Review of Accounting Studies, 7, 195–215, 2002
C 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.
The Role of Volatility in Forecasting
BERNADETTE A. MINTON
minton@cob.ohio-state.edu
Ohio State University
CATHERINE M. SCHRAND∗
schrand@wharton.upenn.edu
University of Pennsylvania
BEVERLY R. WALTHER
bwalther@northwestern.edu
Northwestern University
Abstract. Theories of underinvestment propose a link between cash flow volatility and investment and subsequent
cash flow and earnings levels. Consistent with these theories, our results indicate that forecasting models that include
volatility as an explanatory variable have greater accuracy and lower bias than forecasting models that exclude
volatility. The improvement in forecast accuracy and bias is greatest when the firm is most likely to experience
underinvestment. The profitable implementation of a trading strategy based on these findings, however, suggests
that equity market participants do not incorporate fully the information in historical volatility when forecasting
future firm performance.
Keywords: cash flow, forecasting, underinvestment, volatility
JEL Classification: G31, G35, M41, G19
1.
Introduction
Theories of risk management propose a relation between volatility and investment levels. In
the presence of market imperfections, external capital is more costly than internal capital and
cash flow volatility is associated with underinvestment (see Myers, 1977). Higher volatility
leads to periods in which the firm has insufficient cash flow to fund its “desired” investment.
The result is a lumpy investment pattern over time and a reduction in expected future
cash flow and earnings levels (Froot, Scharfstein and Stein, 1993; Smith and Stulz, 1985).
Minton and Schrand (1999) document a negative relation between cash flow volatility and
investment, suggesting that firms with more volatile cash flows are more likely to experience
internal cash flow shortfalls and forgo investment. Exacerbating the effect of volatility on
underinvestment is the fact that firms with more volatile cash flows or earnings are more
likely to experience a greater external cost of capital (Minton and Schrand, 1999).
Despite the hypothesized link between volatility and future cash flow and earnings, forecasting models in prior research traditionally include only historical cash flow and earnings
∗ Address correspondence to: The Wharton School, University of Pennsylvania, 2427 Steinberg Hall-Dietrich Hall,
Philadelphia, PA 19104.
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levels (Bowen, Burgstahler and Daley, 1986; Dechow, 1994; Finger, 1994; Sloan, 1996;
Wilson, 1987). Although some studies have considered the predictive ability of particular
fundamental variables such as the components of accruals (e.g., Bernard and Stober, 1989;
Barth, Cram and Nelson, 2001), none have considered the role of volatility in forecasting
levels of future cash flows or earnings.
Based on the theories of risk management, we predict that volatility contains incremental
information for forecasts of future firm performance beyond that in historical cash flow,
earnings, or investment levels. As a result, forecasts of cash flow and earnings that explicitly
incorporate historical volatility will be more accurate and less biased than forecasts from
models that exclude volatility as an explanatory variable. We expect greater improvements
in forecasting performance from incorporating volatility in the forecasting model when a
firm is more likely to experience underinvestment. Underinvestment is most likely to occur
when return on assets is low and when noise in cash flow is high.
Empirical analysis of non-financial firms on Compustat over the period 1983–1997 confirms these predictions. We find a statistically negative relation between volatility and future
operating cash flow and operating income levels, even after controlling for historical cash
flow, operating income, investment, or firm characteristics. Forecasting models that incorporate historical volatility yield significantly more accurate and less biased forecasts than
forecasting models that exclude volatility. The incremental predictive power of historical
volatility is especially pronounced for firms with high historical volatility and low return on
assets. Thus, the benefit of using a more complex model is greatest when volatility affects
the firm’s ability to fund investment.
Despite the better predictive accuracy of forecasting models that include historical volatility, the market appears to ignore information on volatility in equity valuation. We document
positive and significant hedge returns to a trading strategy that takes a long (short) position
in firms for which the forecast of future cash flow from models that exclude volatility is less
(greater) than the forecasts from models which incorporate volatility. Positive hedge returns
also result when we base the trading strategy on forecasts of future operating income. These
significant hedge returns are consistent with investors ignoring the information in historical
volatility.
Overall, the results show that investors can improve cash flow and earnings forecasts significantly, and therefore firm valuations, if they explicitly incorporate information about
the effect of volatility on investment and future firm performance. In this regard, our
findings contribute to the fundamental analysis research that identifies factors that improve valuations (see, e.g., Abarbanell and Bushee, 1997, 1998; Lev and Thiagarajan,
1993). The implications of our research, however, are not limited to predictions for
equity valuation. For example, individuals must forecast cash flow levels in a variety
of other contexts, such as option pricing, debt pricing, and capital budgeting. Possible
extensions of this research include further work on how individuals incorporate the information in volatility in cash flow or earnings forecasts in contexts other than equity
valuation.
The remainder of the paper is organized as follows. Section 2 outlines the paper’s predictions about the role of volatility in forecasting. Section 3 examines the predictions using
empirical data. Section 4 analyzes the valuation implications of these results. Section 5
concludes.
THE ROLE OF VOLATILITY IN FORECASTING
2.
2.1.
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The Role of Volatility in Forecasting
The Relation between Volatility and Underinvestment
We rely on the risk management literature, and in particular the underinvestment story
of Myers (1977), to predict a negative relation between volatility and future cash flow and
earnings levels. Based on models that capture underinvestment, Froot, Scharfstein and Stein
(1993) and Smith and Stulz (1985) both assert a negative relation between cash flow volatility
and future cash flow performance to explain why firms engage in costly hedging strategies. In
the presence of market imperfections, cash flow volatility decreases the likelihood that firms
will have sufficient internal capital to fund investment. Assuming external capital is more
costly than internal capital, firms with insufficient internal capital forgo investment. The
result is that firms with higher volatility will forgo (or reduce) investment in some periods,
resulting in a “lumpy” pattern of investment over time. Because the forgone investment is
not recovered in future periods (see Minton and Schrand, 1999), higher volatility leads to
lower average investment, lower future cash flows, and lower future earnings through time.
Critical to the underinvestment story is the assumption that external capital is more costly
than internal capital. Thus, firms do not borrow to fully fund investment in periods of low
internal cash flow realizations. Existing evidence supports this assumption. Empirically,
firms are more likely to forgo investment when costs of accessing external capital are high.
Moreover, a firm’s cost of accessing capital is positively related to its cash flow volatility
(Minton and Schrand, 1999) and its earnings volatility (see, e.g., Beaver, Kettler and Scholes,
1970; Gebhardt, Lee and Swaminathan, 2001). Hence, higher volatility not only increases
the likelihood that a firm will not have sufficient internal cash available to fund investment,1
it also increases the cost of obtaining external capital to fund cash flow shortfalls.
