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Faculty of Business and Law School of Accounting, Economics and Finance
Financial Econometrics Series
SWP 2015/03
Does Cash Flow Predict Returns?
P.K. Narayan and J. Westerlund
The working papers are a series of manuscripts in their draft form. Please do not quote without obtaining the author’s consent as these works are in their draft form. The views expressed in this paper are those of the author and not necessarily endorsed by the School or IBISWorld Pty Ltd.
Does Cash Flow Predict Returns?
Paresh Kumar Narayan Centre for Financial Econometrics, Deakin University, Melbourne, Australia. Email:
narayan@deakin.edu.au
Joakim Westerlund Centre for Financial Econometrics, Deakin University, Melbourne, Australia. Email:
joakim.westerlund@deakin.edu.au
Corresponding Author
Mailing Address
Paresh Kumar Narayan School of Accounting, Economics and Finance
Faculty of Business and Law Deakin University
221 Burwood Highway Burwood, Victoria 3125
Australia Telephone: +61 3 92446180
Fax: +61 3 92446034 Email: narayan@deakin.edu.au
DOES CASH FLOW PREDICT RETURNS?
August 27, 2014
Abstract
In this paper, we propose the hypothesis that cash flow and cash flow volatility pre-
dict returns. We categorize firms listed on the New York Stock Exchange into sectors, and
apply tests for both in-sample and out-of-sample predictability. While we find strong
evidence that cash flow volatility predicts returns for all sectors, the evidence obtained
when using cash flow as a predictor is relatively weak. Estimated profits and utility gains
also suggest that it is cash flow volatility that is more relevant as a source of information
than cash flow.
JEL Classification: C12; C22.
Keywords: Cash Flow Volatility; Returns; Predictability; Panel Data; Sectors.
1 Introduction
There is a body of literature that examines the relationship between cash flow and stock re-
turns (Campbell and Vuolteenaho, 2004; Campbell and Shiller, 1988; Campbell, 1991; Camp-
bell et al., 2010; Santos and Veronesi, 2004; Dechow et al., 2004; Lettau and Wachter, 2007).
The main finding of this literature is that cash flow and cash flow volatility are determinants
of returns, suggesting that they should be useful for forecasting. While limited effort has
been devoted to testing whether or not cash flow predicts returns, quite surprisingly, there
is presently no evidence to suggest whether cash flow volatility predicts returns. This is an
important question, because if predictability can be ascertained, then it should be possible
for investors to make use of this information to devise trading strategies with relatively high
profits when compared to a naive strategy that ignores this information.
The contribution of the present study is to analyze whether cash flow and cash flow
volatility predict returns, and to what extent investors can make use of this information to
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generate profits. We draw on a small and rich literature that establishes the relationship be-
tween cash flow (and its volatility) and returns. The main conclusion from this literature is
that cash flow and cash flow volatility are significantly correlated with returns. A natural
question that this literature has not addressed is whether cash flow volatility actually pre-
dicts returns, as correlation does not necessarily imply predictability. Because we consider
both the first and second moments of cash flow as predictors it allows us to understand the
relative importance of the two, not only in a statistical sense (predictability) but also in terms
of how much economic gains each offers to an investor.
The data that we use consist of firms listed on the New York Stock Exchange (NYSE),
which are grouped into sectors based on the global industry classification standard (GICS)
(see Narayan and Sharma, 2011). To test the null hypothesis of no predictability, we apply a
newly developed in-sample panel predictive test of Westerlund and Narayan (2014). From
this exercise we discover strong evidence that cash flow volatility is in fact able to predict
sectoral returns, a result that holds also out-of-sample. However, we find weak evidence
that cash flow predicts returns. While in in-sample tests, results suggest predictability in
five sectors, out-of-sample tests reveal even weaker evidence. We then undertake an exten-
sive analysis of the economic significance of the predictability. Our main findings based on
cash flow volatility are; (i) in all sectors dynamic trading strategies generate statistically sig-
nificant profits, (ii) investors in all sectors are willing to pay more to hold dynamic trading
strategies over the historical average, and (iii) profits and investor utilities are heteroge-
neous, in that they vary from sector-to-sector. On the other hand, when we consider cash
flow as a predictor, while we find all sectors to be profitable these profits are significantly
less than those obtained using cash flow volatility. The finding that sectors are profitable
even in the absence of predictability corroborates the evidence reported by Cenesizoglu and
Timmermann (2012).
The rest of the paper is organized as follows. In Sections 2 and 3, we introduce the new
hypothesis and the empirical framework that will be used to test it. In Section 4, we report
the results on return predictability and its economic significance. Section 5 concludes.
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2 Hypothesis Development
The goal of this section is to motivate the hypothesis that cash flow and cash flow volatility
predict returns. Most valuation theories, including the simple present value model, identify
either the change in expected cash flows or discount rates or both as the key determinants of
returns. Campbell and Vuolteenaho (2004) developed an intertemporal asset pricing model.
They argued that returns on the market portfolio have two components; permanent shocks,
which reflect news about future cash flows, and temporary shocks, which reflect news about
expected discount rates. Analogously, the required return of a stock is determined by two
separate betas, where one beta is due to the co-variation of individual stock’s return with
the market’s cash flow factor, known as “cash flow risk”, and the other beta is due to the
co-variation with the markets discount rate factor, known as “discount rate risk”. In their
model, the value of the market portfolio may fall either due to poor prospects of cash flow
news, or due to increased discount rates. Both these scenarios have different implications
for a risk averse, long term, investor. In the first scenario, investment opportunities remain
unchanged, whereas in the second scenario they improve. The investor will therefore de-
mand higher returns to hold assets that have high cash flow risk, which represents a source
of uncertainty.
