Macroeconomc Uncertanty and Expected Stock Returns Turan G. Bal Georgetown Unversty Stephen J. Brown New York Unversty Y Tang Fordham Unversty Abstract Ths paper ntroduces a broad ndex of macroeconomc uncertanty based on ex-ante measures of cross-sectonal dsperson n economc forecasts by the Survey of Professonal Forecasters. We estmate ndvdual stock exposure to a newly proposed measure of economc uncertanty ndex and fnd that the resultng uncertanty beta predcts a sgnfcant proporton of the cross-sectonal dsperson n stock returns. After controllng for a large set of stock characterstcs and rsk factors, we fnd the predcted negatve relaton between uncertanty beta and future stock returns remans economcally and statstcally sgnfcant. The sgnfcantly negatve uncertanty premum s robust to alternatve measures of uncertanty ndex and dstnct from the negatve market volatlty rsk premum dentfed by earler studes. Ths draft: December 2014 JEL classfcaton: G11, G12, C13, E20, E30. Keywords: Macroeconomc uncertanty, dsperson n economc forecasts, cross-secton of stock returns, return predctablty. Robert S. Parker Professor of Busness Admnstraton, McDonough School of Busness, Georgetown Unversty, Washngton, D.C. 20057. Emal: tgb27@georgetown.edu. Phone: (202) 687-5388. Fax: (202) 687-4031. Davd S. Loeb Professor of Fnance, Stern School of Busness, New York Unversty, New York, NY 10012, and Professoral Fellow, Unversty of Melbourne, Emal: sbrown@stern.nyu.edu. Assocate Professor of Fnance, Schools of Busness, Fordham Unversty, 1790 Broadway, New York, NY 10019. Emal: ytang@fordham.edu. Phone: (646) 312-8292. Fax: (646) 312-8295. An earler draft of ths paper was crculated under the ttle Cross-Sectonal Dsperson n Economc Forecasts and Expected Stock Returns. We thank Jenne Ba, Geert Bekaert, Nck Bloom, John Campbell, and Sydney Ludvgson for ther extremely helpful comments and suggestons. We also benefted from dscussons wth Senay Agca, Reena Aggarwal, Serdar Aldatmaz, Oya Altnklc, Mke Anderson, Bll Baber, Audra Boone, Yong Chen, Jess Cornagga, Mchael Gordy, Derek Horstmeyer, Shane Johnson, Gergana Jostova, Hagen Km, James Kolar, Yan Lu, Arvnd Mahajan, Paul Peyser, Alexander Phlpov, Lee Pnkowtz, Chrsto Prnsky, Marco Ross, Kevn Sheppard, We Tang, Ashley Wang, Sumudu Watugala, Rohan Wllamson, Kaml Ylmaz, and semnar partcpants at the Federal Reserve Board, George Mason Unversty, George Washngton Unversty, Georgetown Unversty, Koc Unversty, the Offce of Fnancal Research at the U.S. Department of the Treasury, and Texas A&M Unversty. All errors reman our responsblty.
1. Introducton Merton s (1973) semnal paper ndcates that, n a mult-perod economy, nvestors have ncentve to hedge aganst future stochastc shfts n consumpton and nvestment opportunty sets. Ths mples that state varables that are correlated wth changes n consumpton and nvestment opportuntes are prced n captal markets such that an asset s covarance wth these state varables s related to ts expected returns. Macroeconomc varables are wdely accepted canddates for these systematc rsk factors because nnovatons n economc ndcators can generate global mpacts on stock fundamentals, such as cash flows, rsk-adjusted dscount factors, and nvestment opportuntes. Macroeconomc fundamentals, such as output growth, nflaton, and unemployment, have sgnfcant mpacts on expected returns through several channels. To the extent that nvestors pursue opportuntes arsng from changng economc crcumstances, we would expect that returns from nvestment n rsky assets are nfluenced by the extent to whch nvestors vary ther exposure to leadng economc ndcators. Accordng to Merton s (1973) ntertemporal captal asset prcng model (ICAPM), nvestors are concerned not only wth the termnal wealth that ther portfolo produces, but also wth the nvestment and consumpton opportuntes that they wll have n the future. Hence, when choosng a portfolo at tme t, ICAPM nvestors consder how ther wealth at tme t + 1 mght vary wth future state varables. Ths mples that, just as CAPM nvestors, ICAPM nvestors prefer hgh expected return and low return varance but are also concerned wth the covarances of portfolo returns wth state varables that affect future nvestment opportuntes. Bloom, Bond, and Reenen (2007), Bloom (2009), Chen (2010), Allen, Bal, and Tang (2012), Bloom, Floetotto, Jamovch, Saporta-Eksten, and Terry (2012), and Stock and Watson (2012) provde theoretcal and emprcal support for the dea that tme varaton n the condtonal volatlty of macroeconomc shocks s lnked to real economc actvty. Thus, economc uncertanty s a relevant state varable affectng future consumpton and nvestment decsons. Motvated by the aforementoned studes, we examne the role of macroeconomc uncertanty n the cross-sectonal prcng of ndvdual stocks. We argue that dsagreement over changes n macroeconomc fundamentals can be consdered a source of macroeconomc uncertanty. We quantfy ths uncertanty wth ex-ante measures of cross-sectonal dsperson n economc forecasts from the Survey of Professonal Forecasters. These uncertanty measures provded by the Federal Reserve Bank 1
