOA is return on net operating assets. ATO is
asset turnover, PM is profit margin, BM is book-to-market, MVE is the market value of equity. Firm age is calculated as the length between the first record of the
firm on CRSP and the current reporting period. TI/TA is calculated as the sum of capital expenditures, research and development expenditures, and acquisitions,
less the sale of property, plant and equipment, plus amortization and depreciation, scaled by total assets, where missing values of the inputs are set to zero
(Richardson, 2006). ∆Future profit measures the percentage change in earnings before extraordinary items from year t to t+3. Sales growth is measured as
(Salest/Salest-1 -1) following Richardson et al. (2006). ∆NOA is calculated as (NOAt-NOAt-1)/NOAt-1. GP/TA is gross profit (sales less cost of goods sold), scaled
by total assets as the end of year t. Rett, t+12, Rett, t+24, and Rett, t+36 measure future size-adjusted buy-and-hold returns, calculated beginning five months after the
end of the fiscal year. All variables except future returns are winsorized at the 1% and 99% levels. *, **, *** indicate significance at the 10%, 5%, and 1% levels
respectively.
34
Table 2: Persistence of Individual DuPont Ratios by Industry-Adjusted Asset Age Quintiles
Panel A: #
= OK + O, #
+, +
All firms
Loss firms
Q1(Young)
Q2
Q3
Q4
Q5(Old)
(t-statistic)
0.070***
(8.19)
0.528***
(18.78)
-0.243***
(-15.74)
0.418***
(14.13)
0.146***
(16.38)
0.395***
(11.19)
0.141***
(11.58)
0.455***
(10.63)
0.140***
(7.72)
0.448***
(6.48)
0.128***
(11.87)
0.470***
(10.58)
0.155***
(9.45)
0.362***
(5.00)
N
Adj. R2
66,010
0.365
9,710
0.287
11,245
0.269
11,266
0.317
11,269
0.307
11,263
0.307
11,257
0.177
+, +
Loss firms
Q1(Young)
Q2
Q3
Q4
Q5(Old)
(t-statistic)
0.640***
(6.45)
0.761***
(22.19)
0.962***
(7.33)
0.633***
(13.24)
0.646***
(7.35)
0.715***
(19.96)
0.592***
(5.23)
0.770***
(18.65)
0.497***
(5.14)
0.817***
(26.04)
0.496***
(5.25)
0.824***
(24.42)
0.538*** †
(4.91)
0.836*** †††
(25.17)
N
Adj. R2
66,010
0.590
9,710
0.391
11,245
0.598
11,266
0.623
11,269
0.681
11,263
0.688
11,257
0.642
OK
(t-statistic)
#
+,
Panel B:
OK
(t-statistic)
+,
= OK + O,
All firms
Panel C: (F = OK + O, (F +, +
All firms
Loss firms
Q1(Young)
Q2
Q3
Q4
Q5(Old)
(t-statistic)
0.029***
(5.57)
0.584***
(9.82)
-0.127***
(-8.82)
0.479***
(6.85)
0.080***
(15.62)
0.353***
(8.45)
0.063***
(12.38)
0.488***
(11.87)
0.057***
(7.35)
0.520***
(7.80)
0.053***
(9.64)
0.556***
(11.09)
0.074***
(8.77)
0.316***
(3.78)
N
Adj. R2
66,010
0.556
9,710
0.484
11,245
0.286
11,266
0.427
11,269
0.460
11,263
0.501
11,257
0.238
OK
(t-statistic)
(F +,
This table provides regression parameters for the period 1984–2012, where the regressions are estimated for portfolios sorted by industry-adjusted
asset age. The t-statistics (in parentheses) are calculated after accounting for time-series and cross-sectional correlation. RNOA is return on net
operating assets, ATO is asset turnover, PM is profit margin. All variables are winsorized at the 1% and 99% levels. *, **, *** indicate
significance at the 10%, 5%, and 1% levels respectively (two-sided). †, ††, ††† indicate a significant difference between the Q1 and Q5 parameters at
the 10%, 5%, and 1% levels respectively (two-sided).
35
Table 3: Forecasting RNOA with Changes in Asset Turnover by Industry-Adjusted Asset Age Quintiles
Panel A: #
= OK + O, #
OK
(t-statistic)
#
+,
(t-statistic)
?
