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Fundamental uncertainty and stock market volatilityIvo J. M. Arnold
a& Evert B. Vrugt
a
aErasmus School of Economics, Erasmus Universiteit Rotterdam, PO Box 1738, 3000 DR,
Rotterdam, The Netherlands and Nyenrode Business Universiteit, Straatweg 25, 3621 BG,
Breukelen, The Netherlands
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To cite this article: Ivo J. M. Arnold & Evert B. Vrugt (2008): Fundamental uncertainty and stock market volatility, Applied
Financial Economics, 18:17, 1425-1440
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Applied Financial Economics, 2008, 18, 14251440
Fundamental uncertainty and stock
market volatility
Ivo J. M. Arnolda and Evert B. Vrugt*
aErasmus School of Economics, Erasmus Universiteit Rotterdam,
PO Box 1738, 3000 DR, Rotterdam, The Netherlands and Nyenrode
Business Universiteit, Straatweg 25, 3621 BG, Breukelen, The Netherlands
We provide empirical evidence on the link between stock market
volatility and macroeconomic uncertainty. We show that US stock
market volatility is significantly related to the dispersion in economic
forecasts from participants in the Survey of Professional Forecasters
over the period 1969 to 1996. This link is much stronger than that
between stock market volatility and the more traditional time-series
measures of macroeconomic volatility, but disappears from 1997 onwards.
This coincides with a previously documented regime shift in stock
volatility. Macroeconomic uncertainty is also able to explain and forecast
the volatilities of the Fama and French factors SMB, HML and UMD.
I. Introduction
The link between the macroeconomy and the stock
market has intuitive appeal, as macroeconomic
variables affect both expected cash flows accruing
to stockholders and discount rates. A common
framework connecting stock prices to fundamentals
is the dividend discount model. According to this
model, new macroeconomic information will affect
stock prices if it impacts on either expectations
about future dividends, discount rates or both.
Empirically, the evidence linking macroeconomic
factors to the stock market is mixed at best. Chen
et al. (1986) were among the first to explore this
link. Using a multifactor model, they found evidence
that macroeconomic factors are priced in the stockmarket. Pearce and Roley (1985), Hardouvelis
(1987) and Cutler et al. (1989) also conclude that
stock prices respond to macroeconomic news.
Subsequent studies have produced mixed results.
While some confirmed Chen et al.s (1986) findings
(Hamao, 1988; McElroy and Burmeister, 1988),
others have been less successful (Poon and Taylor,
1991; Shanken, 1992).
Moving from first to second moments, Veronesi
(1999) presents a theoretical model that formalizes
the link between economic uncertainty and stock
market volatility. He shows that investors are more
sensitive to news during periods of high uncertainty,
which in turn increases asset price volatility. Yet
establishing an empirical link between the second
moments of stock returns and macroeconomic vari-
ables has proven to be even more challenging than
that between their first moments. Based on US data,
Schwert (1989) concludes that there is a volatility
puzzle, in the sense that stock volatility is not closely
related to other measures of economic volatility.
Davis and Kutan (2003) extend the study of Schwert(1989) and investigate the impact of macroeconomic
volatility (output and inflation) on stock market
volatility in 13 developed and developing countries
since the 50s. Their findings suggest that there is no
international evidence that macroeconomic volatility
causes stock market volatility, consistent with the
*Corresponding author. E-mail: evrugt@xs4all.nl
Applied Financial Economics ISSN 09603107 print/ISSN 14664305 online 2008 Taylor & Francis 1425
http://www.tandf.co.uk/journals
DOI: 10.1080/09603100701857922
7/30/2019 Fundamental Uncertainity and Stock Market
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original findings of Schwert (1989) for the US.
Extending the forecast horizon only worsens the
results. Chan et al. (1998) conclude that in under-
standing the return covariation across stocks, widely
used variables such as industrial production or
inflation are no more useful than a series of random
numbers.
There are a few exceptions to this negativefinding, mainly for countries or periods where
macroeconomic volatility has been higher than in
post-war US. For Europe, Errunza and Hogan
(1998) find a significant influence of monetary and
real macroeconomic volatility on stock market
volatility for the seven largest European countries.
Liljeblom and Stenius (1997) find that between
one-sixth and above two-thirds of the changes
in Finnish stock market volatility is related
to macroeconomic volatility over the period 1920
to 1991. Bittlingmayer (1998) finds significant
effects of economic and political uncertainty on
German stock market volatility for the period 1880to 1940, yet this period includes rather dramatic
economic and political circumstances and may thus
not be representative for more stable times.
More recently, Ahn and Lee (2006) find evidence
that periods of high volatility in real output is
followed by higher stock market volatility for
several countries.
Given the poor results in explaining stock market
volatility, at least for the US, a more recent branch
of the literature focuses on identifying the effect
of macroeconomic announcements on asset volatility
using high frequency data; see Jones et al. (1998) for
fixed income, Andersen et al. (2003) for foreign
exchange and Flannery and Protopapadakis (2002)
for equities. Using macroeconomic surprises
relative to consensus expectations or dummy vari-
ables to account for days with macroeconomic
announcements, this approach has been more suc-
cessful in linking macroeconomic news to asset
volatility. It has been difficult, however, to establish
this link beyond the daily-frequency domain.
Starting with Schwert (1989), the most common
way to extract macroeconomic volatility is by means
of a time-series model. The absolute residuals from
autoregressive models fitted on stock returns andmacroeconomic growth rates are typically used as
volatility estimates. There are some limitations to this
approach (Giordani and So derlind, 2003). First,
a major concern is that time-series models are
backward looking, whereas most applications
are about ex ante uncertainty. Second, time-series
measures present problems when time-series are
subject to structural breaks. Third, there is no
universal time-series model to extract expectations.
Different models will thus yield different uncertainty
estimates leading to different empirical outcomes.
The fourth and, we believe, most important limitation
is that time-series volatility captures the volatility
in just one ex post realization of macroeconomic
developments out of many possible ex ante scenarios.
A single realized path of macroeconomic growth may
appear smooth ex post, notwithstanding significantex ante uncertainty as to which path would occur.
The time-series dimension of the data will not capture
this notion of uncertainty. In this context, Robert
Merton has interpreted the Great Depression as an
example of the Peso problem (Schwert, 1989).
At that time, there was significant uncertainty
whether the economic system as a whole would
survive. This is not apparent by looking at the ex post
data. A similar reasoning has been applied by
Kleidon (1986) on the excess volatility puzzle, where
actual stock prices appear to be much too volatile
compared to the smooth patterns in ex post dividends
which we observe.In this article, we provide empirical evidence on
the link between stock market volatility and
macroeconomic uncertainty. We show that stock
market volatility is significantly related to the
dispersion in economic forecasts from participants
in the Survey of Professional Forecasters (SPF),
rather than to macroeconomic time-series volatility.
Also using the SPF, Giordani and So derlind
(2003) show that disagreement among forecasters
is a reasonable proxy for uncertainty. Commonly
applied time-series models, on the other hand, have
difficulties in capturing macroeconomic uncertainty.