of Phladelpha determne the degree of dsagreement between the expectatons of professonal forecasters. Our emprcal analyss uses seven dfferent measures of cross-sectonal dsperson n quarterly forecasts for output, nflaton, and unemployment as alternatve proxes for economc uncertanty. We quantfy an unexpected change (or nnovaton) n the economc predctons of the professonal forecasters by estmatng an autoregressve process for each dsperson measure. The standardzed resduals from the autoregressve model remove the predctable component of the dsperson measures and can be vewed as a measure of uncertanty shock. We estmate ndvdual stock exposure to the standardzed resduals and fnd that the resultng uncertanty betas from all seven measures of uncertanty shock predct a sgnfcant proporton of the cross-sectonal dsperson n stock returns. In addton to ndvdual measures of dsagreement over macroeconomc fundamentals, we ntroduce two broad ndces of economc uncertanty based on the average and the frst prncpal component of the standardzed resduals for the seven dsperson measures. These economc uncertanty ndces are generated usng past nformaton only, so that there s no look-ahead bas n our emprcal analyses. Moreover, these uncertanty ndces are formed based on ex-ante predctons of professonal forecasters so that we provde the out-of-sample performance of ex-ante measure of the uncertanty beta n predctng the cross-sectonal varaton n future stock returns. Frst, we estmate the uncertanty beta usng 20-quarter rollng regressons of excess returns on the newly proposed economc uncertanty ndex for each stock tradng n the New York Stock Exchange (NYSE), Amercan Stock Exchange (Amex), and Nasdaq. Then, we examne the performance of the quarterly uncertanty beta n predctng the cross-sectonal dsperson n future stock returns. Specfcally, we sort stocks nto decle portfolos by ther uncertanty beta durng the prevous quarter and examne the monthly returns on the resultng portfolos from October 1973 to December 2012. Stocks n the lowest uncertanty beta decle generate about 8% more annual returns compared to stocks n the hghest uncertanty beta decle. After controllng for the well-known market, sze, book-to-market, and momentum factors of Fama and French (1993) and Carhart (1997), we fnd the dfference between the returns on the portfolos wth the hghest and lowest uncertanty beta (4-factor alpha) remans negatve and hghly sgnfcant. 2
The sgnfcantly negatve uncertanty premum s consstent wth ICAPMs of Merton (1973) and Campbell (1993, 1996). An ncrease n economc uncertanty reduces future nvestment and consumpton opportuntes. To the extent that a negatve covarance between asset returns and future consumpton opportuntes mples a postve rsk premum, we should expect that betas wth respect to an approprately defned ndex of economc uncertanty should be negatvely assocated wth rsk prema. In other words, nvestors prefer to hold stocks that have hgher covarance wth economc uncertanty (stocks wth hgher uncertanty beta) and, all other thngs beng equal, demand a lower rsk premum for such stocks. Ths ntertemporal hedgng demand argument mples that nvestors prefer to hold stocks wth hgher covarance wth economc uncertanty and that they pay hgher prces and accept lower returns for stocks wth hgher uncertanty beta. In addton to the ratonal asset prcng explanaton of the negatve uncertanty premum, there exsts a behavoral explanaton based on dfferences of opnon and short-sales constrants along the lnes of Mller (1977). 1 Suppose that stocks wth hgh uncertanty beta are subject to overprcng because nvestor opnons dffer about ther prospects and they are hard to short. When macroeconomc uncertanty ncreases, the range of nvestor opnons about ther prospects broadens. More extreme optmsts end up holdng these stocks, and ther prces ncrease. The uncertanty beta can thus be vewed as an ndrect way to measure dspersed opnon and overprcng. Ths vew suggests that these stocks should have partcularly low returns when economc uncertanty s hgh. Although explorng Mller s hypothess tself s beyond the scope of ths paper, we show later that stocks wth hgh uncertanty beta have partcularly low returns durng economc recessons n whch larger dfferences of opnon are observed among professonal forecasters. To ensure that t s the uncertanty beta that s drvng documented return dfferences rather than well-known stock characterstcs or rsk factors, we perform bvarate portfolo sorts and re-examne the raw return and alpha dfferences. We control for sze and book-to-market (Fama and French 1 Mller (1977) hypotheszes that stock prces reflect an upward bas as long as dvergence of opnon about stock value exsts among nvestors and pessmstc nvestors do not hold suffcent short postons because of nsttutonal or behavoral reasons. In Mller s model, overvaluaton of securtes s observed because pessmsts are restrcted to holdng zero shares although they prefer holdng a negatve quantty, and the prces of securtes are manly determned by the belefs of the most optmstc nvestors. Snce dvergence of opnon s lkely to ncrease wth frm-specfc uncertanty, Mller predcts a negatve relaton between frm-specfc uncertanty and expected stock returns. 3
1992, 1993), momentum (Jegadeesh and Ttman 1993), short-term reversal (Jegadeesh 1990), llqudty (Amhud 2002), co-skewness (Harvey and Sddque 2000), dosyncratc volatlty (Ang, Hodrck, Xng, and Zhang 2006), analyst earnngs forecast dsperson (Dether, Malloy, and Scherbna 2002), market volatlty beta (Ang et al. 2006 and Campbell et al. 2014), frm age (Shumway 2001), and leverage (Bhandar 1988). After controllng for ths large set of stock return predctors, we fnd the negatve relaton between the uncertanty beta and future returns remans hghly sgnfcant. We also examne the cross-sectonal relaton at the stock-level usng the Fama-MacBeth (1973) regressons. After all varables are controlled for smultaneously, the cross-sectonal regressons provde strong corroboratng evdence for an economcally and statstcally sgnfcant negatve relaton between the uncertanty beta and future stock returns. We provde a battery of robustness checks. We nvestgate whether our results are drven by small, llqud, and low-prced stocks, or stocks tradng at the Amex and Nasdaq exchanges. We