Based on these empirical results and aforementioned theories of risk management, we
predict that volatility has a negative relation with future operating cash flows and future
operating income. Further, we predict that incorporating volatility into the forecasting model
will result in more accurate and less biased forecasts of future cash flows and earnings.2
We also predict that the expected improvements from including volatility in the forecasting model will be especially pronounced when a firm’s investment pattern is most
lumpy as a result of periods of underinvestment. One factor that affects the likelihood of
underinvestment is the firm’s cash return on assets. As return on assets increases, investment expenditures from prior periods generate greater future cash flows. Consequently,
for a given level of prior period investment, a firm with a greater return on assets is more
likely to have sufficient internal cash flow to fund investment. Thus, we predict that the
underinvestment problem will be more severe, and thus the improvements from including volatility in a forecasting model will be greatest, as the firm’s cash return on assets
decreases.
The growth rate in a firm’s investment expenditures will affect the likelihood that cash
flow volatility affects investment in two opposing ways. As growth increases, a firm’s
desired level of investment, and thus the probability of underinvestment, increases. However, operating cash flow realizations also increase as growth increases because of higher
prior-period investment, reducing the likelihood of underinvestment. Therefore, the relation
between growth and the likelihood of underinvestment is unclear ex ante.
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Finally, “random” noise in cash flow will increase the probability of underinvestment.
Noisier cash flows increase the likelihood that there will be insufficient cash flow to fund the
desired investment, leading to a lumpy investment pattern. Thus, the inclusion of volatility
in the forecasting model will lead to the greatest improvements for firms with higher levels
of noise in cash flow.
2.2.
Alternative Explanations for a Relation between Volatility
and Future Firm Performance
In addition to the underinvestment story, the risk management literature provides several
alternative explanations for a negative association between volatility and future cash flow
and earnings levels. For example, Smith and Stulz (1985) hypothesize that in the presence
of information asymmetry and risk-averse managers, volatility can increase compensation
costs, thus reducing expected cash flow levels. Smith and Stulz also hypothesize that volatility will be negatively associated with future performance when taxable income volatility
leads to higher expected future tax payments due to progressive tax schedules and net operating loss carryforwards. Graham and Smith (1999) empirically document that the present
value of a firm’s income taxes increases in the volatility of taxable income. If cash flow
volatility is associated with taxable income volatility, then higher cash flow volatility is
negatively related to after-tax cash flows.
Another explanation for a negative relation between volatility and future performance
assumes that firms with higher volatility are perceived to have a higher probability of
financial distress or a higher cost of capital. When the probability of financial distress is
high, suppliers and customers might be unwilling to do business with a firm (Shapiro and
Titman, 1986), resulting in lower future firm performance.
Extant research also indicates higher volatility reduces the information that is available
about a firm, which in turn increases the firm’s cost of capital. For example, Waymire
(1985) documents that firms with less volatile earnings more frequently issue management
earnings forecasts than firms with more volatile earnings. Alford and Berger (1999) indicate
that analysts prefer to follow firms for which earnings are easy to forecast (see also Walther
and Willis, 1999). Less information leads to lower liquidity and a higher cost of capital
(Amihud and Mendelson, 1988). Empirical evidence supports the link between earnings
volatility and a firm’s cost of capital (e.g., Beaver, Kettler and Scholes, 1970; Gebhardt,
Lee and Swaminathan, 2001). The documented association between volatility and a firm’s
cost of capital is consistent with the underinvestment story—firms forgo investment when
volatility is high and cash flow realizations are low because it is costly to borrow to fund
investment.
Despite these other theories on the relation between volatility and future firm performance,
we focus on the underinvestment story because empirical evidence provides the most support
for this explanation. Minton and Schrand (1999) empirically document a negative relation
between cash flow volatility and average discretionary investment. Further, they show that a
positive relation between volatility and the cost of accessing external capital exacerbates the
underinvestment problem associated with cash flow volatility. Their analysis also provides
evidence that the sensitivity of investment to cash flow volatility does not result because
volatility is a proxy for project risk.
THE ROLE OF VOLATILITY IN FORECASTING
199
Indirect evidence also supports the underinvestment story. Firms that use derivatives to
reduce volatility have greater investment opportunities but also face liquidity constraints
(e.g., Geczy, Minton and Schrand, 1997; Guay, 1999; Mian, 1996; Nance, Smith and
Smithson, 1993). These firms are most likely to incur the highest costs from volatility
in the absence of any activities to reduce it. Our analysis on whether the benefits from
incorporating volatility into the forecasting model are associated with the likelihood of
underinvestment also provides indirect evidence on the validity of the underinvestment
story.
3.
Empirical Tests of Predictions
In this section, we test the predictions about the effects of volatility on future cash flow and
earnings levels. Prior literature has assessed the relevance of particular variables for forecasting firm performance by directly examining their relation to stock returns (e.g., Dechow,
1994; Francis, Olsson and Oswald, 2000). Such tests, as acknowledged by Dechow (1994),
are joint tests of the relative predictive power of the forecasting models and whether market
participants use the more accurate model in equity valuation. We separate the joint test into
two parts. In this section, we address the first issue: the predictive power of the forecasting
models. In Section 4, we investigate whether market participants use the information in
volatility in valuation.
3.1.
Sample and Empirical Proxies
The sample contains 3,501 firm-year observations for non-financial institutions from 1983
to 1997 (1,076 distinct firms) with sufficient data to calculate operating cash flow, investment, and operating income levels, cash flow volatility, operating income volatility, and
proxies for firm characteristics as described below. Quarterly operating cash flow (OPCF)
is defined as operating income before depreciation (Compustat data item 21) adjusted for
working capital accruals (see Dechow, 1994).3 We adjust this operating cash flow number
for “investment” expenditures that are expensed as part of operating income by adding
back quarterly research and development and advertising expenses, estimated as the annual
research and development or advertising expense from Compustat divided by four.4 Operating income (OPINC) is operating income before depreciation.5 We scale both OPCF and
OPINC by the firm’s average total assets for the year.
We divide the sample period into 11 overlapping five-year periods (e.g., 1983–1987, 1984–
1988, . . . , 1993–1997), and calculate the firm’s historical and future levels and volatility
measures for each period. The future (historical) level of cash flow or accounting earnings
is the annual measure for the fifth (fourth) year of each five-year period.
Historical volatility is measured as the coefficient of variation over the first four years
(16 quarters) in the five-year period. The coefficient of variation for operating cash flow
(operating income) is the standard deviation of operating cash flow (operating income)
scaled by the absolute value of the mean of operating cash flow (operating income) over the
same period. We require that a firm have data for at least 12 of the 16 quarters to calculate
historical volatility. The coefficient of variation is a unitless measure of volatility that has
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MINTON, SCHRAND AND WALTHER
been used in prior studies (Albrecht and Richardson, 1990; Michelson, Jordan-Wagner and
Wootton, 1995; and Minton and Schrand, 1999).
One potential concern with using quarterly data to calculate the coefficient of variation is
that a firm’s quarterly cash flow and operating income, and therefore investment patterns,
can be seasonal. Minton and Schrand (1999) document that the negative relation between
cash flow volatility and investment is not dependent on whether cash flows are seasonallyadjusted prior to measuring the coefficient of variation. Thus, to maximize the number of
available observations, we use unadjusted quarterly cash flow and income levels.