Driver et al. (2004) caution against the use of time-
series volatility measures as indicators of uncer-
tainty and favour dispersion-based measures. Our
findings extend the literature favouring dispersion-
based measures of uncertainty over time-series
volatility to the field of financial economics.
We take the conclusions from Giordani and
So derlind (2003) and Driver et al. (2004), one step
further to a financial economics context and
test whether uncertainty is better capable of
explaining and forecasting stock market volatility
than macroeconomic volatility. To the best of our
knowledge, this has not been done before. We showthat in periods in which macro-factors are
important, dispersion-based macroeconomic uncer-
tainty is better able to capture the link with stock
market volatility than traditional time-series volati-
lity measures.
Figure 1 shows the gist of our article for one of our
macroeconomic variables. It combines dispersion-
based unemployment uncertainty, time-series based
unemployment volatility and stock market volatility.
1426 I. J. M. Arnold and E. B. Vrugt
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The following observations can be made from
Fig. 1. First, there seems to be more variation in
unemployment uncertainty than in unemployment
volatility. Second, on the face of it, there seems to be
a much stronger link between unemployment uncer-
tainty and stock market volatility than between
unemployment volatility and stock market volatility.
Third, recession periods are associated with large
spikes in unemployment uncertainty. This is compa-
tible with Mertons Peso problem interpretation
and with Veronesis (1999) theoretical model.
Unemployment volatility seems to be much less
strongly associated with recessions. Finally, from
the mid-1990s onwards, stock market volatility
is trending upward with no clear link with either
unemployment uncertainty or unemployment volati-
lity. The behaviour of stock market volatility cannot
be explained by macro factors during this period.
If these results stand up to formal testing, Schwerts
(1989) volatility puzzle can be narrowed down to a
specific sample period that runs from 1997 onwards.
Schwert (2002) also highlights 1997 as an important
year and documents the importance of the technology
sector in explaining stock market volatility during the
late 1990s. Guo and Wohar (2006) support this withstrong statistical evidence of a structural change in
the mean level of volatility in 1997.
This article is organized as follows. Section II
describes the data construction. In Section III
we document the impact of SPF releases on stock
volatility within a GARCH-framework. A significant
impact of SPF releases on the stock market would
increase our confidence in the relevance of this data
source for the stock market. Section IV provides
evidence on whether macroeconomic uncertainty and
macroeconomic volatility are closely related or
distinct pieces of information. Our main results on
the contemporaneous link between macroeconomy
uncertainty and stock market volatility are presented
in Section V. Section VI reports evidence on the
predictability of stock market volatility and on
causality. Section VII extends the analysis to theFama and French (1993) factors size (SMB), value
(HML) and momentum (UMD). In contrast to
earlier studies, we adjust all critical values for small
sample biases and for the generated nature of
macroeconomic volatility. This turns out to be
important, as adjusted critical values are considerably
higher than their asymptotic counterparts. We do so
using a bootstrap experiment that is explained in the
Appendix. Section VIII contains the conclusions.
II. Data
Macroeconomic uncertainty
The SPF was started in 1968 by the American
Statistical Association and the National Bureau
of Economic Research. The Federal Reserve Bank
of Philadelphia took over the SPF in June 1990.
Participants in the survey are professional forecasters
mainly from the business world and Wall Street. They
submit their forecasts anonymously to . . . encourage
people to provide their best forecasts, without fearing
the consequences of making forecast errors. In this
way, an economist can feel comfortable in forecasting
what she really believes will happen to interest
rates, even if it contradicts her firms official position
(Croushore, 1993, p. 8). We take 10 economic
variables from the SPF that are currently included
in the survey. Some have been in the survey since
inception (1968Q4), whereas others have been added
in 1981Q3. Table 1 provides a list of the variables
including their start date and the abbreviations used
in this article.
In terms of the dividend discount model, develop-
ments in nominal GDP, corporate profits, industrial
production and real GDP all potentially affect
current and future cash flows. Interest rates primarilyaffect the discount rate used to value future cash
flows. Additionally, Fama and French (1989) docu-
ment that changes in short-term interest rates are
associated with changes in economic conditions.
Inflation may affect the relative attractiveness
of different investment alternatives and change
the value of real cash flows to stockholders.
As Chen et al. (1986) note, changes in the indirect
marginal utility of wealth will influence pricing.
0.0
0.2
0.4
0.6
0.8
1.0
5
0
5
10
15
20
70 75 80 85 90 95 00
Unemp. uncert. S&P 500 vol. Unemp vol.
Fig. 1. Macroeconomic uncertainty vs. macroeconomicvolatility.Unemployment uncertainty (U4, lhs) and unemploy-ment volatility (V4, rhs) plotted against realized stock marketvolatility (rhs, stock market crash of 1987 excluded). Shadedareas are NBER indicated recession periods
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A possible measure for this is real consumption.
Other variables that may proxy for changes
in marginal utility are the unemployment rate as
information about future human capital and housingas one of the most important components of wealth.
Apart from consumption, the SPF also contains
details on other components of GDP. We do not
separately consider these smaller components.
Furthermore, we exclude the 10-year Treasury
bond rate from the analysis because it is only
available from 1992 onwards. Finally, we exclude
the AAA-corporate bond yield, as the definition was
not uniform across forecasters prior to 1990Q4. This
leaves us with the 10 variables listed in Table 1.
The definitions of NGDP, PGDP and RGDP
deserve more explanation. The SPF definition for
NGDP is nominal GNP prior to 1992 and nominal
GDP thereafter. For PGDP, prior to 1992 it is the
GNP deflator, between 1992 and 1996 the GDP
implicit deflator and from 1996 the GDP price index.
The RGDP definition is GDP in constant Dollars
and real GNP prior to 1992.
Laster et al. (1999) claim that survey participants
may have different incentives when submitting
a forecast. For example, participants may be inclined
to make extreme forecasts, because a bold forecast
that proves to be correct has a higher payoff than
an average forecast that turns out to be correct.
This could influence the accurateness of survey data.We expect, however, that this is not a major concern
for the SPF, as participants are anonymous. Indeed,
Keane and Runkle (1990) and Zarnowitz and Braun
(1992) show that forecasts from the SPF are rational
(both unbiased and efficient). Furthermore, Hafer
and Hein (1985), Rudin (1992) and Su and Su (1975)
show that forecasts generated by time-series models
are different and in general, less accurate than the
forecast from the survey. Using the SPF, Giordani
and So derlind (2003) show that disagreement
among forecasters on a point forecast is a good
proxy for uncertainty. In a comparison of the
conditional variance from an ARCH-type of modelwith disagreement from the survey, Bomberger (1996)
arrives at a similar conclusion. We therefore calculate
cross-sectional standard deviations (SDs) for each
variable in each quarter as our measure of uncer-
tainty. For series that are not reported in percentage
terms (all except unemployment, inflation and the T-
bill rate), we first calculate predicted growth rates for
each forecaster as follows: Ytki, t Ytki, t =Y
t1i, t 1,
where Ytki, t is the predicted growth rate between the
previous quarter and quarter t k of variable Y at
time t by forecaster i. Yt1i, t is the level of variable Yin
the quarter preceding the survey date as observed at
time t by forecaster i. In theory, participants could
disagree on this value but given that it is public
information at the time the survey is taken, this rarely
occurs. Ytki, t is the predicted value of variable Y in
quarter t k made at time t by forecaster i. Below we
use the following notation: U1 refers to uncertainty
for k 1 and U4 refers to uncertainty for k 4. The
cross-sectional SD across forecasters is calculated at
each survey date for each of the 10 variables that we
consider. This is our measure of macroeconomic
uncertainty.