fnd that the negatve uncertanty premum s hghly sgnfcant n the cross-secton of NYSE stocks, Standard & Poor s (S&P) 500 stocks, and the 1,000 and 500 largest and most lqud stocks n the Center for Research n Securty Prces (CRSP) unverse. We show that the cross-sectonal predctablty results are robust across dfferent tme perods, and for both economc recessons and expansons. However, consstent wth theoretcal predctons, the uncertanty premum s hgher durng bad states of the economy. We also examne the long-term predctve power of the uncertanty beta and fnd that the negatve relaton between the uncertanty beta and future stock returns s not just a one-month affar. The uncertanty beta predcts cross-sectonal varatons n stock returns nne months nto the future. Fnally, we show that the negatve uncertanty premum s dstnct from the negatve volatlty rsk premum dentfed by earler studes. The paper s organzed as follows. Secton 2 descrbes the data and varables. Secton 3 presents a smple extenson of Merton s (1973) condtonal asset prcng model wth economc uncertanty. Secton 4 provdes portfolo-level analyses and stock-level cross-sectonal regressons that examne a comprehensve lst of control varables. Secton 5 controls for exposure to stock market volatlty. Secton 6 nvestgates whether our man fndngs reman ntact when we use alternatve measures of the economc uncertanty ndex proposed by other studes. Secton 7 concludes the paper. 4
2. Data and varable defntons Ths secton frst descrbes the data on cross-sectonal dsperson n economc forecasts, and then ntroduces an ndex of macroeconomc uncertanty. Fnally, we provde the defntons of the stock-level predctve varables used n cross-sectonal return predctablty. 2.1. Cross-sectonal dsperson n economc forecasts The Federal Reserve Bank of Phladelpha releases measures of cross-sectonal dsperson n economc forecasts from the Survey of Professonal Forecasters, calculatng the degree of dsagreement between the expectatons of dfferent forecasters. 2 In our emprcal analyses, we use the cross-sectonal dsperson n quarterly forecasts for the U.S. real gross domestc product (GDP) growth, real GDP (RGDP) level, nomnal GDP (NGDP) level, NGDP growth, GDP prce ndex level, GDP prce ndex growth (nflaton rate forecast), and unemployment rate. These dsperson measures are model-ndependent, nonparametrc measures of economc uncertanty obtaned from dsagreements among professonal forecasters. 3 The cross-sectonal dsperson measures are defned as the percent dfference between the 75th and 25th percentles (the nterquartle range) of the projectons for quarterly growth or levels: Dsperson Measure(Growth) = 100 log(75th Growth/25th Growth), (1) Dsperson Measure(Level) = 100 log(75th Level/25th Level). (2) Panel A n Table A1 of the onlne appendx presents the descrptve statstcs of the quarterly crosssectonal dsperson measures for the sample perod 1968:Q4 2012:Q4. The volatlty and max-mn dfferences of the dsperson measures are qute hgh compared to ther means, mplyng sgnfcant tme-seres varaton. Panel B of Table A1 shows that the cross-sectonal dsperson measures are generally hghly correlated wth each other (n the range of 0.74 0.95), and reflect common sources 2 The Survey of Professonal Forecasters s the oldest quarterly survey of macroeconomc forecasts n the Unted States. The survey began n 1968 and used to be conducted by the Amercan Statstcal Assocaton and the Natonal Bureau of Economc Research. The Federal Reserve Bank of Phladelpha took over the survey n 1990. 3 The Federal Reserve Bank of Phladelpha provdes a partal lst of the forecasters who partcpated n the survey. Professonal forecasters are generally academcs at research nsttutons and economsts at major nvestment banks, consultng frms, and central banks n the Unted States and abroad. The number of professonal forecasters who partcpate n the survey changes over tme. Fgure A1 of the onlne appendx presents the number of forecasts for quarterly RGDP growth over the sample perod 1968:Q4 2012:Q4. The numbers of forecasts for the other sx macro varables are almost dentcal for the perod 1968 2012. 5
of ambguty about the state of the aggregate economy. On the other hand, some of the correlatons reported n Panel B of Table A1 are lower, n the range of 0.34 0.59, mplyng that each dsperson measure has the potental to capture dfferent aspects of uncertanty and dsagreement over fnancal and macroeconomc fundamentals. Fgure A2 of the onlne appendx dsplays the quarterly tme-seres plots of the cross-sectonal dsperson measures for the sample perod 1968:Q4 2012:Q4. The vsual depcton of the dsperson measures n Fgure A2 ndcates that these economc uncertanty measures closely follow large falls and rses n fnancal and economc actvty. Specfcally, economc uncertanty s hgher durng economc and fnancal market downturns. Smlarly, uncertanty s hgher durng perods correspondng to hgh levels of default and credt rsk as well as stock market crashes. Lastly, uncertanty about nflaton, uncertanty about output growth, and uncertanty about unemployment are generally hgher durng bad states of the economy, correspondng to perods of hgh unemployment, low output growth, and low economc actvty. 4 2.2. Economc uncertanty ndex In ths secton, we ntroduce a broad ndex of economc uncertanty based on nnovatons n the crosssectonal dsperson n economc forecasts. As presented n the last column of Table A1, Panel A, the cross-sectonal dsperson measures are hghly persstent. The frst-order autocorrelaton, AR(1), coeffcents are n the range of 0.28 0.73. Snce the AR(1) coeffcents are sgnfcantly below one, unexpected change (or nnovaton) n the economc predctons of professonal forecasters s not defned wth a smple change n dsperson measures. Instead, we estmate the followng autoregressve process of order one, AR(1), for each dsperson measure: Z t = ω 0 + ω 1 Z t 1 + ε t, (3) 4 Specfcally, the peaks n Fgure A2 closely follow major economc and fnancal crses such as the 1973 ol crss, the 1973 1974 stock market crash, the 1979 1982 hgh nterest rate perod, the 1980s Latn Amercan debt crss, the 1989-1991 savngs and loan crss n the Unted States, the recesson of the early 1990s, the 1997 1998 Asan and Russan fnancal crses, the recesson of the early 2000s, and the recent global fnancal crss (2007-2009). 6
