Disagreement in Economic Forecasts and Expected Stock
Returns
Turan G. Bali∗
Stephen J. Brown†
Yi Tang‡
Georgetown University
Monash University
Fordham University
Abstract
We estimate individual stock exposure to an economic disagreement index and show that
a zero-cost portfolio that buys stocks in the lowest disagreement-beta decile and shorts
stocks in highest disagreement-beta decile produces a risk-adjusted return of 7.8% per annum. The disagreement premium is induced by the outperformance (underperformance)
by stocks with negative (positive) disagreement beta, indicating that ambiguity-averse investors demand higher (lower) compensation to hold stocks with high disagreement risk
(with large hedging benefits). After controlling for a number of firm characteristics and
risk factors, the negative relation between disagreement beta and future stock returns remains economically and statistically significant.
First draft: January 2014
This version: April 2017
JEL classification: G11, G12, C13, E20, E30.
Keywords: Dispersion in economic forecasts, cross-section of stock returns, return predictability.
∗ Robert S. Parker Professor of Business Administration, McDonough School of Business, Georgetown University, Washington, D.C.
20057. Email: [email protected]. Phone: (202) 687-5388. Fax: (202) 687-4031.
† Professor, Monash Business School, Melbourne, Vic. 3145 Australia, and Emeritus Professor of Finance, NYU Stern School of Business, New York, NY 10012. Phone: +61 3 9903 4953 E-mail: [email protected].
‡ Associate Professor of Finance, Gabelli School of Business, Fordham University, 45 Columbus Avenue, New York, NY 10023. Email:
[email protected]. Phone: (646) 312-8292. Fax: (646) 312-8295.
1. Introduction
Miller (1977) hypothesizes that stock prices reflect an upward bias as long as there exists divergence
of opinion among investors about stock value and pessimistic investors do not hold sufficient short
positions. In Miller’s model, overvaluation of securities is observed because pessimists are restricted to
hold zero shares although they prefer to hold a negative quantity, and the prices of securities are mainly
determined by the beliefs of most optimistic investors. Thus, stocks with greater disagreement have
higher prices and lower subsequent return.1 Using different proxies for disagreement, both Diether,
Malloy, and Scherbina (2002) and Chen, Hong, and Stein (2002) provide cross-sectional evidence that
supports this prediction of Miller’s model.
Most of the literature measures disagreement about individual stocks with the standard deviation
of earnings forecasts made by financial analysts and examines the cross-sectional relation between
this measure and individual stock returns. Unlike prior studies, we focus on disagreement about the
economy instead of disagreement about individual stocks. We investigate if disagreement in economic
forecasts has a significant impact on the cross-sectional pricing of individual stocks. We quantify disagreement about the economy with ex-ante measures of cross-sectional dispersion in economic forecasts from the Survey of Professional Forecasters (SPF). These measures provided by the Federal Reserve Bank of Philadelphia determine the degree of disagreement in the expectations of professional
forecasters.
Our empirical analysis relies on seven different measures of cross-sectional dispersion in quarterly
forecasts for output, inflation, and unemployment. We quantify an unexpected change (or innovation)
in the economic predictions of the professional forecasters by estimating an autoregressive process
for each dispersion measure. The standardized residuals from the autoregressive model remove the
predictable component of the dispersion measures and can be viewed as a measure of disagreement
shock. We estimate individual stock exposure to the standardized residuals and find that the resulting
1 Theoretical models with disagreement and short-sale constraints are also provided by Harrison and Kreps (1978), Harris
and Raviv (1993), Kandel and Pearson (1995), Scheinkman and Xiong (2003), and Hong, Scheinkman, and Xiong (2006).
Hong and Stein (2007) provide an excellent review of this literature.
1
betas from all seven measures of disagreement shock predict a significant proportion of the crosssectional differences in stock returns.
In addition to individual measures of disagreement over economic fundamentals, we introduce two
broad indices of economic disagreement based on the average and the first principal component of
the standardized residuals for the seven dispersion measures. These economic disagreement indices
are generated using past information only, so that there is no look-ahead bias in our asset pricing
tests. Moreover, these disagreement indices are formed based on ex-ante predictions of professional
forecasters so that we provide the out-of-sample performance of ex-ante measure of the disagreement
beta in predicting the cross-sectional variation in future stock returns.
First, we estimate the disagreement beta using 20-quarter rolling regressions of excess returns on
the newly proposed economic disagreement index for each stock trading in the New York Stock Exchange (NYSE), American Stock Exchange (Amex), and Nasdaq. Then, we examine the performance
of the quarterly disagreement beta in predicting the cross-sectional dispersion in future stock returns.
Specifically, we sort stocks into value-weighted decile portfolios by their disagreement beta during
the previous quarter and examine the monthly returns on the resulting portfolios from January 1974
to December 2016. Stocks in the lowest disagreement beta decile generate 50 basis points per month
higher average return compared to stocks in the highest disagreement beta decile. After controlling for
the well-known market, size, book-to-market, momentum, and liquidity factors of Fama and French
(1993), Carhart (1997), and Pastor and Stambaugh (2003), we find the difference between the returns
on the portfolios with the highest and lowest disagreement beta (5-factor alpha) remains negative and
highly significant.
We investigate the source of the risk-adjusted return spread between the high-disagreement beta and
low-disagreement beta portfolios and find that the 5-factor alpha of stocks in decile 1 (with negative
disagreement beta) is significantly positive, whereas the 5-factor alpha of stocks in decile 10 (with positive disagreement beta) is significantly negative, implying that the significantly negative alpha spread
between the high-disagreement beta and low-disagreement beta stocks is due to both the outperfor-
2
mance by negative-disagreement beta stocks and the underperformance by positive-disagreement beta
stocks.
These results are consistent with a well-established literature that distinguishes risk and ambiguity,
showing that investors care not only about the mean and variance of asset returns but also on the ambiguity of events over which the future return distribution occurs. Since the future return distribution is
influenced by the state of the economy, ambiguity about the economy enters an investor’s utility function. In this setting, our results provide a preference-based explanation of the economic disagreement
premium: Due to their negative disagreement beta, the returns of individual stocks in decile 1 correlate
negatively with increases in economic disagreement, hence ambiguity-averse investors would demand
extra compensation in the form of higher expected return to hold these stocks with negative disagreement beta. On the other hand, with their positive disagreement beta, the returns of individual stocks
in decile 10 correlate positively with increases in economic ambiguity. Since stocks with positive disagreement beta would be viewed as relatively safer assets at times of increased economic ambiguity,
investors are willing to pay higher prices for these stocks and accept lower returns.2
In addition to the ambiguity-aversion based explanation of the negative disagreement premium,
there exists an alternative explanation based on differences of opinion and short-sales constraints along
the lines of Miller (1977). Suppose that stocks with high disagreement-beta are subject to overpricing
because investor opinions differ about their prospects and they are hard to short. When economic
ambiguity increases, the range of investor opinions about their prospects broadens. More extreme
optimists end up holding these stocks, and their prices increase. The disagreement beta can thus be
viewed as an indirect way to measure dispersed opinion and overpricing. This view suggests that
these stocks should have particularly low returns when economic disagreement is high. Consistent
with Miller’s hypothesis, our results indicate that stocks with high disagreement-beta have particularly
low returns during economic recessions in which larger differences of opinion are observed among
professional forecasters.
2 Stocks
with negative disagreement beta can be viewed as riskier assets with high disagreement risk because the returns
of these stocks decrease during periods of high economic disagreement. On the other hand, stocks with positive disagreement
beta can be viewed as effective hedging instruments providing large hedging benefits because the returns of these stocks
increase during periods of high economic disagreement.
3
To ensure that it is the disagreement beta that is driving documented return differences rather than
well-known stock characteristics or risk factors, we perform bivariate portfolio sorts and re-examine
the raw return and alpha spreads in long-short equity portfolios. We control for size and book-tomarket (Fama and French 1992, 1993), momentum (Jegadeesh and Titman 1993), short-term reversal
(Jegadeesh 1990), illiquidity (Amihud 2002), co-skewness (Harvey and Siddique 2000), idiosyncratic
volatility (Ang, Hodrick, Xing, and Zhang 2006), analyst earnings forecast dispersion (Diether, Malloy,
and Scherbina 2002), market volatility beta (Ang et al. 2006), and demand for lottery-like stocks (Bali,
Cakici, and Whitelaw (2011)). After controlling for this large set of stock return predictors, we find the
negative relation between the disagreement beta and future returns remains highly significant. We also
examine the cross-sectional relation at the stock-level using the Fama-MacBeth (1973) regressions.
After all variables are controlled for simultaneously, the cross-sectional regressions provide strong
corroborating evidence for an economically and statistically significant negative relation between the
disagreement beta and future stock returns.
We provide a battery of robustness checks. We investigate whether our results are driven by small,
illiquid, and low-priced stocks, or stocks trading at the Amex and Nasdaq exchanges. We find that
the negative disagreement premium is highly significant in the cross-section of NYSE stocks, Standard
& Poor’s (S&P) 500 stocks, and the 1,000 and 500 largest and most liquid stocks in the Center for
Research in Security Prices (CRSP) universe. We also provide evidence of a significant time-series
variation in economic disagreement premium. Consistent with theoretical predictions, the disagreement premium is estimated to be much higher during economic downturns compared to expansionary
periods. We also examine the long-term predictive power of the disagreement beta and find that the
negative relation between the disagreement beta and future stock returns is not just a one-month affair.
The disagreement beta predicts cross-sectional variation in stock returns 12 months into the future. Finally, we show that the negative disagreement premium is robust to controlling for alternative measures
of economic uncertainty and policy uncertainty indices and is distinct from the negative volatility risk
and uncertainty premia identified by earlier studies.
The paper is organized as follows. Section 2 gives a literature review providing theoretical evidence
that supports the cross-sectional relation between disagreement in economic forecasts and expected
4
returns. Section 3 describes the data and variables. Section 4 presents the main empirical results.
Section 5 investigates the significance of disagreement beta after controlling for stock exposures to
economic and policy uncertainty indices. Section 6 concludes the paper.
2. Theoretical evidence
The standard finance theory generally rules out the conditions in which investors are unsure about
the probability distribution of asset returns. There is no meaningful distinction between risk, where
probabilities are available to guide choice, and uncertainty, where information is too imprecise to be
summarized adequately by probabilities. By contrast, Knight (1967) draws a distinction between risk
and true uncertainty and argues that uncertainty is more common in decision-making process. Knight
(1967) points out that risk occurs where the future is unknown, but the probability of all possible outcomes is known. Uncertainty occurs where the probability distribution itself is unknown. Knight’s
distinction between risk and uncertainty implies that risk is related to the objective distribution of returns or the subjective distribution of returns commonly agreed on by all investors, whereas uncertainty
is related to the probability distribution unique to an individual investor. In empirical asset pricing literature, not much attention has been paid to this distinction because in either case the future is unknown
and decisions must be made using the individual’s subjective estimates of the relevant probabilities.
However, the distinction does have significant relevance for the subject of this paper.
In this paper, we essentially rely on one particular class of heterogeneous-agent models, which
is called “disagreement” models by Hong and Stein (2007), focusing on differences in the beliefs of
investors. According to Miller (1977), if differences of opinion reflect limited market participation,
prices of securities are determined by optimistic investors who bid prices up, leading to overvaluation
and subsequent reversal resulting in lower future returns.
Diether, Malloy, and Scherbina (2002) use dispersion in analysts’ earnings forecasts as a proxy for
divergence of opinion and find that stocks with higher dispersion of analysts’ earnings forecasts generate significantly lower future returns than those with lower dispersion. Johnson (2004) questions the
5
interpretation of Diether et al. (2002) results, and argues that dispersion in analyst forecast can proxy
for higher firm-specific idiosyncratic risk and attributes it to higher leverage. Boehme, Danielsen, and
Sorescu (2006) examine the significance of simultaneous effects of differences of opinion and short
sale constraints in the cross-sectional pricing of individual stocks and provide evidence of significant
overvaluation for stocks that are subject to both conditions simultaneously.3 By defining investor uncertainty as the dispersion of predictions of mean market returns obtained from the forecasts of aggregate
corporate profits, Anderson, Ghysels, and Juergens (2009) find that the price of investor uncertainty
is significantly positive. Using measures of uncertainty estimated from a regime-switching model of
market return and of output, Ozoguz (2009) finds a negative relation between investor uncertainty and
asset returns. Overall, there is no clear agreement in the literature on how investor uncertainty and
analyst dispersion affect the cross-sectional variation in future stock returns.4
This paper is motivated by the fact that investors’ decisions, economic outcomes, and asset returns are generally determined by probabilistic assessments of future events, the ambiguity surrounding
them, and disagreement across investors regarding these assessments. Hence, uncertainty about how
the economy will evolve is a key concern for investors. Investors’ views on how likely it is that the
economy will be growing, stagnating, or in recession affect their asset allocation and risk management
decisions. Consequently, how they respond to uncertainty has implications for economic activity and
asset returns. Thus, unlike prior studies, this paper focuses on disagreement about the economy instead
of disagreement about individual stocks. We think that variations over time in the risk premia embedded in stock returns primarily reflect changes in aggregate uncertainty and/or fluctuations in the degree
of the consensus in beliefs about economic fundamentals. As pointed out by Sill (2012), surveys of
expectations (e.g., SPF) offer one potential source for information that could be useful in addressing
such questions.
3 Danielsen
and Sorescu (2001) test the Miller hypothesis by examining the event-window abnormal returns associated
with option introductions. Their empirical findings generally support Miller (1977), but the event-window abnormal returns
are economically small.
4 In a related literature on macroeconomic uncertainty and economic policy uncertainty, Gulen and Ion (2016) document
a strong negative relationship between firm-level capital investment and the aggregate level of uncertainty associated with
future policy and regulatory outcomes. In a conditional asset pricing model with time-varying volatility in the consumption
growth process, Bali and Zhou (2016) find a positive relation between volatility uncertainty and future stock returns. Bali,
Brown, and Tang (2016) show that macroeconomic uncertainty is priced in the cross-section of stock returns.