Another concern with this measure is that scaling by the absolute value of the mean
of either cash flow or income can lead to extreme observations when the variable is near
zero. To minimize the effect of extreme observations, the coefficient of variation measures,
as well as operating cash flow and operating income, are winsorized at the 1st and 99th
percentile values.
3.2.
The Association between Volatility and Future Firm Performance
Table 1 presents the mean coefficient estimates and adjusted R 2 s for the 11 separate annual
regressions that forecast operating cash flow or operating income at t + 1.6 The model
includes historical volatility as well as operating cash flow and operating income levels.
Table 1. Regression analysis of the relation between volatility and future operating performance.
Variable
OPCF Model
OPINC Model
Intercept
0.0699
(6.102)
0.0197
(3.877)
OPCF
0.4863
(7.649)
0.0736
(2.359)
OPINC
0.4049
(9.380)
0.8567
(11.513)
CV(OPCF)
−0.0043
(−5.466)
−0.0023
(−2.164)
CV(OPINC)
Adjusted R 2
60.73%
68.64%
Summary of cross-sectional, rolling window regressions of the future level of operating cash flow or operating
income on historical operating cash flow level, historical operating income level, and historical volatility:
OPCFt+1 = δ0 + δ1 OPCFt + δ2 OPINCt + δ3 CV(OPCF)t + ε
OPINCt+1 = δ0 + δ1 OPCFt + δ2 OPINCt + δ3 CV(OPINC)t + ε
The future levels of operating cash flow (OPCF) and operating income (OPINC) are the annual measures for the
fifth year of each five-year period between 1983 and 1997, scaled by average assets. Historical OPCF and historical
OPINC are the annual measures for the fourth year of each five-year period between 1983 and 1997, scaled by
average assets. The historical coefficient of variation as a proxy for cash flow volatility (CV(OPCF)) or earnings
volatility (CV(OPINC)) is calculated using quarterly data in the first four years of each five-year period between
1983 and 1997. The mean coefficient estimate from the overlapping regressions, the Z statistic in parentheses to
test the hypothesis that the mean estimated coefficient equals zero, and the mean adjusted R 2 are provided.
THE ROLE OF VOLATILITY IN FORECASTING
201
Operating cash flow (OPCF) and operating income (OPINC) are included as controls.
Previous research has documented that both cash flow levels and earnings levels are incrementally relevant for equity valuation (e.g., Bowen, Burgstahler and Daley, 1986; Dechow,
1994; Finger, 1994; Sloan, 1996; Wilson, 1987). Earnings has predictive ability because
the accrual component of earnings provides information about future cash collections and
future required cash payouts.
Table 1 shows that the mean coefficient estimate on historical cash flow volatility is statistically negative for the model predicting future cash flows. The negative relation between
volatility and future cash flow is consistent with the underinvestment story.7 The coefficient
on volatility is negative in ten of the 11 rolling window regressions, and significant in nine
of the 11 estimations. The negative relation exists after controlling for the previously documented positive relations between future cash flow and historical levels of cash flow and
earnings. Thus, there is a role for volatility in forecasting future cash flow levels.
We also estimate an alternative specification of the forecasting model that includes an
interaction term, CV(OPCF)*OPCF (results not reported). This specification allows for the
relation between cash flow volatility and future cash flow performance to be non-linear in
the level of a firm’s cash flow. This specification is consistent with the underinvestment
story in that firms that have large cash flows may be able to withstand volatility shocks
better. In the non-linear specification, the mean coefficient estimate on CV(OPCF) is not
statistically different from zero. However, the mean coefficient estimate on the interaction
term, CV(OPCF)*OPCF, is negative and significant. This finding indicates that as historical
volatility increases, less weight should be placed on historical operating cash flow levels
for forecasting future cash flows.
Since earnings levels are often the performance measure predicted, Table 1 also reports
the results of a model that forecasts future operating income, rather than operating cash
flow, at time t + 1. These results show that historical volatility also has a role in forecasting future earnings levels. The mean coefficient estimate on historical operating income
volatility (CV(OPINC)) is statistically negative for the model predicting future operating
income. Similar to the results for future cash flow levels, this negative association exists
after controlling for historical levels of income and cash flow.
We also estimate a regression that uses CV(OPCF) instead of CV(OPINC) to predict future
operating income levels. This specification increases the explanatory power of the regression
from 68.64% to 81.80%. Furthermore, the mean coefficient estimate on CV(OPCF) remains
significantly negative (−0.0012, Z = −2.156, results not tabulated). This specification
is most consistent with the underinvestment story in which cash flow volatility affects
investment, which in turn affects future performance (as measured by earnings). These
results confirm our conclusion that historical volatility has a negative relation with future
operating cash flow and operating income levels, consistent with the effect of volatility on
the likelihood of underinvestment.
3.3.
The Role of Volatility in Alternative Forecasting Models
of Future Firm Performance
In Table 2, we investigate whether the incremental explanatory power of volatility for future
operating performance documented in Table 1 holds in three alternative forecasting models.
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MINTON, SCHRAND AND WALTHER
Table 2. Analysis of the effects of including volatility in alternative forecasting models of future operating
performance.
Model 1
Variable
Without CV
Model 2
With CV
Without CV
Model 3
With CV
Without CV
With CV
−0.0738
(−1.946)
0.4595
(7.210)
0.3888
(9.348)
−0.0907
(−2.016)
0.4443
(6.935)
0.3881
(8.563)
0.1053
(9.140)
0.1198
(3.511)
0.0001
(0.410)
0.1014
(8.360)
0.1453
(3.798)
0.0001
(−0.049)
−0.0037
(−3.777)
62.90%
3.48
(8/11)
Panel A: Forecasting models of future operating cash flow
Intercept
0.0593
(5.542)
0.5025
(7.670)
0.4155
(10.480)
OPCF
OPINC
0.0699
(6.102)
0.4863
(7.649)
0.4049
(9.380)
INV
0.0286
(3.610)
0.3422
(6.347)
0.4946
(9.886)
0.3527
(6.184)
0.0370
(4.452)
0.3334
(6.402)
0.4828
(9.347)
0.3574
(6.279)
ρ
γ
CV(OPCF)
Adjusted R 2
Median F (versus
model without CV)
60.73%
−0.0043
(−5.466)
60.73%
4.46
(9/11)
64.34%
−0.0037
(−4.110)
64.63%
3.54
(8/11)
0.0172
(3.759)
0.1011
(3.662)
0.8442
(11.342)
−0.0271
(−0.741)
0.0213
(4.373)
0.0911
(2.913)
0.8462
(11.289)
−0.0235
(−0.920)
62.57%
Panel B: Forecasting models of future operating income
Intercept
0.0164
(3.364)
0.0786
(2.457)
0.8566
(11.593)
OPCF
OPINC
0.0197
(3.877)
0.0736
(2.359)
0.8567
(11.513)
INV
ρ
γ
CV(OPINC)
2
Adjusted R
Median F (versus
model without CV)
68.62%
−0.0023
(−2.164)
68.64%
1.95
(8/11)
68.23%
−0.0022
(−2.097)
68.69%
1.96
(8/11)
−0.1056
(−1.649)
0.0661
(2.462)
0.8520
(10.721)
−0.0907
(−1.452)
0.0641
(2.330)
0.8482
(10.467)
0.0177
(2.039)
0.1164
(2.150)
0.0003
(1.866)
0.0211
(2.502)
0.1046
(1.977)
0.0003
(2.001)
−0.0021
(−2.094)
68.70%
1.66
(6/11)
68.39%
Summary of cross-sectional, rolling window regressions of alternative models of future operating cash flow (Panel A) or future
operating income (Panel B) with and without volatility included as an explanatory variable. The alternative forecasting models
considered are:
Model 1: OP PERFt+1 = α0 + α1 OPCFt + α2 OPINCt + ε1
Model 2: OP PERFt+1 = β0 + β1 OPCFt + β2 OPINCt + β3 INVt + ε2
Model 3: OP PERFt+1 = φ0 + φ1 OPCFt + φ2 OPINCt + φ3 ρt + φ4 γt + φ5 t + ε3
where OPCF is the level of operating cash flow, OPINC is the level of operating income, INV is the level of investment, ρ is
the rate of return on assets, γ is the growth rate of underlying activities, and is other accruals besides depreciation. The mean
coefficient estimate from the overlapping regressions, the Z statistic in parentheses to test the hypothesis that the mean estimated
coefficient equals zero, and the mean adjusted R 2 are provided. For each forecasting model, the median F-statistic testing the
restriction that the estimated coefficient on volatility (CV(OPCF) in Panel A; CV(OPINC) in Panel B) equals zero is presented,
with the number of annual F-statistics that are significant at p < 0.10 below in parentheses.
