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 Please do not quote without obtaining the author’s consent as these works are in their draft form.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