The deadline for the SPF is around 20th in the
second month of each quarter. The actual releaseof the SPF is on average a week later. When
the Philadelphia Fed took over the survey in 1990,
the survey was sent out too late for 1990Q2. To
correct for this, the Philadelphia Fed mailed the
survey out together with the 1990Q3 edition.
Therefore, filling in the 1990Q2 data, forecasters
had the benefit of hindsight. We have re-run the
analyses with a dummy included for 1990Q2, but this
did not affect the results materially.
Table 1. List of variables
Code Description Start date
NGDP Nominal GDP (GNP prior to 1992) 1968-Q4PGDP GDP price index (prior to96 GDP implicit
price deflator, prior to 92 GNP deflator)1968-Q4
CPROF Corporate profits after taxes 1968-Q4UNEMP Civilian unemployment rate 1968-Q4INDPROD Industrial production index 1968-Q4HOUSING New private housing units started 1968-Q4CPI Consumer price index,%-change
from previous Quarter1981-Q3
TBILL 3-month Treasury bill rate 1981-Q3RGDP GDP in constant dollars
(GNP prior to 1992)1981-Q3
RCONSUM Real consumption expenditures 1981-Q3
1428 I. J. M. Arnold and E. B. Vrugt
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Stock market volatility
We follow French et al. (1987) in calculating the
volatility of quarterly stock returns,
SP500,t
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiXNii1
rSP500, i t2
r1
where Ni is the number of daily returns in quarter t,
rSP500, i is the price return of the S&P 500 on day
i and t is the average daily return during quarter t.
Figure 2 plots the quarterly SD of the S&P 500.
Overall, the stylized fact that stock market
volatility is persistent and is well reflected in Fig. 2.
This feature of financial data is captured by the
ARCH- and GARCH-models pioneered by Engle
(1982) and Bollerslev (1986). Figure 2 also shows
the impact of the October 1987 crash on
market volatility, which forms a clear outlier from
a statistical point of view. The effects of the crises
in Asia and Russia are also visible. Another observa-
tion is that volatility has trended upward since its lowlevel in the mid-90s. Only since 2002 the volatility
of the S&P 500 has come down. The effects of the
Internet bubble at the turn of the Millennium are also
clear from Fig. 2.
Macroeconomic volatility
We collect realizations for the macroeconomic
variables from two data sources. First, we use the
February 2005 edition of the Real Time Dataset for
Macroeconomists (RTDSM) from the Federal
Reserve Bank in Philadelphia. In this way, we are
able to match 8 out of 10 SPF series. When we
compare median values across forecasters from the
quarter preceding the survey date (that forecasters can
know) with initial unrevised data from the RTDSM,
we observe a perfect fit. We are not able to match theRTDSM with the SPF for industrial production and
new private housing units started. For these two series,
our data source is Thomson Financial Datastream.
These series are also closely related to the correspond-
ing SPF data; correlations of levels (first differences)
between SPF previous quarter values and these series
are in excess of 0.99 (0.94).
Our measure of macroeconomic volatility is
identical to the measure of Bansal et al. (2005). For
each series Y, we estimate an AR(1)-model and
collect the residuals "Yt . Volatility is then calculated as
follows,
Yt1, J logXJj1
"Ytj
! 2We have modified the specification in Equation 2
in two ways to check whether our conclusions remain
the same. First, we have taken values for p based on
the Schwarz Information Criterion. This changes the
optimal lag length for five series. For these series,
correlations between the two measures based on
different lag lengths are on average 0.76. Second, we
1970 1975 1980 1985 1990 1995 2000 2005
5
10
15
20
25
Fig. 2. Realized stock market volatility. Quarterly realized volatility of S&P 500 stock returns based ondaily returns for January 1969April 2004
Fundamental uncertainty and stock market volatility 1429
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have dropped the log from Equation 2. We have
re-run the analyses in and found that both modifica-
tions did not change the results in any material way.
If anything, results are worse for macroeconomic
volatility under these alternative specifications. Since
we contrast our new measure (macroeconomic
uncertainty) with macroeconomic volatility, we take
the best performing specification for macroeconomicvolatility, which is the original specification in
Equation 2. In the rest of the article, we consider
lag values for J 1 and 4. This matches the horizons
from the SPF (U1 and U4). The lag value for J 1 is
also consistent with prior studies (Errunza and
Hogan, 1998). Alternatively, different weights could
be chosen in the summation of absolute residuals, but
Andersen et al . (2002) show that our current
specification is more informative about ex ante
volatility.
III. Does the Release of the SPF Matter tothe Stock Market?
In order to establish whether the stock market reacts
to the actual release of the SPF, we collect daily
values of the S&P 500 index from January 1990 to
January 2005 as well as the release dates for the
survey. If the release of the SPF contains a relevant
piece of new information to the stock market, its
announcement should have an impact on daily stock
returns. Ideally, we would like to construct a measure
that captures the unexpected component of the SPF
contents, containing only information new to the
market. This is the route taken by Andersen et al.
(2003) using high-frequency exchange-rate data and
market participant expectations for series to be
announced during the subsequent week. For the
SPF, that contains 18 different economic indicators,
no such summary measure of expectations is avail-
able. We therefore follow Jones et al. (1998) and
Flannery and Protopapadakis (2002), and analyse the
behaviour of conditional stock market risk on SPF
release days. A GARCH(1, 1) model is estimated
adding a set of calendar dummies,
Rt, S&P 1ItSPF
X5i2
iIday i
t
6IJANt "t 3
2t ! "2t1
2t1 1I
SPFt
X5j2
jIday jt 6I
JANt 4
where Rt, S&P is the continuously compounded daily
price return on the S&P 500, ISPFt is an indicator
variable that equals 1 on days when the SPF is
released and 0 otherwise, Iday it are day-of-the-week
dummies to account for possible interactions between
the SPF release and the well-documented day-of-the-
week effects. Of the total number of 59 SPF releases
since January 1990, 22 occurred on Monday, 9 onTuesday, 7 on Wednesday, 5 on Thursday and 16 on
Friday. By the same token, IJANt is an indicator
variable that equals 1 in January and 0 otherwise, to
account for the January-effect. All parameters are
estimated using maximum likelihood assuming nor-
mally distributed errors. Table 2 summarizes the
results.