where Z t s one of the seven measures of cross-sectonal dsperson n economc forecasts, that s, the RGDP growth and level, the NGDP growth and level, the GDP prce ndex growth and level (proxyng for the nflaton rate), and the unemployment rate. For each dsperson measure and for each quarter, we estmate equaton (3) usng the quarterly rollng regressons over a 20-quarter fxed wndow and generate the standardzed resduals from the AR(1) model. The economc uncertanty ndex (UNC AV G ) s defned as the average of the standardzed resduals for the seven dsperson measures and can be vewed as a broad measure of the shock to dsperson n the forecasts of output, nflaton and unemployment. The frst-order autocorrelaton coeffcents of the nnovatons n dsperson measures are n the range from 0.04 to 0.18, much lower than the seral correlatons n the raw measures of dsperson (n absolute magntude). Ths result ndcates that the standardzed resduals from the AR(1) model successfully remove the predctable component of the dsperson measures so that the economc uncertanty ndex (UNC AV G ) s a measure of uncertanty shock that captures dfferent aspects of dsagreement over macroeconomc fundamentals and also reflects unexpected news or surprse about the state of the aggregate economy. It s mportant to note that the economc uncertanty ndex s generated for each quarter usng past nformaton only, so that there s no look-ahead bas n our emprcal analyses. Moreover, the economc uncertanty ndex s formed based on ex-ante predctons of professonal forecasters so that the exposure of stocks to nnovatons n dsperson measures s an ex-ante measure of the uncertanty beta. Thus, we nvestgate the purely out-of-sample cross-sectonal predctve power of economc uncertanty. One may argue that not all dsperson measures contrbute equally to overall uncertanty n the macro economy. To address ths potental concern, we ntroduce an alternatve measure of the economc uncertanty ndex usng prncpal component analyss (PCA). Specfcally, we extract the frst prncpal component of the nnovatons n seven dsperson measures wthout mposng equal weghts. Ths alternatve ndex s defned as the frst prncpal component of the standardzed resduals from AR(1) 7
regressons, Stdres, whch explans about two-thrds of the total varaton n these measures. Hence, we obtan a broad measure of economc uncertanty usng ths frst component: 5 UNC PCA t = 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 weghts attached to the standardzed resduals are not reported, the economc uncertanty ndex obtaned from the frst prncpal component (UNC PCA ) loads farly evenly on the nnovatons n seven dsperson measures, suggestng a strong correlaton wth the smpler uncertanty ndex (UNC AV G ) defned as the average of the standardzed resduals. Fgure 1 depcts the two broad ndces of economc uncertanty (UNC AV G and UNC PCA ) whch are almost dentcal (wth a sample correlaton of 0.98). Smlar to our fndngs for ndvdual dsperson measures (shown n Fgure A2), the broad ndex of economc uncertanty s generally hgher durng bad states of the economy, correspondng to perods of hgh unemployment, low output growth, and low economc actvty. The economc uncertanty ndex also tracks large fluctuatons n busness condtons. 2.3. Cross-sectonal return predctors Our stock sample ncludes all common stocks traded on the NYSE, Amex, and Nasdaq exchanges from July 1963 through December 2012. We elmnate stocks wth a prce per share less than $5 or more than $1,000. The daly and monthly return and volume data are from the CRSP. We adjust stock returns for delstng to avod survvorshp bas (Shumway 1997). 6 Accountng varables are obtaned from the merged CRSP-Compustat database. Analysts earnngs forecasts come from the Insttutonal Brokers 5 Note that we do not have a look-ahead bas when estmatng the frst prncpal component of the resduals because we use the expandng wndow wth the frst estmaton wndow set to be the frst 20 quarters and then updated on a quarterly bass. Hence, the weghts (w 1,t..w 7,t ) attached to the standardzed resduals n equaton (4) are tme dependent. 6 Specfcally, when a stock s delsted, we use the delstng return from the CRSP, f avalable. Otherwse, we assume the delstng return s -100%, unless the reason for delstng s coded as 500 (reason unavalable), 520 (went over the counter), 551 573, 580 (varous reasons), 574 (bankruptcy), or 584 (does not meet exchange fnancal gudelnes). For these observatons, we assume that the delstng return s -30%. 8