+
+
+,
(t-statistic)
(F +,
(t-statistic)
+
N
Adj. R2
66,010
0.415
Panel B: #
OK
(t-statistic)
#
+,
(t-statistic)
R +,
(t-statistic)
S
+,
(t-statistic)
R +, ∗ S
(t-statistic)
+, + OP
All firms
0.030***
(5.30)
0.398***
(10.55)
0.015***
(5.60)
0.383***
(5.29)
= OK + O, #
+
–
–
+,
F-test (OP = OQ )
–
+, + OQ (F +, +
Loss firms
Q1 (Young)
-0.144***
0.091***
(-6.20)
(9.69)
0.292***
0.280***
(8.04)
(5.17)
-0.025***
0.024***
(-3.20)
(5.45)
0.305***
0.183**
(3.91)
(2.13)
9,710
0.348
+, + OP R +, + OQ S
All firms
Loss firms
0.084***
-0.221***
(10.33)
(-15.79)
0.525***
0.405***
(16.92)
(13.52)
-0.037***
-0.067***
(-3.06)
(-4.44)
-0.074***
0.022
(-4.82)
(1.02)
0.067**
0.079**
(2.53)
(2.47)
0.056
0.000
11,245
0.306
Q2
0.075***
(5.01)
0.325***
(4.90)
0.026***
(4.84)
0.247*
(1.94)
Q3
0.051***
(3.59)
0.290***
(3.20)
0.031***
(6.60)
0.416***
(2.60)
Q4
0.064***
(5.45)
0.342***
(5.91)
0.024***
(4.91)
0.284***
(3.61)
Q5 (Old)
0.076***
(5.26)
0.239***
(2.95)
0.032***
(7.79)
0.182
(1.36)
11,266
0.355
11,269
0.364
11,263
0.347
11,257
0.249
Q3
0.144***
(8.23)
0.460***
(6.11)
-0.024
(-1.12)
-0.150***
(-6.33)
0.027
(0.29)
Q4
0.131***
(11.08)
0.480***
(9.91)
-0.025
(-1.21)
-0.117***
(-5.57)
0.061
(1.19)
Q5 (Old)
0.154***
(9.62)
0.371***
(4.91)
-0.055** †
(-1.98)
-0.117*** ††
(-3.90)
-0.104*
(-1.68)
0.002
0.001
0.134
+ OT R +, ∗ S
+, +
Q1 (Young)
Q2
0.146***
0.137***
(17.31)
(11.94)
0.390***
0.475***
(9.47)
(11.14)
0.001
0.001
(0.05)
(0.06)
-0.041***
-0.061***
(-3.85)
(-3.35)
-0.063***
-0.041
(-5.49)
(-1.04)
+,
0.014
0.000
N
62,174
8,800
9,977
10,492
10,822
11,035
11,048
Adj. R2
0.361
0.278
0.262
0.332
0.328
0.339
0.197
This table provides regression parameters for the period 1984–2012, where the regressions are estimated for portfolios sorted by industry-adjusted
asset age. The t-statistics (in parentheses) are calculated after accounting for time-series and cross-sectional correlation. RNOA is return on net
operating assets, ATO is asset turnover, PM is profit margin, SGt-1 is sales growth, measured as (Salest-1/Salest-2 -1) and ∆ATOt-1 is measured as 1*(ATOt-1-ATOt-2)/ATOt-2 following Richardson et al. (2006). All variables are winsorized at the 1% and 99% levels. *, **, *** indicate
significance at the 10%, 5%, and 1% levels respectively (two-sided). †, ††, ††† indicate a significant difference between the Q1 and Q5 parameters at
the 10%, 5%, and 1% levels respectively (two-sided).
