International Stock Return PredictabilityWhat is the Role of the United States?

International Stock Return Predictability
What is the Role of the United States?
David E. Rapach?
Jack K. Strauss
Saint Louis University
Saint Louis University
rapachde@slu.edu
strausjk@slu.edu
Guofu Zhou
Washington University in St. Louis
zhou@wustl.edu
September 18, 2009
PRELIMINARY—COMMENTS WELCOME
?Corresponding author. Send correspondence to Guofu Zhou, Olin School of Business, Washington University
in St. Louis, St. Louis, MO 63130; e-mail: zhou@wustl.edu; phone: 314-935-6384. We thank participants at the
2009 Midwest Econometric Group Meetings for helpful comments. The usual disclaimer applies. Rapach and Strauss
acknowledge ?nancial support from the Simon Center for Regional Forecasting at Saint Louis University.

---

International Stock Return Predictability:
What is the Role of the United States?
Abstract
We present signi?cant evidence of out-of-sample equity premium predictability for a host
of industrialized countries over the postwar period. There are important differences, however,
in the nature of equity premium predictability between the United States and other developed
countries. Taken collectively, U.S. economic variables are signi?cant out-of-sample predictors
of the U.S. equity premium that clearly outperform lagged international stock returns. In con-
trast, lagged international stock returns—especially lagged U.S. returns—substantially outper-
form economic variables as out-of-sample equity premium predictors for non-U.S. countries,
pointing to a leading role for the United States with respect to international return predictabil-
ity. These predictability patterns are enhanced during economic downturns, linking return
predictability to business-cycle ?uctuations and information frictions involving the diffusion
of news on macroeconomic fundamentals across countries. The leading role of the United
States stands out during the recent global ?nancial crisis: lagged U.S. stock returns deliver
especially sizable gains for forecasting the monthly equity premium in other countries, evi-
denced by out-of-sample R2 statistics of 10% or greater, more than triple the postwar average.
JEL classi?cations: C22, C53, G14, G15, G17
Keywords: Equity premium; Predictive regression model; Combination forecast; Information
diffusion; Granger causality; Business cycle; Global ?nancial crisis

---

International Stock Return Predictability:
What is the Role of the United States?
1
Introduction
Stock return predictability is a central issue in ?nancial economics. Correspondingly, a vast em-
pirical literature exists on the predictability of U.S. aggregate stock market returns using eco-
nomic variables. In summarizing this literature, Campbell (2000), Cochrane (2007), and Lettau
and Ludvigson (2009) argue that U.S. returns contain a statistically and economically signi?cant
predictable component. Fama and French (1989), Campbell and Cochrane (1999), and Cochrane
(2007), among others, contend that economic variables—such as valuation ratios, nominal interest
rates, in?ation rates, term and default spreads, and the consumption-wealth ratio1—predict returns
because they capture rational ?uctuations in expected returns relating to time-varying macroeco-
nomic risk premiums. A number of researchers argue that market inef?ciencies and information
frictions also play an important role in generating return predictability; see, for example, Baker
and Wurgler (2000) and Hong, Torous, and Valkanov (2007).
Several important studies consider stock return predictability in countries outside the United
States, including Cutler, Poterba, and Summers (1991), Harvey (1991), Bekaert and Hodrick
(1992), Campbell and Hamao (1992), Ferson and Harvey (1993), Solnik (1993), Ang and Bekaert
(2007), and Hjalmarsson (2008). While these studies provide intriguing evidence that stock returns
are predictable in other countries, they typically consider a limited number of countries or potential
predictors, use relatively short data samples, and rely only on in-sample tests. It is thus dif?cult to
ascertain the signi?cance of return predictability in countries outside the United States.
To better understand the extent and nature of international stock return predictability, we exten-
sively analyze stock return predictability in the United States and eleven other industrialized coun-
tries during the postwar period. Our analysis provides answers the following questions: Is stock
return predictability an economically signi?cant feature of countries outside the United States? Do
similar variables predict returns in the Unites States and other countries? Are there important links
1Representative studies include Fama and French (1988, 1989), Campbell and Shiller (1988, 1998), Kothari and
Shanken (1997), Cochrane (2008), and P´astor and Stambaugh (2009) for valuation ratios; Fama and Schwert (1977),
Campbell (1987), Breen, Glosten, and Jagannathan (1989), and Ang and Bekaert (2007) for nominal interest rates;
Nelson (1976), Fama and Schwert (1977), and Campbell and Vuolteenaho (2004) for in?ation rates; Campbell (1987)
and Fama and French (1989) for term and default spreads; Baker and Wurgler (2000) and Boudoukh, Michaely,
Richardson, and Roberts (2007) for corporate issuing activity; and Lettau and Ludvigson (2001) for the consumption-
wealth ratio.
1