THE ROLE OF VOLATILITY IN FORECASTING
203
Model 1 is a benchmark model that includes historical operating cash flow and historical
operating income. This forecasting model represents a specification that is traditionally
examined in accounting research.
The second alternative model (Model 2) includes the firm’s historical investment level
in addition to the variables in the benchmark model. Historical investment may represent
a reasonable substitute for historical volatility with respect to its ability to forecast future
operating performance. Investment is defined as quarterly capital expenditures plus estimates of quarterly research and development and advertising expenses, deflated by average
assets. Quarterly capital expenditures are estimated as the change in net property, plant, and
equipment plus depreciation.8
Finally, Model 3 includes fundamental variables that drive the cash flow generation process: return on assets and growth. The cash flow return on assets variable is calculated as
cash flow from operations (cash flow from operations plus cash interest paid) at year t divided by the value of gross PPE minus accumulated depreciation (“net PPE”) at year t − 1.
The growth variable is calculated as the annual growth rate of investment opportunities,
measured by net PPE at time t divided by net PPE at time t − 1.
Model 3 also includes a proxy for other accruals, . The variable is calculated as
the ratio of other accruals (defined as current assets minus current liabilities) to operating
cash flow, and captures differences between firms’ trade cycles (see Minton, Schrand and
Walther, 2001). It is included in Model 3 because both operating cash flow and its derivative,
operating income, are included in the model.
For each of the overlapping five-year periods, we measure return on assets, growth, and
other accruals as the mean of the quarterly values for the first four years of the period. We
require that a firm have at least 12 quarters of data to calculate each mean. Although the
results are similar if we measure these variables as the mean value over the entire five-year
period, measuring the characteristics over only the first four years creates a proxy that is
more consistent with the information that investors would have available for prediction
purposes. To minimize the effect of extreme observations, all of the empirical proxies are
winsorized at the 1st and 99th percentile values.
Table 2 reports the estimation results for each of the three alternative models, with and
without cash flow volatility as an additional explanatory variable. Panel A provides the
regression results for predicting future operating cash flow. Panel B provides the regression
results for predicting future operating income.
On average, historical levels of cash flow and operating income provide reasonable estimates of future operating cash flow (Panel A) and operating income (Panel B)
levels. The mean adjusted R 2 of Model 1 for the overall sample is 60.73% for the operating cash flow model, and 68.62% for the operating income model. Consistent with
prior research, the estimated coefficients on OPCF and OPINC are statistically positive
( p < 0.02).
Historical volatility contains incremental explanatory power for future operating levels
beyond that in historical cash flow and earnings levels, as previously documented in Table 1.
Although the average overall explanatory power of Model 1 (as measured by the adjusted R 2 )
with and without volatility is similar, the F-statistic testing the restriction that the coefficient
volatility is zero is significant in nine (eight) of the 11 annual regressions for the cash flow
(income) model.
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Adding historical investment to the model (Model 2) provides incremental explanatory
power for future cash flow levels relative to Model 1. The mean adjusted R 2 increases
from 60.73% for Model 1 to 64.34% for Model 2 in Panel A. The partial F-test rejects
the restriction that the coefficient on INV in the cash flow model equals zero at the 10%
probability level in all 11 annual regressions (not reported). In Panel A, the mean estimated
coefficient on INV is positive and statistically significant at p < 0.01, indicating that higher
investment is associated with higher future operating cash flows. By contrast, the mean
estimated coefficient on INV is insignificant in Panel B, suggesting that after controlling for
historical cash flow and earnings levels, investment does not contain incremental explanatory
power for future operating income.
When volatility is added to Model 2, the coefficient is statistically negative and significant
in both the operating cash flow and operating income models. In both panels, the partial
F-test rejects the restriction that the coefficient on volatility equals zero at the 10% probability level in eight of the 11 annual regressions. Therefore, historical volatility contains
information incremental to that in historical investment for future operating performance.
Incorporating firm characteristics (Model 3) improves the predictability of future operating performance, and especially operating cash flow, over Model 1. For the operating cash
flow (operating income) model, the partial F-statistic rejects the restriction that the coefficients on ρ, γ , and ω equal zero in ten (seven) of the 11 annual regressions (not tabulated).
In both panels, the mean annual estimated coefficients on ρ and γ are positive and significant, indicating that increases in the rate of return or growth are associated with increases
in future operating cash flow and operating income levels. The mean estimated coefficient
on other accruals is insignificant in Panel A, but is significantly positive in Panel B. The
positive coefficient indicates that higher levels of other accruals are associated with higher
levels of future operating income.
In both panels, the mean coefficient on volatility is significant and negative when it is
added to Model 3. Thus, the variables that characterize the cash flow generation process do
not fully capture the information about future operating performance in historical volatility.
Table 3 provides the forecast accuracy and bias statistics for the models with and without volatility included as an explanatory variable. This comparison allows us to assess
whether adding volatility to a forecasting model is not only statistically significant but also
economically significant in that it generates a forecast that dominates forecasts from other
possibly more parsimonious models.