Table 2 reveals significant SPF announcement
effects on both the stock market mean and its
conditional variance. While the stock market return
is significantly higher on days when the SPF is
released, conditional variance is significantly lower.The January indicator is insignificant in both
the mean and the variance equation. Although none
of the individual day-of-the-week dummies is sig-
nificant, a Wald test rejects the null hypothesis that
the coefficients are jointly equal to zero for the
conditional variance equation (p 0.02). This cannot
be rejected for the mean equation (p 0.57).
Table 2. The impact of SPF releases on the stock market
Mean equation Variance equation
0.087*** ! 0.0331 0.287*** 0.055***2 0.047 0.940***3 0.015 1 0.114**4 0.049 2 0.0625 0.055 3 0.0696 0.007 4 0.108
5 0.0996 0.004
Hypothesis tests2 3 4 5 0 2 3 4 5 0p-value: 0.57 p-value: 0.02
Notes: The table provides Gaussian maximumlikelihood estimates of the parameters of the GARCH
(1, 1) model from equations: Rt,S&P 1ItSPF
P5i2 iI
day it 6I
JANt "t and
2t ! "
2t1
2t1
1ItSPF
P5j2 jI
day jt 6I
JANt . The sample period is
1 January 199028 February 2005 with a total number of
3955 observations.
** and *** denote parameter estimates different from zero
at the 5 and 1% level of significance, respectively, using
Bollerslev and Wooldrige (1992) robust SEs. The lower part
of the table reports Wald tests for joint significance of the
day-of-the-week effects.
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The release of the SPF may reveal new
information (either positive or negative) to market
participants not previously incorporated into the
stock market. The negative coefficient for the SPF
release in the conditional variance equation indi-
cates that the release of the SPF reduces condi-
tional risk. This is consistent with Flannery and
Protopapadakis (2002), who find that announce-ments of the consumer price index, new home
sales, industrial production, leading indicators,
producer price index and real GNP/GDP macro-
economic variables reduce conditional volatility.
Except for the leading indicators, these variables
are also part of the SPF. Furthermore, out of three
series for which Flannery and Protopapadakis
(2002) find a statistically significant positive effect
on conditional volatility, only one (employment)
is included in the SPF. This indicates that the SPF
is essentially a collection of variables for which
the release reduces the conditional variance of thestock market, consistent with the evidence on the
release of its constituents documented in Flannery
and Protopapadakis (2002).
As a robustness check, we have also estimated an
exponential GARCH (or EGARCH) specification to
allow the conditional variance of the index to respond
asymmetrically to positive and negative return
shocks. Although some of the estimated coefficients
are less significant in this specification, the main
results from the analysis remain unchanged. Finally,
we have included the SPF release dummy with a one-
day lead and lag. This would account for potential
leakage prior to the official announcement or for aslow response of the equity market. Neither lead nor
lag was significant. We do not report these results.
IV. The Relation between MacroeconomicUncertainty and MacroeconomicVolatility
Schwert (1989) also presents evidence that stock
market volatility is significantly higher during NBER
recessions. This suggests that the link between
macroeconomic volatility and recessions is not verytight. Dispersion-based macroeconomic uncertainty
may have a closer link to both recessions and stock
market volatility. As a prelude to our main analysis,
Table 3 reports empirical results on the mutual
relationships between macroeconomic uncertainty,
macroeconomic volatility and NBER recessions. We
estimate the following regression,
Yt NBERt "t 5
where Yt measures either the cross-sectional SD from
the SPF (U1 and U4) or the corresponding macro-
economic volatility (V1 and V4). The one-quarter
horizon corresponds to the metric often used in
empirical research (Schwert, 1989; Errunza and
Hogan, 1998), but we also report the results for
quarter four as a robustness check. NBER is
a dummy variable that equals 1 during NBERindicated recession periods and 0 otherwise. In
order to use as many recession periods as possible,
the analysis is confined to series that start in 1969.
Panel A shows that macroeconomic uncertainty is
significantly higher during recessions, for all macro-
economic variables, confirming Veronesis (1999)
model. Volatility is significantly higher during reces-
sions only for unemployment and industrial produc-
tion. For quarter four, the results are somewhat
stronger for V4 and somewhat weaker for U4.
This might be caused by to the lower number of
participating forecasters for U4.
Further evidence in panels BC shows correlationsbetween uncertainty and volatility (panel B), among
the uncertainty measures (upper triangle of panel C)
and among the volatility measures (lower triangle of
panel C). Coefficients significant at a 5% level are in
bold. With the exception of two correlation
coefficients between volatility and uncertainty of the
deflator and corporate profits, all correlations coeffi-
cients in panel B are significantly different from zero
at a 5% level. Comparing panels B and C, the
correlations among the uncertainty measures
of different macroeconomic variables are higher
than the correlations between uncertainty and
volatility of the same macroeconomic variable and
correlations among the volatility measures of
different macroeconomic variables. Although not as
strong, the conclusions are the same for U4 and V4 in
panels E and F. This suggests that uncertainty
measures are better able to capture moments of
what we could call general economic unease, where
forecasters disagree about the general direction in
which the economy will go. Summing up, the results
so far indicate that dispersion-based uncertainty
measures are more closely related to recessions than
time-series based volatility measures. In the next
section we will analyse whether this conclusion can beextended to stock market volatility.
V. Linking Stock Volatility toMacroeconomic Uncertaintyand Volatility
In this section, we test the explanatory power
of macroeconomic uncertainty and volatility
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for stock market volatility. We present results
of contemporaneous regressions of stock market
volatility on a constant, lagged stock market volatility
and both macroeconomic uncertainty and volatility.
This answers the question whether there is any
information in the macroeconomic variables beyond
the information that is contained in lagged stockmarket volatility. In addition, it explicitly contrasts the
abilities of uncertainty and volatility in explaining
stock market volatility.
We run regressions of the following form,
SP500, t uncert:Y, uncert:t
vol:Y, vol:t SP500, t1 "t 6
where SP500, t is the stock market volatility for
quarter t based on daily returns from Equation 1,
Y, uncert:t is macroeconomic uncertainty of variable
Y(U1/U4), and Y,vol:t is macroeconomic volatility of
variable Y (V1/V4). We take calendar quarters for
stock market volatility, macroeconomic uncertainty
and macroeconomic volatility. One should keep in
mind that the SPF results are released around 27th of
each second month in a quarter. We use calendarquarters in this section and address the issue of SPF
release dates in Section VI.
The spike in stock market volatility as a result of
the 1987 stock market crash has a potentially
distorting effect. We follow Campbell et al. (2001)
and substitute the second highest quarterly stock
market volatility from the sample for 1987 Q4. This is
an ad hoc solution, but avoids a disproportionate
influence of a single observation, while leaving in an
Table 3. Relationships between uncertainty, volatility and recessions.