6
3. Data and variable definitions
This section first describes the data on cross-sectional dispersion in economic forecasts, and then introduces an index of economic disagreement. Finally, we provide the definitions of the stock-level
predictive variables used in cross-sectional return predictability.
3.1. Cross-sectional dispersion in economic forecasts
The Federal Reserve Bank of Philadelphia releases measures of cross-sectional dispersion in economic
forecasts from the Survey of Professional Forecasters, calculating the degree of disagreement between
the expectations of different forecasters.5 In our empirical analyses, we use the cross-sectional dispersion in quarterly forecasts for the U.S. real gross domestic product (GDP) growth, real GDP (RGDP)
level, nominal GDP (NGDP) level, NGDP growth, GDP price index level, GDP price index growth (inflation rate forecast), and unemployment rate. These measures are model-independent, nonparametric
measures of economic disagreement obtained from divergence of opinion among professional forecasters.6 The cross-sectional dispersion measures are defined as the percent difference between the 75th
and 25th percentiles (the interquartile range) of the projections for quarterly growth or levels:
Dispersion Measure(Growth) = 100 × log(75th Growth/25th Growth),
Dispersion Measure(Level) = 100 × log(75th Level/25th Level).
(1)
(2)
Panel A in Table A1 of the online appendix presents the descriptive statistics of the quarterly crosssectional dispersion measures for the sample period 1968:Q4−2016:Q4. The volatility and max-min
differences of the dispersion measures are quite high compared to their means, implying significant
5 The
Survey of Professional Forecasters is the oldest quarterly survey of macroeconomic forecasts in the United States.
The survey began in 1968 and used to be conducted by the American Statistical Association and the National Bureau of
Economic Research. The Federal Reserve Bank of Philadelphia took over the survey in 1990.
6 The Federal Reserve Bank of Philadelphia provides a partial list of the forecasters who participated in the survey. Professional forecasters are generally academics at research institutions and economists at major investment banks, consulting
firms, and central banks in the United States and abroad. The number of professional forecasters who participate in the
survey changes over time. Figure A1 of the online appendix presents the number of forecasts for quarterly RGDP level over
the sample period 1968:Q4−2016:Q4. The numbers of forecasts for the other six macro variables are almost identical for the
period 1968−2016.
7
time-series variation. Panel B of Table A1 shows that the cross-sectional dispersion measures are
generally highly correlated with each other (in the range of 0.76 and 0.95), and reflect common sources
of ambiguity about the state of the aggregate economy. On the other hand, some of the correlations
reported in Panel B of Table A1 are lower, in the range of 0.35 and 0.53, implying that each dispersion
measure has the potential to capture different aspects of disagreement over economic fundamentals.
Figure A2 of the online appendix displays the quarterly time-series plots of the cross-sectional
dispersion measures for the sample period 1968:Q4−2016:Q4. The visual depiction of the dispersion
measures in Figure A2 indicates that these economic disagreement measures closely follow large falls
and rises in financial and economic activity. Specifically, economic disagreement is higher during economic and financial market downturns. Similarly, disagreement is higher during periods corresponding
to high levels of default and credit risk as well as stock market crashes. Lastly, disagreements about
inflation, output growth and unemployment are generally higher during bad states of the economy,
corresponding to periods of high unemployment, low output growth, and low economic activity.7
3.2. Economic disagreement index
In this section, we introduce a broad index of economic disagreement based on innovations in the
cross-sectional dispersion in economic forecasts. As presented in the last column of Table A1, Panel
A, the cross-sectional dispersion measures are highly persistent. The first-order autocorrelation, AR(1),
coefficients are in the range of 0.29 and 0.74. Since the AR(1) coefficients are significantly below one,
unexpected change (or innovation) in the economic predictions of professional forecasters is not defined
with a simple change in dispersion measures. Instead, we estimate the following autoregressive process
of order one, AR(1), for each dispersion measure:8
Zt
= ω0 + ω1 Zt−1 + εt ,
7 Specifically,
(3)
the peaks in Figure A2 closely follow major economic and financial crises such as the 1973 oil crisis, the
1973−1974 stock market crash, the 1979−1982 high interest rate period, the 1980s Latin American debt crisis, the 1989-1991
savings and loan crisis in the United States, the recession of the early 1990s, the 1997−1998 Asian and Russian financial
crises, the recession of the early 2000s, and the recent global financial crisis (2007-2009).
8 At an earlier stage of the study, we replicate our main findings using MA(1) and ARMA(1,1) specifications and the
results turn out to be very similar to those reported in our tables.
8
where Zt is one of the seven measures of cross-sectional dispersion in economic forecasts, that is, the
RGDP growth and level, the NGDP growth and level, the GDP price index growth and level (proxying
for the inflation rate), and the unemployment rate.
For each dispersion measure and for each quarter, we estimate equation (3) using the expanding
window with the first estimation window set to be the first 20 quarters and then updated on a quarterly
basis, and generate the standardized residuals from the AR(1) model. The economic disagreement index (DSGRAV G ) is defined as the average of the standardized residuals for the seven dispersion measures
and can be viewed as a broad measure of the shock to dispersion in the forecasts of output, inflation
and unemployment.
The first-order autocorrelation coefficients of the innovations in dispersion measures are in the
range from −0.07 to −0.20, much lower than the serial correlations in the raw measures of dispersion (in absolute magnitude). This result indicates that the standardized residuals from the AR(1)
model successfully remove the predictable component of the dispersion measures so that the economic
disagreement index (DSGRAV G ) is a measure of disagreement shock that captures different aspects of
disagreement over economic fundamentals and also reflects unexpected news or surprise about the state
of the aggregate economy.
It is important to note that the economic disagreement index is generated for each quarter using past
information only, so that there is no look-ahead bias in our empirical analyses. Moreover, the economic
disagreement index is formed based on ex-ante predictions of professional forecasters so that the exposure of stocks to innovations in dispersion measures is an ex-ante measure of the disagreement beta.
Thus, we investigate the out-of-sample cross-sectional predictive power of economic disagreement.
One may argue that not all dispersion measures contribute equally to overall disagreement in the
macro economy. To address this potential concern, we introduce an alternative measure of the economic disagreement index using principal component analysis (PCA). Specifically, we extract the first
principal component of the innovations in seven dispersion measures without imposing equal weights.
This alternative index is defined as the first principal component of the standardized residuals from
9
AR(1) regressions, Stdres, which explains about two-thirds of the total variation in these measures.
Hence, we obtain a broad measure of economic disagreement using this first principal component:9
DSGRtPCA = w1,t × StdrestRGDP−growth + w2,t × StdrestRGDP−level +
(4)
w3,t × StdrestNGDP−growth + w4,t × StdrestNGDP−level +
w5,t × StdrestPGDP−growth + w6,t × StdrestPGDP−level +
w7,t × StdresUNEMP
.
t
Although the weights attached to the standardized residuals are not reported, the economic disagreement index obtained from the first principal component (DSGRPCA ) loads fairly evenly on the
innovations in seven dispersion measures, suggesting a strong correlation with the simpler disagreement index (DSGRAV G ) defined as the average of the standardized residuals.10
Figure 1 depicts the two broad indices of economic disagreement (DSGRAV G and DSGRPCA ) which
are almost identical (with a correlation of 0.98). Similar to our findings for individual dispersion measures (shown in Figure A2), the broad index of economic disagreement is generally higher during
bad states of the economy, corresponding to periods of high unemployment, low output growth, and
low economic activity. The economic disagreement index also tracks large fluctuations in business
conditions. Since these two indices of economic disagreement (DSGRAV G and DSGRPCA ) are almost
identical, in our follow-up empirical analyses, we use DSGRAV G and call it DSGR for notational simplicity.
9 Note
that we do not have a look-ahead bias when estimating the first principal component of the residuals because we
use the expanding window with the first estimation window set to be the first 20 quarters and then updated on a quarterly
basis. Hence, the weights (w1,t ...w7,t ) attached to the standardized residuals in equation (4) are time dependent.
10 Ex-ante measures of dispersion provided by the Federal Reserve Bank of Philadelphia are based on the 1-, 2-, 3-, and
4-quarter ahead predictions of professional forecasters on output growth, inflation, and unemployment. At an earlier stage
of the study, we examined the predictive power of the disagreement beta obtained from alternative forecast horizons and our
main finding from 2-, 3-, and 4-quarter ahead predictions turned out to be similar to those reported in the paper. We also used
raw measures of dispersion, instead of the index of disagreement shock. The cross-sectional return predictability results from
the level of dispersion measures and the index of disagreement level turned out to be similar to those presented in our tables.
10
3.3. Cross-sectional return predictors
Our stock sample includes all common stocks traded on the NYSE, Amex, and Nasdaq exchanges from
July 1963 through December 2016. We eliminate stocks with a price per share less than $5 or more
than $1,000. The daily and monthly return and volume data are from the CRSP. We adjust stock returns
for delisting to avoid survivorship bias (Shumway 1997).11 Accounting variables are obtained from the
merged CRSP-Compustat database. Analysts’ earnings forecasts come from the Institutional Brokers’
Estimate System (I/B/E/S) dataset and cover the period from 1983 to 2016. In this section, we provide
the definitions of the stock-level variables used in predicting cross-sectional returns.
For each stock and for each quarter in our sample, we estimate the disagreement beta from the
quarterly rolling regressions of excess stock returns on the economic disagreement index over a 20quarter fixed window:
Ri,t = αi,t + βDSGR
· DSGRt + βMKT
· MKTt + εi,t ,
i,t
i,t
(5)
where Ri,t is the excess return on stock i in quarter t, DSGRt is the economic disagreement index
in quarter t, defined as the average of the standardized residuals in equation (3) for seven dispersion
measures, and MKTt is the excess market return in quarter t; βDSGR
and βMKT
are, respectively, the
i,t
i,t
disagreement beta and the market beta for stock i in quarter t.
Following Fama and French (1992), we estimate the market beta of individual stocks using monthly
returns over the prior 60 months if available (or a minimum of 24 months). Firm size (SIZE) is computed as the natural logarithm of the product of the price per share and the number of shares outstanding
(in millions of dollars). Following Fama and French (1992, 1993, 2000), the natural logarithm of the
book-to-market equity ratio at the end of June of year t, denoted BM, is computed as the book value
of stockholder equity plus deferred taxes and investment tax credit (if available) minus the book value
of preferred stock at the end of the last fiscal, t − 1, scaled by the market value of equity at the end of
11 Specifically,
when a stock is delisted, we use the delisting return from the CRSP, if available. Otherwise, we assume the
delisting return is -100%, unless the reason for delisting is coded as 500 (reason unavailable), 520 (went over the counter),
551–573, 580 (various reasons), 574 (bankruptcy), or 584 (does not meet exchange financial guidelines). For these observations, we assume that the delisting return is -30%.
11
December of year t − 1. Depending on availability, the redemption, liquidation, or par value (in that
order) is used to estimate the book value of preferred stock.
Following Jegadeesh and Titman (1993), momentum (MOM) is the cumulative return of a stock
over a period of 11 months ending one month prior to the portfolio formation month. Following Jegadeesh (1990), short-term reversal (REV ) is defined as the stock return over the prior month.
Following Harvey and Siddique (2000), the stock’s monthly co-skewness (COSKEW ) is defined
as:
E εi,t R2m,t
,
COSKEWi,t = r h i
2 2
E εi,t E Rm,t
(6)
where εi,t = Ri,t − (αi + βi Rm,t ) is the residual from the regression of the excess stock return (Ri,t )
against the contemporaneous excess return on the CRSP value-weighted index (Rm,t ) using the monthly
return observations over the prior 60 months (if at least 24 months are available). The risk-free rate is
measured by the return on one-month Treasury bills.12
Following Amihud (2002), we measure the illiquidity of stock i in month t, denoted ILLIQ, as the
ratio of the daily absolute stock return to the daily dollar trading volume averaged within the month:
|Ri,d |
,
ILLIQi,t = Avg
VOLDi,d
(7)
where Ri,d and VOLDi,d are the daily return and dollar trading volume for stock i on day d, respectively.13 A stock is required to have at least 15 daily return observations in month t. Amihud’s illiquidity measure is scaled by 106 .
12 At
an earlier stage of the study, following Mitton and Vorkink (2007), co-skewness is defined as the estimate of γi,t in
the regression using the monthly return observations over the prior 60 months with at least 24 monthly return observations
available: Ri,t = αi + βi Rm,t + γi,t R2m,t + εi,t , where Ri,t and Rm,t are the monthly excess returns on stock i and the CRSP
value-weighted index, respectively. The risk-free rate is measured by the return on one-month Treasury bills. In addition to
using monthly returns over the past five years, we use continuously compounded daily returns over the past 12 months when
estimating the co-skewness of individual stocks. Our main findings from these two alternative measures of co-skewness turn
out to be very similar to those reported in our tables and they are available upon request.
13 Following Gao and Ritter (2010), we adjust for institutional features so that the Nasdaq and NYSE/Amex volumes are
counted. Specifically, divisors of 2.0, 1.8, 1.6, and 1.0 are applied to the Nasdaq volume for the periods prior to February
2001, between February 2001 and December 2001, between January 2002 and December 2003, and in January 2004 and later
years, respectively.
12
Following Diether, Malloy, and Scherbina (2002), analyst earnings forecast dispersion (DISP) is
defined as the standard deviation of annual earnings-per-share forecasts scaled by the absolute value of
the average outstanding forecast.
Following Ang, Hodrick, Xing, and Zhang (2006), the monthly idiosyncratic volatility of stock i
(IVOL) is computed as the standard deviation of the daily residuals in a month from the regression:
Ri,d = αi + βi Rm,d + γi SMBd + ϕi HMLd + εi,d ,
(8)
where Ri,d and Rm,d are, respectively, the excess daily returns on stock i and the CRSP value-weighted
index, and SMBd and HMLd are, respectively, the daily size and book-to-market factors of Fama and
French (1993).