Operating cash flow (operating income) forecast accuracy is measured for each observation as the absolute percentage error, APE, of the forecast, defined as the absolute value
of actual OPCF (OPINC) less predicted OPCF (OPINC), scaled by the absolute value of
actual OPCF (OPINC). Higher APEs correspond to less accurate forecasts. The forecast is
based on a model that forecasts operating performance at time t + 2 using the coefficient
estimates from the model that estimates operating performance at time t + 1.9
Operating cash flow (operating income) forecast bias is actual OPCF (OPINC) less predicted OPCF (OPINC), scaled by the absolute value of actual OPCF (OPINC). Thus, a
positive (negative) bias measure indicates that the model under predicts (over predicts)
the actual future operating performance level. We examine improvements in both accuracy
and bias because these are important dimensions that analysts must potentially trade off in
forecasting (Lim, 2001).
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THE ROLE OF VOLATILITY IN FORECASTING
Table 3. Accuracy and bias of forecasts from alternative forecasting models of future operating performance.
Model 1
Variable
Without CV
With CV
Model 2
Model 3
Without CV
With CV
Without CV
With CV
1.4410
0.2505
−0.9917
0.0006
0.7412*
0.2443†
−0.4251*
0.0029
1.3211
0.2666
−0.8722
−0.0120
0.8693*
0.2607
−0.5491†
−0.0123
1.5587
0.2356
−0.8315
0.0140
0.9267*
0.2308†
−0.4358*
0.0148
1.6964
0.2420
−0.9547
0.0231
0.9252*
0.2330†
−0.4365*
0.0232
Panel A: Operating cash flow forecasts
Mean APE
Median APE
Mean bias
Median bias
1.3498
0.2662
−0.9186
−0.0214
0.7618*
0.2592†
−0.4595*
−0.0217
Panel B: Operating income forecasts
Mean APE
Median APE
Mean bias
Median bias
1.5703
0.2335
−0.8155
0.0176
1.0085*
0.2288†
−0.3676*
0.0156
The mean and median absolute percentage error (APE) and bias of alternative models of future operating cash flow
(Panel A) or future operating income (Panel B) with and without volatility included as an explanatory variable. The
alternative forecasting models are defined in Table 2. The table reports the mean and median absolute percentage
error (APE) and bias of the forecasts from each model.
† (*) statistically different from the corresponding value for the model without CV using a t-test (Z statistic) for
means (medians) at p < 0.10 (0.05).
Both operating cash flow and operating income forecasts based on models that include
volatility are more accurate and less biased than forecasts from the corresponding models that exclude volatility. In both panels, the mean and median APEs are lower for the models
that include historical volatility as an explanatory variable than for the counterpart models that exclude volatility. While the median forecast bias statistics are similar across the
models with and without volatility, the mean bias is less negative when volatility is included as an explanatory variable. These findings supplement those in Table 2, and indicate
that not only is the relation between future operating performance and historical volatility
statistically significant, it is also economically significant.
3.4.
Cross-Sectional Variation in the Relation between Volatility
and Future Firm Performance
Table 4 examines under what conditions the models that include volatility outperform models that exclude volatility in terms of increased accuracy and reduced bias. In Section 2, we
predict that incorporating volatility into the forecasting model will have the greatest impact
on forecast accuracy and bias when underinvestment is most likely to occur. Underinvestment is most likely to occur when the return on assets (ρ) is low and when the noise in
cash flow (ω) is high. As discussed in Section 2, the relation between growth (γ ) and the
likelihood of underinvestment is unclear ex ante. Thus, Table 4 shows the improvements in
forecast accuracy and bias from adding volatility to the model across quartiles of return on
assets (ρ) and growth (γ ), and on the basis of historical volatility (CV) as a substitute for
noise in operating cash flow (ω).
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MINTON, SCHRAND AND WALTHER
Table 4. Accuracy and bias of forecasts from forecasting models of future operating performance by firm
characteristics.
Accuracy Statistics (APE)
Variable
Bias Statistics
Without CV
With CV
Without CV
With CV
Panel A: Operating cash flow forecasts
ρ
Lowest quartile
Quartile 2
Quartile 3
Highest quartile
0.4057
0.2517
0.2323
0.2519
0.3873†
0.2468
0.2320
0.2466
−0.1444
−0.0688
0.0063
0.0749
−0.1249
−0.0696
−0.0007
0.0769
γ
Lowest quartile
Quartile 2
Quartile 3
Highest quartile
0.3658
0.2430
0.2113
0.2884
0.3453†
0.2387
0.2079
0.2842
−0.1069
−0.0397
0.0095
0.0180
−0.0907
−0.0461
0.0055
0.0207
CV(OPCF)
Lowest quartile
Quartile 2
Quartile 3
Highest quartile
0.1776
0.2331
0.3260
0.4747
0.1783
0.2334
0.3147
0.4304*
0.0376
−0.0302
−0.0768
−0.1191
0.0287
−0.0352
−0.0786
−0.0562†
Panel B: Operating income forecasts
ρ
Lowest quartile
Quartile 2
Quartile 3
Highest quartile
0.3307
0.2195
0.1952
0.2445
0.3187
0.2158
0.1870
0.2379
−0.0020
0.0251
0.0205
0.0173
0.0113
0.0176
0.0172
0.0160
γ
Lowest quartile
Quartile 2
Quartile 3
Highest quartile
0.3447
0.1928
0.1790
0.2814
0.3310
0.1870
0.1767
0.2744
−0.0812
0.0262
0.0297
0.0794
−0.0678
0.0195
0.0239
0.0812
CV(OPINC)
Lowest quartile
Quartile 2
Quartile 3
Highest quartile
0.1311
0.1933
0.2960
0.6060
0.1296
0.1884
0.2789
0.5673†
0.0352
0.0401
0.0157
−0.1125
0.0274
0.0285
0.0135
−0.0898
Median accuracy and bias statistics for firm-specific forecasts of future operating cash flow levels (Panel A) and
future operating income levels (Panel B) from Model 1 (defined in Table 2) with and without volatility. The table
reports the median absolute percentage error (APE) and bias of the forecasts from the model for quartiles formed
on the basis of return on assets (ρ), growth (γ ), and historical volatility.
† (*) statistically different from the corresponding value for the model without CV using a Z statistic at p < 0.10
(0.05).
Table 4 reports the findings for Model 1, which only includes historical operating cash
flow and operating income levels as independent variables. The results for Models 2 and 3
are similar and not reported. Panel A reports the results for operating cash flows; Panel B
reports the results for operating income. Only the median accuracy and bias statistics are
provided in Table 4; results based on the mean statistics are discussed in the text.
Overall, the results suggest that incorporating volatility into the forecasting model yields
the greatest improvement when underinvestment is most likely to occur. First, the largest
improvement in forecast accuracy and bias from including volatility occurs at low values
of return on assets. In the lowest quartile of ρ, the median APE for the cash flow forecasting model that includes volatility (APE = 0.3873) is significantly lower than that for
THE ROLE OF VOLATILITY IN FORECASTING
207
the cash flow forecasting model that excludes volatility (APE = 0.4057, Panel A). In this
subsample, the mean APE is also significantly lower when volatility is included in the cash
flow forecasting model (APE = 0.9597) than when it is not (APE = 1.6536, not tabulated).