36
Table 4: DuPont Ratio Mean Forecast Errors by Industry-Adjusted Change in Asset Age
Quintiles
Panel A: Random Walk Forecast Errors
Q1
Q2
(Younger)
-0.005
-0.004
#
−#
+,
-0.139
-0.086
−
+,
0.006
0.004
(F − (F +,
Panel B: AR(1) Forecast Errors
Q1
(Younger)
V
-0.009
#
−#
-0.119
−V
W
-0.001
(F − (F
Panel C: Additional Variables
Q1
(Younger)
∆Asset Aget
-1.397
Asset Aget
6.131
TI/TAt
0.179
Sales growtht
0.235
Rett-1, t
0.201
Rett, t+12
0.029
Rett, t+24
0.066
Rett, t+36
0.092
Q2
-0.005
-0.073
0.000
Q2
-0.127
5.480
0.172
0.170
0.186
0.052
0.099
0.155
Q3
0.001
-0.042
0.005
Q3
-0.005
-0.043
-0.002
Q3
0.227
5.412
0.165
0.153
0.200
0.051
0.106
0.144
Q4
0.012
0.002
0.009
Q5
(Older)
0.061
0.128
0.026
Difference
(Q5 - Q1)
0.066***
0.268***
0.020***
Q4
-0.007
-0.012
-0.001
Q5
(Older)
0.015
0.073
0.005
Difference
(Q5 - Q1)
0.023***
0.192***
0.006***
Q4
0.553
5.903
0.152
0.121
0.220
0.050
0.105
0.159
Q5
(Older)
1.569
7.980
0.140
0.097
0.254
0.055
0.107
0.137
Difference
(Q5 - Q1)
2.965***
1.848***
-0.039***
-0.138***
0.053***
0.026***
0.040***
0.046**
Table 3 presents mean forecast errors and descriptive statistics for the period 1984-2012 for quintiles of
industry-adjusted change in asset age (excluding loss firms). Change in industry-adjusted asset age quintiles
are sorted annually. Asset age is the ratio of accumulated depreciation over depreciation expense, and industry
−#
adjusted using the Fama-French 48 Industry Classification. #
+, is the change in return on net
operating assets,
−
+, is the change in asset turnover, (F − (F +, is the change in profit margin.
W are calculated as the difference between the realized ratio value
#
− #V ,
− V , and (F − (F
in year t and the predicted value, where the predicted value is calculated using the univariate persistence
parameters estimated using data from year t-1 for the corresponding industry-adjusted asset age quintile in year
t-1. Thus, these forecast errors are calculated for the sample period 1985-2012. TI/TA is calculated as the sum
of capital expenditures, research and development expenditures, and acquisitions, less the sale of property,
plant and equipment, plus amortization and depreciation, scaled by total assets, where missing values of the
inputs are set to zero (Richardson, 2006). Sales growth is measured as (Salest/Salest-1 -1) following Richardson
et al. (2006). Ret measures the concurrent 12-month buy-and-hold return ending four months after the end of
fiscal year t. Rett, t+12, Rett, t+24, and Rett, t+36measure future size-adjusted buy-and-hold returns, calculated
beginning five months after the end of the fiscal year. All variables except future returns are winsorized at the
1% and 99% levels. *, **, *** indicate significance at the 10%, 5%, and 1% levels respectively after adjusting
for cross-sectional and time-series correlation.
37
Table 5: Buy and Hold Returns
Panel A: Returns by Changes in Asset Turnover
Q1
(Low)
Q2
0.141
0.133
Rett-1, t
0.024
0.031
Rett, t+12
0.062
0.064
Rett, t+24
0.109
0.093
Rett, t+36
Q3
0.181
0.021
0.070
0.092
Q4
0.257
0.063
0.117
0.140
Q5
(High)
0.394
0.065
0.116
0.132
Difference
(Q5 – Q1)
0.254***
0.041***
0.054**
0.023
Panel B: Returns by ATO AR(1) Forecast Error Quintiles