Estmate System (I/B/E/S) dataset and cover the perod from 1983 to 2012. In ths secton, we provde the defntons of the stock-level varables used n predctng cross-sectonal returns. For each stock and for each quarter n our sample, we estmate the uncertanty beta from the quarterly rollng regressons of excess stock returns on the economc uncertanty ndex over a 20-quarter fxed wndow: R,t = α,t + β UNC,t UNCt AV G + ε,t, (5) where R,t s the excess return on stock n quarter t, UNC AV G t s the economc uncertanty ndex n quarter t, defned as the average of the standardzed resduals n equaton (3) for seven dsperson measures, and β UNC,t s the uncertanty beta for stock n quarter t. 7 Followng Fama and French (1992), we estmate the market beta of ndvdual stocks usng monthly returns over the pror 60 months f avalable (or a mnmum of 24 months). The sze (SIZE) s computed as the natural logarthm of the product of the prce per share and the number of shares outstandng (n mllons of dollars). Followng Fama and French (1992, 1993, 2000), the natural logarthm of the book-to-market equty rato at the end of June of year t, denoted BM, s computed as the book value of stockholder equty plus deferred taxes and nvestment tax credt (f avalable) mnus the book value of preferred stock at the end of the last fscal, t 1, scaled by the market value of equty at the end of December of year t 1. Dependng on avalablty, the redempton, lqudaton, or par value (n that order) s used to estmate the book value of preferred stock. Followng Jegadeesh and Ttman (1993), momentum (MOM) s the cumulatve return of a stock over a perod of 11 months endng one month pror to the portfolo formaton month. Followng Jegadeesh (1990), short-term reversal (REV) s defned as the stock return over the pror month. 7 As dscussed n Sectons 4.5 and 5, we use alternatve specfcatons of equaton (5) when estmatng β UNC. Specfcally, we control for market return and market volatlty factors and show that alternatve measures of uncertanty beta generate very smlar results n cross-sectonal return predctablty. Secton 4.5 also shows that our man fndngs reman ntact when we replace UNC AV G wth UNC PCA n the estmaton of the uncertanty beta. 9
Followng Amhud (2002), we measure the llqudty of stock n month t, denoted ILLIQ, as the rato of the daly absolute stock return to the daly dollar tradng volume averaged wthn the month: [ ] R,d ILLIQ,t = Avg, (6) VOLD,d where R,d and VOLD,d are the daly return and dollar tradng volume for stock on day d, respectvely. 8 A stock s requred to have at least 15 daly return observatons n month t. Amhud s llqudty measure s scaled by 10 6. as: Followng Harvey and Sddque (2000), the stock s monthly co-skewness (COSKEW) s defned COSKEW,t = E E [ ε,t R 2 ] m,t [ ε 2,t ] E [ R 2 m,t ], (7) where ε,t = R,t (α + β R m,t ) s the resdual from the regresson of the excess stock return (R,t ) aganst the contemporaneous excess return on the CRSP value-weghted ndex (R m,t ) usng the monthly return observatons over the pror 60 months (f at least 24 months are avalable). The rsk-free rate s measured by the return on one-month Treasury blls. 9 Followng Ang, Hodrck, Xng, and Zhang (2006), the monthly dosyncratc volatlty of stock (IVOL) s computed as the standard devaton of the daly resduals n a month from the regresson: R,d = α + β R m,d + γ SMB d + ϕ HML d + ε,d, (8) 8 Followng Gao and Rtter (2010), we adjust for nsttutonal features so that the Nasdaq and NYSE/Amex volumes are counted. Specfcally, dvsors of 2.0, 1.8, 1.6, and 1.0 are appled to the Nasdaq volume for the perods pror to February 2001, between February 2001 and December 2001, between January 2002 and December 2003, and n January 2004 and later years, respectvely. 9 At an earler stage of the study, followng Mtton and Vorknk (2007), co-skewness s defned as the estmate of γ,t n the regresson usng the monthly return observatons over the pror 60 months wth at least 24 monthly return observatons avalable: R,t = α + β R m,t + γ,t R 2 m,t + ε,t, where R,t and R m,t are the monthly excess returns on stock and the CRSP value-weghted ndex, respectvely. The rsk-free rate s measured by the return on one-month Treasury blls. In addton to usng monthly returns over the past fve years, we use contnuously compounded daly returns over the past 12 months when estmatng the co-skewness of ndvdual stocks. Our man fndngs from these two alternatve measures of co-skewness turn out to be very smlar to those reported n our tables and they are avalable upon request. 10
where R,d and R m,d are, respectvely, the excess daly returns on stock and the CRSP value-weghted ndex, and SMB d and HML d are, respectvely, the daly sze and book-to-market factors of Fama and French (1993). Followng Dether, Malloy, and Scherbna (2002), analyst earnngs forecast dsperson (DISP) s defned as the standard devaton of annual earnngs-per-share forecasts scaled by the absolute value of the average outstandng forecast. Followng earler studes, we also control for frm age, leverage and ndustry effect. Frm age (AGE) s defned as the total number of months between the date when a stock frst appears n the CRSP database and the portfolo formaton month. We use a proxy for leverage (LEV) defned as the rato of net total assets to the market captalzaton of a stock. We control for the ndustry effect by assgnng each stock to one of the 10 ndustres based on ts four-dgt Standard Industral Classfcaton (SIC) code. The ndustry defntons are obtaned from the onlne data lbrary of Kenneth French. 3. A condtonal asset prcng model wth economc uncertanty Merton s (1973) ICAPM mples the followng equlbrum relaton between expected return and rsk for any rsky asset : µ = A σ m + B σ x, (9) where µ denotes the uncondtonal expected excess return on rsky asset, σ m denotes the uncondtonal covarance between the excess returns on rsky asset and the market portfolo m, and σ x denotes the (1 k)th row of uncondtonal covarances between the excess returns on rsky asset and the k-dmensonal state varables x. The varable A s the relatve rsk averson of market nvestors and B measures the market s aggregate reacton to shfts n a k-dmensonal state vector that governs the stochastc nvestment opportunty set. Equaton (9) states that n equlbrum, nvestors are compensated n terms of expected returns for bearng market rsk and the rsk of unfavorable shfts n the nvestment opportunty set. 11