While the median APE and bias are not significantly different in Panel B, the mean APE
is significantly lower (1.7198 versus 1.0185) and the mean bias is significantly closer to
zero (−0.9883 versus −0.3712) at p < 0.05 for the operating income model that includes
volatility (not tabulated). At lower levels of return (ρ), a firm is more likely to be forced
to forgo investment because of lower cash levels. Thus, the results support the hypothesis
that incorporating volatility into the forecast model improves the relative accuracy and bias
when underinvestment is most likely to occur.
Second, the results suggest that incorporating volatility into the forecasting model improves forecasts the most for firms experiencing low growth. Panel A reports that for the
lowest quartile of γ , the mean and median APE are significantly lower for the cash flow
forecasting model that includes volatility. While the reported median bias statistics are not
significantly different in Panel A, the mean bias is significantly less negative (−1.9063
versus −0.8434, not tabulated) when volatility is included in the cash flow forecasting
model.
While the median APE statistics are not significantly different in Panel B, the mean APE
for the operating income model with volatility (1.2870) is significantly lower than the mean
APE without volatility (2.3336, p < 0.05) for the lowest quartile of γ . Further, the mean bias
statistic is significantly improved from incorporating volatility into the operating income
model for firms with the lowest level of growth (−1.7484 versus −0.7627, not tabulated).
Overall, these results suggest that the improvement from incorporating volatility is greatest
at low levels of growth.
Finally, forecast accuracy is most improved from incorporating volatility into the model
for firms with volatility in the highest quartile. For both operating cash flow and operating
income forecasts, the mean and median APEs for the model that excludes volatility are
significantly greater than the mean and median APEs for the model that includes volatility
in the highest quartile of CV.
Forecast bias also is most improved in the highest quartile of CV. The median bias statistic
in Panel A for the cash flow forecasting model without volatility is −0.1191, compared to
−0.0562 for the model with volatility ( p < 0.10). While the median bias is improved in
Panel B as well, only the mean bias is significantly different for the highest quartile of
CV(OPINC) (−1.7192 versus −0.5955, p < 0.10, results not tabulated).
As discussed in Section 2, a firm is more likely to experience underinvestment at higher
levels of cash flow volatility. Therefore, these findings support the conclusion that volatility
improves the relative accuracy of the forecasting models when underinvestment, and thus
a lumpy investment pattern, is likely to occur.
4.
Valuation Implications
The results of the previous section indicate a role for volatility in forecasting, especially in
cases when underinvestment is most likely to occur. In this section, we test whether investors
incorporate information about volatility in their estimates of future firm performance. Prior
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MINTON, SCHRAND AND WALTHER
research suggests that individuals have difficulty incorporating information about variance
into their decisions and judgments (see Ashton, 1982, pp. 101–108 for a summary of the
findings). We examine the profitability of trading strategies that assume market participants
do not incorporate volatility into forecasts of future operating cash flows and future operating
income. In Section 4.2, we investigate the relation between our findings and other previously
documented anomalies.
4.1.
Trading Strategies Based on Historical Volatility
We implement a trading strategy that assumes investors ignore the information in volatility
in setting prices. We forecast one-year ahead operating performance levels for each firm
using specifications of the forecasting models that include and exclude volatility. We buy
(sell) firms for which the forecast from the model that includes volatility is greater (less)
than the forecast from the same model without volatility, and calculate excess returns for
the portfolio. We implement this trading strategy for both forecasts of future operating cash
flows and future operating income, and for all three forecasting models.
Size-adjusted portfolio excess returns in year t + 1 are measured over two windows. The
annual window begins four months after the firm’s fiscal year-end of the year in which
we measure the level of earnings, level of cash flow, level of investment, and historical
volatility. The second window is the sum of the three-day excess return around each of the
four quarterly earnings announcement dates in year t + 1. The size-adjusted excess return
for each sample observation is the firm’s raw buy-hold return minus the buy-hold return on
a size-matched, value-weighted portfolio of firms based on market value of equity deciles
of NYSE, AMEX, and NASDAQ firms from CRSP.
The significant hedge returns in Panel A of Table 5 suggest that investors do not consider
the information in historical cash flow volatility when forecasting future operating cash
flow, despite greater accuracy and lower bias from the models that include volatility. The
trading strategy returns over the annual window range from 2.88% for Model 1 to 5.86%
for Model 3. All are significantly different from zero with the exception of the mean return
for Model 1.
All trading strategy returns over the earnings announcement date window also are statistically significant at p < 0.10, and range from 1.85% for Model 1 to 2.91% for Model 3.
Thus, regardless of the underlying model we assume investors use to forecast cash flows,
the results suggest that investors do not incorporate the information in historical cash flow
volatility in price, even though it has value for predicting future cash flow performance and
thus returns.
This conclusion holds if we instead assume that investors predict earnings and value the
earnings predictions to set a price. In Panel B, we recompute the trading strategy results
using forecasting models that predict future operating income rather than cash flows.10
The mean and median hedge returns for the annual window are positive and significant for
Models 1 and 3. The mean and median hedge returns around the earnings announcement
date range from 2.05% to 3.26%, and are significantly positive regardless of the forecasting
model examined. These findings again suggest that investors do not fully incorporate the
information in volatility for future firm performance.
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THE ROLE OF VOLATILITY IN FORECASTING
Table 5. Trading strategy returns based on predicted operating performance.
Earnings Announcement
Date Returns
Annual Returns
Portfolio
Mean
Median
Mean
Median
Model 1: With v. without CV
Long
1.04%
Short
−1.84
Hedge return
2.88
−0.26%
−4.11
3.85†
2.79%
0.71
2.08†
2.32%
0.47
1.85*
Model 2: With v. without CV
Long
1.90%
Short
−2.34
Hedge return
4.24*
0.49%
−4.27
4.76*
2.89%
0.87
2.02†
2.73%
0.37
2.36*
Model 3: With v. without CV
Long
1.72%
Short
−2.27
Hedge return
3.99†
0.83%
−5.03
5.86*
2.91%
0.63%
2.28*
3.28%
0.37
2.91*
Model 1: With v. without CV
Long
2.28%
Short
−0.47
Hedge return
2.75†
0.37%
−2.26
2.63*
2.42%
0.30
2.12*
2.95%
0.08
2.87*
Model 2: With v. without CV
Long
Short
Hedge return
1.12%
0.87
0.25
0.34%
−0.27
0.61
2.59%
0.54
2.05*
3.45%
0.92
2.53†
Model 3: With v. without CV
Long
1.81%
Short
−2.75
Hedge return
4.56*
0.29%
−1.45
1.74*
2.60%
0.11%
2.49*
2.93%
−0.33
3.26*
Panel A: Operating cash flow forecasts
Panel B: Operating income forecasts
Excess returns to trading strategies that use forecasting models that include volatility as an independent variable
instead of forecasting models that exclude volatility. Table 2 provides the forecasting models. In Panel A, a long
(short) position is taken in firms for which the forecasted cash flow level for t + 1 from the model with volatility
is greater (less) than the forecasted cash flow level for t + 1 from the model without volatility. In Panel B, a long
(short) position is taken in firms for which the forecasted operating income level for t + 1 from the model with
volatility is greater (less) than the forecasted operating income level for t + 1 from the model without volatility.