Q1
Q2
Q3
(Low)
0.123
0.145
0.183
Rett-1, t
0.037
0.032
0.043
Rett, t+12
0.071
0.072
0.081
Rett, t+24
0.109
0.105
0.105
Rett, t+36
Q4
0.247
0.056
0.118
0.163
Q5
(High)
0.369
0.074
0.147
0.201
Difference
(Q5 – Q1)
0.247***
0.037***
0.076***
0.092***
Panel C: Returns by Change in ATO Quintiles and Industry Adjusted Change in Asset Age Quintiles
Change in Asset Age Quintile
Q5
Difference
Q1
Rett, t+12
Q2
Q3
Q4
(High)
(Q5 - Q1)
(Low)
0.017
0.041
0.043
0.067
0.035
0.018
Q1
Change in Q2
0.021
0.047
0.029
0.030
0.044
0.023
Asset
0.018
0.026
0.055
0.040
0.025
0.007
Q3
Turnover
0.037
0.060
0.060
0.060
0.082
0.045***
Q4
Quintile
0.056
0.094
0.069
0.055
0.072
0.017
Q5
0.038**
0.053***
0.026*
-0.013
0.037*
Difference (Q5 – Q1)
Panel D: Returns by ATO AR(1) Forecast Error Quintiles and Industry Adjusted Change in Asset Age
Quintiles
Change in Asset Age Quintile
Q1
Q5
Difference
Rett, t+12
(Low)
Q2
Q3
Q4
(High)
(Q5 - Q1)
0.021
0.043
0.053
0.035
0.041
0.020*
Q1
ATO
0.028
0.027
0.032
0.051
0.023
-0.005
Q2
AR(1)
0.020
0.052
0.034
0.050
0.056
0.036*
Forecast
Q3
Error
0.030
0.068
0.068
0.049
0.062
0.032***
Q4
Quintile
0.053
0.077
0.079
0.068
0.091
0.038*
Q5
0.032
0.034**
0.025
0.033**
0.050**
Difference (Q5 – Q1)
This table estimates average concurrent and future returns for various portfolios (excluding loss firms). Rett-1, t
measures the concurrent 12-month buy-and-hold return ending four months after the end of fiscal year t. Rett, t+N
measures the future size-adjusted buy-and-hold abnormal return held for N months beginning five months after the
end of fiscal year t for N = 12, 24 and 36. Panel A (B) sorts firm-years into quintiles on the basis of the change in
ATO (AR(1) forecast errors) for the period 1984-2012 (1985–2012). Panel C (D) presents the mean Rett, t+12 by
double independent sorts of the change in ATO (ATO AR(1) forecast errors) and industry adjusted change in asset
age quintiles. *, **, *** indicate significance at the 10%, 5%, and 1% levels respectively after adjusting for crosssectional and time-series correlation.
38
Table 6: Multivariate returns analysis
Profitable sample
(1)
(2)
VARIABLES
−
+,
Predicted Sign
Rett, t+12
+
0.017
(1.52)
-0.016
(-0.96)
(F − (F +,
+
− V
+
V
(F − (F
+
∆Asset Aget
+
∆NOAt
-
SGt
?
Firm Aget
TI/TAt
-
Constant
?
Risk controls
N
Adj. R2
∆Asset Age Quintile
Q1
Q5
(3)
(4)
Rett, t+12
Rett, t+12
Rett, t+12
0.013
(0.62)
-0.010
(-0.51)
0.041**
(2.51)
0.010
(0.47)
-0.004
(-0.42)
-0.087***
(-4.68)
-0.035***
(-2.87)
-0.020**
(-2.21)
0.038*
(1.69)
0.059
(1.46)
0.027***
(2.84)
-0.004
(-0.33)
-0.006
(-0.57)
-0.084***
(-4.57)
-0.040***
(-2.75)
-0.022**
(-2.30)
0.040*
(1.75)
0.050
(1.21)
-0.102***
(-4.38)
-0.040**
(-2.37)
-0.028
(-1.31)
0.050**
(2.01)
0.045
(1.17)
-0.091***
(-2.74)
-0.014**
(-2.26)
-0.018
(-0.65)
-0.037**
(-2.42)
0.026
(0.71)
Yes
Yes
Yes
Yes
52,259
0.010
52,259
0.010
10,438
0.010
10,406
0.013
This table estimates the association between one-year ahead size-adjusted returns and asset turnover forecast errors,
including various control variables for the period 1985-2012 and excluding loss firms.
−
+, is the
W are calculated as
change in asset turnover, (F − (F +, is the change in profit margin.