Following Ang et al. (2006), we estimate the implied market volatility beta from the bivariate
time-series regressions of excess stock returns on the excess market returns and the changes in implied
volatility using daily data in a month:
V XO
V XO
Ri,d = αi,daily + βMKT
+ εi,d ,
i,daily · Rm,d + βi,daily · ∆VARd
(9)
where Ri,d is the excess return of stock i on day d, Rm,d is the excess market return on day d, ∆VARVd XO
XO is the implied
is the change in the S&P 100 index option implied variance (VXO) on day d, and βVi,daily
market volatility beta of stock i in month t.
Following Bali, Cakici, and Whitelaw (2011) and Bali, Brown, Murray, and Tang (2016), we measure demand for lottery-like stocks using MAX, calculated as the average of the five highest daily
returns of the stock during the given month t. We require a minimum of 15 daily return observations
within the given month to calculate MAX.
We control for the industry effect by assigning each stock to one of the 10 industries based on its
four-digit Standard Industrial Classification (SIC) code. The industry definitions are obtained from the
online data library of Kenneth French.
13
4. Empirical results
In this section, we conduct parametric and nonparametric tests to assess the predictive power of the
disagreement beta over future stock returns. First, we start with a univariate portfolio-level analysis.
Second, we examine the average characteristics of stocks with low vs. high disagreement beta. Third,
we conduct bivariate portfolio-level analyses to examine the predictive power of the disagreement beta
after controlling for well-known stock characteristics and risk factors. Fourth, we present firm-level
Fama-MacBeth cross-sectional regression results. Fifth, we investigate the significance of time-series
variation in economic disagreement premium. Sixth, we provide a summary of the results from a
battery of robustness checks. Finally, we introduce a factor capturing the returns associated with the
disagreement beta and then investigate the ability of well-known factor models to explain the newly
proposed disagreement beta factor.
4.1. Univariate portfolio-level analysis
Exposures of individual stocks to economic disagreement are obtained from quarterly rolling regressions of excess stock returns on the economic disagreement index using a 20-quarter fixed window
estimation. The first set of disagreement betas (βDSGR ) are obtained using the sample from 1969:Q1
to 1973:Q4. Then, these quarterly disagreement betas are used to predict the monthly cross-sectional
stock returns in the following three months (January 1974, February 1974, and March 1974). This
quarterly rolling regression approach is used until the sample is exhausted in December 2016. The
cross-sectional return predictability results are reported from January 1974 to December 2016.
Table 1 presents the univariate portfolio results. For each month, we form decile portfolios by
sorting individual stocks based on their disagreement betas (βDSGR ), where decile 1 contains stocks
with the lowest βDSGR during the past quarter, and decile 10 contains stocks with the highest βDSGR
during the previous quarter. The first column in Table 1 reports the average disagreement betas for the
decile portfolios formed on βDSGR using the CRSP breakpoints with an equal number of stocks in the
14
decile portfolios. The last four columns in Table 1 present the average excess returns and the 5-factor
alphas on the value-weighted and equal-weighted portfolios, respectively.
The first column of Table 1 shows that moving from decile 1 to decile 10, there is significant
cross-sectional variation in the average values of βDSGR ; the average disagreement beta increases from
−23.95 to 30.27. Another notable point in Table 1 is that for the value-weighted portfolio, the nextmonth average excess return decreases almost monotonically from 0.93% to 0.44% per month, when
moving from the lowest to the highest βDSGR decile. The average return difference between decile
10 (high-βDSGR ) and decile 1 (low-βDSGR ) is −0.50% per month with a Newey-West (1987) t-statistic
of −2.45.14 This result indicates that stocks in the lowest βDSGR decile generate about 6.24% higher
annual returns compared to stocks in the highest βDSGR decile.
In addition to the average raw returns, Table 1 presents the magnitude and statistical significance of
the differences in intercepts (5-factor alpha) from the regression of the high-minus-low portfolio returns
on a constant, excess market return (MKT), a size factor (SMB), a book-to-market factor (HML), a
momentum factor (MOM), and a liquidity factor (LIQ), following Fama and French (1993), Carhart
(1997), and Pastor and Stambaugh (2003).15 As shown in the third column of Table 1, for the valueweighted portfolio, the 5-factor alpha decreases almost monotonically from 0.33% to −0.32% per
month, when moving from the lowest to the highest βDSGR decile. The difference in alphas between the
high-βDSGR and low-βDSGR portfolios is −0.65% per month with a Newey-West t-statistic of −3.06,
indicating that a zero-cost portfolio that buys stocks in the lowest disagreement-beta decile and shorts
stocks in highest disagreement-beta decile generates a risk-adjusted return of 7.8% per annum. This
also shows that after controlling for the well-known market, size, book-to-market, momentum, and
liquidity factors, the return difference between the high-βDSGR and low-βDSGR stocks remains negative
and statistically significant.
As presented in the last two columns of Table 1, similar results are obtained from the equalweighted portfolios of βDSGR . The average excess returns and the 5-factor alphas on the disagreement
beta portfolios decrease almost monotonically. The average return and alpha differences between the
14 Newey-West
(1987) adjusted standard errors are computed using six lags.
excess market returns (MKT) and the factors small-minus-big (SMB), high-minus-low (HML), and winner-minuslosers (UMD) are from Kenneth French’s data library. The liquidity factor (LIQ) is from Lubos Pastor’s data library.
15 The
15
high-βDSGR and low-βDSGR portfolios are negative and highly significant with Newey-West t-statistics
larger than three in absolute magnitude.
Next, we investigate the source of the risk-adjusted return difference between the high-βDSGR and
low- βDSGR portfolios: Is it due to outperformance by low-βDSGR stocks, underperformance by highβDSGR stocks, or both? For this, we focus on the economic and statistical significance of the riskadjusted returns of decile 1 versus decile 10. As reported in Table 1, for both value-weighted and
equal-weighted portfolios, the 5-factor alphas of stocks in decile 1 (low-βDSGR stocks) are significantly positive, whereas the 5-factor alphas of stocks in decile 10 (high-βDSGR stocks) are significantly
negative. Hence, we conclude that the significantly negative alpha spread between high-βDSGR and
low-βDSGR stocks is due to both the outperformance by low-βDSGR stocks and the underperformance by
high-βDSGR stocks.16
These results are consistent with a well-established literature that distinguishes risk and uncertainty.
Due to their negative disagreement betas, the returns of individual stocks in decile 1 are negatively associated with increases in economic disagreement, hence ambiguity-averse investors would demand extra
compensation in the form of higher expected return to hold these stocks with negative βDSGR (stocks
with high disagreement risk). On the other hand, with their positive disagreement betas, the returns
of individual stocks in decile 10 are positively associated with increases in economic disagreement.
Since stocks with positive βDSGR would be viewed as good hedging instruments at times of increased
economic disagreement, investors are willing to pay higher prices for these stocks with large hedging
benefits and accept lower returns.
Of course, the disagreement betas documented in Table 1 are for the portfolio formation month
and, not for the subsequent month over which we measure average returns. Investors may pay high
prices for stocks that have exhibited high disagreement beta in the past in the expectation that this
behavior will be repeated in the future, but a natural question is whether these expectations are rational.
Table A2 of the online appendix investigates this issue by presenting the average quarter-to-quarter
16 At an earlier stage of the study, we form decile portfolios based on the NYSE breakpoints, which are used to alleviate the
concerns that the CRSP decile breakpoints are distorted by the large number of small Nasdaq and Amex stocks (Fama and
French, 1992). The results from the NYSE breakpoints turn out to be similar to those reported in Table 1 and available upon
request.
16
portfolio transition matrix. Specifically, Panel A of Table A2 presents the average probability that a
stock in decile i (defined by the rows) in one quarter will be in decile j (defined by the columns) in
the subsequent quarter. If the disagreement betas were completely random, then all the probabilities
should be approximately 10%, since a high or low disagreement beta in one quarter should say nothing
about the disagreement beta in the following quarter. Instead, all the diagonal elements of the transition
matrix exceed 10%, illustrating that the disagreement beta is highly persistent. Of greater importance,
this persistence is especially strong for the extreme portfolios. Panel A shows that for the one-quarterahead persistence of βDSGR , stocks in decile 1 (decile 10) have a 74.11% (72.98%) chance of appearing
in the same decile next quarter. Similarly, Panel D of Table A2 shows that for the four-quarter-ahead
persistence of βDSGR , stocks in decile 1 (decile 10) have a 53.82% (54.42%) chance of appearing in the
same decile the next four quarters.
These results show that the estimated historical disagreement betas successfully predict future disagreement betas and hence are good proxies for the true conditional betas. Persistence identified from
transition matrices also indicate that the disagreement betas are not simply characteristics of firms that
result in differences in expected returns, but proxies for a source of economic disagreement.
4.2. Average stock characteristics
In this section, we examine the average characteristics of stocks with low vs. high disagreement beta
based on the Fama and MacBeth (1973) cross-sectional regressions. We present the time-series averages of the slope coefficients from the regressions of the disagreement beta (βDSGR ) on the stock-level
characteristics and risk factors. Monthly cross-sectional regressions are run for the following econometric specification and nested versions thereof:
βDSGR
= λ0,t + λ1,t Xi,t + εi,t ,
i,t
(10)
where βDSGR
is the disagreement beta of stock i in month t and Xi,t is a collection of stock-specific
i,t
variables observable at time t for stock i (market beta, size, book-to-market, momentum, short-term
reversal, illiquidity, co-skewness, idiosyncratic volatility, analyst dispersion, market volatility beta, and
17
MAX). The cross-sectional regressions are run at a monthly frequency from January 1974 to December
2016.
Columns (1) and (10) of Table 2 show that the average slope coefficients on βMKT
and βVi,tXO are
i,t
positive and significant, implying that stocks with high disagreement beta (and low returns/alpha) have
high market beta and high market volatility beta. This result is in line with earlier studies (e.g., Frazzini
and Pedersen (2014) and Ang et al. (2006)), providing evidence that stocks with higher βMKT
and
i,t
higher βVi,tXO generate lower one-month-ahead returns and alpha. Column (3) reports that the average
slope coefficient on BM is significantly negative. This result, indicating that stocks with low disagreement beta (and high returns/alpha) are value stocks, is also consistent with Fama and French (1992,
1993) that value stocks generate higher average returns and alpha, compared to growth stocks. Column
(7), (8), and (11) show that the average slopes on COSKEW, IVOL, and MAX are positive and significant, indicating that stocks with low disagreement beta (and high returns/alpha) are negatively skewed,
and they have low volatility and low MAX. These results are in agreement with Harvey and Siddique
(2000), Ang et al. (2006), and Bali et al. (2011) that stocks with high co-skewness, high volatility, and
high MAX generate lower one-month-ahead returns and alpha.
The last column in Table 2 shows that when we include all variables simultaneously, the crosssectional relations between the disagreement beta and most of the aforementioned firm characteristics
become weaker or insignificant. The only variables that remain significantly connected to the disagreement beta are the market beta, co-skewness, and idiosyncratic volatility, indicating that stocks with
high disagreement beta have high market beta, high co-skewness, and high idiosyncratic volatility after
controlling for all other variables.
4.3. Bivariate portfolio-level analysis
This section examines the relation between the disagreement beta and future stock returns after controlling for the well-known cross-sectional return predictors. We perform bivariate portfolio sorts on the
disagreement beta (βDSGR ) in combination with the market beta (βMKT ), the log market capitalization
(SIZE), the log book-to-market ratio (BM), momentum (MOM), short-term reversal (REV), illiquidity
18
(ILLIQ), co-skewness (COSKEW), analyst dispersion (DISP), idiosyncratic volatility (IVOL), market
volatility beta (βV XO ), and lottery demand (MAX). Table 3 reports the value-weighted portfolio results
from these conditional bivariate sorts.
We control for the market beta (βMKT ) by first forming decile portfolios ranked based on βMKT .
Then, within each βMKT decile, we sort stocks into decile portfolios ranked based on the disagreement
beta (βDSGR ) so that decile 1 (decile 10) contains stocks with the lowest (highest) βDSGR values. The
first column of Table 3 averages the value-weighted portfolio returns across the ten βMKT deciles to
produce decile portfolios with dispersion in βDSGR but that contain all the stocks’ market betas. This
procedure creates a set of βDSGR portfolios with very similar levels of market beta, and hence these
βDSGR portfolios control for differences in market beta. The row (High−Low) in the first column of
Table 3 shows that after controlling for the market beta, the 5-factor alpha spread between the highβDSGR and low-βDSGR value-weighted portfolios is −0.57% per month with a Newey-West t-statistic
of −3.55. Thus, the market beta does not explain the high (low) returns on low disagreement (high
disagreement) beta stocks.
Table 3 shows that after controlling for the other cross-sectional return predictors (size, book-tomarket, momentum, short-term reversal, illiquidity, co-skewness, analyst dispersion, volatility, market
volatility beta, and lottery demand), the 5-factor alpha differences between the high-βDSGR and lowβDSGR portfolios are in the range of −0.40% and −0.70% per month and highly significant. These
results indicate that the well-known cross-sectional effects (including market beta, co-skewness, and
idiosyncratic volatility) cannot explain the low returns to stocks with high disagreement beta.
4.4. Stock level cross-sectional regressions
In this section, we examine the cross-sectional relation between the disagreement beta and expected
returns at the stock level using the Fama and MacBeth (1973) regressions. We present the time-series
averages of the slope coefficients from the regressions of one-month-ahead stock returns the disagreement beta (βDSGR ) and the market beta (βMKT ) with and without control variables. The average slopes
provide standard Fama-MacBeth tests for determining which explanatory variables on average have
19
non-zero premiums. Monthly cross-sectional regressions are run for the following econometric specification and nested versions thereof:
Ri,t+1 = λ0,t + λ1,t · βDSGR
+ λ2,t · βMKT
+ λ3,t · Xi,t + εi,t+1 ,
i,t
i,t
(11)
where Ri,t+1 is the realized excess return on stock i in month t + 1, βMKT
is the market beta of stock
i,t
i in month t, βDSGR
is the quarterly disagreement beta of stock i in months t, t − 1, and t − 2, and Xi,t
i,t
is a collection of stock-specific control variables observable at time t for stock i (size, book-to-market,
momentum, short-term reversal, illiquidity, co-skewness, analyst dispersion, idiosyncratic volatility,
market volatility beta, and lottery demand). The cross-sectional regressions are run at a monthly frequency from January 1974 to December 2016. When calculating the standard errors of the average
slope coefficients, we take into account autocorrelation and heteroscedasticity in the time-series slope
coefficients from cross-sectional regressions. The Newey-West (1987) adjusted standard errors are
computed with six lags.