Then there is the work of Da (2009), which is based on the idea that cash flow more di-
rectly underlie the risk compensation of assets. Da (2009) decomposes the role that cash flow
plays into two important components. The first component is the degree of comovement of
cash flow with consumption, known as “cash flow variance” (see, for example, Abel, 1999;
Bansal and Yaron, 2004; Bansal et al., 2005). The second cash flow component is cash flow
duration, that is, the timing of the cash flow. Dechow et al. (2004), and Lettau and Wachter
(2007) link cash flow duration to stock returns. Value stocks have short duration, whereas
growth stocks have high duration. Value stocks, therefore, vary more with fluctuations in
cash flows that investors fear the most and have high expected returns.
Like cash flow, the effects of cash flow volatility has generated much interest in the litera-
ture. Botshekan et al. (2012) study the impact of cash flow risk on returns. Their idea is based
on the well-documented fact that investors react asymmetrically to unexpected movements
in upside and downside markets (see, for example, Roy, 1952; Markowitz, 1952; Kahneman
and Tversky, 1979). Investors are loss averse and therefore sensitive to downside market
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movements (Ang et al., 2006). Botshekan et al. (2012) decompose the beta into four compo-
nents; upside and downside cash flow betas, and upside and downside discount rate betas.
They argue that the impact of cash flow risk versus discount rate risk may be different in up
and down markets, and therefore highest returns are expected for downside cash flow risk.
The relationship between volatility and investments is also captured by theories of risk
management. Popularised by Myers (1977), risk management theories suggest that when
markets are imperfect, external capital is expensive relative to internal capital, and cash flow
volatility is associated with underinvestment. Cash flow volatility therefore leads to cash
flow problems, hurting investments. Risk management theories consequently posit a neg-
ative relationship between cash flow volatility and investment (returns) (see Minton and
Schrand, 1999, for empirical evidence). Other channels through which cash flow volatility
impacts firm performance have been provided by Graham and Smith (1999). Their main ar-
gument, motivated by Smith and Stulz (1985), is that if cash flow volatility is associated with
taxable income volatility, then higher cash flow volatility is negatively related to after-tax
cash flow.
Finally, there is the cost of capital argument linked to cash flow volatility and firm perfor-
mance. Several studies show how volatility affects a firm’s cost of capital (see, for example,
Gebhardt et al., 2001). The main idea is that with a higher cash flow volatility and lower
cash flow realizations, because it is costly to borrow investment funds, firms have to forego
investments.
The main implication of work done on cash flow and returns is that both cash flows and
cash flow risk matter to returns. What is unclear, though, is how much does each matter? For
example, can investors use cash flow and its volatility to predict returns? Which of the two
predictors will predict returns most? Which of the two predictors will offer more economic
gains to investors? To answer these questions we test if cash flow and cash flow volatility
predict sectoral returns on the NYSE.
3 Empirical Framework
The panel data predictive regression model that we consider has the following form:
yi,t = αi + βixi,t−1 + ϵi,t,
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where i = 1, ..., N and t = 1, ..., T indexes the cross-section and time series dimensions,
respectively, xi,t = ρixi,t−1 + ε i,t, and ϵi,t and ε i,t are mean zero disturbances, which could
potentially be correlated with each other, and serially and/or cross-section correlated. This
is a panel extension of the prototypical predictive regression model that has been widely
used in the time series literature, in which xi,t is a variable believed to be able to predict
returns, yi,t. In our case, xi,t will be either cash flow or cash flow volatility.
3.1 A test of in-sample predictability
The problem of testing the null hypothesis of no predictability is equivalent to the problem
of testing the restriction that β1 = ... = βN = 0, which in-sample is typically done by
means of a pooled ordinary least squares (OLS) t-test (see, for example, Hjalmarsson, 2010).
However, this procedure has the drawback that positive and negative deviations may cancel
out. Specifically, assuming that βi is randomly distributed with mean β and variance σ2, tests
of this type has no power if σ2 > 0 but β = 0. This is rather problematic, because, since the
sign of βi is generally indetermine, one cannot rule out the possibility of such a cancelation,
in which case t-tests will incorrectly lead to the conclusion that there is no predictability,
when in fact βi ̸= 0 for all i.
In view of this drawback Westerlund and Narayan (2014) propose a Lagrange multiplier
(LM) test for the joint hypothesis of H0 : β = σ2 = 0 versus H1 : β ̸= 0 and/or σ2 > 0.
The random specification βi is extremely convenient because it means that the original N-
dimensional problem of testing whether β1 = ... = βN = 0 can be reformulated using only
two parameters, β and σ2, which means that the problems associated with the estimation of
parameters that are superfluous under the null can be kept to a minimum. Interestingly, the
Hessian of the log-likelihood function with respect to β and σ2 is (asymptotically) diagonal,
which implies that the (joint) LM test statistic for testing H0, LMJ say, has the following
convenient form: LMJ = LMβ + LMσ2 , where LMβ (LMσ2) is the appropriate LM test statistic
for testing β = 0 given σ2 = 0 (σ2 = 0 given β = 0). That is, while LMβ tests the no
predictability null against the alternative of a homogenous predictive slope different from
zero, with LMσ2 the null is tested versus the alternative that there is predictability but not
on average. Thus, with this approach there is not just one way in which the no predictability
null can be tested, but several, and it will therefore be used in this paper.