The second term n equaton (9) reflects nvestors demand for the asset as a vehcle to hedge aganst unfavorable shfts n the nvestment opportunty set. Merton (1973) uses the example of a stochastc nterest rate to llustrate the role of ntertemporal hedgng demand. He ponts out that a postve covarance of asset returns wth nterest rate shocks (or nnovatons n nterest rate) predcts a lower return on the rsky asset. In the context of Merton s ICAPM, an ncrease n nterest rate predcts a decrease n nvestment demand (snce the cost of borrowng s hgh) and a decrease n optmal consumpton, whch leads to an unfavorable shft n the nvestment opportunty set. Rsk-averse nvestors wll demand more of an asset the more postvely correlated the asset s return s wth changes n the nterest rate, because they wll be compensated by a hgher level of wealth through the postve correlaton of the returns. That asset can be vewed as a hedgng nstrument. In other words, an ncrease n the covarance of returns wth nterest rate rsk leads to an ncrease n the hedgng demand, whch, n equlbrum, reduces the expected return on the asset. 10,11 There s substantal evdence that economc uncertanty s a relevant state varable affectng future consumpton and nvestment decsons. Bloom, Bond, and Reenen (2007), Bloom (2009), and Bloom et al. (2012) ntroduce a theoretcal model lnkng macroeconomc shocks to aggregate output, employment and nvestment dynamcs. Chen (2010) proposes a model that shows how busness cycle varatons n economc uncertanty and rsk premums nfluence frms fnancng decsons. Chen (2010) also shows that countercyclcal fluctuatons n rsk prces arse through stocks responses to macroeconomc condtons. Stock and Watson (2012) fnd that the declne n aggregate output and employment durng the recent crss perod s drven by fnancal and macroeconomc shocks. Allen, Bal, and Tang (2012) show that downsde rsk n the fnancal sector predcts future economc downturns, lnkng economc uncertanty to the future nvestment opportunty set. 12 10 Assets that covary postvely wth nterest rates may have hgher or lower average returns (controllng for ther covarance wth current wealth) dependng on whether the coeffcent of relatve rsk averson s greater or less than one. Thus, Merton (1973) ponts out that the relaton between changes n nterest rates and optmal consumpton depends on preferences, but hs footnote 34 (Merton 1973, p.885) ndcates that the relaton holds for most people. 11 We note that the consumpton-based nterpretaton of the role of ntertemporal hedgng demand s not general, because wth Epsten-Zn preferences, nvestors may choose to ether ncrease current consumpton, lower t, or mantan t (for a gven level of wealth) n response to unfavorable shfts n nvestment opportuntes. Hence, our dscusson here depends on nvestor preferences n the context of a consumpton-based asset prcng model too. 12 By defnng nvestor uncertanty as the dsperson of predctons of mean market returns obtaned from the forecasts of aggregate corporate profts, Anderson, Ghysels, and Juergens (2009) fnd a postve ntertemporal relaton between the level of uncertanty and excess market returns. In a condtonal asset prcng model wth tme-varyng volatlty n the consumpton growth process, Bal and Zhou (2014) fnd a postve relaton between volatlty uncertanty and future stock returns. 12
Hence, our fndng that ndvdual stocks that have greater exposure to nnovatons n the economc uncertanty ndex earn commensurately lower returns than other stocks s consstent wth Merton s (1973) ntertemporal hedgng demand argument. To the extent that negatve covarance between asset returns and future consumpton opportuntes mples a postve rsk premum, we should expect that betas wth respect to an approprately defned ndex of economc uncertanty should be negatvely assocated wth rsk prema. Followng the aforementoned studes, we argue that an ncrease n economc uncertanty s an unfavorable shft n the nvestment opportunty set. Snce an ncrease n economc uncertanty makes nvestors concerned about future outcomes, t reduces optmal consumpton. Investors cut ther consumpton and nvestment demand so that they can save more to hedge aganst possble future downturns n the economy. To hedge aganst such an unfavorable shft, nvestors prefer holdng stocks that have hgher covarance wth economc uncertanty. Ths s because an ncrease n economc uncertanty wll ncrease the returns on these stocks due to postve ntertemporal correlaton. 13 Hence, when economc uncertanty ncreases, although ther optmal consumpton and future nvestment opportuntes declne, nvestors compensate for ths loss by obtanng a stronger wealth effect through an ncrease n the returns on those stocks that have postve correlaton wth economc uncertanty. Therefore, through ntertemporal hedgng demand, nvestors are wllng to hold stocks wth hgher covarance wth economc uncertanty, and they pay hgher prces and accept lower returns for stocks wth hgher uncertanty beta. 14 Followng Bal and Engle (2010), we model tme varatons n expected returns and covarances by ncludng tme-varyng parameters n the condtonal ICAPM: E[R,t+1 Ω t ] = A cov[r,t+1,r m,t+1 Ω t ] + B cov[r,t+1, X t+1 Ω t ], (10) 13 We compute the contemporaneous and predctve correlatons between the quarterly growth rate of consumpton and the economc uncertanty ndex. For the sample perod 1968:Q4 2012:Q4, the ntertemporal correlatons between consumpton growth and the economc uncertanty ndex are postve, n the range of 0.18 0.20, and hghly sgnfcant. 14 Campbell s (1993, 1996) two-factor ICAPM model uses a smlar argument for an ncrease n stock market volatlty beng an unfavorable shft n the nvestment opportunty set. Campbell, Gglo, Polk, and Turley (2014) extend the earler work of Campbell (1993, 1996) to allow for stochastc volatlty. 13