Panel A of Table 4 reports the time series averages of the slope coefficients and the Newey-West
t-statistics in parentheses. The univariate regression results reported in the first column indicate a
negative and statistically significant relation between the disagreement beta and the cross-section of
future stock returns. The average slope from the monthly regressions of realized returns on βDSGR
i,t
alone is −0.011 with a t-statistic of −3.11.
To determine the economic significance of this average slope coefficient, we use the average values
of the disagreement betas in the decile portfolios. Table 1 shows that the difference in βDSGR
values bei,t
tween average stocks in the first and 10th deciles is 54.22[= 30.27 − (−23.95)]. If a stock were to move
from the first to the 10th decile of βDSGR
, what would be the change in that stock’s expected return?
i,t
The average slope coefficient of −0.011 on βDSGR
in Panel A of Table 4 represents an economically
i,t
significant decrease of 0.60% per month, [−0.011 × 54.22 = −0.60%], in the average stock’s expected
return for moving from the first to the 10th decile of βDSGR
.
i,t
The second column in Panel A of Table 4 controls for the market beta (βMKT ), a cross-sectional
regression specification corresponding to an extended CAPM. The third column in Panel A of Table
20
4 controls for the market beta (βMKT ), market capitalization (SIZE), and the book-to-market (BM),
a cross-sectional regression specification corresponding to the 3-factor model of Fama and French
(1993). The fourth column controls for the market beta (βMKT ), market capitalization (SIZE), the bookto-market (BM), and momentum (MOM), a cross-sectional regression specification corresponding to
the 4-factor model of Fama and French (1993) and Carhart (1997). In all three specifications, the
average slopes from the monthly regressions of realized returns on βDSGR
are negative and highly
i,t
significant; in the range of −0.011 and −0.013 with Newey-West t-statistics ranging from −3.60 to
−3.81.
Columns (5) through (11) include each control variable one-by-one to the baseline multivariate
specification with βDSGR , βMKT , SIZE, BM, and MOM. Columns (5)−(11) show that including REV,
ILLIQ, COSKEW, DISP, IVOL, βV XO , and MAX one-by-one, the average slope coefficient on βDSGR
remains negative, in the range of −0.006 and −0.012, and highly significant with t-statistics ranging
from −3.36 to −4.00.
In Columns (2) to (11), the coefficients of the individual control variables are also as expected;
the size effect is negative and significant, the value effect is positive and significant, stocks exhibit
intermediate-term momentum and short-term reversals, and the average slopes of co-skewness, idiosyncratic volatility, MAX, analyst dispersion, and the market volatility beta are negative and significant.
The average slope of the market beta is positive but statistically insignificant, which contradicts the
implications of the CAPM but is consistent with prior empirical evidence. The average slope of illiquidity is negative and significant, contradicting the positive illiquidity premium identified by theoretical
models but is consistent with some prior empirical evidence.
The last column of Table 4 controls for all variables simultaneously, including the market beta, size,
book-to-market, momentum, short-term reversal, illiquidity, co-skewness, idiosyncratic volatility, analyst dispersion, market volatility beta, and MAX. In this more general specification, the average slope
of βDSGR remains negative, −0.006, and highly significant with a Newey-West t-statistic of −3.06.
The average slope coefficient of −0.006 for βDSGR implies that a portfolio short-selling stocks with the
21
highest disagreement beta (in decile 10) and buying stocks with the lowest disagreement beta (in decile
1) generates a return in the following month of about 0.33%, controlling for all else.
In Panel B of Table 4, we control for the industry effect. For each month, we assign each stock to
one of the 10 industries based on the four-digit SIC code and replicate our firm-level cross-sectional
regressions with and without the large set of firm characteristics and risk factors.
The univariate regression results reported in the first column of Table 4, Panel B indicate a negative
and statistically significant relation between the disagreement beta and future stock returns after controlling for the industry effect; the average slope coefficient is −0.010 with a Newey-West t-statistic
of −3.43, implying an economically and statistically significant decrease of 0.54% per month in the
average stock’s expected return for moving from the first to the 10th decile of βDSGR .
Columns (2) through (12) in Panel B of Table 4 examine the significance of disagreement beta after
controlling for the industry effect and a sequential set of other cross-sectional predictors. Columns (2),
(3), and (4) show that when the industry as well as the market, size, book-to-market and momentum
effects are controlled for, the average slopes from the monthly regressions of returns on βDSGR are
negative and highly significant. Columns (5) through (11) show that after controlling for the industry
effect and other well-known predictors (REV, ILLIQ, COSKEW, DISP, IVOL, βV XO , and MAX) oneby-one in the baseline multivariate specification with βDSGR , βMKT , SIZE, BM, and MOM, the average
slope coefficient on βDSGR remains negative, in the range of −0.006 and −0.010, and highly significant
with t-statistics ranging from −3.35 to −3.95. The last column presents results from the most general
specification including all other control variables along with the industry effect. As shown in Column
(12), the average slope of βDSGR remains negative at −0.006 and highly significant with a t-statistic of
−3.02. This average slope coefficient on βDSGR implies that a portfolio short-selling stocks with the
highest disagreement beta and buying stocks with the lowest disagreement beta generates a return in
the following month of about 30 basis points, controlling for the industry effect and all else.
22
4.5. Does disagreement premium vary over time?
We have so far provided an average estimate of the disagreement premium over the period 1974−2016.
In this section, we test if the cross-sectional relation between the disagreement beta and future stock
returns changes over time. Specifically, we investigate whether the disagreement premium is higher
during recessions, when economic activity (including investment and consumption) is low and the
marginal utility of wealth is high. We determine the states of the economy based on the National
Bureau of Economic Research (NBER) recession dummy taking the value of one if the U.S. economy
is in recession as determined by the NBER.
To provide a robustness check, the states of the economy are also determined based on the Chicago
FED National Activity Index (CFNAI).17 In Figure 2, the solid line depicts the 3-month moving average of the monthly slope coefficients of the disagreement beta and the dashed line depicts the 3-month
moving average of the monthly CFNAI. The monthly slope coefficients move very closely with the
CFNAI and become negative and large in absolute magnitude when the CFNAI takes negative values indicating economic downturns. We also compute the correlation between the 3-month moving
average of the monthly slope coefficients and the 3-month moving average of the CFNAI, and find
a significantly positive correlation of 0.33, indicating higher disagreement premium during economic
recessions.
In addition to the results from firm-level Fama-MacBeth regressions, we now test if the portfoliolevel analyses provide evidence suggesting higher disagreement premium during economic downturns.
Specifically, we had a closer look at the univariate portfolios of stocks sorted by βDSGR during recessionary and expansionary periods. The 5-factor alpha spread between the high-βDSGR and low-βDSGR
portfolios is −1.29% per month (t-statistic = −2.66) during the NBER recessions and −0.97% per
month (t-statistic = −2.34) during the CFNAI-based recessionary periods, whereas the 5-factor alpha
spreads are much smaller in absolute magnitude during expansionary periods; −0.63% per month (t17 The CFNAI is a monthly index designed to assess overall economic activity. It is the weighted average of 85 monthly
economic indicators and is constructed to have an average value of zero and a standard deviation of one. Since economic
activity tends toward the trend growth rate over time, a positive index reading corresponds to growth above the trend and
a negative index reading corresponds to growth below the trend. A CFNAI index value below −0.7 following a period of
economic expansion indicates the increasing likelihood that a recession has begun.
23
statistic = −2.70) during the NBER expansions and −0.64% per month (t-statistic = −2.59) during the
CFNAI-based expansionary periods.
Both portfolio-level analyses and cross-sectional regression results are consistent with the theoretical prediction that the disagreement premium is higher during bad states of the economy. During
recessions, economic disagreement is much higher and the returns of individual stocks with negative
disagreement beta decrease substantially with increases in economic disagreement. Hence, ambiguityaverse investors would demand extra compensation in the form of higher expected return to hold these
stocks with negative βDSGR (stocks with extremely high disagreement risk). On the other hand, during
economic downturns, the returns of individual stocks with positive disagreement beta increase with
increases in economic disagreement. Since stocks with positive βDSGR would be viewed as important
hedging instruments at times of increased economic disagreement, investors would be willing to pay
higher prices for these stocks with positive βDSGR (stocks with extremely large hedging benefits) and
accept lower returns during economic downturns.
4.6. Robustness checks
We provide a battery of robustness checks in this section. First, we test whether using a different
factor model in the estimation of risk-adjusted returns of βDSGR -sorted portfolios changes our main
findings. We have so far used the 5-factor model of Fama-French (1993), Carhart (1997), and Pastor and
Stambaugh (2003) with the market (MKT), size (SMB), book-to-market (HML), momentum (UMD),
and liquidity (LIQ) factors.
In Table 5, we present results from the CAPM with MKT; the 3-factor (FF3) model of Fama and
French (1993) with MKT, SMB, and HML; the 4-factor (FFC) model of Fama-French (1993) and
Carhart (1997) with MKT, SMB, HML, and UMD; the 5-factor model of Fama and French (2015) with
MKT, SMB, HML, the profitability (RMW) and investment (CMA) factors; the 7-factor (FF5CPS)
model, which combines the 5-factor (FF5) model of Fama and French (2015) with Carhart (1997) and
Pastor and Stambaugh (2003), with MKT, SMB, HML, UMD, LIQ, RMW, and CMA factors; the 4factor (Q-factor) model of Hou, Xue, and Zhang (2015) with MKT, the size (Rsize ), the profitability
24
(Rroa ) and the investment (Ria ) factors; and the 6-factor (QCPS) model, which combines the Q-factor
model of Hou, Xue, and Zhang (2015) with Carhart (1997), and Pastor and Stambaugh (2003), with
MKT, Rsize , Rroa , Ria , UMD, and LIQ factors.
The last row of Table 5 shows that the alpha spreads for the value-weighted portfolios of βDSGR
are in the range of −0.53% and −0.63% per month and highly significant with t-statistics ranging
from −2.35 to −2.82. These results indicate that our main finding is not sensitive to the choice of a
factor model, i.e., the cross-sectional relation between the disagreement beta and risk-adjusted returns
is negative and highly significant with respect to a number of factor models widely used in the literature.
Second, we investigate whether our results are driven by small, illiquid, and low-priced stocks, or
stocks trading at the Amex and Nasdaq exchanges. As shown in Table 6, the disagreement premium is
highly significant in the cross-section of NYSE stocks, large stocks (with market capitalization greater
than the median NYSE size breakpoints), S&P 500 stocks, and the 1,000 and 500 largest and most
liquid stocks in the CRSP universe.
Third, we examine the long-term predictive power of the disagreement beta in Fama-MacBeth
cross-sectional regressions controlling for all variables used in Table 4. The results indicate that the
negative relation between the disagreement beta and future stock returns is not just a one-month affair.
Table 7 shows that the disagreement beta predicts cross-sectional variation in stock returns 12 months
into the future after controlling for a large set of well-known cross-sectional predictors.
Finally, we investigate the significance of disagreement premium for stocks in each of the 10 industries determined based on the four-digit SIC code; Non-durable, Durable, Manufacturing, Energy,
Hi-Tech, Telecom, Shops, Health, Utilities, and Other. The results provide evidence of a negative relation between the disagreement beta and future stock returns for all 10 industries except for the Utilities
industry, but the disagreement premium is significant for four industries out of 10. More specifically,
the disagreement premium is statistically significant and economically larger for stocks in Manufacturing, Shops, Hi-Tech, and Energy industry groups (in the range of −0.52% and −1.15% per month).
For the remaining five industries (Non-durable, Durable, Telecom, Health, and Other), the disagreement premium is negative, in the range of −0.16% and −0.46%, but statistically weak.
25
4.7. The disagreement beta factor
In this section, we propose a factor capturing the returns associated with the disagreement beta and
then investigate the ability of well-known factor models to explain the newly proposed disagreement
beta factor. We form a disagreement beta factor, using the factor-forming technique pioneered by
Fama and French (1993). At the end of each month, we sort all stocks into two groups based on
market capitalization (size), with the breakpoint dividing the two groups being the median market
capitalization of stocks traded on the NYSE. We independently sort all stocks into three groups based
on an ascending sort of the disagreement beta (βDSGR ) using the NYSE 30th and 70th percentile values
of βDSGR . The intersections of the two size groups and the three βDSGR groups generate six portfolios.
The disagreement beta factor return is taken to be the average return of the two value-weighted highβDSGR portfolios minus the average return of the two value-weighted low-βDSGR portfolios. As such, the
disagreement beta factor is designed to capture returns associated with disagreement premium while
maintaining neutrality to market capitalization.
The first column of Table 8 shows that the disagreement beta factor generates an average monthly
return of 0.24% with a Newey-West t-statistic of 2.55. We also estimate the alpha of the disagreement
beta factor with respect to a large set of well-known factors, including the market (MKT), the size
(SMB), the book-to-market (HML), the profitability (RMW) and the investment (CMA) factors of
Fama and French (1993, 2015); the momentum (UMD) factor of Carhart (1997); the liquidity (LIQ)
factor of Pastor and Stambaugh (2003); the size (Rsize ), the profitability (Rroa ) and the investment (Ria )
factors of Hou, Xue, and Zhang (2015); and the betting-against-beta (BAB) factor of Frazzini and
Pedersen (2014).18
Columns (2) through (7) in Table 8 demonstrate that without the BAB factor, the alphas of the
disagreement beta factor are significant from alternative models, in the range of 0.26% and 0.34% per
month, and highly significant with t-statistics ranging from 2.42 to 3.56.19 Similar results are obtained
18 MKT, SMB, HML, RMW, CMA and UMD factors are obtained from the online data library of Kenneth French. LIQ
and BAB factors are obtained from Lubos Pastor’s data library and AQR’s website, respectively. Rsize , Rroa , and Ria factors
are calculated following Hou, Xue, and Zhang (2015).