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3.2 Two measures of out-of-sample forecasting ability
Following the bulk of the previous literature (see, for example, Welch and Goyal, 2008; West-
erlund and Narayan, 2012), the out-of-sample forecasting performance of the (unrestricted)
predictive regression model using a constant and xi,t−1 as predictors is compared to that of
the (restricted) constant-only model obtained by setting β1 = ... = βN = 0. Two measures of
the relative forecasting performance of these two models are considered. The first is the aver-
age relative Theil U measure, defined as RTU = ∑Ni=1 RTUi/N, where RTUi = TUi,U/TUi,R
is the relative U for firm i, and TUi,U (TUi,R) is the U measure from the unrestricted (re-
stricted) predictive model. It follows that if RTU < 1, then the forecasts based on the un-
restricted model are on average more accurate than those of the restricted model. The sec-
ond measure is the average out-of-sample R2, and is given by OR2 = ∑Ni=1 OR2
i /N, where
OR2i = 1 − RMSEi,U/RMSEi,R with RMSEi,U (RMSEi,R) being the root mean square error
(RMSE) of the unrestricted (restricted) predictive model when applied to firm i (see Camp-
bell and Thompson, 2008 for a time series version of this measure). If OR2 > 0, this means
that the forecast based on the unrestricted model is on average relatively more accurate.
3.3 A measure of economic significance
To deduce the economic significance of any statistical differences in in- and out-of-sample
predictive ability we follow, for example, Narayan et al. (2013), Campbell and Thompson
(2008), and Marquering and Verbeek (2004), and compute the realized utility gain for a mean-
variance investor and the profits possible for that same investor if using a dynamic trading
strategy.
The utility function of the investor is given by E(y∗i,t+1|It)− var(y∗i,t+1|It), where y∗i,t de-
notes excess returns, It is the information set available in the same month, and γ is the coeffi-
cient of relative risk aversion. The investor invests in two assets, one is risky, the other is risk-
free. The proportion invested in the risky asset is set optimally to E(y∗i,t+1|It)/γvar(y∗t+1|It),
where y∗t+1 denotes market (excess) returns (Marquering and Verbeek, 2004). Our (out-of-
sample) estimate of this quantity simply replaces E(y∗i,t+1|It) and var(y∗t+1|It) by the esti-
mated mean and variance of the return forecasts. Borrowing and short selling are not al-
lowed, and therefore the estimated portfolio weights in each time period are constrained to
lie between 0% and 100%. We do not allow for short-selling and borrowing because it leads
to an increase in profits and investor utility (see Narayan et al., 2013; Narayan et al., 2014, for
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empirical evidence on this). Therefore, by not allowing for short-selling and borrowing we
provide a sort of worst case scenario in which the economic value of return forecasts will be
tested. Hence, if profits and investor utility are positive without short-selling and borrow-
ing, relaxing this restriction will only further increase profits and utility. As in Section 3.2, the
utility derived from the forecasts based on the unrestricted model using a constant and xi,t−1
as predictors is compared to the utility derived from the restricted constant-only model. The
utility gain, or “certainty equivalent return”, is simply the difference between the estimated
utilities, and can be interpreted as the portfolio management fee that an investor would be
willing to pay to have access to the additional information contained in xi,t−1 relative to the
information in the historical average.
Next, we estimate profits from a dynamic trading strategy for the same mean-variance
investor. The trading strategy optimizes a portfolio based on predicted excess returns. The
profits are computed as in Marquering and Verbeek (2004), and use a transaction cost of
0.1%. As in Section 3.2, the estimated utilities and profits are averaged across firms.
4 Empirical results
4.1 Data
The hypotheses that cash flow and cash flow volatility predict returns are tested for firms
listed on the NYSE. We use monthly data covering the period August 1996 to August 2010.1
The size of the cross-section is dictated by data availability. While there are several thousand
firms listed on the New York Stock Exchange, consistent time series data were only available
for 1,559 firms. Our data filtering process is as follows; (a) exclude all stocks that were priced
at less than five US dollar, (b) exclude all stocks that were priced greater than 500 dollar, and
(c) exclude all stocks which had three consecutive days of missing values. Approaches (a)
and (b) ensured that results are not influenced by unduly high and low priced stocks. We
extract data on two variables, namely, firm returns and the cash flow-to-price (CFP) ratio,
our measure of cash flow.
All the data are downloaded from the Datastream database and are organized by sec-
tor based on the GICS (see Narayan and Sharma, 2011). In general, it is quite reasonable to
1While it is possible to consider data prior to 1996, there are two reasons we do not do this; (1) given our paneldata approach it was important to maximize the number of firms in each sector, and (2) 14-years of monthly timeseries data is more than sufficient to implement the Westerlund and Narayan (2014) approach.
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group firms that are homogeneous in the sense that they share some common characteristics.
Homogeneous firms are likely to have similar predictability patterns compared to heteroge-
neous firms. It is therefore common to group firms by sector. We end up with 15 sectors. The
number of firms range from as low as seven in the case of mining sector to as large as 51 in
the case of the retail sector. In all cases, T >> N, which is consistent with the requirement
of the in-sample LM test that we consider (see Westerlund and Narayan, 2014).