where R,t+1 and R m,t+1 are, respectvely, the return on rsky asset and the market portfolo m n excess of the rsk-free nterest rate, Ω t denotes the nformaton set at tme t that nvestors use to form expectatons about future returns, E[R,t+1 Ω t ] s the expected excess return on rsky asset at tme t + 1 condtonal on the nformaton set at tme t, cov[r,t+1,r m,t+1 Ω t ] measures the tme-t expected condtonal covarance between the excess returns on rsky asset and the market portfolo m, and cov[r,t+1, X t+1 Ω t ] measures the tme-t expected condtonal covarance between the excess returns on rsky asset and the nnovaton n the state varable X that affects future nvestment opportuntes. We re-wrte equaton (10) n terms of condtonal betas, nstead of condtonal covarances: E[R,t+1 Ω t ] = à E[β m,t+1 Ω t ] + B E[β x,t+1 Ω t ], (11) where à = A var[r m,t+1 Ω t ], B = B var[ X t+1 Ω t ], E[β m,t+1 Ω t ] s the condtonal market beta of asset, defned as the rato of the condtonal covarance between R,t+1 and R m,t+1 to the condtonal varance of R m,t+1, and E[β x,t+1 Ω t ] s the condtonal beta of asset wth respect to the nnovaton n the state varable X, defned as the rato of the condtonal covarance between R,t+1 and X t+1 to the condtonal varance of X t+1 : 15 E[β m,t+1 Ω t ] = cov[r,t+1,r m,t+1 Ω t ], var[r m,t+1 Ω t ] (12) E[β x,t+1 Ω t ] = cov[r,t+1, X t+1 Ω t ]. var[ X t+1 Ω t ] (13) Other studes (e.g., Bloom, Bond, and Van Reenen 2007; Bloom 2009; Bloom et al. 2012; Bekaert, Engstrom, and Xng 2009; Ludvgson and Ng 2009; Chen 2010; Stock and Watson 2012; and Allen, Bal, and Tang 2012) provde theoretcal and emprcal evdence that economc uncertanty s a relevant state varable proxyng for consumpton and nvestment opportuntes n the condtonal ICAPM framework. Hence, the economc uncertanty ndex used n ths paper can be vewed as a proxy for the state varable X n equaton (13). The beta n equaton (12) s referred to as the market beta, whle the beta n equaton (13) s referred to as the uncertanty beta. 15 Note that à and B are tme-varyng parameters that are estmated for each month usng the cross-secton of stock returns, the market beta, and the uncertanty beta n multvarate Fama-MacBeth regressons. 14
4. Emprcal results In ths secton, we conduct parametrc and nonparametrc tests to assess the predctve power of the uncertanty beta over future stock returns. Frst, we start wth unvarate portfolo-level analyses. Second, we dscuss average portfolo characterstcs to obtan a clear pcture of the composton of uncertanty beta portfolos. Thrd, we conduct bvarate portfolo-level analyses to examne the predctve power of the uncertanty beta after controllng for well-known stock characterstcs and rsk factors. Fourth, we present the unvarate and multvarate cross-sectonal regresson results. Fnally, we provde the results from a battery of robustness checks. 4.1. Unvarate portfolo-level analyss Exposures of ndvdual stocks to macroeconomc uncertanty are obtaned from quarterly rollng regressons of excess stock returns on the economc uncertanty ndex usng a 20-quarter fxed wndow estmaton. The frst set of uncertanty betas (β UNC ) are obtaned usng the sample from 1968:Q4 to 1973:Q3. Then, these quarterly uncertanty betas are used to predct the monthly cross-sectonal stock returns n the followng three months (October 1973, November 1973, and December 1973). Ths quarterly rollng regresson approach s used untl the sample s exhausted n December 2012. The cross-sectonal return predctablty results are reported from October 1973 to December 2012. Table 1 presents the unvarate portfolo results. For each month, we form decle portfolos by sortng ndvdual stocks based on ther uncertanty betas (β UNC ), where decle 1 contans stocks wth the lowest β UNC durng the past quarter, and decle 10 contans stocks wth the hghest β UNC durng the prevous quarter. The frst column n Table 1 reports the average uncertanty betas for the decle portfolos formed on β UNC usng the CRSP breakponts wth equal numbers of stocks n the decle portfolos. The last four columns n Table 1 present the average excess returns and the 4-factor alphas on the value-weghted and equal-weghted portfolos, respectvely. The frst column of Table 1 shows that movng from decle 1 to decle 10, there s sgnfcant crosssectonal varaton n the average values of β UNC ; the average uncertanty beta ncreases from 22.70 to 26.06. Another notable pont n Table 1 s that for the value-weghted portfolo, the next-month average excess return decreases almost monotoncally from 0.98% to 0.32% per month, when movng from the 15
lowest to the hghest β UNC decle. The average return dfference between decle 10 (hgh-β UNC ) and decle 1 (low-β UNC ) s 0.66% per month wth a Newey-West (1987) t-statstc of 2.75. 16 Ths result ndcates that stocks n the lowest β UNC decle generate about 7.92% hgher annual returns compared to stocks n the hghest β UNC decle. In addton to the average raw returns, Table 1 presents the magntude and statstcal sgnfcance of the dfferences n ntercepts (Fama-French-Carhart, or (FFC) four-factor alphas) from the regresson of the hgh-mnus-low portfolo returns on a constant, excess market return (MKT), a sze factor (SMB), a book-to-market factor (HML), and a momentum factor (MOM), followng Fama and French (1993) and Carhart (1997). 