− V and (F − (F
the difference between the realized ratio value in year t and the predicted value, where the predicted value is
calculated using the univariate persistence parameters estimated using data from year t-1 for the corresponding
industry-adjusted asset age quintile in year t-1. ∆Asset age is the change in the ratio of accumulated depreciation
over depreciation expense and is industry adjusted, ∆NOA is calculated as (NOAt-NOAt-1)/NOAt-1, Firm age is
calculated as the length between the first record of the firm on CRSP and the current reporting period TI/TA is
calculated as the sum of capital expenditures, research and development expenditures, and acquisitions, less the sale
of property, plant and equipment, plus amortization and depreciation, scaled by total assets, where missing values of
the inputs are set to zero (Richardson, 2006). Risk controls include the market value of equity, book-to-market, beta,
idiosyncratic risk, and concurrent 12-month buy-and-hold returns. All independent variables are sorted into quintiles
annually, t-statistics are presented in parentheses, using standard errors that are clustered by firm and time. *, **,
*** indicate significance at the 10%, 5%, and 1% levels respectively.
39
Table 7: International evidence linking future returns, asset age and DuPont ratios
∆Asset Age Quintilet
+
∆ATOt
+
∆PMt
+
MVEt
–
BMt
+
Constant
?
N
Adj. R2
(1)
Low Inf.
(2)
Mid Inf.
(3)
High Inf.
(10)
Low Inf.
(11)
Mid Inf.
(12)
High Inf.
Rett, t+12
Rett, t+12
Rett, t+12
Rett, t+12
Rett, t+12
Rett, t+12
0.022***
(2.86)
0.059***
(7.67)
-0.014
(-1.04)
-0.066***
(-6.48)
-0.019*
(-1.81)
0.046***
(4.34)
0.029***
(2.90)
†††
0.059***
(6.42)
††
0.002
(0.07)
†††
-0.076***
(-5.99)
-0.003
(-0.24)
0.084***
(6.45)
33,971
0.006
23,093
0.018
0.047***
(4.99)
†††
0.019***
(3.63)
0.041***
(6.15)
0.045***
(13.82)
0.015***
(4.07)
0.059***
(12.13)
0.020***
(3.78)
0.025***
(4.62)
-0.057***
(-4.42)
-0.036***
(-5.20)
0.017**
(2.35)
0.045***
(6.74)
52,806
0.006
33,971
0.003
23,093
0.015
52,806
0.007
This table estimates the association between future buy-and-hold returns asset age and asset turnover forecast errors, for the period 2001-2012. ∆ATO
is the change in asset turnover, ∆PM is the change in profit margin, ∆Asset age is the change in the ratio of accumulated depreciation over
depreciation expense and is industry adjusted. We include the following countries in this analysis: Australia, Canada, Brazil, Switzerland, Chile,
China, Germany, Denmark, Egypt, France, UK, Greece, Hong Kong, Indonesia, Israel, India, Italy, Japan, Korea, Cayman Islands, Mexico, Malaysia,
Netherlands, Norway, Pakistan, Sweden, Singapore, Thailand, Taiwan, Vietnam, Bermuda, and South Africa. Each regression is estimated using
country fixed effects and standard errors are clustered by firm. *, **, *** indicate significance at the 10%, 5%, and 1% levels respectively. †, ††, †††
indicate a significant difference between the High and Low inflation parameters at the 10%, 5%, and 1% levels respectively (two-sided).