We use two measures of CFP volatility. First, we compute the volatility of CFP by tak-
ing a 12-month rolling window of standard deviation (SD); see, for example, Westerlund
and Narayan (2012) for similar approaches. Second, we use the RV approach of Schwert
(1989), variants of which have been employed by Taylor (1986) and Nelson (1992). This ap-
proach has three steps. In the first step, one estimates a 12th-order (since we using monthly
data) autoregressive (AR) model for returns, including dummy variables to allow for dif-
ferent monthly means. In the second step, one estimates another 12th-order AR model with
monthly dummies, but this time for the absolute values of the first-step residuals. The final
step amounts to extracting the fitted values from the second step, which is effectively the
conditional standard deviation of stock returns. We run all regressions for each of the sec-
tors, consisting of panels of firms. Following Schwert (1989), the absolute errors are scaled
by√
π/2 ≈ 1.2533.
4.2 Preliminary results
We begin by considering some preliminary results on the persistency and endogeneity of the
predictors, which are important aspects when testing the null hypothesis of no predictabil-
ity. Consider persistency. Intuitively, the higher the persistency, the easier it is to detect
deviations from the no predictability null. Therefore, in order to ascertain the order of inte-
gration of the variables, we apply the Im et al. (2003, IPS) panel unit root test. To account
for some degree of heterogeneity and cross-section dependence, the test regression is fitted
with both firm- and time-specific fixed effects. The order of the lag augmentation used to
account for serial correlation is chosen using the Schwarz information criterion (SIC). The
results, reported in Table 1, suggest that the null hypothesis of a unit root has to be rejected
at the 1% level for all four variables except in the case of software and telecom sectors for
which CFP turns out to be unit root non-stationary. We therefore conclude that there is evi-
dence of stationarity not only for returns but also for our two measures of CFP volatility and
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for CFP of most sectors. However, we also note that in all sectors, the estimated first-order
AR coefficient is still very close to one for the CFP and SD predictors, suggesting that while
statistically different from one, the actual difference is not very large. The AR coefficient for
RV is neither close to one nor close to zero; it mostly falls in the 0.3–0.6 range. Therefore, RV
also exhibits persistence, although it is not as strong as in the case of SD and CFP.
Let us denote by ϵ̂i,t (ε̂ i,t) the estimator of ϵi,t (ε i,t) obtained by applying OLS to the pre-
dictive (predictor) equation. Table 1 reports the estimated slope coefficient, θ̂ say, obtained
when regressing ϵ̂i,t onto ε̂ i,t, which can be seen as a measure of endogeneity; if θ = 0, then
ϵi,t and ε i,t are uncorrelated and therefore there is no endogeneity, while if θ ̸= 0, then the
opposite is true. When considering the volatility predictors, the results appear to be mixed
with evidence of endogeneity in about half of the 15 sectors. However, when using CFP as
a predictor, endogeneity is relatively stronger. Fortunately, the statistics considered here are
(asymptotically) robust to the presence of such endogeneity.
Another important consideration, especially when implementing the in-sample LM ap-
proach, is that of cross-sectional dependence. A pre-test of cross-sectional dependence is
therefore necessary to choose the most appropriate test statistics from a range of tests pro-
posed by Westerlund and Narayan (2014). We apply the Pesaran et al. (2008) CD test for
testing the null hypothesis of no cross-correlation in returns. The (unreported) results sug-
gest that across all 15 sectors, the average of the pair-wise correlation coefficients ranges
between 0.3 and 0.5, and the associated CD p-values are all less than 1%, suggesting that
the null of no cross-correlation must be rejected. This implies that we should choose the
cross-correlation robust versions of the LM tests of Westerlund and Narayan (2014).
4.3 In-sample results
The results obtained from the LM tests are presented in Table 2. The appropriate lag aug-
mentation required to account for serial correlation is again selected by the SIC, and in order
to also account for the cross-correlation the test regression is further augmented by the cross-
section averages of the observables (see Westerlund and Narayan, 2014).
The key findings can be summarized as follows. First, looking at the results for RV, while
LMσ2 is generally highly significant, LMβ is generally insignificant. Hence, while there is
evidence of predictability at the level of the individual firms, the predictive slopes average
to zero. This means that existing pooled t-tests for predictability (see, for example, Hjalmars-
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son, 2010) are likely to be misleading in the sense that the no predictability null is unlikely to
be rejected. By contrast, the LM tests considered here suggest that while for six of the sectors
(hardware, mining, retail, travel, engineering, and utility) there is no evidence against the
null hypothesis of no predictability, for the remaining nine sectors there is quite strong evi-
dence of predictability. Second, looking at SD, there is more of an agreement between LMσ2
and LMβ. Thus, in this case, if returns can be predicted, then it is with heterogeneous slopes
with a mean different from zero. The evidence is stronger not only because in this case both
the mean and variance of βi are generally different from zero, but also in terms of the num-
ber of sectors whose returns can be predicted. In fact, there is only one sector, chemicals, for
which returns cannot be predicted. Third, for eight sectors (banking, real estate, transport,
energy, electricity, household, software and telecom) both measures of CFP volatility predict
returns. These findings, on the whole, suggest that CFP volatility can be used to predict re-
turns for most sectors but not all. The same conclusion cannot be drawn when considering
CFP itself as a predictor. Indeed, results suggest that in only three sectors the mean and the
variance of βi are different from zero and that at best a limited level of predictability is found
in four of 15 sectors.