---

among national equity markets with respect to return predictability? These questions relate to an
overarching issue: Does the United States play a special role with respect to international stock re-
turn predictability? The recent global ?nancial crisis highlights the importance of these questions,
as the crisis has been characterized by deteriorating macroeconomic fundamentals—originating
primarily in the United States—and sharply falling share prices across many countries.
For the equity premium in each country, we consider three groups of potential predictors. The
?rst group comprises ten domestic economic variables representative of the literature, such as the
dividend yield, nominal interest rates, in?ation rate, and term spread. The second group consists
of U.S. economic variables. This is motivated by Harvey (1991) and Ferson and Harvey (1993),
who ?nd that U.S. economic variables help to predict returns in other countries. The ?nal group of
potential predictors includes lagged excess stock returns from all twelve countries. Our consider-
ation of lagged excess returns from multiple countries allows us to study lead-lag relationships in
international stock returns.
Following a number of recent studies (e.g., Campbell and Thompson, 2008; Goyal and Welch,
2008; Rapach, Strauss, and Zhou, 2009), we focus on out-of-sample tests of equity premium pre-
dictability, which are less susceptible than in-sample tests to data mining and over?tting.2 We
use the historical average forecast, which corresponds to the well-known random walk (with drift)
model, as a natural benchmark. The historical average forecast is a stringent out-of-sample bench-
mark: Goyal and Welch (2008) show that a large number of economic variables with in-sample
predictive ability in the literature fail to consistently outperform the historical average forecast of
the U.S. equity premium in out-of-sample tests.3
In addition to individual predictive regression model forecasts, we employ combination fore-
casts. This is motivated by Rapach, Strauss, and Zhou (2009), who show that simple combinations
of individual predictive regression model forecasts of the U.S. equity premium consistently outper-
form the historical average benchmark, despite the inability of individual forecasts to consistently
beat the historical average.4 For each country, we consider combination forecasts based on the
three different groups of potential predictors, as well as all potential predictors taken together.
2While it is widely believed that out-of-sample tests are more reliable than in-sample tests, there are some philo-
sophical issues relating to the choice of in-sample versus out-of-sample tests (e.g., Inoue and Kilian, 2004; Lettau and
Ludgivson, 2009).
3The in?uential study of Goyal and Welch (2008) won the Michael Brennan Best Paper Prize for the Review of
Financial Studies.
4The success of the combination forecast approach stems in part from its ability to improve forecast accuracy
in environments with substantial model uncertainty and instability; see, for example, Hendry and Clements (2004),
Clements and Hendry (2006), Timmermann (2006), and Rapach, Strauss, and Zhou (2009).
2

---

Previewing our results, we ?nd statistically and economically signi?cant evidence of out-of-
sample predictability in the monthly equity premium for eleven of the twelve industrialized coun-
tries during the 1966:01–2009:05 period.5 Nevertheless, we identify important differences across
countries in the ability of the various groups of predictors to forecast excess returns. Consider the
?rst group of predictors, ten domestic economic variables for each country. Despite the inability of
individual U.S. economic variables to consistently outperform the historical average benchmark for
forecasting the U.S. equity premium, a combination forecast based on all ten economic variables
collectively beats the historical average benchmark by statistically and economically signi?cant
margins, similar to Rapach, Strauss, and Zhou (2009). Individual domestic economic variables also
fail to consistently outperform the historical average equity premium forecast for the eleven other
industrialized countries. In contrast to the United States, however, combination forecasts based on
domestic economic variables also fail to signi?cantly outperform the historical average benchmark
for nine of the eleven other countries. The exceptions are Belgium and Germany; even for these
countries, however, the magnitudes of the out-of-sample gains are considerably smaller than those
for the United States. In short, while domestic economic variables in combination signi?cantly
predict the U.S. equity premium, they exhibit substantially weaker out-of-sample predictive ability
for the equity premium in other industrialized countries.
The second group of predictors, U.S. economic variables, generally demonstrate greater out-of-
sample predictive ability than domestic economic variables for non-U.S. countries. Combination
forecasts based on U.S. economic variables signi?cantly outperform the historical average bench-
mark equity premium forecast for Belgium, Canada, Germany, and the Netherlands. Nevertheless,
the magnitudes of the out-of-sample forecasting gains are limited compared to the predictive power
of U.S. economic variables for the U.S. equity premium. Overall, economic variables produce sub-
stantial out-of-sample forecasting gains for the U.S. equity premium, but they generate smaller or
no gains for the equity premium in non-U.S. countries.
A different pattern emerges with respect to the out-of-sample predictive ability of the third
group of predictors, lagged international stock returns. Taken individually or in combination,
lagged international excess stock returns do not signi?cantly outperform the historical average
benchmark for forecasting the U.S. equity premium. In sharp contrast, a number of individual
lagged international excess stock returns, as well as combination forecasts based on lagged inter-
5The fact that we ?nd substantial evidence of return predictability at a monthly horizon is important, since much of
the signi?cant in-sample evidence of return predictability in the literature occurs at longer horizons, and long-horizon
predictability raises a number of econometric issues due to overlapping observations (e.g., Richardson and Stock,
1989; Valkanov, 2003; Ang and Bekaert, 2007; Boudoukh, Richardson, and Whitelaw, 2008).
3

