Fundamental Uncertainity and Stock Market

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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: [email protected]

Applied Financial Economics ISSN 09603107 print/ISSN 14664305 online 2008 Taylor & Francis 1425

http://www.tandf.co.uk/journals

DOI: 10.1080/09603100701857922


3/17

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


4/17

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

Fundamental uncertainty and stock market volatility 1427


5/17

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



6/17

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



7/17

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.



8/17

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



9/17

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.



10/17

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.



11/17

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.



12/17

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


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



14/17

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


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


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.



15/17

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



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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.


Fundamental Uncertainity and Stock Market

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