The above conclusion raises two questions: (i) is the in-sample evidence of predictability
corroborated by the out-of sample results, and, if so, (ii) can investors gain by utilizing pre-
dictive information contained in CFP and its volatility? Answers to these questions occupy
subsequent sections.
4.4 Out-of-sample results
In this section, we use the RTU and OR2 measures to investigate whether in-sample evidence
of predictability extends also out-of-sample. The results are reported in Table 3. We begin by
considering the RTU measure, which is less than one in 13 of the 15 sectors when using RV as
a predictor, in nine out of 15 sectors when using SD as a predictor, and in one out of 15 sectors
when using CFP. With the RV predictor, no evidence of predictability is found in the case of
energy and hardware sectors, while in the case of SD, no evidence of predictability is found
for chemicals, engineering, hardware, mining, software and utilities. In the case of CFP, on
the other hand, predictability is only found in the hardware sector. These findings imply
that when considering the volatility-based predictors, the evidence in favor of predictability
is quite strong, and it is even stronger when considering OR2. Specifically, when using RV,
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OR2 > 0 for all but four sectors (banking, mining, software and telecom), while when us-
ing SD, OR2 < 0 only for the banking sector. The out-of-sample evidence of predictability
therefore corroborates the evidence obtained from the in-sample tests. By comparison, the
evidence of weak in-sample predictability when using CFP is consistent with the weak out-
of-sample evidence. On the whole these results suggest that it is the second moment of cash
flow that contains greater information content than the first moment.
4.5 Economic significance results
Investor utility is computed as described in Section 3.3. The risk aversion parameter is set
to γ = 6 and we use the US three-month Treasury bill rate as a proxy for the risk-free rate
of return.2 The results reported in Table 4 show strong support for the forecast based on
the unrestricted predictive regression model in the case of volatility predictors. Take, as
an example, the case when CFP volatility is measured by RV, in which investors prefer the
unrestricted forecast in all but one sector (mining). The support is weaker when volatility
is measured by SD. However, the results are still rather encouraging with the forecast based
on the unrestricted model being preferred in seven out of the 15 sectors. The support is
weakest when we use the CFP as a predictor. In this case, the restricted model is preferred
by investors in all sectors.
Consider next the results for the estimated profits (Table 4). We have three predictive re-
gression models, one for each measure of CFP volatility and one for CFP itself, so we obtain
three profit estimates. The first thing to note is that all profits are statistically significant on
average and have positive Sharpe ratios. This is true regardless of how CFP volatility is mea-
sured and holds even when using CFP itself as a predictor. This implies that by accounting
for the information contained in CFP and CFP volatility investors can make non-negligible
profits. We also see that the two measures of volatility lead to different profits. On the one
hand, with SD profits range from 0.4% (electricity, energy, engineering, real estate and util-
ity) to over 1% in the case of household and retail sectors. On the other hand, with RV profits
range from 0.08% (telecom) to 1.3% (mining). The range of profits for RV is therefore wider
than when using SD. However, the results are still rather similar with a majority of sectors
having profits that are in the 0.5–1.0% range. Indeed, while in four sectors (mining, energy,
engineering, and telecom) the difference in profits from the two models is relatively large,
2The results for γ = 1, 3 and 12 were very similar, and are therefore omitted.
11
for the remaining 10 sectors, the difference is very small. By comparison, profits obtained
using the CFP predictor are all small and less than 0.132. This finding is not surprising given
recent empirical evidence presented by Cenesizoglu and Timmermann (2012), who show
that even statistically insignificant predictors have some information content that translates
into economic significance.
Three messages emerge from our empirical analysis of investor profitability. First, CFP
volatility not only predicts returns, but also allows a mean-variance investor to make non-
negligible (positive) profits. This means that the investor is willing to pay more to have
access to information contained in the CFP volatility-based forecast as opposed to using
the historical average forecast. Second, while profits and utilities (to a lesser extent) are all
positive, they do differ across sectors. This implies that both investor utility and profits are
not homogeneous but sector-dependent. Third, while CFP does not predict returns of most
sectors, CFP still contains some information content leading to statistically significant profits
in all 15 sectors, although profits are significant less than profits obtained from CFP volatility
based predictors. On the whole, in a relative sense, what matters most to investors is not the
first moment but the second moment of CFP.
4.6 An explanation of the results
In this section, we have two goals. First, since we discover that cash flow volatility is a better
predictor of returns than cash flow, we begin by explaining why this is the case. Second, we
focus on the volatility-based predictor which offers strong results in support of predictabil-
ity, both statistically and economically. We clearly observe that profits and indeed investor
utilities are different depending on the sector in which one invests. What this implies is that
the role played by CFP volatility in terms of predicting returns is different for different sec-
tors. We provide some explanations for this finding. This appears in the second part of this
section.
This is not the only study that finds cash flow volatility to be a superior contributor
to returns compared to cash flow. That cash flow volatility is relatively more important
has been shown by Minton et al. (2002: p.196), who argue that: “... volatility contains
incremental information for forecasts of future firm performance beyond that in historical
cash flow ...”. This idea has roots in theories of risk management where the main argument
is that forecasts and earnings (returns) that explicitly incorporate historical volatility will be
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more accurate and less biased than corresponding forecasts from models that exclude the
role of volatility (see Minton et al., 2002).