---

national excess returns, signi?cantly outperform the historical average benchmark for the equity
premium in other industrialized countries. Lagged U.S. excess returns appear especially impor-
tant: they produce statistically and economically sizable forecasting gains in ten of the eleven
other countries. These gains are typically larger than those associated with other countries’ lagged
excess returns. The United States thus appears to play a leading role with respect to international
return predictability.
Our ?nding that U.S. returns lead returns in other countries has an interesting parallel in the
literature on cross-serial correlation in portfolios of individual U.S. stocks sorted on size, ana-
lyst coverage, volume, and/or industry (e.g., Lo and MacKinlay, 1990; Brennan, Jegadeesh, and
Swaminathan, 1993; Chordia and Swaminathan, 2000; Hou, 2007). This literature ?nds that re-
turns on particular portfolios lead returns on other portfolios; for example, Lo and MacKinlay
(1990) present evidence that returns on portfolios of U.S. large-cap stocks lead returns on portfolios
of U.S. small-cap stocks. We extend this literature by showing that important lead-lag relationships
also exist across countries.
An explanation for lead-lag relationships among portfolios is information frictions: certain
stocks adjust more slowly to economy-wide information. For example, Hong, Torous, and Valka-
nov (2007) recently posit that many investors specialize in particular segments of the equity market;
information-processing limitations can then cause information originating in particular segments
to diffuse slowly across the broader market, thereby creating return predictability. In our interna-
tional context, if many investors focus more intently on the U.S. equity market, information on
macroeconomic fundamentals relevant for equity markets worldwide diffuses more slowly to other
countries. Lagged U.S. returns will then have predictive ability with respect to returns in other
countries.
To further analyze lead-lag relationships in international returns, we test for Granger causal-
ity between U.S. and non-U.S. excess returns, following Brennan, Jegadeesh, and Swaminathan
(1993), Hameed (1997), and Chordia and Swaminathan (2000) in the U.S. domestic context. This
guards against spurious evidence of lead-lag relationships in portfolio returns that arises from au-
tocorrelation in portfolios returns combined with contemporaneously correlated portfolio returns
(Boudoukh, Richardson, and Whitelaw, 1994; Hameed, 1997; Chordia and Swaminathan, 2000).
Our results continue to point to a leading role for the United States: U.S. returns Granger cause
returns in nearly every other country (using both in-sample and out-of-sample tests), while the
converse does not hold.
4