NGDP PGDP CPROF UNEMP INDPROD HOUSING
Panel A:(U1) 0.32 0.26 1.51 0.12 0.49 3.34t-value 2.61 3.23 2.74 5.63 3.98 3.67(V1) 0.45 0.41 0.09 1.00 0.78 0.55t-value 1.53 1.78 0.30 4.87 4.64 1.85
Panel B:(U1,V1) 0.24 0.12 0.00 0.40 0.39 0.30
Panel C:NGDP 0.58 0.36 0.67 0.67 0.68PGDP 0.01 0.30 0.49 0.55 0.53CPROF 0.15 0.05 0.42 0.43 0.43UNEMP 0.01 0.18 0.07 0.75 0.70INDPROD 0.30 0.06 0.10 0.28 0.71HOUSING 0.01 0.05 0.07 0.02 0.19
Panel D:(U4) 0.68 0.48 0.62 0.19 0.34 6.69t-value 2.38 2.32 0.63 4.55 1.20 3.06(V4) 0.47 0.23 0.01 0.34 0.40 0.36
t-value 2.86 1.78 0.08 2.40 2.98 2.22
Panel E(U4,V4) 0.57 0.29 0.39 0.39 0.49 0.56
Panel F:NGDP 0.58 0.47 0.69 0.66 0.71PGDP 0.52 0.27 0.50 0.48 0.46CPROF 0.11 0.00 0.31 0.42 0.40UNEMP 0.31 0.24 0.33 0.59 0.67INDPROD 0.66 0.51 0.23 0.56 0.60HOUSING 0.48 0.46 0.10 0.46 0.52
Notes: Panel A shows s and Newey and West (1987) corrected t-values for in theregression Yt
NBERt "t, where Yt is either macroeconomic uncertainty (U1) or
macroeconomic volatility (V1) and NBER is a dummy variable with value 1 if the economy is
in a recession and 0 otherwise. Panel B provides correlations between macroeconomicuncertainty and macroeconomic volatility. The upper triangle of panel C holds the correlationmatrix for the uncertainty series, the lower triangle holds the correlation matrix for thevolatility series. Panels D, E and F shows the same information, but for U4 and V1 rather thanU1 and V1. Bold numbers indicate significance at the 5%-level at least. All results are for theperiod 19692004.
1432 I. J. M. Arnold and E. B. Vrugt
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important event. We experimented with different
treatments of the 1987 stock market crash, but this
did not affect our results materially.
Table 4 contains parameter estimates for uncert: and
vol:
, as well as the Newey and West (1987)
corrected t-values. Panel A shows the results for the
period up to April 1996 and panel B for the period
January 1997 to April 2004. We use a bootstrap
experiment to determine the finite sample properties of
the Newey and West (1987) t-statistics. Based on fitted
time-series models, we simulate stock market volati-
lity, macroeconomic volatility and macroeconomic
uncertainty 10 000 times. These processes are simu-
lated independently from each other. In each run, we
collect parameter estimates and t-values, which form
the bootstrap distributions under the null that the
macroeconomic risks are unrelated to stock market
volatility. For macroeconomic volatility, we simulatethe macroeconomic variable itself (rather than its
volatility series) and construct the volatility measure in
each run. Hence, t-values from the simulation take
into account the two-step procedure to generate
macroeconomic volatility, just as in the original
data. The Appendix provides more details on the
bootstrap procedure.
Table 4 shows that uncertainty about future
macroeconomic conditions contains information in
addition to the information from lagged stock market
volatility itself. In addition, information about macro-
economic uncertainty largely subsumes the informa-
tion from macroeconomic volatility. For U1, none of
the traditional macroeconomic volatility measures is
significant vs. four uncertainty variables (nominal
GDP, corporate profits, real GDP and consumption).
For U4, uncertainty about nominal GDP, unemploy-
ment, the T-bill rate, real GDP and consumption are
significant, compared to the volatility of only infla-
tion. In particular, uncertainty about corporate
profits, output and consumption have a strong link
with stock market volatility. Corporate profits is the
most direct measure of cash-flows accruing to stock-
holders that we have in our database. Consumption
based asset pricing models imply a strong link between
consumption and asset prices. The evidence in Table 4
indicates that this carries over to second moments;more uncertainty about future consumption is asso-
ciated with higher stock market volatility. The
marginal significance of the 2.15 t-value of Q4 nominal
GDP illustrates the effect of taking into account small
sample properties.
These results are consistent with Schwerts (1989)
findings that macroeconomic volatility has a weak
link with stock market volatility, once lagged stock
market volatility is included. But perhaps the more
Table 4. Macroeconomic uncertainty vs. macroeconomic volatility
NGDP PGDP CPROF UNEMP I NDPROD HOUSING CPI TBILL RGDP RCONSUM
Panel A 1969Q11996Q4 1981Q31996Q4
U1 1.02 1.14 0.36 3.05 0.40 0.09 0.57 1.28 1.42 1.31t-value 2.49** 1.49 2.99*** 1.30 0.98 1.30 1.33 1.73 2.57** 3.11**V1 0.22 0.13 0.02 0.19 0.11 0.10 0.15 0.02 0.16 0.23t-value 1.43 1.42 0.24 1.56 0.72 0.63 1.10 0.06 1.06 1.31U4 0.57 0.43 0.15 2.55 0.15 0.05 0.23 1.56 1.20 0.42t-value 2.15* 1.22 1.68 2.55** 0.67 1.20 0.60 2.83** 3.35*** 2.33**V4 0.27 0.38 0.16 0.14 0.01 0.01 0.80 0.59 0.10 0.48t-value 0.65 1.22 0.53 0.60 0.05 0.03 2.55** 1.46 0.29 1.44
Panel B 1997Q12004Q4 1997Q12004Q4
U1 0.58 4.31 0.17 0.26 0.24 2.10 2.76 7.82 1.03 1.23t-value 0.18 0.53 0.85 0.05 0.14 1.95 2.06 1.41 0.29 0.22V1 0.20 0.32 0.07 0.14 0.50 0.16 0.39 0.23 0.13 0.64t-value 0.43 0.72 0.30 0.21 1.21 0.62 0.54 0.68 0.40 2.29*U4 0.30 0.14 0.03 8.33 0.27 0.64 3.22 6.21 2.99 1.81t-value 0.20 0.03 0.16 0.82 0.19 1.08 1.45 2.06 1.29 0.36V4 1.52 1.59 0.74 0.57 0.03 1.14 1.36 0.83 0.70 0.95
t-value 1.85 1.20 0.80 0.31 0.06 1.29 1.21 1.85 0.44 0.80
Notes: The table reports beta-coefficients and Newey and West (1987) t-values for the regression model SP500, t uncert:
Y, uncertt vol:
Y,volt SP500, t1 "t with for each macroeconomic variable both uncertainty and volatility included
(U1 & V1 and U4 & V4) as well as lagged stock market volatility. Panel A runs the regression for the period 1969Q11996Q4and panel B for the period 1997Q12004Q4.*, ** and *** indicate significance at the 10-, 5- and 1%- level, respectively. Significance levels are based on bootstrappedcritical values (parametric) with 10 000 replications. The parameter estimates and t-values for the constant and lagged stockmarket volatility are not shown in the table.