There are other influential studies that support the relative importance of cash flow
volatility in predicting stock returns. For example, De Santis (1997) argues that most models
of asset pricing predict that expected returns on an asset are related to its covariance with
one or more of the pricing factors. Nissim (2002) argues that cash flow volatility may serve
as a proxy for the persistence of cash flows thereby containing more information as opposed
to cash flow itself. Ali (1994) argues against cash flow’s impact on returns by suggesting that
large changes in cash flows are not expected to persist thereby having a subdued effect on
stock returns.
That the role of CFP volatility is different for different sectors is related to a branch of
the financial economics literature on market response to cash flow news announcements,
including increases in research and development expenditure that is funded from an increase
in cash flow. In particular, Szewczyk et al. (1996) argue that the reaction of firms to cash
flow announcements depends on the industry to which firms belong. They write: “Free
cash flow agency costs may depend on the firm’s investment opportunities. Firms with
relatively more growth opportunities are less likely to have free cash flow” (page 105). Free
cash flow is effectively cash flow in excess of that required to fund all projects that have
positive net present value when discounted at the relevant cost of capital. At the sector
level, then, growth opportunities differ. Some sectors, such as, for example, oil, have higher
growth opportunities (see Jensen, 1986). When there are large increases in cash flows in a
sector, the result is an increase in free cash flow. Jensen (1986) focuses on the oil industry and
argues that with reforms and oil price hikes of the 1970s, the oil sector experienced a steady
increase in cash flows. His main point is that when a sector experiences free cash flow,
firm managers have a tendency to engage in wasteful investments at the expense of higher
shareholder payments. This behavior subsequently depresses share prices and profitability.
Therefore, the oil sector is likely to have much higher free cash flow than other sectors.3
The main message from the work of Jensen (1986) and Szewczyk et al. (1996) is that sector
cash flows behave differently, which in turn dictates the actions of managers. Subsequently,
these chain of activities have implications for sectoral profitability. This is consistent with
3Narayan and Sharma (2011) show that not only oil but those sectors related to oil, experience higher growthwhen, for example, oil prices increase. They show that an increase in oil price leads to a rise in returns for oiland transport sectors on the NYSE.
13
our findings; CFP volatility has different predictive content depending on the sector, leading
to differing profits.
That return predictability is sector-specific is nothing new. The study that comes closest
to our work is Westerlund and Narayan (2014), who use a range of financial ratio predic-
tors to test stock return predictability for stocks listed on the NYSE. In agreement with our
results they discover that stock returns are more predictable for some sectors than others.
The main reason for this finding has roots in the investor underreaction and overreaction to
cash flow (volatility) news. Investors in different sectors perceive and interpret cash flow
news differently, that is, the speed at which news flows and is interpreted is different for
investors in different sectors. Some investors end up underreacting to cash flow (volatil-
ity) news while others overreact. The overreaction to news is explained by the positive-
feedback-trader model of DeLong et al. (1990). The main argument is that prices initially
react to news about fundamentals and then continues to overreact for some time due to
positive feedback from investors. Clearly, as several studies have shown (see, for example,
Narayan and Sharma, 2011), the magnitude of positive feedback is not homogeneous, rather
it is sector-specific. Our results are merely reflecting this type of behavior and are therefore
consistent with the findings of Westerlund and Narayan (2014), and Narayan and Sharma
(2011).
5 Concluding remarks
This paper is motivated by the lack of empirical evidence on whether or not CFP and CFP
volatility predict returns. We form panels of firms listed on the NYSE based on sectors
and apply tests for both in-sample and out-of-sample predictability. Two measures of CFP
volatility are considered, SD and RV. We discover strong evidence that CFP volatility predicts
sectoral returns for at least 14 of the 15 sectors, but weak evidence that CFP predicts sectoral
returns. We further show that the information contained in the CFP volatility can be used
to generate non-negligible profits. Profits are, however, heterogeneous. Investors in some
sectors can make relatively large profits compared to others. A similarly heterogeneous
evidence of investor utility is also found. Therefore, while the information contained in
cash flow volatility is useful for investors on the NYSE, its usefulness is sector-dependent.
Our results have a serious implication: As much as our results reveal the important role of
14
cash flow volatility in predicting returns, they also provide a practical guide for investors.
The key implication has roots in the fact that investors forecast returns. In doing so, they
depend on a wide range of fundamentals, including cash flow. Our results imply that using
cash flow volatility as opposed to cash flow will offer investors relatively more accurate
forecasts. This is important because the more accurate the forecasts, the greater the precision
in estimating profits and investor utility. These are important economic considerations for
attracting shareholders.
In concluding, we believe that one limitation of our study is that it is focussed on a
developed country market. Therefore, to build consensus on our finding that cash flow
volatility is more important predictor than cash flow, future studies should consider testing
this hypothesis using data from other developed and emerging markets.
15
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19
Tabl
e1:
Prel
imin
ary
pers
iste
ncy
and
endo
gene
ity
resu
lts.
SDRV
CFP
Ret
urn
Sect
orA
RSE
θ̂t-
test
IPS
AR
SEθ̂
t-te
stIP
SA
RSE
θ̂t-
test
IPS
AR
SEIP
S
Bank
ing
0.98
0.00
0.13
4.37
0.00
0.54
0.01
0.17
4.83
0.00
0.88
0.01
−0.
15−
17.2
10.