---

We glean additional insight into the nature of international stock return predictability by ana-
lyzing predictability in each country over different phases of the business cycle. More speci?cally,
we compute out-of-sample forecasting gains separately over “classical” business-cycle expansions
and recessions. The classical business cycle corresponds to the basic approach of the National
Bureau of Economic Research with respect to the “of?cial” dating of U.S. business-cycle peaks
and troughs. Using classical business-cycle dates from various sources for the twelve industrial-
ized countries, we ?nd that out-of-sample return predictability is often markedly enhanced during
recessions. Moreover, the differences in the forecasting ability of the various predictors that we
identify over the full out-of-sample period are magni?ed during recessions. In particular, lagged
U.S. returns generate even more sizable forecasting gains during recessions in non-U.S. countries.
The enhanced predictive power of lagged U.S. returns during recessions suggests that U.S. eq-
uity prices quickly incorporate information relevant for changing worldwide economic conditions,
while this information diffuses more slowly to other countries.
As a ?nal exercise, we analyze out-of-sample stock return predictability during the recent
global ?nancial crisis by using a 2007:01–2009:05 forecast evaluation period. Given the interna-
tional scope of the crisis and rapidly deteriorating macroeconomic conditions, this is an especially
informative period. We are particularly interested in the relevance of the information ?ow frictions
during the recent crisis, and, indeed, we ?nd that lagged U.S. returns are especially useful for fore-
casting the equity premium in other countries during the crisis. Over the full out-of-sample period,
Campbell and Thompson (2008) out-of-sample R2 statistics based on lagged U.S. returns range
from approximately 1% to 3% for many other industrialized countries, which are statistically and
economically signi?cant. These R2 statistics jump to approximately 10% to 13% during the recent
crisis. This is a very high range, highlighting the leading role played by the United States with
respect to international return predictability.
The remainder of the paper is organized as follows. Section 2 outlines the formation and
evaluation of out-of-sample equity premium forecasts. Section 3 describes the data and reports
out-of-sample results for the twelve industrialized countries over the 1966:01–2009:05 forecast
evaluation period. Section 4 presents Granger causality test results for country excess returns.
Section 5 examines the out-of-sample equity premium predictability separately over business-cycle
expansions and contractions, as well as during the recent global crisis. Section 6 concludes.
5

---

2
Econometric Methodology
We begin with a conventional predictive regression model for country i’s monthly equity premium:
ri,t+1 = ? + ? xt + ?i,t+1,
(1)
where ri,t is the return on a broad stock market index for country i in excess of the risk-free interest
rate for country i, xt is a potential predictor of ri,t+1, and ?i,t+1 is a disturbance term. Observe that,
following Solnik (1993), Ang and Bekaert (2007), and Hjalmarsson (2008), among others, the
equity premium is measured in the national currency. As noted by Solnik (1993), the national cur-
rency equity premium is approximately equal to the currency-hedged equity premium for investors
from any country due to interest rate parity, where the forward premium equals the difference in
the risk-free interest rates. The approximation becomes more accurate for shorter time periods
(monthly returns in our case). Solnik (1993) also points out that working with national currency
returns obviates the need to develop a risk premium model for exchange rates, allowing us to focus
on time-varying expected returns in equity markets.
Following the recent studies of Campbell and Thompson (2008), Goyal and Welch (2008),
and Rapach, Strauss, and Zhou (2009), we generate out-of-sample equity premium forecasts for
country i using a recursive (expanding) estimation window. More speci?cally, we ?rst divide the
total sample of T observations into in-sample and out-of-sample components comprised of the
?rst m and last q observations, respectively. The initial out-of-sample forecast of country i’s equity
premium is given by
ˆri,m+1 = ˆ
?m + ˆ
?mxm,
(2)
where ˆ
?m and ˆ
?m are the ordinary least squares (OLS) estimates of ? and ? , respectively, in (1)
generated by regressing {ri,t}m
on a constant and {x
. The next out-of-sample forecast is
t=2
t }m?1
t=1
given by
ˆri,m+2 = ˆ
?m+1 + ˆ
?m+1xm+1,
(3)
where ˆ
?m+1 and ˆ
?m+1 are generated by regressing {ri,t }m+1 on a constant and {x
. We pro-
t=2
t }m
t=1
ceed in this manner through the end of the out-of-sample period, leaving us with a series of q
out-of-sample forecasts for country i’s equity premium, { ˆri,t+1}T?1
t=m . Apart from data reporting
conventions and revisions, this out-of-sample exercise simulates the situation of a forecaster in
real time.6 As indicated in Section 1, our focus on out-of-sample tests follows a number of recent
6Data reporting conventions and revisions are only relevant for a few of the predictors we consider, namely, in?ation
and industrial production. To allow for the lag in the reporting of these data, we also computed equity premium
forecasts with with xt?1 replacing xt in (1). The results are qualitatively unchanged.
6