19 Note that the factor construction methodologies somewhat differ across these factors. In particular, the BAB factor is
rank-weighted, while the others are formed based on the value-weighted portfolios and NYSE breakpoints. That’s why we
investigate the explanatory power of the factor models with and without the BAB factor in Table 8.
26
after including the BAB to each factor model. As presented in columns (8)−(11), with the BAB factor,
the alphas are in the range of 0.27% and 0.29% per month and remain significant.
Another notable point in Table 8 is that the factor loadings are statistically insignificant for all
factors, except for the liquidity (LIQ) factor of Pastor and Stambaugh (2003) and for the market factor
in some specifications.20 This implies the SMB, HML, RMW, and CMA factors of Fama and French
(1993, 2015), the UMD factor of Carhart (1997), the Rsize , Rroa , and Ria factors of Hou, Xue, and Zhang
(2015), and the BAB factor of Frazzini and Pedersen (2014) are not significantly correlated with the
disagreement beta factor. That is, the disagreement beta factor contains distinct information that is
orthogonal to the existing stock market factors. Consistent with this finding, the adjusted R2 values are
very low from these prominent factor models, ranging from 1.79% to 5.48%. Overall, the significant
alpha estimates and the low R2 values indicate that the disagreement beta factor is not explained by the
long-established factors in the equity market.
5. Controlling for Exposures to Economic and Policy Uncertainty
Jurado, Ludvigson, and Ng (2015) develop a factor-based estimate of economic uncertainty index
(henceforth referred to as the JLN index) using a rich set of time-series that represent broad categories
of macroeconomic activities. They estimate the conditional volatility of the unpredictable component
of the future value of each series, and then aggregate individual conditional volatilities into a macro
uncertainty index. Bali, Brown, and Tang (2016) show that stocks with larger exposures to the JLN
index earn significantly lower future returns. On the other hand, Baker, Bloom, and Davis (2016) develop a new index of economic policy uncertainty based on newspaper coverage frequency. They find
that policy uncertainty is associated with greater stock price volatility and reduced investment and employment in policy-sensitive sectors. At the macro level, innovations in policy uncertainty foreshadow
declines in investment, output and employment.
20 The
slope on LIQ factor is negative and significant in all specifications, which implies that a decrease in liquidity risk
leads to a higher return on the disagreement beta factor, indicating a higher (lower) risk-adjusted return on low-βDSGR (highβDSGR ) stocks.
27
Intuitively, economic disagreement, economic uncertainty, and economic policy uncertainty are
expected to be correlated with each other. For example, Baker, Bloom, and Davis (2016) show that
the correlation between their policy uncertainty index and the JLN index during their sample period is
0.42. The quarterly economic disagreement index proposed in this paper is highly correlated with the
quarterly JLN index; the correlation between DSGR and JLN indices is 0.50 for the common sample
period, 1969:Q1 − 2016:Q4. The quarterly disagreement index is also significantly correlated with the
quarterly policy uncertainty index, measured by averaging the values of the monthly policy uncertainty
index within the same quarter; the correlation between DSGR and policy uncertainty indices is 0.39 for
the common sample period, 1985:Q1 − 2016:Q4.
In this section, we investigate the robustness of our findings after controlling for stock exposures
to economic and policy uncertainty indices. We obtain the one-month-ahead JLN index for the period
July 1960−December 2016 from Sydney Ludvigson’s website, and the monthly economic policy uncertainty index for the period January 1985−December 2016 from http://www.policyuncertainty.com/.
For each stock and for each month in our sample, we estimate the policy uncertainty beta from
the monthly rolling regressions of excess stock returns on the policy uncertainty index (EPU) over a
60-month fixed window updated on a monthly basis after controlling for the market (MKT ):
Ri,t = αi,t + βEPU
· EPUt + βMKT
· MKTt + εi,t ,
i,t
i,t
(12)
where EPUt is the monthly residuals from the AR(1) model of the economic policy uncertainty index
using the expanding window with the first estimation window set to be the first 60 months.
Following Bali, Brown, and Tang (2016), for each stock and for each month in our sample, we estimate the uncertainty beta from the monthly rolling regressions of excess stock returns (R) on the economic uncertainty index (JLN) over a 60-month fixed window after controlling for the market (MKT ),
size (SMB), book-to-market (HML), momentum (UMD), liquidity (LIQ), investment (RI/A ), and prof-
28
itability (RROE ) factors of Fama and French (1993), Carhart (1997), Pastor and Stambaugh (2003), and
Hou, Xue, and Zhang (2015):
Ri,t
MKT
HML
= αi,t + βJLN
· MKTt + βSMB
· HMLt +
i,t · JLNt + βi,t
i,t · SMBt + βi,t
(13)
R
I/A
RROE
βUMD
·UMDt + βLIQ
· RROE,t + εi,t .
i,t
i,t · LIQt + βi,t · RI/A,t + βi,t
We first perform bivariate sorts on the disagreement beta (βDSGR ) after controlling for the economic
policy uncertainty beta (βEPU ) and the economic uncertainty beta (βJLN ). Specifically, we sort stocks
into deciles based on βEPU or βJLN . We then further sort stocks within each control variable decile into
deciles based on βDSGR . Panel A of Table 9 reports the 5-factor alphas of the value-weighted monthly
returns (in percentage) for each disagreement beta decile, averaged across the ten control groups. The
last column of Panel A reports the 5-factor alpha differences between decile 1 (Low) and decile 10
(High) βDSGR portfolios. Panel A shows that after controlling for the economic policy uncertainty beta
(βEPU ) and the economic uncertainty beta (βJLN ), the 5-factor alpha differences between the high-βDSGR
and the low-βDSGR value-weighted portfolios are −0.74% per month (t-stat.=−2.74) and −0.35% per
month (t-stat.=−2.14), respectively. Thus, the policy uncertainty beta and the economic uncertainty
beta do not explain the negative cross-sectional relation between the economic disagreement beta and
future stock returns. This is because the cross-sectional correlations between βDSGR and βJLN /βEPU are
very low, especially compared to the correlations between DSGR and JLN/EPU indices.21
Next, we estimate the firm-level Fama-MacBeth regressions of one-month-ahead excess returns
(in percentage) on βDSGR , βEPU and βJLN after controlling for the set of lagged predictive variables
specified in equation (11) and the industry effect. Panel B of Table 9 reports the time-series averages
of the slope coefficients. Column (1) of Panel B reports the results from univariate Fama-MacBeth
regressions of excess returns on βEPU ; column (2) reports the results from Fama-MacBeth regressions of excess returns on βEPU after controlling for the market beta (βMKT ), log market capitalization
(SIZE), log book-to-market ratio (BM), and momentum (MOM); and column (3) reports the results
21 Although
the economic disagreement and economic uncertainty/policy uncertainty indices are highly/moderately correlated, the cross-sectional correlations among βDSGR , βJLN , and βEPU are much lower. Specifically, the average cross-sectional
correlation between βDSGR and βJLN is 0.32, that between βDSGR and βEPU is 0.02, and that between βJLN and βEPU is 0.05.
29
from Fama-MacBeth regressions of excess returns on βEPU after controlling for the large set of lagged
predictive variables, including βMKT , SIZE, BM, MOM, short-term reversal (REV), illiquidity (ILLIQ),
co-skewness (COSKEW), analyst dispersion (DISP), idiosyncratic volatility (IVOL), and demand for
lottery-type stocks (MAX). Columns (1) to (3) show that the average slope coefficients of βEPU are
negative, but statistically insignificant.
The results reported in columns (4) to (6) of Table 9, Panel B are based on the same models as
those corresponding to columns (1) to (3) except that βEPU is replaced by the economic uncertainty
beta (βJLN ). Consistent with Bali, Brown, and Tang (2016), the average slope coefficients of βJLN are
negative, in the range of −0.235 and −0.470, and they are highly significant with t-statistics ranging
from −2.49 to −3.44.
Finally, columns (7) to (9) of Table 9, Panel B, respectively, report the results from Fama-MacBeth
regressions of excess returns on βDSGR and βEPU ; βDSGR and βJLN ; and βDSGR , βEPU and βJLN after
controlling for everything else. Columns (7) to (9) show that the average slope coefficients of βDSGR
remain significantly negative, in the range of −0.004 and −0.006, with t-statistics ranging from −2.24
to −2.93. The average slope coefficients of βEPU are negative but statistically insignificant, whereas
those of βJLN are negative and statistically significant.22
Overall, the results from bivariate portfolio sorts and multivariate Fama-MacBeth regressions indicate that stock exposures to the economic uncertainty and policy uncertainty indices fail to absorb the
predictive power of the economic disagreement beta.
6. Conclusion
This paper investigates the role of economic disagreement in the cross-sectional pricing of individual stocks. Economic disagreement is quantified with ex-ante measures of cross-sectional dispersion
in economic forecasts from the Survey of Professional Forecasters, determining the degree of disagreement among professional forecasters over changes in economic fundamentals. Seven different
22 Comparing
the results in Columns (4)-(6) and Column (8) versus (9) indicates that the relatively weaker average slope
coefficient of βJLN in Column (9) is due to the shorter sample period when βEPU is controlled for.
30
measures of economic disagreement are used in our empirical analyses: the cross-sectional dispersion in quarterly forecasts for the RGDP growth/level, the NGDP growth/level, the GDP price index
growth/level, and the unemployment rate.
We introduce a broad index of economic disagreement based on the innovations in the crosssectional dispersion of economic forecasts so that the index is a shock measure that captures different
aspects of disagreement over economic fundamentals and also reflects unexpected news or surprise
about the state of the aggregate economy. After building the broad index of economic disagreement,
we test its out-of-sample performance in predicting the cross-sectional variation in future stock returns.
Univariate portfolio-level analyses indicate that decile portfolios that are long in stocks with the
lowest disagreement beta and short in stocks with the highest disagreement beta yield a risk-adjusted
return of 7.8% per annum. This economically and statistically significant disagreement premium is
driven by the outperformance by stocks with negative disagreement beta and the underperformance by
stocks with positive disagreement beta. Consistent with theoretical predictions, these results indicate
that ambiguity-averse investors demand extra compensation to hold stocks with negative disagreement
beta (stocks with high disagreement risk) and they are willing to pay high prices for stocks with positive
disagreement (stocks with large hedging benefits).
Bivariate portfolio-level analyses and stock-level cross-sectional regressions that control for wellknown pricing effects, including market beta, size, book-to-market, momentum, short-term reversal,
liquidity, co-skewness, idiosyncratic volatility, dispersion in analysts’ earnings estimates, and demand
for lottery-like stocks generate similar results. After controlling for each of these variables one-by-one
and then controlling for all variables simultaneously, the results provide evidence of a significantly
negative link between the disagreement beta and future stock returns. Our main findings also hold
for different stock samples including the NYSE stocks, S&P 500 stocks, and large and liquid stocks.
The monthly Fama-MacBeth regressions provide evidence of a significant time-series variation in the
economic disagreement premium. As expected, we find the disagreement premium to be significantly
higher during economic downturns, compared to non-recessionary and expansionary periods.
31
We also test whether the predictive power of the disagreement beta remains intact after controlling
for the exposure of individual stocks to changes in aggregate stock market volatility, economic uncertainty, and policy uncertainty. The results show that the predictive power of the disagreement beta is
not driven by the market volatility beta, the economic uncertainty beta, or the policy uncertainty beta,
implying that the significantly negative premium of economic disagreement in the cross-section of individual stocks is distinct from the negative volatility risk and uncertainty premia identified by earlier
studies.
32
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34
Figure 1. Economic Disagreement Index. In the figure, the solid line depicts the quarterly economic
disagreement index, defined as the average of the standardized residuals from the AR(1) model for the
seven dispersion measures; the dashed line depicts the quarterly economic disagreement index, defined
as the first principal component of the standardized residuals from the AR(1) model for the seven
dispersion measures. The seven dispersion measures are the cross-sectional dispersion in the quarterly
forecasts of RGDP growth and level, NGDP growth and level, GDP price index (PGDP) growth and
level, and unemployment rate (UNEMP). The sample period is from 1969:Q1 to 2016:Q4.
35
Figure 2. Slope coefficient of Disagreement Beta In the figure, the solid line depicts the 3-month
moving average of the monthly slope coefficients of the disagreement beta (Column (1) in Table 4) and
the dashed line depicts the 3-month moving average of the monthly CFNAI index.
36
Table 1
Univariate Portfolios of Stocks Sorted by Disagreement Beta
For each month, decile portfolios are formed by sorting individual stocks based on their disagreement
betas (βDSGR ), where decile 1 contains stocks with the lowest βDSGR during the past quarter, and decile
10 contains stocks with the highest βDSGR during the previous quarter. The first column reports the
average disagreement beta of individual stocks in each βDSGR decile; the next four columns present the
average value-weighted and equal-weighted excess return (RET−RF) and the corresponding 5-factor
alpha for each βDSGR decile, respectively. The last row presents the average return differences and
the 5-factor alpha differences between Decile 1 (Low) and Decile 10 (High). Newey-West adjusted
t-statistics are given in parentheses. The sample period is January 1974−December 2016.