000.
000.
010.
00
Che
mic
al0.
990.
000.
00−
0.80
0.00
0.37
0.01
0.28
7.69
0.00
0.88
0.01
0.00
−3.
380.
000.
000.
010.
00
Elec
tric
ity
0.97
0.00
0.20
1.96
0.00
0.50
0.01
0.03
0.93
0.00
0.91
0.01
−0.
56−
14.7
90.
000.
060.
010.
00
Ener
gy0.
970.
00−
0.07
−0.
340.
000.
430.
020.
101.
870.
000.
930.
01−
1.97
−35
.48
0.01
0.07
0.02
0.00
Engi
neer
ing
0.96
0.00
0.22
1.36
0.00
0.32
0.02
0.12
2.51
0.00
0.94
0.01
−1.
47−
21.2
40.
000.
000.
020.
00
Rea
lest
ate
0.98
0.00
0.46
4.67
0.00
0.51
0.01
0.31
0.06
0.00
0.85
0.01
−0.
75−
29.7
30.
00−
0.02
0.01
0.00
Har
dwar
e0.
960.
000.
974.
840.
000.
330.
020.
378.
920.
000.
940.
01−
1.99
−20
.56
0.02
0.02
0.02
0.00
Hou
seho
ld0.
970.
000.
143.
850.
000.
490.
010.
369.
840.
000.
880.
01−
0.24
−22
.68
0.00
0.06
0.01
0.00
Min
ing
0.00
0.00
0.46
1.48
0.00
0.20
0.03
−0.
26−
1.12
0.00
0.93
0.01
−2.
67−
12.7
10.
04−
0.01
0.03
0.00
Ret
ail
0.96
0.00
0.13
3.42
0.00
0.39
0.01
0.46
17.2
20.
000.
830.
01−
0.29
−23
.42
0.00
0.05
0.01
0.00
Soft
war
e0.
960.
011.
752.
680.
000.
390.
030.
392.
480.
000.
970.
01−
3.00
−18
.52
0.13
0.00
0.03
0.00
Tele
com
0.97
0.01
−0.
20−
0.81
0.00
0.42
0.03
−0.
06−
0.35
0.00
0.97
0.01
−1.
34−
25.8
50.
790.
020.
030.
00
Tran
spor
t0.
930.
000.
285.
140.
000.
420.
020.
001.
450.
000.
910.
01−
0.42
−16
.10
0.00
0.10
0.02
0.00
Trav
el0.
980.
000.
211.
620.
000.
380.
020.
5113
.21
0.00
0.91
0.01
−1.
38−
32.3
20.
010.
060.
020.
00
Uti
litie
s0.
960.
00−
0.08
−1.
000.
000.
270.
02−
0.05
−1.
110.
000.
950.
01−
0.35
−10
.83
0.00
−0.
030.
010.
00
Not
es:“
AR
”an
d“S
E”re
fer
toth
ees
tim
ated
first
-ord
erA
Rco
effic
ient
and
its
stan
dard
erro
r,re
spec
tive
ly,θ̂
and
“t-t
est”
refe
rto
the
esti
mat
edsl
ope
whe
n
regr
essi
ngth
ere
sidu
alof
the
pred
icti
veeq
uati
onon
the
resi
dual
ofth
epr
edic
tor
equa
tion
,and
the
asso
ciat
edze
rosl
ope
t-te
st,r
espe
ctiv
ely,
and
“IPS
”re
fers
toth
ep-
valu
eof
the
Imet
al.(
2003
)pan
elun
itro
otte
st.“
SD”
and
“RV
”re
fer
toth
est
anda
rdde
viat
ion
and
Schw
ert(
1989
)mea
sure
sof
CFP
vola
tilit
y.
20
Table 2: In-sample predictability test results.
RV SD CFPSector LMσ2 LMJ LMβ LMσ2 LMJ LMβ LMσ2 LMJ LMβ
Banking 0.00 0.00 0.08 0.00 0.00 0.00 0.84 0.91 0.56Chemical 0.00 0.00 0.96 0.12 0.26 0.58 0.42 0.59 0.23Electricity 0.00 0.00 0.85 0.01 0.00 0.08 0.36 0.53 0.20Hardware 0.06 0.16 0.84 0.00 0.00 0.01 0.85 0.95 0.56Household 0.01 0.02 1.00 0.00 0.00 0.00 0.30 0.44 0.18Mining 0.06 0.17 0.89 0.04 0.03 0.09 0.03 0.52 0.01Retail 0.24 0.49 0.94 0.00 0.00 0.00 0.00 0.00 0.98Software 0.00 0.00 0.74 0.02 0.04 0.38 0.61 0.42 0.56Telecom 0.00 0.00 0.74 0.20 0.09 0.08 0.67 0.55 0.51Transport 0.01 0.02 0.83 0.00 0.00 0.07 0.48 0.72 0.25Travel 0.06 0.13 0.46 0.00 0.00 0.00 0.00 0.73 0.00Utility 0.36 0.66 0.95 0.00 0.00 0.08 0.25 0.37 0.16Energy 0.02 0.07 0.68 0.00 0.00 0.00 0.17 0.18 0.19Engineering 0.04 0.12 0.62 0.01 0.00 0.00 0.62 0.42 0.58Real estate 0.00 0.00 0.20 0.00 0.00 0.00 0.01 0.39 0.00
Notes: LMσ2 and LMβ tests the null hypothesis that σ2 = 0 (β = 0) given β = 0 (σ2 = 0),where β and σ2 are the mean and variance of βi, respectively. LMJ tests the joint hypo-thesis that σ2 = β = 0.