---

studies and is designed to provide more reliable inferences regarding return predictability.
Following Campbell and Thompson (2008) and Goyal and Welch (2008), we use the historical
average forecast, ¯r
t
i,t+1 = ?
r
j=1 i, j, as the benchmark forecast. This benchmark corresponds to the
random walk with drift or constant expected excess return model. Intuitively, if xt contains infor-
mation useful for forecasting ri,t+1, the predictive regression model forecast, which incorporates
information from xt, should deliver superior forecasts relative to the historical average forecast,
which ignores xt. Goyal and Welch (2008) show that the historical average forecasts is a stringent
benchmark.
In Section 3, we consider a large number of potential predictors and thus a large number of
individual predictive regression model forecasts. In this setting, it can be bene?cial to combine
information from individual predictive regression model forecasts. In particular, Rapach, Strauss,
and Zhou (2009) show that while numerous individual predictive regression models based on pop-
ular economic variables are unable to consistently outperform the historical average with respect
to forecasting the U.S. equity premium, a simple combination of individual forecasts does consis-
tently outperform the historical average. Rapach, Strauss, and Zhou (2009) provide an extended
analysis of how combination forecasts can improve equity premium prediction. Intuitively, com-
bining forecasts incorporates useful information from many predictors while stabilizing individual
forecasts and thus avoiding the numerous “false signals” in individual forecasts. In light of this,
we consider combination forecasts that take the form of simple averages of various groups of in-
dividual predictive regression model forecasts. While more sophisticated combining methods are
available, simple combining methods often outperform more complicated methods (e.g., Timmer-
mann, 2006).
To evaluate the individual predictive regression model and combination forecasts against the
historical average benchmark, we calculate the Campbell and Thompson (2008) out-of-sample R2
statistic, R2 . This statistic measures the reduction in mean square prediction error (MSPE) for
OS
an individual predictive regression model or combination forecast relative to the historical average
forecast:
q
?
(ri,m+k ? ˆri,m+k)2
R2
k=1
OS = 1 ?
q
,
(4)
?
(r
k=1
i,m+k ? ¯
ri,m+k)2
where ˆri,m+k represents an individual predictive regression model or combination forecast. When
R2 > 0, the predictive regression model or combination forecast thus has a lower MSPE than the
OS
historical average benchmark.
To test the null hypothesis that the predictive regression model or combination forecast is not
7

---

more accurate than the historical average benchmark (R2 ? 0) against the alternative hypothesis
OS
that the predictive regression model or combination forecast has a lower MSPE (R2 > 0), we
OS
use the Clark and West MSPE-adjusted statistic. This is a variant of the popular Diebold and
Mariano (1995) and West (1996) statistic. While the Diebold and Mariano (1995) and West (1996)
statistic has a standard normal asymptotic distribution when comparing forecasts from nonnested
models, it has a nonstandard distribution when comparing forecast from nested models (Clark and
McCracken, 2001; McCracken, 2007). Our forecast comparison clearly involves nested models,
since setting ? = 0 in (1) yields the constant expected excess return model. Clark and West (2007)
modify the Diebold and Mariano (1995) and West (1996) statistic to develop a test based on the
standard normal distribution that produces valid asymptotic inferences when comparing forecast
from nested models. More speci?cally, the Clark and West (2007) MSPE-adjusted statistic is
conveniently computed by ?rst de?ning
fi,t+1 = (ri,t+1 ? ¯ri,t+1)2 ? [(ri,t+1 ? ˆri,t+1)2 ? (¯ri,t+1 ? ˆri,t+1)2]
(5)
and then regressing { fi,s+1}T?1
s=m on a constant; the t -statistic corresponding to the constant is the
MSPE-adjusted statistic. A p-value for a one-sided (upper-tail) test is generated using the standard
normal distribution. In Monte Carlo simulations, Clark and West (2007) ?nd that the MSPE-
adjusted statistic has good ?nite-sample properties.
Given the nature of stock return predictability, R2 statistics are typically small at the monthly
OS
horizon. Nevertheless, Kandel and Stambaugh (1996), Xu (2004), and Campbell and Thompson
(2008) demonstrate that even an apparently small degree of predictability can be economically
important. For example, Campbell and Thompson (2008) show that an R2 greater than approxi-
OS
mately 0.5% for monthly returns corresponds to economically meaningful predictability gains with
respect to the U.S. equity premium.
3
Out-of-Sample Forecasting Results
3.1
Data
We employ monthly data for 1956:02–2009:05 for twelve industrialized countries (Australia, Bel-
gium, Canada, France, Germany, Italy, Japan, the Netherlands, Sweden, Switzerland, the United
Kingdom, and the United States). The selection of countries and sample period are dictated by data
availability and our desire to analyze out-of-sample return predictability for a relatively large num-
ber of countries for a relatively long postwar sample. Most of the data are from Global Financial
8

---