βDSGR
Decile
Low
-23.95
2
-11.09
3
-6.67
4
-3.56
5
-0.91
6
1.66
7
4.48
8
7.92
9
13.06
High
30.27
High−Low
Value-weighted
RET−RF
Alpha
0.93
0.33
(3.23)
(2.04)
0.79
0.30
(3.30)
(2.87)
0.74
0.18
(3.50)
(2.20)
0.68
0.06
(3.32)
(0.70)
0.63
0.03
(3.10)
(0.26)
0.52
-0.05
(2.51)
(-0.53)
0.67
0.09
(3.25)
(1.36)
0.54
-0.12
(2.44)
(-1.39)
0.51
-0.18
(2.00)
(-1.95)
0.44
-0.32
(1.47)
(-2.88)
-0.50
-0.65
(-2.45)
(-3.06)
37
Equal-weighted
RET−RF
Alpha
1.02
0.21
(3.69)
(2.32)
1.06
0.30
(4.51)
(3.75)
0.97
0.24
(4.52)
(4.03)
1.02
0.28
(4.78)
(4.81)
0.95
0.21
(4.55)
(3.80)
0.87
0.12
(4.04)
(2.03)
0.92
0.15
(4.23)
(2.83)
0.88
0.08
(3.79)
(1.41)
0.82
-0.04
(3.29)
(-0.62)
0.65
-0.20
(2.24)
(-2.84)
-0.37
-0.42
(-3.25)
(-3.40)
Table 2
Average Stock Characteristics
This table reports the time-series averages of the slope coefficients from the regressions of the disagreement beta (βDSGR ) on the stock-level
characteristics and risk factors. Monthly cross-sectional regressions are run for the following econometric specification and nested versions
thereof: βDSGR
= λ0,t + λ1,t Xi,t + εi,t , where βDSGR
is the disagreement beta of stock i in month t and Xi,t is a collection of stock-specific
i,t
i,t
variables observable at time t for stock i (market beta (βMKT ), size (SIZE), book-to-market (BM), momentum (MOM), short-term reversal
(REV), illiquidity (ILLIQ), co-skewness (COSKEW), idiosyncratic volatility (IVOL), analyst dispersion (DISP), market volatility beta (βV XO ),
and maximum daily return in a month (MAX)). The cross-sectional regressions are run at a monthly frequency from January 1974 to December
2016. Newey-West adjusted t-statistics are given in parentheses.
Variable
βMKT
(1)
2.781
(6.46)
SIZE
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
-0.117
(-1.03)
38
BM
-0.482
(-2.70)
MOM
-0.005
(-0.75)
REV
-0.002
(-0.43)
ILLIQ
-0.002
(-0.06)
COSKEW
4.853
(3.86)
DISP
0.064
(0.73)
IVOL
0.514
(3.56)
βV XO
12.807
(1.77)
MAX
Adj. R2
(11)
5.32%
1.44%
0.96%
5.08%
0.85%
0.31%
2.30%
0.10%
1.16%
0.14%
0.332
(3.61)
1.18%
(12)
2.719
(5.03)
-0.162
(-0.94)
-0.239
(-1.02)
-0.006
(-0.67)
0.000
(-0.03)
-0.234
(-1.37)
3.617
(2.49)
0.064
(0.73)
0.259
(2.06)
3.214
(0.72)
-0.122
(-0.74)
13.64%
Table 3
Bivariate Portfolio Sorts
In this table, stocks are first sorted into deciles based on one control variable, and then stocks within each control variable decile are further sorted
into deciles based on disagreement beta (βDSGR ). This table reports the 5-factor alphas of value-weighted monthly returns (in percentage) for each
disagreement beta decile, averaged across the ten control groups, and the 5-factor alpha differences between decile 1 (Low) and decile 10 (High).
The control variables are market beta (βMKT ), log market capitalization (SIZE), log book-to-market ratio (BM), momentum (MOM), short-term
reversal (REV), illiquidity (ILLIQ), co-skewness (COSKEW), analyst dispersion (DISP), idiosyncratic volatility (IVOL), market volatility beta
(βV XO ), and demand for lottery-like stocks (MAX). The control variables are defined in Section 3.3. Newey-West adjusted t-statistics are given
in parentheses. The sample period is January 1974−December 2016.
βDSGR
Low
2
39
3
4
5
6
7
8
9
High
High-Low
βMKT
0.35
(3.03)
0.19
(2.26)
0.12
(1.97)
0.13
(1.86)
-0.04
(-0.75)
-0.03
(-0.50)
-0.01
(-0.20)
-0.07
(-1.21)
-0.15
(-2.32)
-0.22
(-2.47)
-0.57
(-3.55)
SIZE
0.22
(2.62)
0.27
(3.83)
0.27
(4.29)
0.28
(4.97)
0.20
(3.50)
0.12
(2.10)
0.08
(1.22)
0.10
(1.80)
-0.01
(-0.12)
-0.23
(-3.21)
-0.44
(-3.73)
BM
0.23
(2.07)
0.20
(2.41)
0.14
(2.04)
0.10
(1.31)
0.15
(2.23)
-0.06
(-1.07)
0.00
(0.06)
-0.01
(-0.12)
-0.14
(-1.84)
-0.37
(-3.73)
-0.60
(-3.56)
MOM
0.13
(1.26)
0.11
(1.57)
0.12
(1.79)
0.17
(2.40)
-0.02
(-0.27)
0.02
(0.36)
0.03
(0.54)
-0.16
(-2.44)
-0.11
(-1.34)
-0.27
(-2.92)
-0.40
(-2.64)
REV
0.29
(2.45)
0.20
(2.26)
0.09
(1.31)
0.13
(1.70)
0.15
(2.56)
-0.08
(-1.34)
0.04
(0.71)
-0.13
(-1.90)
-0.13
(-1.67)
-0.23
(-2.33)
-0.52
(-2.98)
ILLIQ
0.18
(2.20)
0.17
(2.33)
0.25
(4.24)
0.17
(2.85)
0.09
(1.58)
0.05
(0.80)
0.03
(0.48)
0.00
(-0.07)
-0.07
(-1.29)
-0.29
(-3.96)
-0.46
(-3.64)
COSKEW
0.25
(2.25)
0.22
(2.18)
0.11
(1.68)
0.22
(3.32)
0.06
(0.99)
0.03
(0.49)
0.07
(1.16)
-0.04
(-0.54)
-0.13
(-1.78)
-0.34
(-3.23)
-0.59
(-3.63)
DISP
0.26
(2.40)
0.20
(2.51)
0.11
(1.57)
0.07
(0.88)
-0.01
(-0.20)
0.01
(0.22)
-0.08
(-1.22)
-0.03
(-0.45)
-0.21
(-2.82)
-0.27
(-2.76)
-0.53
(-3.59)
IVOL
0.30
(2.60)
0.10
(1.00)
0.05
(0.65)
0.12
(1.56)
-0.04
(-0.55)
-0.07
(-1.16)
-0.05
(-0.89)
-0.18
(-2.37)
-0.26
(-3.20)
-0.40
(-4.66)
-0.70
(-4.71)
βV XO
0.33
(2.40)
0.18
(1.73)
-0.05
(-0.47)
0.11
(1.39)
0.09
(1.21)
0.03
(0.36)
-0.02
(-0.34)
-0.04
(-0.43)
-0.22
(-2.55)
-0.24
(-1.93)
-0.56
(-2.70)
MAX
0.28
(2.36)
0.13
(1.53)
0.12
(1.66)
-0.01
(-0.09)
0.08
(1.04)
-0.12
(-1.92)
-0.01
(-0.13)
-0.19
(-2.67)
-0.18
(-2.39)
-0.28
(-3.16)
-0.57
(-3.51)
Table 4
Fama-MacBeth Cross-Sectional Regressions
This table reports the time-series averages of the slope coefficients obtained from regressing monthly excess returns (in percentage) on a set of
lagged predictive variables using the Fama-MacBeth methodology. In Panel A, the control variables are the market beta (βMKT ), log market capitalization (SIZE), log book-to-market ratio (BM), momentum (MOM), short-term reversal (REV), illiquidity (ILLIQ), co-skewness (COSKEW),
analyst dispersion (DISP), idiosyncratic volatility (IVOL), market volatility beta (βV XO ), and demand for lottery-like stocks (MAX). Panel B
presents the same set of regression results controlling for the industry effect. Newey-West adjusted t-statistics are reported in parentheses. The
sample period is January 1974−December 2016.
40
Panel A. Monthly Fama-MacBeth regressions
Variable
(1)
(2)
(3)
DSGR
β
-0.011
-0.013
-0.012
(-3.11)
(-3.81)
(-3.72)
βMKT
0.109
0.105
(0.88)
(0.92)
SIZE
-0.053
(-2.09)
BM
0.176
(2.72)
MOM
REV
ILLIQ
COSKEW
DISP
IVOL
βV XO
MAX
(4)
-0.011
(-3.60)
0.066
(0.63)
-0.057
(-2.30)
0.182
(2.90)
0.006
(4.30)
(5)
-0.010
(-3.83)
0.090
(0.79)
-0.053
(-2.09)
0.208
(3.20)
0.005
(4.02)
-0.038
(-9.49)
(6)
-0.012
(-3.86)
0.036
(0.35)
-0.093
(-3.41)
0.179
(2.75)
0.006
(4.17)
(7)
-0.010
(-3.36)
0.065
(0.62)
-0.055
(-2.22)
0.188
(3.04)
0.006
(4.45)
(8)
-0.011
(-4.00)
-0.016
(-0.14)
-0.092
(-3.07)
0.097
(1.42)
0.006
(3.85)
(9)
-0.011
(-3.69)
0.159
(1.60)
-0.113
(-4.72)
0.148
(2.46)
0.006
(4.32)
(10)
-0.006
(-3.58)
0.082
(0.67)
-0.009
(-0.36)
0.120
(1.77)
0.005
(3.05)
(11)
-0.011
(-3.75)
0.238
(2.29)
-0.095
(-3.90)
0.148
(2.48)
0.006
(4.29)
-0.039
(-4.03)
-0.245
(-2.23)
-0.205
(-2.13)
-0.255
(-9.68)
-6.856
(-2.06)
-0.217
(-11.10)
(12)
-0.006
(-3.06)
0.131
(1.12)
-0.091
(-2.83)
0.036
(0.48)
0.005
(2.60)
-0.013
(-2.11)
-0.139
(-1.53)
-0.020
(-0.16)
-0.084
(-2.33)
-0.016
(-0.25)
-5.627
(-1.64)
-0.118
(-1.76)
Table 4 – continued
Panel B. Controlling for the industry effect
Variable
(1)
(2)
(3)
DSGR
β
-0.010
-0.011
-0.011
(-3.43)
(-3.81)
(-3.57)
βMKT
0.118
0.097
(1.13)
(0.98)
SIZE
-0.050
(-2.03)
BM
0.207
(3.74)
MOM
41
REV
ILLIQ
COSKEW
DISP
IVOL
βV XO
MAX
(4)
-0.009
(-3.59)
0.060
(0.66)
-0.053
(-2.19)
0.209
(3.85)
0.005
(4.10)
(5)
-0.009
(-3.95)
0.083
(0.82)
-0.047
(-1.91)
0.241
(4.22)
0.005
(3.70)
-0.043
(-11.06)
(6)
-0.010
(-3.84)
0.020
(0.23)
-0.090
(-3.36)
0.215
(3.75)
0.005
(3.98)
(7)
-0.009
(-3.35)
0.059
(0.64)
-0.052
(-2.15)
0.216
(4.01)
0.005
(4.23)
(8)
-0.009
(-3.71)
-0.014
(-0.15)
-0.090
(-3.11)
0.131
(2.23)
0.006
(3.73)
(9)
-0.010
(-3.76)
0.147
(1.69)
-0.110
(-4.70)
0.185
(3.48)
0.005
(4.12)
(10)
-0.006
(-3.70)
0.079
(0.76)
-0.006
(-0.27)
0.145
(2.55)
0.004
(2.83)
(11)
-0.010
(-3.87)
0.226
(2.46)
-0.092
(-3.85)
0.187
(3.51)
0.005
(4.07)
-0.038
(-3.94)
-0.172
(-1.93)
-0.215
(-2.44)
-0.263
(-11.18)
-5.225
(-1.91)
-0.229
(-13.11)
(12)
-0.006
(-3.02)
0.097
(0.99)
-0.092
(-3.02)
0.077
(1.15)
0.004
(2.26)
-0.020
(-3.34)
-0.134
(-1.54)
0.082
(0.79)
-0.087
(-2.59)
-0.050
(-0.85)
-4.863
(-1.55)
-0.096
(-1.59)
Table 5
Alphas from Alternative Factor Models
For each month, decile value-weighted portfolios are formed by sorting individual stocks based on
their disagreement betas (βDSGR ), where decile 1 contains stocks with the lowest βDSGR during the past
quarter, and decile 10 contains stocks with the highest βDSGR during the previous quarter. This table
presents results from the CAPM, the 3-factor (FF3) model of Fama and French (1993), the 4-factor
(FFC4) model of Fama-French (1993) and Carhart (1997), and the 5-factor (FF5) model of Fama and
French (2015), the 7-factor (FF5CPS) model of the 5-factor (FF5) model of Fama and French (2015),
Carhart (1997), and Pastor and Stambaugh (2003), the 4-factor model (Q) of Hou, Xue, and Zhang
(2015), and the 6-factor model (QCPS) of Hou, Xue, and Zhang (2015), Carhart (1997), and Pastor
and Stambaugh (2003). The last row presents the alpha differences between Decile 1 (Low) and Decile
10 (High). Newey-West adjusted t-statistics are given in parentheses. The sample period is January
1974−December 2016.