21
Table 3: Out-of-sample predictability test results.
RV SD CFPSector N RTU OR2 RTU OR2 RTU OR2
Banking 36 0.991 −0.001 0.969 −0.003 1.041 0.012Chemicals 35 0.965 0.002 1.000 0.000 1.030 0.010Electricity 38 0.962 0.002 0.986 0.006 1.017 −0.002Energy 22 1.006 0.000 0.928 0.011 1.002 −0.003Engineering 25 0.982 0.000 1.008 0.002 1.012 0.004Real Estate 39 0.987 0.001 0.952 0.006 1.012 0.003Hardware 23 1.002 0.000 1.019 0.006 1.000 0.000Household 35 0.965 0.002 0.937 0.007 1.000 0.000Mining 7 0.972 −0.009 1.015 0.003 1.004 0.001Retail 51 0.981 0.003 0.946 0.012 1.000 0.001Software 9 0.915 −0.005 1.003 0.006 1.005 0.006Telecom 8 0.953 −0.007 0.932 0.006 1.008 0.007Transport 26 0.983 0.003 0.995 0.005 1.016 −0.005Travel 23 0.970 0.002 0.969 0.011 1.012 −0.002Utilities 29 0.993 0.001 1.005 0.002 1.011 0.004
Notes: RTU and OR2 refer to the relative Theil U and out-of-sample R2
measures, respectively.
22
Tabl
e4:
Esti
mat
edpr
ofits
and
utili
ties
for
γ=
6.
RV
SDC
FP
Sect
orM
ean
t-te
stSD
Shar
peU
tilit
yM
ean
t-te
stSD
Shar
peU
tilit
yM
ean
t-te
stSD
Shar
peU
tilit
y
Bank
ing
0.66
613
.968
0.24
20.
097
0.13
50.
769
8.37
32.
229
0.61
20.
618
0.13
012
.115
0.00
20.
963
−1.
211
Che
mic
al0.
764
14.0
531.
218
1.00
93.
735
0.50
314
.053
0.23
70.
083
−0.
757
0.12
79.
003
0.00
00.
737
−1.
202
Elec
tric
ity
0.44
95.
735
0.77
00.
149
0.52
90.
421
14.0
530.
237
0.08
30.
288
0.12
63.
451
0.00
10.
654
−0.
760
Ener
gy0.
942
13.9
210.
243
0.09
70.
617
0.36
19.
846
0.86
50.
548
−1.
368
0.12
77.
892
0.00
40.
502
−1.
638
Engi
neer
ing
0.71
74.
569
1.29
80.
191
0.06
30.
388
14.0
530.
237
0.08
3−
0.49
90.
124
8.88
90.
001
0.00
8−
1.16
7
Rea
lest
ate
0.70
014
.060
0.23
70.
084
0.28
00.
444
9.26
71.
522
0.63
4−
0.03
70.
126
17.2
180.
000
1.10
4−
1.09
0
Har
dwar
e0.
917
3.10
81.
937
0.13
20.
264
0.92
018
.791
2.27
01.
528
3.52
90.
133
19.2
200.
000
10.1
94−
1.67
6
Hou
seho
ld1.
241
14.7
000.
595
0.83
10.
549
1.03
412
.495
0.83
30.
769
0.96
40.
132
9.02
70.
000
28.6
10−
1.94
2
Min
ing
1.32
014
.087
0.23
70.
084
−1.
311
0.71
114
.053
0.23
70.
083
−0.
691
0.13
123
.455
0.00
037
.084
−2.
336
Ret
ail
0.93
414
.517
0.40
40.
599
0.37
21.
040
19.0
050.
289
0.72
20.
253
0.13
116
.230
0.00
21.
151
−1.
633
Soft
war
e0.
697
14.7
160.
294
0.36
20.
579
0.79
715
.659
0.42
60.
733
−1.
537
0.13
312
.111
0.00
22.
111
−1.
129
Tele
com
0.07
99.
118
0.41
90.
150
0.00
20.
521
15.9
480.
220
0.16
0−
0.22
60.
132
16.5
440.
003
1.02
4−
0.23
1
Tran
spor
t0.
850
14.5
350.
292
0.34
00.
324
0.53
714
.065
0.24
50.
118
0.16
70.
125
5.56
60.
001
0.17
1−
1.41
7
Trav
el1.
016
14.5
670.
261
0.23
10.
565
0.81
315
.563
1.14
71.
127
0.57
20.
131
13.3
010.
001
1.81
6−
1.65
5
Uti
lity
0.51
66.
597
0.71
00.
194
0.14
80.
429
14.0
530.
237
0.08
3−
0.67
90.
126
5.10
00.
003
1.13
1−
0.81
4
Not
es:“
Mea
n”,“
t-te
st”,
“SD
”an
d“S
harp
e”re
fer
toth
eav
erag
ees
tim
ated
profi
t,th
et-
test
for
test
ing
the
null
that
the
aver
age
profi
tis
zero
,th
est
anda
rdde
viat
ion
ofpr
ofit,
and
the
Shar
pera
tio,
resp
ecti
vely
.γre
fers
toth
eco
effic
ient
ofre
lati
veri
skav
ersi
on.
23