The annual abnormal return to each portfolio is the mean one-year size-adjusted excess return beginning four
months after the fiscal year-end. The earnings announcement date abnormal return is the sum of the mean threeday size-adjusted excess return around the four earnings announcements for t + 1.
† (*) statistically different from zero using a t-test (Z statistic) for means (medians) at p < 0.10 (0.05).
Our results are closely related to the previously documented “predictability bias” in stock
returns. Huberts and Fuller (1995) document that firms with the least predictable earnings
per share have the greatest positive analyst forecast errors and related negative abnormal
returns (see also Weary, 1998). The lower than expected earnings for firms with high earnings
volatility is consistent with analysts ignoring the impact of volatility on the likelihood of
underinvestment and thus future cash flows and future earnings. The negative abnormal
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MINTON, SCHRAND AND WALTHER
returns are consistent with our evidence that investors also fail to incorporate in prices the
information in historical volatility.
4.2.
Relation of Our Results with Other Trading Strategies
In this section, we relate our findings to Sloan’s (1996) profitable trading strategy and a
subsequent examination of his results by Ali, Hwang and Trombley (2000). Sloan (1996)
documents an abnormal return of approximately 11% from a trading strategy that takes a
long position in firms with low earnings but high cash flow and a short position in firms
with high earnings but low cash flow.11 The profitability of this trading strategy suggests
that investors ignore information in cash flow for future firm performance.
We predict that the accuracy of models of future operating cash flow that exclude volatility
as an explanatory variable is greatest when historical cash flow volatility is low, and the
empirical analysis supports this prediction. If investors also ignore the effect of historical
volatility on the relation between historical and future measures, then the profitability of
Sloan’s (1996) trading strategy will be greatest when cash flow volatility is low and thus
historical cash flow is most relevant for future cash flow.
We analyze the returns to Sloan’s (1996) trading strategy conditioning on historical cash
flow volatility. For each sample year, we separate firms into quintiles based on historical
accruals and historical cash flow volatility, resulting in 25 portfolios.12 We take a long
position in low-volatility firms that have low accruals and a short position in low-volatility
firms that have high accruals (i.e., high earnings but low cash flow). While we expect that
the strategy will be more profitable for low-volatility firms, we implement the same strategy
with respect to accruals for high-volatility firms as a benchmark. Following Sloan (1996),
we examine the size-adjusted excess annual return beginning four months after the firm’s
fiscal year-end of the year in which the level of earnings, level of cash flow, and historical
cash flow volatility are measured.
Panel A of Table 6 provides the mean and median excess returns for each accrual portfolio,
separately for firms with low and high cash flow volatility. For firms with low cash flow
volatility, the average annual size-adjusted excess return to the long position is +3.94%
and the return to the short position is −9.51%, for a hedge return of +13.45% (t =
2.37, p < 0.04, Panel A).13 The hedge return is positive in 15 of 18 years. By contrast, the
average annual hedge return for the high-volatility firms is insignificantly different from
zero (4.93%, t = 1.01, p > 0.10).
To ensure that the difference in hedge returns between low and high volatility firms is not
attributable to an omitted risk factor, Panel B of Table 6 regresses the annual size-adjusted
excess return on firm characteristics (see Sloan, 1996).14 The characteristics considered are
size (measured as the logarithm of total assets), book-to-market (measured as the log of the
ratio of the book value of equity to the market value of equity), and firm beta (measured by
estimating the market model on the prior 100 trading days). Consistent with the findings in
Panel A, the estimated coefficient on accruals is significant only for the low volatility firms.
Replacing the continuous measure of accruals with a variable that represents the accrual
portfolio rank yields similar results (not tabulated). Thus, the ability of accruals to predict
future returns for low volatility firms but not high volatility firms is not due to differences
in risk characteristics.
211
THE ROLE OF VOLATILITY IN FORECASTING
Table 6. Replication of Sloan’s (1996) trading strategy results conditional on volatility.
Low Volatility
Portfolio
Mean
High Volatility
Median
Mean
Median
Panel A: Annual returns to accrual strategy
1 (Low accruals: High CF, Low AE)
3.94%
0.02%
3.59%
1.47%
2
4.73
4.49
6.73
7.65
3
5.26
2.77
9.59
4.92
4
2.25
2.79
3.12
4.73
5 (High accruals: Low CF, High AE)
−9.51
−13.33
−1.34
−2.21
Hedge return
13.45%*
Variable
13.35%*
Low Volatility
4.93%
3.68%
High Volatility
Panel B: Annual returns to accrual strategy controlling for firm characteristics
Intercept
−0.0758
(−3.74)
−0.0393
(−1.52)
Accruals
−0.0921
(−1.82)
0.0080
(0.13)
Size
0.0195
(6.08)
0.0015
(0.28)
Book-to-market
0.0347
(3.77)
−0.0371
(−2.70)
−0.0403
(−3.50)
0.0006
(0.05)
Beta
Excess returns to Sloan’s (1996) trading strategy conditioning on historical cash flow volatility. Firms are sorted
annually into quintiles on the basis of historical cash flow volatility and accruals, which indicate the relative levels of
cash flow (CF) and accounting earnings (AE). Panel A provides the mean and median annual cumulative abnormal
return for each accrual portfolio for firms with low and high cash flow volatility. The annual cumulative abnormal
return to each portfolio is the one-year size-adjusted excess return beginning four months after the end of the
fiscal period. Panel B provides the coefficient estimate and t-statistic in parentheses from a regression of the
annual cumulative abnormal return on an intercept, accruals, size, book-to-market ratio, and beta. Size is the log
of total assets. The book-to-market ratio is the log of total common equity (from Compustat) divided by share
price times number of common shares outstanding. Betas are estimated using daily returns and a value-weighted
market index from CRSP over the 100 trading days prior to each firm’s year end.
*Statistically different from zero at p < 0.05 using a t-test (for means) or a Wilcoxon Z -test (for medians).
Recent work by Ali, Hwang and Trombley (2000) examines whether the profitability of
Sloan’s (1996) trading strategy is negatively related to the richness of the firm’s information
environment. They find that investors in larger firms are more likely to ignore the information
in cash flows relative to earnings. Because larger firms are more likely to be followed by
analysts and held by institutional investors, they conclude that the problem Sloan documents
is not more pronounced for firms with naı̈ve investors.
However, Ali et al. analysis ignores the endogeneity between volatility and the richness of a firm’s information environment. Given the negative relation between volatility and analyst following or institutional ownership (e.g., O’Brien and Bhushan, 1990;
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MINTON, SCHRAND AND WALTHER
Minton and Schrand, 1999), firms with richer information sets also are more likely to have
lower cash flow volatility. Therefore, a more intuitive and economically appealing explanation for the greater abnormal returns for large firms found by Ali, Hwang and Trombley
(2000) is that historical cash flows are better predictors of future cash flow levels for these
firms.