Decile
Low
2
3
4
5
6
7
8
9
High
High−Low
CAPM
0.22
(1.45)
0.18
(1.71)
0.17
(2.25)
0.11
(1.34)
0.07
(0.76)
0.00
(-0.05)
0.12
(1.73)
-0.04
(-0.50)
-0.12
(-1.25)
-0.31
(-2.35)
-0.53
(-2.57)
FF3
0.24
(1.58)
0.23
(2.33)
0.18
(2.29)
0.08
(1.19)
0.00
(-0.01)
-0.05
(-0.67)
0.08
(1.14)
-0.10
(-1.20)
-0.15
(-1.49)
-0.29
(-2.39)
-0.53
(-2.69)
FFC
0.30
(1.79)
0.27
(2.63)
0.15
(2.04)
0.07
(0.98)
0.01
(0.07)
-0.04
(-0.42)
0.10
(1.51)
-0.10
(-1.20)
-0.14
(-1.52)
-0.29
(-2.54)
-0.59
(-2.78)
FF5
0.39
(2.59)
0.25
(2.58)
0.14
(1.32)
0.00
(-0.05)
-0.10
(-1.25)
-0.13
(-1.54)
0.01
(0.09)
-0.15
(-1.68)
-0.17
(-1.61)
-0.14
(-1.11)
-0.53
(-2.39)
42
FF5CPS
0.44
(2.80)
0.30
(2.78)
0.14
(1.41)
-0.02
(-0.25)
-0.06
(-0.75)
-0.11
(-1.31)
0.02
(0.33)
-0.16
(-1.78)
-0.20
(-1.95)
-0.19
(-1.57)
-0.63
(-2.82)
Q
0.36
(2.03)
0.27
(2.52)
0.16
(1.39)
-0.01
(-0.16)
-0.04
(-0.48)
-0.06
(-0.78)
0.05
(0.73)
-0.13
(-1.54)
-0.22
(-1.81)
-0.20
(-1.62)
-0.57
(-2.35)
QCPS
0.42
(2.43)
0.31
(2.88)
0.18
(1.47)
-0.06
(-0.78)
-0.06
(-0.78)
-0.11
(-1.26)
0.01
(0.18)
-0.17
(-2.01)
-0.26
(-2.13)
-0.20
(-1.37)
-0.62
(-2.40)
Table 6
Different Stock Samples
In this table, sensitivity of our main findings is tested using univariate portfolios of stocks sorted by βDSGR for seven different stock samples:
(i) NYSE stocks only; (ii) Large stocks, defined as those with market capitalization greater than the 50th NYSE size percentile at the beginning
of each month; (iii) the S&P 500 stocks; (iv) Largest 500 stocks based on market capitalization in the CRSP universe; (v) Largest 1, 000 stocks
based on market capitalization in the CRSP universe; (vi) 500 most liquid stocks in the CRSP universe based on the Amihud’s (2002) illiquidity
measure; and (vii) 1, 000 most liquid stocks in the CRSP universe based on the Amihud’s (2002) illiquidity measure. This table reports the
5-factor alpha for the univariate decile value-weighted portfolios formed on βDSGR . The last row presents the 5-factor alpha differences between
Decile 1 (Low) and Decile 10 (High). Newey-West adjusted t-statistics are given in parentheses. The sample period is January 1974−December
2016.
Decile
Low
2
43
3
4
5
6
7
8
9
High
High−Low
NYSE
0.31
(1.72)
0.23
(1.96)
0.12
(1.33)
0.01
(0.15)
-0.03
(-0.36)
-0.12
(-1.38)
0.06
(0.75)
-0.15
(-1.74)
-0.21
(-2.07)
-0.37
(-2.79)
-0.68
(-3.01)
Large
0.36
(1.92)
0.31
(2.79)
0.17
(1.98)
0.04
(0.48)
0.01
(0.07)
-0.05
(-0.59)
0.10
(1.35)
-0.13
(-1.45)
-0.17
(-1.72)
-0.28
(-2.20)
-0.64
(-2.63)
S&P500
0.42
(1.77)
0.36
(3.08)
0.21
(2.25)
0.05
(0.57)
0.00
(0.03)
-0.04
(-0.44)
0.12
(1.42)
-0.13
(-1.26)
-0.17
(-1.45)
-0.33
(-2.12)
-0.74
(-2.43)
500 largest
0.42
(1.97)
0.31
(2.66)
0.18
(1.99)
0.04
(0.47)
0.01
(0.10)
-0.06
(-0.60)
0.10
(1.36)
-0.15
(-1.58)
-0.16
(-1.52)
-0.33
(-2.31)
-0.74
(-2.72)
1,000 largest
0.37
(2.08)
0.31
(2.87)
0.18
(2.09)
0.05
(0.62)
0.02
(0.18)
-0.05
(-0.55)
0.09
(1.35)
-0.12
(-1.40)
-0.18
(-1.83)
-0.30
(-2.47)
-0.67
(-2.89)
500 most liquid
0.47
(2.25)
0.32
(2.62)
0.18
(2.00)
0.04
(0.50)
0.01
(0.11)
-0.05
(-0.55)
0.11
(1.42)
-0.14
(-1.41)
-0.17
(-1.60)
-0.33
(-2.44)
-0.81
(-3.02)
1,000 most liquid
0.39
(2.15)
0.30
(2.75)
0.18
(2.13)
0.05
(0.62)
0.02
(0.20)
-0.05
(-0.58)
0.10
(1.39)
-0.12
(-1.39)
-0.18
(-1.86)
-0.31
(-2.56)
-0.69
(-2.98)
Table 7
Long-term Predictive Power of Disagreement Beta
This table reports the time-series averages of the slope coefficients obtained from regressing two-month-ahead up to 12-month-ahead excess
returns (in percentage) on a set of lagged predictive variables using the Fama-MacBeth methodology. The control variables are the market beta
(βMKT ), log market capitalization (SIZE), log book-to-market ratio (BM), momentum (MOM), short-term reversal (REV), illiquidity (ILLIQ),
co-skewness (COSKEW), analyst dispersion (DISP), idiosyncratic volatility (IVOL), market volatility beta (βV XO ), and demand for lottery-like
stocks (MAX). Newey-West adjusted t-statistics are given in parentheses.
Variable
βDSGR
βMKT
44
SIZE
BM
MOM
REV
ILLIQ
COSKEW
DISP
IVOL
βV XO
MAX
n=2
-0.006
(-3.49)
0.034
(0.29)
-0.084
(-2.80)
0.026
(0.36)
0.004
(2.28)
0.006
(0.91)
-0.065
(-0.83)
0.034
(0.30)
-0.102
(-2.96)
-0.123
(-2.16)
4.530
(1.03)
-0.056
(-0.87)
n=3
-0.005
(-2.68)
0.034
(0.31)
-0.053
(-1.78)
0.042
(0.58)
0.003
(1.65)
0.021
(3.92)
0.056
(0.71)
-0.076
(-0.67)
-0.107
(-2.80)
0.031
(0.62)
-1.845
(-0.44)
-0.125
(-2.19)
n=4
-0.005
(-2.65)
0.025
(0.25)
-0.051
(-1.62)
0.041
(0.58)
0.003
(1.90)
0.007
(1.39)
-0.063
(-0.83)
0.012
(0.11)
-0.052
(-1.31)
0.015
(0.30)
-3.492
(-1.11)
-0.095
(-1.65)
n=5
-0.005
(-2.50)
0.005
(0.05)
-0.055
(-1.78)
0.033
(0.46)
0.002
(1.31)
0.000
(0.01)
0.030
(0.52)
0.156
(1.36)
-0.032
(-0.97)
-0.260
(-4.46)
5.461
(1.27)
0.091
(1.49)
n-month-ahead
n=6
n=7
n=8
-0.005
-0.007
-0.007
(-2.76)
(-3.48)
(-3.33)
0.030
0.080
0.051
(0.30)
(0.78)
(0.50)
-0.038
-0.052
-0.054
(-1.24)
(-1.51)
(-1.68)
0.053
0.061
0.026
(0.72)
(0.84)
(0.35)
0.001
0.001
0.001
(0.73)
(0.62)
(0.53)
0.018
0.009
0.004
(3.60)
(1.71)
(0.64)
-0.015
0.050
0.078
(-0.17)
(0.66)
(1.43)
0.156
0.132
0.167
(1.27)
(1.12)
(1.32)
-0.008
-0.080
-0.066
(-0.22)
(-2.39)
(-1.38)
0.026
-0.053
-0.099
(0.49)
(-0.82)
(-1.79)
7.426
-5.471
-0.204
(1.33)
(-1.37)
(-0.05)
-0.076
-0.015
0.008
(-1.43)
(-0.26)
(0.16)
n=9
-0.007
(-3.58)
0.068
(0.67)
-0.025
(-0.77)
0.052
(0.68)
0.000
(-0.03)
0.015
(2.92)
-0.019
(-0.30)
0.205
(1.69)
-0.038
(-1.15)
0.020
(0.37)
-1.656
(-0.71)
-0.043
(-0.88)
n=10
-0.006
(-3.43)
0.072
(0.69)
-0.031
(-0.97)
0.071
(0.93)
0.000
(0.39)
0.006
(1.02)
0.092
(1.69)
0.136
(1.19)
0.033
(0.84)
-0.052
(-0.96)
3.411
(1.21)
-0.005
(-0.09)
n=11
-0.005
(-3.15)
0.120
(1.17)
-0.039
(-1.24)
0.049
(0.64)
-0.001
(-1.13)
0.016
(2.96)
0.068
(1.12)
0.151
(1.29)
-0.040
(-0.72)
-0.058
(-1.03)
1.096
(0.51)
-0.031
(-0.56)
n=12
-0.006
(-3.03)
0.084
(0.85)
-0.037
(-1.11)
0.053
(0.68)
-0.001
(-1.49)
0.012
(2.29)
-0.001
(-0.01)
0.138
(1.12)
-0.048
(-1.19)
-0.015
(-0.30)
-1.899
(-0.82)
-0.026
(-0.46)
Table 8
Alphas and Factor Loadings for the Disagreement Beta Factor
Column (1) of the table below reports the time-series average of the monthly economic disagreement
factor (FDSGR) for the period January 1974−December 2016. Columns (2)−(11) report the alphas
(row labeled Alpha) and the factor loadings for FDSGR after controlling for a large set of well-known
factors, including the market (MKT), the size (SMB), the book-to-market (HML), the profitability
(RMW), and the investment (CMA) factors of Fama and French (1993, 2015), the momentum (UMD)
factor of Carhart (1997), the liquidity (LIQ) factor of Pastor and Stambaugh (2003), the size (Rsize ), the
profitability (Rroa ), and the investment (Ria ) factors of Hou, Xue, and Zhang (2015), and the bettingagainst-beta factor (BAB) factor of Frazzini and Pedersen (2014). MKT, SMB, HML, RMW, CMA
and UMD are from the online data library of Kenneth French, LIQ is from Lubos Pastor’s data library,
and BAB is from AQR’s website. Rsize , Rroa , and Ria are calculated following Hou, Xue, and Zhang
(2015). The last two rows present the number of monthly observations (N) used in each factor model
regression and the corresponding adjusted r-squared (Adj. R2 ). Newey-West adjusted t-statistics are
given in parentheses.
Alpha
βMKT
βSMB
βHML
βUMD
βLIQ
βRMW
βCMA
βRsize
βRroa
βRia
βBAB
N
Adj R2
(1)
(2)
(3)
(4)
0.24
0.28
0.29
0.30
(2.55) (3.03) (3.06) (3.27)
-0.06 -0.05 -0.05
(-1.82) (-1.57) (-1.78)
-0.07 -0.07
(-1.76) (-1.76)
0.00
0.00
(0.04) (-0.08)
-0.02
(-0.38)
(5)
0.34
(3.56)
-0.06
(-1.97)
-0.07
(-1.78)
0.00
(-0.09)
-0.02
(-0.42)
-0.07
(-2.86)
(6)
0.26
(2.42)
-0.05
(-1.59)
-0.04
(-1.07)
0.02
(0.25)
(7)
0.31
(2.91)
-0.05
(-1.86)
-0.04
(-0.99)
0.00
(-0.09)
-0.02
(-0.52)
-0.07
(-2.83)
0.08
0.09
(1.14) (1.11)
-0.04 -0.01
(-0.43) (-0.13)
(8)
(9)
(10)
(11)
0.29
0.27
0.29
0.28
(2.47) (2.38) (2.42) (2.12)
-0.06 -0.06 -0.06 -0.06
(-2.08) (-1.95) (-2.16) (-2.40)
-0.04
(-1.21)
-0.03
0.05
0.02
(-0.46)
(0.92) (0.42)
-0.03
-0.05 -0.05
(-0.69)
(-0.84) (-0.88)
-0.07
-0.07 -0.07
(-2.95)
(-2.85) (-2.97)
0.06
(0.82)
-0.03
(-0.28)
-0.03 -0.01 -0.02
(-0.74) (-0.23) (-0.42)
0.07
0.12
0.10
(0.90) (1.43) (1.24)
-0.05 -0.09 -0.10
(-0.58) (-0.91) (-1.09)
0.06
0.06
(1.22)
(1.28)
516
516
516
516
504
516
504
504
516
504
504
1.39% 1.79% 2.53% 2.47% 4.12% 3.07% 4.08% 5.13% 2.54% 4.86% 5.48%
45
Table 9
Controlling for Exposures to Economic and Policy Uncertainty Indices
In Panel A, stocks are first sorted into deciles based on the economic policy uncertainty beta (βEPU ) or
the economic uncertainty beta (βJLN ), and then stocks within each control variable decile are further
sorted into deciles based on the disagreement beta (βDSGR ). Panel A reports the 5-factor alphas of the
value-weighted monthly returns (in percentage) for each disagreement beta decile, averaged across the
ten control groups, and the 5-factor alpha differences between decile 1 (Low) and decile 10 (High). In
Panel B, one-month-ahead excess returns (in percentage) are regressed on βDSGR , βEPU , and βJLN after
controlling for a set of lagged predictive variables and the industry effect using the Fama-MacBeth
methodology. The control variables are the market beta (βMKT ), log market capitalization (SIZE),
log book-to-market ratio (BM), momentum (MOM), short-term reversal (REV), illiquidity (ILLIQ),
co-skewness (COSKEW), analyst dispersion (DISP), idiosyncratic volatility (IVOL), market volatility
beta (βV XO ), and demand for lottery-like stocks (MAX). Panel B reports the time-series averages of the
slope coefficients from Fama-MacBeth regressions. Newey-West adjusted t-statistics are reported in
parentheses.