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important conclusion from Table 4 is that macro-
economic uncertainty matters in explaining stock
market volatility. Previous disappointing results
might therefore at least partially be explained by the
way macroeconomic uncertainty is measured.
Overall, the message from panel A in Table 4 is
that stock market volatility is more closely related
to macroeconomic uncertainty than to macroeco-nomic volatility. In panel B we examine the same
set of regressions for the period since 1997. The
results are now completely different. For the full set
of estimates, only one entry is significantly different
from zero (V4 consumption), but it has the wrong
sign. These findings correspond to the pattern that
we already observed in Fig. 1; from the mid-90s
onwards, stock market volatility is trending upward
without a clear link with either macroeconomic
uncertainty or macroeconomic volatility. Recent
work by Guo and Wohar (2006) formally tests
for structural breaks in volatility indexes using the
Bai and Perron (1998) framework. They also
document a significant break in S&P 500 volatility
in 1997. A similar observation has been made by
Schwert (2002), who attributes the unusual beha-
viour of stock market volatility from that point
onwards to technology. As the SPF does not
contain dotcom-related information, our variables
are unlikely to capture the behaviour of stock
market volatility during this episode. Nevertheless,
previous attempts in the literature to associate
macroeconomic factors with stock market volatility
have met with little success even for pre-1997
samples. Our results for the period 1969 to 1996suggest that we can solve at least part of the
volatility puzzle. Using dispersion-based uncertainty
measures instead of the times-series based volatility
measures, a strong link can be established with
stock market volatility for much of the post-1969
period. We conclude that the behaviour of stock
market volatility since 1997 cannot be adequately
explained using macro-variables and proceed by
further analysing the pre-1997 sample.
VI. Causality and Forecasting StockMarket Volatility
In this section, we forecast stock market volatility
using macroeconomic uncertainty and volatility.
The move to forecasting requires a different
timing for measuring stock market volatility.
Above we have calculated stock market volatility
from daily returns during calendar quarters. We
recalculate stock market volatility over periods that
match the deadlines for the survey. For example,
the 1993Q1 and 1993Q2 survey deadlines were,
respectively, 19 February 1993 and 5 May 1993. We
now calculate 1993Q2 stock market volatility usingthe daily returns between these two dates. In
contrast, our calendar measure would take returns
between 1 April and 30 June. From 1990Q2
onwards, when the Philadelphia Fed took over
the survey, deadline dates are available exactly. For
the period prior to that we take 20th as the
deadline, which is the average date in the post-1990
period. This is an assumption, but varying this date
does not have an impact on our conclusions.1 We
proceed in two steps. First, we investigate the
causality between macroeconomic variability (either
uncertainty or volatility) and stock market volati-
lity; subsection Granger causality reports the
results of Granger causality tests. Second, in
subsection Forecasting stock market volatility we
forecast stock market volatility with macroeco-
nomic uncertainty and volatility.
Granger causality
To answer the question whether stock market
volatility causes macroeconomic variability or vice
versa we run Granger causality tests. We estimate
first-order bivariate vector autoregressions for stock
market volatility and macroeconomic uncertaintyand for stock market volatility and macroeconomic
volatility. The latter specification is comparable to
previous studies on stock market volatility and the
macroeconomy (Schwert, 1989; Errunza and Hogan,
1998). The specification is,
SP500, t1 1 1Yt 1SP500, t "1, t1
Yt1 2 2Yt 2SP500, t "2, t1 7
where Yt is either macroeconomic uncertainty or
volatility. We test whether macroeconomic uncer-
tainty or volatility does not Granger cause stock
market volatility (H0 : 1 0), and whether stockmarket volatility does not Granger cause macroeco-
nomic uncertainty or volatility (H0 : 2 0). The lag
length is comparable to previous studies and since
a higher order VAR can always be re-written
as a first-order VAR, our choice for the lag length
1 We have re-run the analyses in sections Granger causality and Forecasting stock market volatility with calendar quarters(instead of SPF deadline matched quarters). The results are slightly weaker, but the conclusions are in line with the reportedresults.
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is not restrictive. Furthermore, tests for residual
autocorrelation (both univariate BreuschGodfrey
and multivariate Portmanteau) show no sign
of serial autocorrelation for most equations.
Since we estimate VAR(1)s, the Granger causality
F-value is equal to the square of the t-statistic
(which are reported in Table 5). Significance levels
again are bootstrapped.Table 5 shows that causality runs one way from
macroeconomic uncertainty (U1 and U4) to stock
market volatility for inflation, the T-bill rate and
nominal GDP (for U4 only). Causality runs both
ways for nominal GDP for U1, the deflator for both
U1 and U4 and industrial production for U4. For U1
corporate profits and industrial production and U4
consumption higher stock market volatility Granger
causes more uncertainty in these variables. For
the remaining four variables, no causality relationship
can be established. For the volatility variables, only
V4 inflation volatility Granger causes higher stock
market volatility. In summary, there are four (five)
macroeconomic uncertainty variables at U1 (U4)
that significantly predict subsequent stock market
volatility. For macroeconomic volatility, just one
variable is significantly associated with subsequent
stock market volatility. This suggests that investors
can improve on their volatility forecasts by adding
information on macroeconomic uncertainty during
times when macroeconomic information matters.
More accurate volatility forecasts help in constructing
portfolios with better risk/return trade-offs, in pricing
derivatives, and in risk management, where volatility
forecasts play a major role.
Forecasting stock market volatility
How do macroeconomic uncertainty and volatility
compare when both are included to forecast stock
market volatility? We employ the following frame-
work to forecast stock market volatility,
SP500, t1 uncert:Y, uncert:t
vol:Y,vol:t SP500, t "t1 8
Equation 8 again takes the form of a horse race
between uncertainty and volatility. Lagged stock
market volatility is also included. Table 6 summarizes
the results.
Uncertainty remains dominant over volatility in the
forecasting context; none of the volatility series is
significantly different from zero. At the one-quarter
horizon, four uncertainty variables are significant.
Remarkably, in comparison to the contemporaneous
regression results from Table 4, only two variables
(NGDP for both U1 and U4 and TBILL for U4)
have both explanatory and forecasting power.
Uncertainty about the deflator, industrial production
and inflation is significant in predicting stock market
volatility, but not in explaining stock market
volatility. Apparently, these variables are more
forward-looking in nature. Also note that since the
deadline for the survey is in the second month of the
quarter, not all information is known to forecasters
even in the contemporaneous setting. Combined with
the Granger causality tests, we conclude that macro-
economic uncertainty outperforms volatility not only
in a contemporaneous setting, but also in a prediction
context.