40
Table 8: Investigation of the link between asset age and trading strategies based on asset
growth
Panel A: Average monthly returns to asset growth portfolios
∆Asset Age
∆NOA
Q1
Q5
∆TA
(Younger)
Q3
(Older)
P1
0.0149
0.0162
0.0153
P1
P2
0.0140
0.0162
0.0190
P2
P3
0.0133
0.0163
0.0147
P3
P4
0.0140
0.0151
0.0143
P4
P5
0.0128
0.0137
0.0167
P5
P6
0.0129
0.0144
0.0144
P6
P7
0.0131
0.0135
0.0115
P7
P8
0.0108
0.0127
0.0144
P8
P9
0.0082
0.0120
0.0123
P9
P10
0.0059
0.0123
0.0105
P10
P10-P1
-0.0090***
-0.0039**
-0.0049*
P10-P1
(t)
(-3.55)
(-2.10)
(-1.72)
(t)
Q1
(Younger)
0.0150
0.0131
0.0113
0.0162
0.0138
0.0136
0.0094
0.0139
0.0078
0.0056
-0.0094***
(-3.68)
Panel B: Estimates of alpha from four-factor asset pricing models
∆Asset Age
∆NOA
Q1
Q5
∆TA
(Younger)
Q3
(Older)
P1
0.0045
0.0049
0.0063
P1
P2
0.0032
0.0084
0.0061
P2
P3
0.0036
0.0054
0.0066
P3
P4
0.0034
0.0040
0.0051
P4
P5
0.0028
0.0066
0.0041
P5
P6
0.0028
0.0040
0.0051
P6
P7
0.0046
0.0013
0.0039
P7
P8
0.0008
0.0044
0.0030
P8
P9
-0.0022
0.0022
0.0029
P9
P10
-0.0035
0.0014
0.0031
P10
P10-P1
-0.0080***
-0.0035*** -0.0032*** † P10-P1
(t)
(-3.82)
(-3.56)
(-4.05)
(t)
Q1
(Younger)
0.0041
0.0030
0.0008
0.0058
0.0039
0.0036
0.0004
0.0044
-0.0017
-0.0045
-0.0086***
(-4.03)
∆Asset Age
Q3
0.0173
0.0174
0.0148
0.0141
0.0134
0.0150
0.0137
0.0136
0.0115
0.0115
-0.0058**
(-2.72)
Q5
(Older)
0.0139
0.0195
0.0170
0.0154
0.0155
0.0145
0.0127
0.0134
0.0135
0.0077
-0.0062**
(-2.23)
∆Asset Age
Q3
0.0068
0.0075
0.0048
0.0047
0.0040
0.0054
0.0040
0.0042
0.0023
0.0023
-0.0046***
(-4.42)
Q5
(Older)
0.0029
0.0088
0.0056
0.0060
0.0068
0.0044
0.0032
0.0031
0.0042
-0.0023
-0.0051***
(-3.32)
This table reports average monthly returns of portfolios sorted by asset growth and changes in asset age. ∆Asset age
is the change in the ratio of accumulated depreciation over depreciation expense and is industry adjusted, ∆DNOA is
the percentage change in net operating assets, and ∆TA is the percentage change total assets. In Panel B, we report
estimates of the abnormal return spread between portfolio P10 minus portfolio P1 based on the four factor asset
pricing model where MKTRF is the market return less the risk-free rate of return, SMB is the small minus big factor
(based on market value), HML is the high minus low factor (based on book-to-price) and UMD is the up minus
down factor (based on price momentum). The intercepts report the monthly average abnormal return. *, **, ***
indicate significance in the portfolio spreads at the 10%, 5%, and 1% levels respectively. . †, ††, ††† indicate a
significant difference between the Q1 and Q5 alphas at the 10%, 5%, and 1% levels respectively (two-sided).
41
Table 9: Statistics for Gross Profit Scaled by Total Assets (Novy-Marx, 2013)
Panel A: Univariate Persistence Parameters by Industry Adjusted Asset Age Quintiles
R( = OK + O, R( +, +
Q1
All firms
Loss firms
(Young)
Q2
Q3
0.039***
0.036***
0.057***
0.044***
0.034***
OK
(t-statistic)
(15.32)
(6.30)
(15.90)
(13.95)
(10.74)
0.903***
0.856***
0.864***
0.899***
0.920***
R( +,
(t-statistic)
(159.12)
(59.61)
(113.24)
(141.09)
(131.24)
Q4
0.028***
(12.77)
0.934***
(190.30)
Q5
(Old)
0.036*** †††
(8.42)
0.913*** †††
(105.66)
11,269
0.880
11,263
0.892
11,257
0.882
Panel B: Forecast Errors by Industry-Adjusted Change in Asset Age Quintiles
Q1
(Younger)
Q2
Q3
∆GPt
0.000
0.000
-0.001
W
-0.003
0.000
-0.001
R(Y − R(
Q4
0.001
-0.001
Q5
(Older)
0.004
0.001
Difference
(Q5 - Q1)
0.004
0.004*
Panel C: Returns by Change in Gross Profit Scaled by Total Assets
Q1
(Low)
Q2
Rett-1, t
0.168
0.145
Rett, t+12
0.031
0.036
Rett, t+24
