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Cross-correlations and Predictability ofStock Returns
D. OLSON1
AND C. MOSSMAN2
1American University of Sharjah, United Arab Emirates2University of Manitoba, Canada
ABSTRACT
Studies have shown that small stock returns can be partially predicted by thepast returns of large stocks (cross-correlations), while a larger body ofliterature has shown that macroeconomic variables can predict future stockreturns. This paper assesses the marginal contribution of cross-correlationsafter controlling for predictability inherent in lagged macroeconomicvariables. Macroeconomic forecasting models generate trading rule protso f u p t o 0431% per month, while the inclusion of cross-correlationsincreases returns to 0516% per month. Such results suggest that cross-correlations may serve as a proxy for omitted macroeconomic variables instudies of stock market predictability. Macroeconomic variables are moreimportant than cross-correlations in forecasting small stock returns andencompassing tests suggest that the small marginal contribution of cross-correlations is not statistically signicant. Copyright # 2001 John Wiley &Sons, Ltd.
INTRODUCTION
Recent studies, such as Lo and MacKinlay (1990), have shown that small stock returns can be
predicted, in part, by the past returns of larger stocks. The cross-correlations are asymmetric in
the sense that returns to small stocks are correlated with lagged returns on large stocks, but
lagged returns for small stocks do not help predict returns to large stocks. The existence of this
leadlag relationship between large and small stocks raises questions about market eciency and
to date, two studies have examined whether trading rules can exploit the predictability inherent in
cross-correlations. McQueen, Pinegar, and Thorley (1996) devise a trading rule that yields
annualized abnormal returns of 68%, while Knez and Ready's (1996) non-parametricforecasting technique generates trading rule prots of up to 21% per year. However, Knez and
Ready (1996) argue that the inclusion of realistic transaction costs eectively eliminates trading
rule prots.
In addition to the predictability arising from past stock returns, macroeconomic variables have
been shown to predict the time series of stock returns, while stock market fundamentals help
Copyright # 2001 John Wiley & Sons, Ltd.
Journal of Forecasting
J. Forecast. 20, 145160 (2001)
* Correspondence to: Dennis Olson, School of Business, PO Box 26666, American University of Sharjah, Sharjah,United Arab Emirates.
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explain the cross-section of stock returns. Connor (1995) categorizes models designed to capture
these sources of predictability as statistical factor models, macroeconomic factor models, and
fundamental factor models. For a pooled cross-sectional time series of US stock returns for
19851993, he nds that macroeconomic variables contain no marginal explanatory power when
added to either fundamental or statistical factor models. In contrast, Lo and MacKinlay (1990)
hypothesize that macroeconomic information impacts large companies rst and is transmitted
with a lag to smaller companies. If this hypothesis is correct, with the `right' set of
macroeconomic variables as predictors, the proper lag structure, and functional form, any
economically signicant prediction from cross-correlations should be eliminated. Following this
argument, one would expect macroeconomic variables to forecast small stock returns better than
statistical models involving cross-correlations, which is the opposite of Connor's (1995) ndings.
This study examines the relative importance of cross-correlations versus macroeconomic
variables in models that forecast returns for portfolios of US small stocks. Unlike previous
studies that examine predictability within-sample, comparisons between these two sources of
predictability are made using out-of-sample tests.1
Following an approach developed byPesaran and Timmermann (1995), various models are tted within-sample and tested for one-
month-ahead out-of-sample predictability. The models are updated monthly using a rolling
120-month estimation window. Small stocks are purchased and held as long as one-month-
ahead portfolio returns are predicted to be positive, while the risk-free asset is held whenever
the forecast for excess stock returns (returns above the risk-free rate) is negative. Base-case
forecasting models are developed for both macroeconomic variables and cross-correlations.
Then, lagged large stock returns and macroeconomic variables are included in the same model
to determine the marginal contribution of each source of predictability. The models are judged
on the basis of directional forecast accuracy and trading rule prots before and after the
inclusion of trading costs.
LITERATURE REVIEW
Cross-correlations
Cross-correlations are perhaps the least researched of the many sources of predictability in stock
returns that are now well documented in the nance literature. Badrinath, Kale, and Noe (1995)
suggest that cross-autocorrelations between large and small stocks arise primarily from levels of
institutional ownership, rather than stock market value. Institutionally favoured stocks tend to
be larger than institutionally unfavoured rms, so that the leadlag eect in size portfolios may
be caused more by the level of institutional ownership than rm size. In contrast, McQueen et al.
(1996) document that observed leadlag relationships between large and small stocks are more
size related than the result of institutional ownership. They also discovered a directional
asymmetry in cross-correlations. Small stocks respond quickly to bad macroeconomic news, but
respond with a delay to common good news. Hence, the observed leadlag relationship applies
only to positive returns to large stocks.In an attempt to understand why small stock returns can be predicted using cross correlations,
Boudoukh, Richardson, and Whitelaw (1994) categorize possible explanations into three
1 For example, Ferson and Korajczyk (1995) use factor models to determine which variables are most responsible forwithin-sample returns predictability. Similarly, Connor's (1995) analysis of three types of factor models involves in-sample comparisons.
146 D. Olson and C. Mossman
Copyright # 2001 John Wiley & Sons, Ltd. J. Forecast. 20, 145160 (2001)
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groups loyalists, revisionists, and heretics according to their relationship with the ecient
market hypothesis. The loyalist group looks to data mismeasurement or specic institutional
features such as dierential bidask spreads to defend market eciency. Non-synchronous
trading is consistent with this explanation, but Lo and MacKinley (1990) argue that the
frequency of non-trading is not sucient to be the primary source of observed stock cross-
correlations.
Revisionist arguments expressed by Conrad, Gultekin, and Kaul (1991) suggest that
predictability arises from time-varying expected returns and does not violate market eciency.
More recently, Hameed (1997) has shown that predictability from cross-correlations can likely be
attributable to dierences in the level of time variation in expected returns. However, McQueen et
al. (1996) note that such an explanation does not indicate why returns to large stocks can not be
predicted in the same way. Also, their formal test for this theory fails to support the time-varying
risk premium argument.
The heretic explanations for predictability rest on over-reaction, under-reaction, noise trader
response, or feedback strategies that lead to a form of market ineciency. Over-reaction couldlead to contrarian prots, and under-reaction to protability of momentum strategies. For
example, Grinblatt, Titman, and Wermers (1995) argue that mutual fund managers follow each
other in buying winners, but make independent decisions about selling losers. Since less
information is available for small stocks, herding occurs once managers have observed a rather
imprecise signal, such as a positive return on large stocks in the previous period. This behaviour is
consistent with the directional asymmetry in cross-correlations, as identied by McQueen et al.
(1996).
Macroeconomic variables
Studies such as Fama and French (1989) demonstrate that macroeconomic variables
representing general business conditions can help predict the time series of stock returns.Perhaps the most important of these variables are the levels and changes in interest rates.
Short-term rates (yields on T-bills or commercial paper), term spreads (yields on long-term
government bonds less short-term yields), and default spreads (yields on high-risk corporate
bonds versus low-risk corporate or government bonds) have been shown to have predictive
power in numerous studies. For example, Kairys (1993) shows that changes in commercial
paper rates help explain excess stock returns in the USA from the 1830s to the present. Lo and
MacKinlay (1990) show that large stocks respond to macroeconomic news in the same month
that the news is received, while the response of small stocks can take up to eight weeks (based
upon the signicance of lagged autocorrelations). Jegadeesh and Titman (1995) n