Table 5. Granger causality tests
1969Q21996Q4 1981Q31996Q4
NGDP PGDP CPROF UNEMP INDPROD HOUSING CPI TBILL RGDP RCONSUM
Macroeconomic variability does not Granger cause stock market volatilityU1 2.31** 2.38** 1.73 1.05 1.70 0.90 4.44*** 1.95* 0.11 1.67V1 0.33 0.76 0.97 0.09 0.57 0.81 1.57 0.47 0.35 0.72U4 1.99* 1.94* 0.91 1.72 1.85* 0.90 3.13*** 2.24** 1.36 0.04V4 0.57 0.54 0.09 0.44 0.24 0.58 2.20* 0.02 0.59 0.93
Stock market volatility does not Granger cause macroeconomic variabilityU1 1.92* 2.95*** 1.91* 1.52 2.15* 1.35 0.66 1.36 0.81 0.92
V1 1.75* 2.26** 1.42 2.46** 1.70 2.16** 1.15 1.04 1.27 2.16**U4 1.00 1.78* 0.37 0.87 2.99*** 0.69 0.55 0.94 0.35 1.95*V4 0.96 1.89* 1.06 2.68** 1.63 2.64** 1.23 1.16 1.24 1.53
Notes: The table reports Newey and West (1987) t-values and associated levels of significance for the hypotheses 1 0 in thefirst equation and 2 0 in the second equation of the bivariate first-order VAR:
SP500, t1 1 1Yt 1SP500, t "1, t1
Yt1 2 2Yt 2SP500, t "2, t1:
*, ** and *** indicate significance at the 10-, 5- and 1%- level, respectively. Significance levels are based on bootstrappedcritical values (parametric) with 10 000 replications as described in the Appendix.
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VII. The Fama and French Factors andMacroeconomic Uncertainty
This section investigates whether groups of stocks are
affected differently by macroeconomic uncertainty.
Several recent studies show that the dispersion in
analysts earnings forecasts matter for future stock
returns. These effects are most prevalent for
small stocks and stocks with positive momentum
(Diether et al ., 2002) and small value stocks
(Qu et al., 2003). Anderson et al. (2005) examine
whether disagreement among analysts about expectedearnings affects expected returns and risk of equities.
They show that dispersion of analysts earnings
forecasts is a priced risk factor and is able to predict
return volatility out-of-sample.
We extend this research by considering the link
between macroeconomic measures of uncertainty and
the volatility of the Fama and French (1993) factors
SMB (small minus big), HML (high minus low book-
to-market) and UMD (up minus down). Daily return
series are from Kenneth Frenchs website.2 Volatility is
constructed as in (1). We repeat the analyses from
Paragraph 5 and subsection Granger causality for the
Fama and French factors by estimating the followingregressions,
FFi, t uncert:Y, uncert:t
vol:Y, vol:t FFi, t1 "t 9
FFi, t1 1 1Yt 1FFi, t "1, t1
Yt1 2 2Yt 2FFi, t "2, t1 10
where FFi, t is the volatility of Fama and French
factor i (SMB, HML or UMD) in quarter t. The
remaining variables are as described before.
Consistent with the reasons from subection Granger
causality, we use a lag length of one for the VAR
of Equation 10. We take quarter 1 uncertainty and
volatility (U1 and V1) in Equation 9 and quarter 1
uncertainty in Equation 10; Tables 7 and 8 show the
results for Equations 9 and 10, respectively.
The results from Table 7 reinforce the conclusions
for the S&P from Section V; uncertainty is dominant
over volatility and contains information beyond whatis contained in lagged volatility. There is a significant
contemporaneous relation between the volatility of
SMB and UMD and uncertainty about corporate
profits. Apparently, the risk of small companies and
companies that have experienced strong past returns
are exposed to uncertainty about future corporate
profits. For value stocks (HML), uncertainty about
inflation, real GDP and the T-bill rate are significant.
Since the T-bill rate is determined primarily by
monetary policy expectations, this suggests that
uncertainty about monetary policy is relevant for the
volatility of the value-growth portfolio. The reason for
this may be that there are differences in the access tofunds that value and growth firms have and hence, the
impact that monetary policy. Jensen et al. (1997) show
that there is a strong link between the performance of
size and value portfolios and the monetary policy
stance. For the value factor, this conclusion carries
over to second moments as well, as Table 7 shows.
Interestingly, for momentum 7 out of 10 uncertainty
Table 6. Forecasting stock market volatility
1969Q21996Q4 1981Q31996Q4
NGDP PGDP CPROF UNEMP INDPROD HOUSING CPI TBILL RGDP RCONSUM
Panel AU1 0.85 1.85 0.22 2.60 0.77 0.04 1.46 1.36 0.04 1.21
t-value 2.49** 2.35** 1.76 1.11 1.91* 0.81 4.30*** 1.83 0.06 1.71V1 0.11 0.11 0.07 0.09 0.17 0.10 0.02 0.12 0.09 0.15t-value 0.71 0.78 0.72 0.56 1.22 0.72 0.13 0.53 0.35 0.80
Panel BU4 0.59 0.56 0.05 2.20 0.40 0.04 0.67 1.53 0.76 0.00t-value 2.53** 2.09* 0.67 1.83 1.87* 1.04 1.68 2.68** 1.58 0.02V4 0.25 0.62 0.12 0.21 0.31 0.08 0.48 0.58 0.03 0.37t-value 0.49 1.44 0.30 0.81 0.91 0.20 1.21 1.35 0.07 0.91
Notes: Panel A (B) reports beta-coefficients and Newey and West (1987) t-values for the regression model SP500, t1 uncert:
Y, uncertt vol:
Y,volt SP500, t "t1, with for each macroeconomic variable both U1 uncertainty (U4) and
V1 volatility (V4) included.*, ** and *** indicate significance at the 10-, 5- and 1%- level, respectively. Significance levels are based on bootstrappedcritical values (parametric) with 10 000 replications. The constant and lagged stock market volatility are not shown in thetable.
2 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
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variables are significant at the 10% level at least. This
seems to suggest that the risk of the momentum factor
can be explained to some extent by exposure to
macroeconomic uncertainty variables.
Table 8 reports the results for the Granger causality
tests. Uncertainty about corporate profits and the
deflator Granger cause SMB volatility at the 10%
level. For HML, inflation and T-bill uncertainty
Granger cause volatility. These variables were also
significant in the contemporaneous regression
reported in Table 7. For UMD, four uncertainty
variables Granger cause volatility (PGDP, CPROF,
CPI, TBILL), but UMD volatility Granger causes
CPROF and INDPROD uncertainty. Overall, there
seems to be a link between the volatility of the Fama
and French (1993) factors and macroeconomic uncer-
tainty. These results suggest a risk-based explanation
for the factors SMB, HML and UMD. Especially for
Table 7. Macroeconomic uncertainty and the Fama and French factors.