0.063
0.076
Rett, t+36
0.103
0.115
Q4
0.220
0.058
0.118
0.157
Q5
(High)
0.348
0.074
0.148
0.202
Difference
(Q5 - Q1)
0.180***
0.042***
0.084***
0.099***
N
Adj. R2
66,009
0.842
9,709
0.725
11,245
0.796
11,266
0.857
Q3
0.179
0.037
0.078
0.109
Panel A provides regression parameters for the period 1984–2012, where the regressions are estimated for portfolios sorted by industry-adjusted asset age. The tstatistics (in parentheses) are calculated after accounting for time-series and cross-sectional correlation. GP/TA is gross profit (sales less cost of goods sold),
scaled by total assets as the end of year t. All variables are winsorized at the 1% and 99% levels prior to estimating the parameters. In Panel A *, **, *** indicate
significance from the parameters in Q1 at the 10%, 5%, and 1% levels respectively. Panel B provides forecast errors, both random walk (i.e., ∆GP) and out-ofsample AR(1) forecast errors (for 1985-2012) based on persistence parameters estimated in the following year and industry-adjusted asset age quintile, by
industry-adjusted asset age quintile. Panel C estimates average concurrent and future returns for various portfolios for the period 1984–2012. Ret measures the
concurrent 12-month buy-and-hold return ending four months after the end of fiscal year t. Rett, t+N measures the future size-adjusted buy-and-hold abnormal
return held for N months beginning four months after the end of fiscal year t for N = 12, 24 and 36. *, **, *** indicate significance at the 10%, 5%, and 1% levels
respectively. †, ††, ††† indicate a significant difference between the Q1 and Q5 parameters at the 10%, 5%, and 1% levels respectively (two-sided).
42
Appendix A
Table A1: Descriptive Statistics by the Fama and French 48 industry groups (Excluding:
Other, Banks, and Utilities)
Industry Group
Healthcare
Business Services
Construction
Personal Services
Computers
Communication
Entertainment
Retail
Medical Equipment
Pharmaceutical Products
Restaurants, Hotels, Motels
Transportation
Precious Metals
Wholesale
Apparel
Recreation
Candy & Soda
Printing and Publishing
Electronic Equipment
Coal
Automobiles and Trucks
Measuring and Control Equipment
Real Estate
Consumer Goods
Rubber and Plastic Products
Agriculture
Beer & Liquor
Petroleum and Natural Gas
Food Products
Electrical Equipment
Machinery
Textiles
Tobacco Products
Business Supplies
Aircraft
Shipping Containers
Construction Materials
Defense
Chemicals
Steel Works Etc
Shipbuilding, Railroad Equipment
Non-Metallic and Industrial Metal Mining
Fabricated Products
N
1545
7985
851
924
3079
2330
1094
4515
2625
2725
1454
2020
180
2768
1110
502
194
687
5111
135
1379
2066
386
1347
695
247
315
3106
1519
1303
3159
429
104
1330
538
295
1785
227
1825
1188
166
256
229
43
Average
Asset Age
4.569
4.783
4.857
4.939
5.117
5.228
5.274
5.331
5.411
5.479
5.488
5.504
5.621
5.753
5.875
5.994
6.015
6.112
6.329
6.332
6.412
6.425
6.589
6.856
6.941
6.955
7.078
7.145
7.247
7.352
7.444
7.492
7.497
7.686
7.733
7.869
8.033
8.061
8.241
8.390
8.428
8.625
8.697
Std. Dev. of
Asset Age
2.537
3.044
2.703
2.805
3.754
3.035
3.486
2.625
3.293
3.297
2.502
2.917
2.985
3.314
3.154
4.458
2.769
3.232
4.030
3.152
3.189
3.364
4.862
3.440
3.414
3.476
2.660
4.207
3.432
3.540
3.722
3.937
2.949
3.747
3.302
3.335
3.709
4.517
3.964
4.056
4.597
3.779
4.772
Average
ATO
2.400
3.653
3.531
2.402
3.311
1.183
1.434
4.594
2.183
2.342
2.316
2.730
0.728
4.720
2.817
2.569
2.305
2.197
2.307
2.125
2.902
2.003
0.962
2.780
2.108
1.647
1.726
1.273
2.697
2.019
2.161
2.036
2.465
2.140
2.130
1.790
2.311
2.981
1.992
2.122
2.760
1.222
2.297