Disagreement in Economic Forecasts and Expected Stock Returns

Transcription

1 Disagreement in Economic Forecasts and Expected Stock Returns Turan G. Bali Georgetown University Stephen J. Brown Monash University Yi Tang 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 tgb27@georgetown.edu. Phone: (202) Fax: (202) Professor, Monash Business School, Melbourne, Vic Australia, and Emeritus Professor of Finance, NYU Stern School of Business, New York, NY Phone: stephen.brown@monash.edu. Associate Professor of Finance, Gabelli School of Business, Fordham University, 45 Columbus Avenue, New York, NY ytang@fordham.edu. Phone: (646) Fax: (646)

2 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

3 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 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

4 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

5 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

6 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

7 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

8 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 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), (1) Dispersion Measure(Level) = 100 log(75th Level/25th Level). (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 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

9 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 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 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 Z t = ω 0 + ω 1 Z t 1 + ε t, (3) 7 Specifically, the peaks in Figure A2 closely follow major economic and financial crises such as the 1973 oil crisis, the stock market crash, the high interest rate period, the 1980s Latin American debt crisis, the savings and loan crisis in the United States, the recession of the early 1990s, the Asian and Russian financial crises, the recession of the early 2000s, and the recent global financial crisis ( ). 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

10 where Z t 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 (DSGR AV 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 (DSGR AV 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

11 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 DSGRt PCA = w 1,t Stdrest RGDP growth + w 2,t Stdres RGDP level t + (4) w 3,t Stdrest NGDP growth + w 4,t Stdrest NGDP level + w 5,t Stdrest PGDP growth + w 6,t Stdrest PGDP level + w 7,t Stdres UNEMP t. Although the weights attached to the standardized residuals are not reported, the economic disagreement index obtained from the first principal component (DSGR PCA ) loads fairly evenly on the innovations in seven dispersion measures, suggesting a strong correlation with the simpler disagreement index (DSGR AV G ) defined as the average of the standardized residuals. 10 Figure 1 depicts the two broad indices of economic disagreement (DSGR AV G and DSGR PCA ) 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 (DSGR AV G and DSGR PCA ) are almost identical, in our follow-up empirical analyses, we use DSGR AV 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 (w 1,t...w 7,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

12 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 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 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 20- quarter fixed window: R i,t = α i,t + β DSGR i,t DSGR t + β MKT i,t MKT t + ε i,t, (5) where R i,t is the excess return on stock i in quarter t, DSGR t is the economic disagreement index in quarter t, defined as the average of the standardized residuals in equation (3) for seven dispersion measures, and MKT t is the excess market return in quarter t; β DSGR i,t disagreement beta and the market beta for stock i in quarter t. and β MKT i,t are, respectively, the 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), , 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

13 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. as: Following Harvey and Siddique (2000), the stock s monthly co-skewness (COSKEW) is defined COSKEW i,t = E E [ ε i,t R 2 ] m,t [ ε 2 i,t ] E [ R 2 m,t ], (6) where ε i,t = R i,t (α i + β i R m,t ) is the residual from the regression of the excess stock return (R i,t ) against the contemporaneous excess return on the CRSP value-weighted index (R m,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 ILLIQ i,t = Avg, (7) VOLD i,d where R i,d and VOLD i,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 At an earlier stage of the study, following Mitton and Vorkink (2007), co-skewness is defined as the estimate of γ i,t in the regression using the monthly return observations over the prior 60 months with at least 24 monthly return observations available: R i,t = α i + β i R m,t + γ i,t R 2 m,t + ε i,t, where R i,t and R m,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

14 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: R i,d = α i + β i R m,d + γ i SMB d + ϕ i HML d + ε i,d, (8) where R i,d and R m,d are, respectively, the excess daily returns on stock i and the CRSP value-weighted index, and SMB d and HML d 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: R i,d = α i,daily + β MKT i,daily R m,d + β V i,daily XO XO VARVd + ε i,d, (9) where R i,d is the excess return of stock i on day d, R m,d is the excess market return on day d, VAR V XO d is the change in the S&P 100 index option implied variance (VXO) on day d, and β V i,daily XO is the implied 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

15 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 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 (β DSGR ) 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 The cross-sectional return predictability results are reported from January 1974 to December Table 1 presents the univariate portfolio results. For each month, we form decile portfolios by sorting individual stocks based on their disagreement betas (β DSGR ), where decile 1 contains stocks with the lowest β DSGR during the past quarter, and decile 10 contains stocks with the highest β DSGR during the previous quarter. The first column in Table 1 reports the average disagreement betas for the decile portfolios formed on β DSGR using the CRSP breakpoints with an equal number of stocks in the 14