1969Q11996Q4 1981Q31996Q4
NGDP PGDP CPROF UNEMP INDPROD HOUSING CPI TBILL RGDP RCONSUM
Small minus BigU1 0.27 0.11 0.12 0.39 0.07 0.00 0.08 0.46 0.30 0.54t-value 1.22 0.48 2.29** 0.36 0.34 0.10 0.37 0.97 0.94 1.81
V1 0.09 0.05 0.02 0.10 0.02 0.04 0.01 0.06 0.12 0.00t-value 1.69 1.04 0.46 1.38 0.21 0.51 0.26 0.49 1.95* 0.01
High minus LowU1 0.30 0.48 0.06 1.02 0.02 0.06 0.54 1.37 1.09 0.34t-value 1.28 1.01 1.07 0.69 0.07 1.48 2.42** 2.65** 2.68** 0.91V1 0.01 0.00 0.02 0.18 0.05 0.02 0.03 0.06 0.14 0.10t-value 0.11 0.08 0.31 2.13* 0.50 0.30 0.47 0.39 1.39 1.20
Up minus DownU1 0.77 0.95 0.15 3.25 0.08 0.12 0.60 0.94 1.27 0.41t-value 1.89* 2.82** 2.49** 2.40** 0.21 2.18** 2.22* 1.55 3.26*** 1.35V1 0.08 0.09 0.07 0.15 0.21 0.07 0.05 0.05 0.16 0.20t-value 0.89 1.44 0.73 1.74 1.37 0.73 0.48 0.32 1.50 1.60
Notes: The table reports parameter estimates and Newey and West (1987) t-values for the regressionFFi, t uncert:
Y, uncert:t vol:
Y, vol:t FFi, t1 "t, where FFi, t is the volatility of Fama and French (1993) factor
i in period t, Y, uncert:t (Y,vol:t ) uncertainty (volatility) for Q1 (V1) about macroeconomic variable Y and "t is the error term.*, ** and *** indicate significance at the 10%-, 5%- and 1%-level, respectively, and critical values are based on the parametricbootstrap experiment described in the appendix with 10 000 replications. Small minus Big, High minus Low and Up minusDown are realized volatilities for size, value and momentum portfolios and are described in more details in the text.
Table 8. Granger causality tests for the Fama and French factors
1969Q21996Q4 1981Q31996Q4
NGDP PGDP CPROF UNEMP INDPROD HOUSING CPI TBILL RGDP RCONSUM
Macroeconomic variability does not Granger cause stock market volatilitySMB 0.34 1.92* 1.05 0.61 0.79 0.05 1.53 0.47 0.50 0.62HML 0.10 1.50 1.44 0.24 0.02 0.83 3.30*** 2.73** 0.77 0.27
UMD 1.68 2.96** 1.81* 1.65 1.76 1.78 3.39*** 2.02* 0.97 0.44Stock market volatility does not Granger cause macroeconomic variability
SMB 0.38 0.15 1.85* 0.19 0.80 0.90 0.41 1.56 0.31 0.21HML 0.37 0.08 1.35 0.57 1.59 0.99 0.71 0.26 1.28 0.61UMD 0.46 0.24 2.48** 1.18 2.64** 1.11 0.34 0.18 0.31 0.87
Notes: The table reports Newey and West (1987) t-values and associated levels of significance for the hypotheses 1 0 inthe first equation and 2 0 in the second equation of the bivariate first-order VAR:
FFi, t1 1 1Y, U1t 1FFi, t "1, t1
Y, U1t1 2 2
Y, U1t 2FFi, t "2, t1,
where symbols are as defined before.*, ** and *** indicate significance at the 10, 5 and 1% level, respectively. Significance levels are based on bootstrapped criticalvalues (parametric) with 10 000 replications as described in the Appendix.
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momentum, macroeconomic uncertainty seems to
impact volatility. For the value factor uncertainty
about monetary policy seems relevant. For investors,
the important message is that variation in Fama and
French factor returns may be driven by the same
underlying macroeconomic force (i.e. uncertainty)
that also drives return variation in the general equity
market when macroeconomic information is relevant.Furthermore, causality implies that investors can
improve their volatility forecasts by using information
on macroeconomic uncertainty from the SPF.
VIII. Conclusions
In linking stock market volatility to macroeconomic
factors, it is important to make a distinction between
dispersion-based measures of macroeconomic uncer-
tainty and time-series based measures of macroeco-
nomic volatility. For much of the post-1969 sample
period, stock market volatility is more closely related
to contemporaneous uncertainty measures than
to the more commonly used volatility measures.
Uncertainty measures also outperform volatility
measures in a prediction context. Additionally,
macroeconomic uncertainty increases more strongly
during recessions than macroeconomic volatility.
This result is compatible with earlier work showing
that stock market volatility increases during
recessions. Macroeconomic uncertainty measures
also have more theoretical appeal than volatility
measures, mainly because of the Peso-problem inusing time-series data. We conclude that in periods in
which macro-factors are important, dispersion-based
macroeconomic uncertainty is more likely to capture
economic reality than macroeconomic volatility.
Schwerts (1989) volatility puzzle can thus be reduced
to the period since 1997, in which developments
in the technology sector instead of macro-factors
seem to have driven stock market volatility.
In addition to this, uncertainty about macroeconomic
variables also holds important information about the
Fama and French (1993) factors size, value and
momentum. Since the volatility of these factors is
related to macroeconomic uncertainty, this mightsuggests a risk-based explanation for the returns on
these portfolios. This seems to be an interesting
avenue for further research.
Acknowledgement
We thank the editor and two anonymous referees for
useful comments and suggestions.
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Appendix
Bootstrapping critical values
In order to provide evidence on the finite sample
properties of the t-values from our regressions, webootstrap critical values. As Stambaugh (1999) points
out, least squares estimates may be biased if
regressors are persistent. Furthermore, standard
errors should take into account that macroeconomic
volatility is calculated rather than observed.
We build bootstrap distributions for the quantities
of interest using the following steps, see also
Mark (1995),
(1) Estimate SP500, t SP500, t1 "t in the
actual data set.
(2) For each run i of the 10 000 replications,
bootstrap a residuals sequence of lengthT 50: f"itg
T50t1 , either parametric (using a
normal distribution with variance equal to that
of the errors from the regression of the previous
step) or nonparametric (resampling the original
errors). T is the length of the original series.
(3) Generate fiSP500, tgT50t1
iSP500, t1
f"itgT50t1 using the parameters from the first
step, the last available observation on stock
Fundamental uncertainty and stock market volatility 1439
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market volatility and the generated residuals
from the second step.
(4) Delete the first 50 observations to prevent any
dependence on starting values for the recursions.
(5) Do the same for the uncertainty series of
macroeconomic variable Y.
For macroeconomic volatility, we simulate themacroeconomic series itself rather than its volatility.
In an additional step after step 3, macroeconomic
volatility is generated as in Equation 2. Just as in the
original data, we thus explicitly take into account the
fact that macroeconomic volatility is generated,
instead of measured, in the bootstrap.
(6) EstimateiSP500, t i iY, it
iiSP500, t1 "it
for each bootstrap run i. Collect estimates of
i, the Newey and West (1987) t-value ti.
The 10 000 observations of ti form the bootstrap
distribution for the t-value under the null-hypothesis,
that macroeconomic risk factors have no relation
with stock market volatility. The quantiles from thesedistributions are used as small sample corrected
critical values.
In the main text, critical values are taken
from the parametric bootstrap experiment, but
conclusions are insensitive to using the nonpara-
metric procedure.
1440 I. J. M. Arnold and E. B. Vrugt