5.
Conclusions
This paper links results from the risk management literature that show a relation between
volatility, investment, and firm value to the literature on forecasting. When current period
investment decisions are a function of current period cash flow realizations, a firm’s investment pattern through time depends on cash flow volatility. Thus, volatility will affect future
cash flows and future income levels. As a result, we predict that volatility has explanatory
power for future operating performance incremental to that in historical cash flow, earnings, investment, or other firm characteristics related to the cash flow generation process
(such as return on assets and growth). Further, we predict that incorporating volatility into a
forecasting model improves forecast accuracy and bias most when volatility causes periods
of underinvestment and thus a lumpy investment pattern. Lumpy investment is most likely
to occur when return on assets is low and noise in cash flow is high.
Four main results emerge from our empirical analysis. First, consistent with our predictions, volatility has incremental explanatory power for future operating cash flows and
operating income beyond traditional forecasting models. Second, forecasting models that
incorporate volatility provide more accurate and less biased forecasts than corresponding
models that exclude volatility as an explanatory variable. Third, the relative improvements
from incorporating volatility are greater when underinvestment is most likely to occur.
Finally, the profitability of a trading strategy that relies on the first three findings suggests
that investors do not fully incorporate information on volatility in equity valuation. The
results from our empirical analyses can be used to improve existing forecasts of cash flow
and earnings levels in equity valuation as well as in other contexts.
Acknowledgments
The authors appreciate comments from Mary Barth, Ted Goodman, Adam Koch, Lisa
Koonce, Rick Lambert, James Livingston, Doron Nissim, Richard Sloan, René Stulz,
Ro Verrecchia, Karen Wruck, two anonymous reviewers, and seminar participants at American Accounting Association 2000 annual meetings, Australian Graduate School of Management, Baruch College, Carnegie-Mellon, University of Chicago, Columbia University’s Burton Workshop, Duke University/University of North Carolina’s fall camp, Emory
University, Georgetown University, University of Illinois, University of Melbourne, University of Minnesota’s mini-conference, New York University, Review of Accounting Studies
2001 conference, and University of Texas, and the computer assistance of Jim Noonan.
Minton thanks the Dice Center for Financial Economics for financial support. Walther
thanks the Accounting Research Center at the Kellogg School of Management for financial
support.
THE ROLE OF VOLATILITY IN FORECASTING
213
Notes
1. Prior work also has documented a positive association between liquidity and investment levels (e.g., Fazzari,
Hubbard and Peterson, 1988, 1998; Hoshi, Kashyap and Scharfstein, 1991; Kaplan and Zingales, 1997; Lamont,
1997). Unlike Minton and Schrand (1999), these results indicate that firms time investments to match cash flow
levels but do not necessarily imply that firms forgo investments when cash flow realizations are low. Lumpy
investment also can be a rational choice because of the real options embedded in certain investment projects,
such as when to invest, whether to abandon a project, or whether to modify a product midstream (e.g., Berger,
Ofek and Swary, 1996; Dixit and Pindyck, 1993; Majd and Pindyck, 1987; Pindyck, 1988; Trigeorgis, 1996).
2. The predictions were originally based on a model of a firm’s cash flow generation process that incorporated
underinvestment. A detailed description of the model and the simulation analysis used to develop the predictions
is provided in Minton, Schrand and Walther (2001).
3. The adjustment for working capital accruals subtracts the changes in accounts receivable, inventory, and other
current assets, and adds back the changes in accounts payable and other current liabilities.
4. We estimate quarterly advertising expense since these Compustat data are available only on an annual basis.
Quarterly research and development data are available from Compustat beginning in the first quarter of 1989.
The mean of the actual quarterly amount for all firms on Compustat from 1989 to 1997 is virtually identical
to that of our estimated amount ($7.03 million versus $7.05 million), and the Pearson (Spearman) correlation
between these two numbers is 0.96 (0.99).
5. The results in Sections 3.2 through 3.4 are qualitatively similar if we calculate operating cash flow using operating income before depreciation (defined as net sales minus cost of goods sold minus selling and administrative
expenses) adjusted for the change in accruals, and/or if we do not adjust the operating cash flow number for
research and development or advertising expenses. The results also are insensitive to alternative definitions of
operating income, including net income or net income before extraordinary items and discontinued operations.
6. In the tabulated results, we eliminate observations with studentized residuals greater than two in absolute value
or Cook’s D greater than one; the results are not sensitive to this outlier elimination.
7. To provide additional evidence on the underinvestment story, we examine the relation between historical cash
flow volatility and future investment levels, after controlling for historical operating cash flow and operating
income levels. As expected, the mean estimated coefficient on CV(OPCF) in this specification is negative
and statistically significant (−0.0017, Z = − 2.910, p < 0.01). Thus, higher levels of cash flow volatility are
associated with lower levels of future investment, consistent with Minton and Schrand (1999).
8. The results are robust to alternative measures of quarterly capital expenditures, including the amount reported
by Compustat (available the first quarter of 1984) or annual capital expenditures from 10-K Schedule V divided
by four, and to the exclusion of research and development and advertising expenses from the definition of
investment.
9. Using the mean of the coefficients from the prior three or five yearly regressions result in more accurate and
less biased forecasts, but does not change any of our inferences.
10. We also computed the hedge returns from taking a long (short) position in firms for which both the cash flow
forecast and the earnings forecast from the model that includes volatility are greater than the cash flow and
earnings forecasts, respectively, from the same model that excludes volatility. All inferences are unchanged.
11. In our sample, the average hedge return to Sloan’s (1996) strategy is 10.76% when we divide observations
into separate deciles for historical cash flow and historical earnings levels. We use quintiles for the remainder
of the tests due to the small sample size in each combination of decile classifications. Implementing Sloan’s
strategy for quintiles is lower but still positive (8.76%).
12. The minimum number of observations per portfolio is five in 1993, the maximum is 53 in 1989, and the average
over all years is 23.7. Our conclusions are unchanged if we segregate sample firms into portfolios based on
historical cash flow and earnings levels.
13. There are also significant excess returns to a trading strategy that relies only on historical cash flow volatility
and historical cash flow levels and ignores earnings. The average annual hedge return for a strategy that takes
a long position in firms with high cash flow levels and low volatility (+7.33%) and a short position in firms
with low cash flow levels and low volatility (−6.14%) is +13.47%.
14. As an alternative means of assessing whether our findings are due to differences in risk, we implemented a
trading strategy based solely on historical volatility. This trading strategy takes a long (short) position in firms
in the lowest (highest) quintile of historical volatility. Regardless of whether we form the quintiles on the basis
214
MINTON, SCHRAND AND WALTHER
of CV(OPCF) or CV(OPINC), the mean and median hedge returns over the annual window are insignificantly
different from zero.
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