16 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 β DSGR ; the average disagreement beta increases from to 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 β DSGR decile. The average return difference between decile 10 (high-β DSGR ) and decile 1 (low-β DSGR ) is 0.50% per month with a Newey-West (1987) t-statistic of This result indicates that stocks in the lowest β DSGR decile generate about 6.24% higher annual returns compared to stocks in the highest β DSGR 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 β DSGR decile. The difference in alphas between the high-β DSGR and low-β DSGR 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-β DSGR and low-β DSGR 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 β DSGR. 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. 15 The 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

17 high-β DSGR and low-β DSGR 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-β DSGR and low- β DSGR portfolios: Is it due to outperformance by low-β DSGR stocks, underperformance by highβ DSGR 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-β DSGR stocks) are significantly positive, whereas the 5-factor alphas of stocks in decile 10 (high-β DSGR stocks) are significantly negative. Hence, we conclude that the significantly negative alpha spread between high-β DSGR and low-β DSGR stocks is due to both the outperformance by low-β DSGR stocks and the underperformance by high-β DSGR 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 β DSGR (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 β DSGR 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

18 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 β DSGR, 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 β DSGR, 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 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 (β DSGR ) on the stock-level characteristics and risk factors. Monthly cross-sectional regressions are run for the following econometric specification and nested versions thereof: β DSGR i,t = λ 0,t + λ 1,t X i,t + ε i,t, (10) where β DSGR i,t is the disagreement beta of stock i in month t and X i,t is a collection of stock-specific 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

19 MAX). The cross-sectional regressions are run at a monthly frequency from January 1974 to December Columns (1) and (10) of Table 2 show that the average slope coefficients on β MKT i,t and β V XO 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 β MKT i,t higher β V XO i,t 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. are and 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 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 (β DSGR ) in combination with the market beta (β MKT ), the log market capitalization (SIZE), the log book-to-market ratio (BM), momentum (MOM), short-term reversal (REV), illiquidity 18

20 (ILLIQ), co-skewness (COSKEW), analyst dispersion (DISP), idiosyncratic volatility (IVOL), market volatility beta (β V XO ), and lottery demand (MAX). Table 3 reports the value-weighted portfolio results from these conditional bivariate sorts. We control for the market beta (β MKT ) by first forming decile portfolios ranked based on β MKT. Then, within each β MKT decile, we sort stocks into decile portfolios ranked based on the disagreement beta (β DSGR ) so that decile 1 (decile 10) contains stocks with the lowest (highest) β DSGR values. The first column of Table 3 averages the value-weighted portfolio returns across the ten β MKT deciles to produce decile portfolios with dispersion in β DSGR but that contain all the stocks market betas. This procedure creates a set of β DSGR portfolios with very similar levels of market beta, and hence these β DSGR 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 highβ DSGR and low-β DSGR value-weighted portfolios is 0.57% per month with a Newey-West t-statistic of 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-β DSGR and lowβ DSGR 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 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 (β DSGR ) and the market beta (β MKT ) with and without control variables. The average slopes provide standard Fama-MacBeth tests for determining which explanatory variables on average have 19

21 non-zero premiums. Monthly cross-sectional regressions are run for the following econometric specification and nested versions thereof: R i,t+1 = λ 0,t + λ 1,t β DSGR i,t + λ 2,t β MKT i,t + λ 3,t X i,t + ε i,t+1, (11) where R i,t+1 is the realized excess return on stock i in month t + 1, β MKT i,t i in month t, β DSGR i,t is the market beta of stock is the quarterly disagreement beta of stock i in months t, t 1, and t 2, and X 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 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 β DSGR i,t alone is with a t-statistic of 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 β DSGR i,t values between average stocks in the first and 10th deciles is 54.22[= ( 23.95)]. If a stock were to move from the first to the 10th decile of β DSGR i,t, what would be the change in that stock s expected return? The average slope coefficient of on β DSGR i,t in Panel A of Table 4 represents an economically significant decrease of 0.60% per month, [ = 0.60%], in the average stock s expected return for moving from the first to the 10th decile of β DSGR i,t. The second column in Panel A of Table 4 controls for the market beta (β MKT ), a cross-sectional regression specification corresponding to an extended CAPM. The third column in Panel A of Table 20