Panel A. Bivariate portfolio sorts
Low
βDSGR
2
3
4
5
6
7
8
EPU
β
0.31 0.23 0.17 0.15 -0.02 0.11 0.03 0.04
(1.93) (1.96) (1.70) (1.42) (-0.21) (1.26) (0.36) (0.43)
βJLN 0.17 0.27 0.13 0.21 0.00 0.04 0.06 -0.04
(1.64) (3.06) (1.73) (3.16) (-0.05) (0.65) (0.91) (-0.61)
46
9
-0.23
(-2.10)
-0.15
(-1.87)
High
βDSGR High−Low
-0.43
-0.74
(-2.64)
(-2.74)
-0.18
-0.35
(-1.86)
(-2.14)
Table 9 – continued
Panel B. Monthly Fama-MacBeth regressions controlling for the industry effect
Variable
(1)
(2)
(3)
(4)
(5)
(6)
(7)
DSGR
β
-0.006
(-2.93)
βEPU
-0.206 -0.267 -0.277
-0.211
(-0.57) (-0.80) (-0.86)
(-0.64)
-0.470 -0.357 -0.235
βJLN
(-3.44) (-2.86) (-2.49)
βMKT
0.096
0.090
0.064
0.091
0.107
(0.85)
(0.87)
(0.69)
(0.93)
(1.03)
SIZE
-0.013 -0.103
-0.033 -0.091 -0.106
(-0.47) (-3.22)
(-1.34) (-2.98) (-3.30)
BM
0.125
0.056
0.182
0.073
0.055
(2.01)
(0.81)
(3.55)
(1.09)
(0.79)
MOM
0.003
0.003
0.005
0.004
0.003
(2.05)
(1.67)
(4.48)
(2.45)
(1.76)
REV
-0.019
-0.020 -0.019
(-2.92)
(-3.29) (-2.91)
ILLIQ
-0.160
-0.139 -0.161
(-1.59)
(-1.60) (-1.58)
COSKEW
0.104
0.106
0.124
(0.94)
(0.94)
(1.10)
DISP
-0.089
-0.086 -0.089
(-2.31)
(-2.57) (-2.34)
IVOL
-0.024
-0.053 -0.025
(-0.38)
(-0.90) (-0.39)
βV XO
-4.759
-4.787 -4.867
(-1.37)
(-1.54) (-1.40)
MAX
-0.095
-0.092 -0.094
(-1.41)
(-1.52) (-1.39)
47
(8)
-0.004
(-2.24)
-0.219
(-2.28)
0.103
(1.05)
-0.093
(-3.05)
0.074
(1.11)
0.004
(2.46)
-0.020
(-3.29)
-0.137
(-1.58)
0.112
(0.99)
-0.086
(-2.59)
-0.051
(-0.87)
-4.869
(-1.56)
-0.093
(-1.54)
(9)
-0.005
(-2.50)
-0.188
(-0.57)
-0.161
(-1.84)
0.115
(1.11)
-0.108
(-3.37)
0.051
(0.75)
0.003
(1.94)
-0.018
(-2.87)
-0.164
(-1.62)
0.142
(1.17)
-0.088
(-2.32)
-0.025
(-0.39)
-4.870
(-1.41)
-0.091
(-1.36)
Disagreement in Economic Forecasts and Expected Stock
Returns
Turan G. Bali
Stephen J. Brown
Yi Tang
Online Appendix
To save space in the paper, we present some of our findings in the Online Appendix. Section I
presents summary statistics for the cross-sectional dispersion in economic forecasts. Section II investigates if the estimated historical disagreement betas successfully predict future disagreement betas
based on the portfolio transition matrices.
1
I. Summary statistics for the cross-sectional dispersion in economic forecasts
The Federal Reserve Bank of Philadelphia releases measures of cross-sectional dispersion in economic
forecasts from the Survey of Professional Forecasters, calculating the degree of disagreement between
the expectations of different forecasters. In our empirical analyses, we use the cross-sectional dispersion in quarterly forecasts for the U.S. real gross domestic product (GDP) growth, real GDP (RGDP)
level, nominal GDP (NGDP) level, NGDP growth, GDP price index level, GDP price index growth
(inflation rate forecast), and unemployment rate.
Panel A in Table A1 of the online appendix presents the descriptive statistics of the quarterly crosssectional dispersion measures for the sample period 1968:Q4−2016:Q4. Panel B of Table A1 reports
the correlation coefficients between these dispersion measures.
The Federal Reserve Bank of Philadelphia provides a partial list of the forecasters who participated
in the survey. Professional forecasters are generally academics at research institutions and economists
at major investment banks, consulting firms, and central banks in the United States and abroad. The
number of professional forecasters who participate in the survey changes over time. Figure A1 of the
online appendix presents the number of forecasts for quarterly RGDP growth over the sample period
1968:Q4−2016:Q4. The numbers of forecasts for the other six macro variables are almost identical for
the period 1968−2016.
Figure A2 of the online appendix displays the quarterly time-series plots of the cross-sectional
dispersion measures for the sample period 1968:Q4−2016:Q4. The visual depiction of the dispersion
measures in Figure A2 indicates that these economic disagreement measures closely follow large falls
and rises in financial and economic activity.
II. Portfolio transition matrix
In this section, we investigate if the estimated historical disagreement betas successfully predict future
disagreement betas and hence are good proxies for the true conditional betas. Table A2 of the online
1
appendix investigates this issue by presenting the average quarter-to-quarter portfolio transition matrix.
Specifically, Panel A of Table A2 presents the average probability that a stock in decile i (defined by
the rows) in one quarter will be in decile j (defined by the columns) in the subsequent quarter. If
the disagreement betas were completely random, then all the probabilities should be approximately
10%, since a high or low disagreement beta in one quarter should say nothing about the disagreement
beta in the following quarter. Instead, all the diagonal elements of the transition matrix exceed 10%,
illustrating that the disagreement beta is highly persistent. Of greater importance, this persistence is
especially strong for the extreme portfolios. Panels B, C, and D of Table A2 present two-quarter,
three-quarter, and four-quarter ahead transition matrices, respectively.
2
Table A1
Summary Statistics for the Cross-Sectional Dispersion in Economic Forecasts
3
Panel A reports the descriptive statistics for the cross-sectional dispersion in the quarterly forecasts of real GDP (RGDP) growth
and level, nominal GDP (NGDP) growth and level, GDP price index (PGDP) growth and level, and unemployment rate (UNEMP).
Panel B reports the correlation coefficients between these dispersion measures. The sample period is January 1974−December 2016.
Panel A. Descriptive statistics
Mean
Std. dev.
Minimum
Median
Maximum
AR(1)
RGDP growth
1.40
0.81
0.38
1.14
4.89
0.74
RGDP level
0.35
0.21
0.09
0.28
1.23
0.73
NGDP growth
1.70
0.74
0.68
1.50
5.16
0.63
NGDP level
0.41
0.18
0.17
0.36
1.16
0.64
PGDP growth
1.05
0.58
0.00
0.91
3.40
0.47
PGDP level
0.26
0.15
0.00
0.23
0.81
0.36
UNEMP
2.43
1.51
0.00
2.06
11.33
0.29
Panel B. Correlation coefficients
RGDP level
RGDP growth
0.94
RGDP level
NGDP growth
NGDP level
PGDP growth
PGDP level
NGDP growth
0.78
0.76
NGDP level
0.78
0.81
0.95
PGDP growth
0.58
0.57
0.46
0.47
PGDP level
0.54
0.61
0.43
0.50
0.75
UNEMP
0.50
0.53
0.35
0.38
0.47
0.40
Table A2
Transition Matrix
This table reports the average quarter-to-quarter portfolio transition matrix in one to four quarters ahead.
The table presents the average probability that a stock in decile i (defined by the rows) in one quarter
will be in decile j (defined by the columns) in the subsequent quarter. If the disagreement betas were
completely random, then all the probabilities should be approximately 10%, since a high or low disagreement beta in one quarter should say nothing about the disagreement beta in the following quarter.
Instead, all the diagonal elements of the transition matrix exceed 10%, illustrating that the disagreement
beta is highly persistent. The sample period is January 1974-December 2016.
Panel A. One-quarter ahead
Decile Low
2
3
Low 74.11% 13.67% 3.25%
2
12.87% 53.79% 17.57%
3
3.14% 16.88% 45.64%
4
1.75% 5.16% 17.74%
5
1.39% 2.75% 6.17%
6
1.23% 1.85% 3.14%
7
1.09% 1.61% 2.22%
8
1.33% 1.55% 1.84%
9
1.10% 1.47% 1.49%
High 1.99% 1.77% 1.48%
4
1.97%
5.29%
18.45%
41.61%
17.84%
6.39%
3.33%
2.12%
1.70%
1.24%
5
1.41%
2.76%
6.32%
18.52%
39.71%
18.28%
6.37%
3.11%
2.06%
1.45%
6
1.14%
2.15%
3.17%
6.68%
18.72%
40.47%
17.68%
5.84%
2.64%
1.57%
7
1.22%
1.63%
2.15%
3.29%
6.37%
18.17%
42.68%
17.73%
5.12%
1.97%
8
1.07%
1.57%
1.66%
2.24%
3.39%
6.10%
18.13%
46.81%
16.45%
3.20%
9
0.98%
1.21%
1.46%
1.60%
2.16%
2.72%
4.96%
16.47%
55.95%
12.35%
High
1.16%
1.14%
1.13%
1.41%
1.51%
1.65%
1.93%
3.21%
12.02%
72.98%
Total
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
Panel B. Two-quarter ahead
Decile Low
2
3
Low 65.81% 17.56% 5.17%
2
16.39% 41.63% 20.35%
3
4.54% 19.55% 33.45%
4
2.48% 7.68% 19.57%
5
1.81% 4.13% 8.65%
6
1.38% 2.80% 4.78%
7
1.30% 1.99% 3.16%
8
1.40% 1.84% 2.41%
9
1.48% 1.70% 1.74%
High 1.90% 1.97% 1.74%
4
2.61%
8.12%
20.04%
30.06%
18.84%
9.03%
4.88%
2.94%
2.42%
1.64%
5
1.84%
4.16%
9.19%
19.44%
28.47%
19.27%
9.06%
4.53%
2.54%
1.97%
6
1.44%
2.80%
5.10%
9.57%
19.49%
28.53%
19.37%
8.28%
3.74%
2.12%
7
1.45%
1.98%
2.96%
4.81%
9.34%
19.58%
30.55%
19.55%
7.35%
2.85%
8
1.33%
1.86%
2.12%
2.83%
4.85%
8.69%
19.90%
34.97%
19.46%
4.57%
9
1.32%
1.44%
1.75%
2.07%
2.67%
4.00%
7.30%
19.91%
44.12%
15.70%
High
1.47%
1.26%
1.30%
1.51%
1.73%
1.93%
2.48%
4.18%
15.43%
65.54%
Total
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
4
Table A2 – continued
Panel C. Three-quarter ahead
Decile Low
2
3
Low 59.45% 19.02% 6.87%
2
17.10% 34.92% 20.25%
3
6.18% 19.11% 27.63%
4
3.15% 9.63% 18.77%
5
2.24% 5.28% 10.19%
6
1.80% 3.48% 6.18%
7
1.71% 2.55% 3.97%
8
1.53% 2.06% 3.05%
9
1.81% 1.95% 2.33%
High 2.32% 2.43% 1.89%
4
3.52%
10.03%
19.27%
24.64%
18.03%
10.48%
6.32%
3.93%
2.68%
2.06%
5
2.42%
5.62%
11.02%
18.23%
23.46%
18.28%
10.63%
5.76%
3.39%
2.38%
6
2.05%
3.64%
6.51%
11.11%
18.16%
23.58%
18.37%
10.13%
4.78%
2.62%
7
1.71%
2.68%
3.83%
6.16%
10.76%
18.50%
25.21%
19.41%
9.05%
3.52%
8
1.66%
2.28%
2.75%
3.79%
6.28%
10.15%
19.32%
28.82%
19.94%
5.90%
9
1.60%
1.81%
2.20%
2.60%
3.51%
5.35%
8.87%
19.87%
37.59%
17.14%
High
1.71%
1.67%
1.49%
1.94%
2.10%
2.17%
3.04%
5.44%
16.48%
59.73%
Total
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
Panel D. Four-quarter ahead
Decile Low
2
3
Low 53.82% 19.77% 8.27%
2
17.26% 30.01% 19.76%
3
7.21% 18.36% 23.47%
4
3.86% 10.43% 17.69%
5
2.75% 6.42% 11.26%
6
2.03% 4.32% 7.12%
7
2.07% 3.17% 4.91%
8
1.87% 2.58% 3.64%
9
2.00% 2.46% 2.70%
High 2.74% 2.77% 2.32%
4
4.58%
11.11%
18.49%
20.97%
16.88%
11.37%
7.42%
4.82%
3.29%
2.41%
5
3.09%
6.84%
11.80%
17.38%
20.00%
17.19%
11.52%
6.92%
4.13%
2.74%
6
2.48%
4.50%
7.80%
11.88%
17.10%
20.42%
17.01%
11.23%
6.02%
3.24%
7
2.05%
3.33%
4.90%
7.51%
11.54%
17.37%
22.06%
18.32%
10.18%
4.30%
8
2.03%
2.76%
3.47%
4.88%
7.29%
11.15%
18.23%
24.75%
19.62%
7.02%
9
1.81%
2.35%
2.70%
3.24%
4.40%
6.28%
9.82%
19.39%
32.59%
18.06%
High
2.09%
2.07%
1.81%
2.17%
2.37%
2.74%
3.80%
6.48%
17.02%
54.42%
Total
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
5
Figure A1. Number of Forecasts This figure depicts the number of forecasts for the quarterly real
GDP level over the sample period 1968:Q4−2016:Q4.
6
Figure A2. Cross-Sectional Dispersion in Economic Forecasts. The four panels (moving from
top to bottom) depict the cross-sectional dispersion in the quarterly forecasts of RGDP growth and
level, NGDP growth and level, GDP price index (PGDP) growth and level, and unemployment rate
(UNEMP). The sample period is 1968:Q4−2016:Q4.
7