17 As shown n the thrd column of Table 1, for the value-weghted portfolo, the 4-factor (FFC) alpha decreases almost monotoncally from 0.44% to 0.33% per month, when movng from the lowest to the hghest β UNC decle. The dfference n alphas between the hgh-β UNC and lowβ UNC portfolos s 0.77% per month wth a Newey-West t-statstc of 2.99. Ths ndcates that after controllng for the well-known sze, book-to-market, and momentum factors, the return dfference between the hgh-β UNC and low-β UNC stocks remans negatve and statstcally sgnfcant. The last two columns of Table 1 show that smlar results are obtaned from the equal-weghted portfolos of β UNC. The average excess returns and the FFC alphas on the uncertanty beta portfolos decrease almost monotoncally. The average return and alpha dfferences between the hgh-β UNC and low-β UNC portfolos are about the same, 0.58% per month, and hghly sgnfcant wth Newey-West t-statstcs larger than three n absolute magntude. Next, we nvestgate the source of the rsk-adjusted return dfference between the hgh-β UNC and low- β UNC portfolos: Is t due to outperformance by low-β UNC stocks, underperformance by hghβ UNC stocks, or both? For ths, we focus on the economc and statstcal sgnfcance of the rsk-adjusted returns of decle 1 versus decle 10. As reported n Table 1, for both value-weghted and equal-weghted portfolos, the FFC alphas of stocks n decle 1 (low-β UNC stocks) are sgnfcantly postve, whereas the FFC alphas of stocks n decle 10 (hgh-β UNC stocks) are sgnfcantly negatve. Hence, we conclude 16 Newey-West (1987) adjusted standard errors are computed usng sx lags. 17 The factors small mnus bg (SMB), hgh mnus low (HML), and wnner mnus loser (MOM) are descrbed n and obtaned from Kenneth French s data lbrary: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/. 16
that the sgnfcantly negatve alpha spread between hgh-β UNC and low-β UNC stocks s due to both the outperformance by low-β UNC stocks and the underperformance by hgh-β UNC stocks. 18 Of course, the uncertanty betas documented n Table 1 are for the portfolo formaton month and, not for the subsequent month over whch we measure average returns. Investors may pay hgh prces for stocks that have exhbted hgh uncertanty beta n the past n the expectaton that ths behavor wll be repeated n the future, but a natural queston s whether these expectatons are ratonal. Table A2 of the onlne appendx nvestgates ths ssue by presentng the average quarter-to-quarter portfolo transton matrx. Specfcally, Panel A of Table A2 presents the average probablty that a stock n decle (defned by the rows) n one quarter wll be n decle j (defned by the columns) n the subsequent quarter. If the uncertanty betas were completely random, then all the probabltes should be approxmately 10%, snce a hgh or low uncertanty beta n one quarter should say nothng about the uncertanty beta n the followng quarter. Instead, all the dagonal elements of the transton matrx exceed 10%, llustratng that the uncertanty beta s hghly persstent. Of greater mportance, ths persstence s especally strong for the extreme portfolos. Panel A shows that for the one-quarter-ahead persstence of β UNC, stocks n decle 1 (decle 10) have a 73.95% (73.53%) chance of appearng n the same decle next quarter. Smlarly, Panel D of Table A2 shows that for the four-quarter-ahead persstence of β UNC, stocks n decle 1 (decle 10) have a 54.03% (54.68%) chance of appearng n the same decle the next four quarters. These results ndcate that the estmated hstorcal uncertanty betas successfully predct future uncertanty betas and hence are good proxes for the true condtonal betas, whch s mportant for nterpretatons of the results n terms of an equlbrum model such as the ICAPM. These results also show that the uncertanty betas are not smply characterstcs of frms that result n dfferences n expected returns, but proxes for a source of macroeconomc uncertanty. 18 As shown n Table A3 of the onlne appendx, very smlar results are obtaned when decle portfolos are formed based on the NYSE breakponts, whch are used to allevate the concerns that the CRSP decle breakponts are dstorted by the large number of small Nasdaq and Amex stocks (Fama and French, 1992). 17
4.2. Average portfolo characterstcs To obtan a clearer pcture of the composton of the uncertanty beta portfolos, Table 2 presents summary statstcs for the stocks n the decles. Specfcally, Table 2 reports the cross-sectonal averages of varous characterstcs for the stocks n each decle averaged across the months. We report average values for the uncertanty beta (β UNC ), the market share (Mkt. shr.), the prce n dollars (PRC), the market beta (BETA), the log market captalzaton (SIZE), the log book-to-market rato (BM), the return over the 11 months pror to portfolo formaton (MOM), the return n the portfolo formaton month (REV), a measure of llqudty (ILLIQ), co-skewness (COSKEW), dosyncratc volatlty (IVOL), analyst dsperson (DISP), frm age (AGE), and leverage (LEV). The defntons of these varables are gven n Secton 2.3. The portfolos exhbt nterestng patterns. Average market betas are hgher for the low-β UNC and hgh-β UNC portfolos, compared to decles 2 to 9. Not surprsngly, stocks n the hgh-β UNC portfolo have somewhat hgher market betas than those n the low-β UNC portfolo. Stocks n the extreme decles (decles 1 and 10) are smaller compared to those n decles 2 to 9. As expected, Table 2 shows that stocks n the low-β UNC and hgh-β UNC portfolos have somewhat lower share prces compared to those n decles 2 to 9, but there s no monotoncally ncreasng or decreasng pattern n the average prces of the stocks n the uncertanty beta portfolos. Average book-to-market and leverage ratos are lower for the low-β UNC and hgh-β UNC portfolos, compared to decles 2 to 9. Snce there s no sgnfcant dfference between the sze, value, and leverage characterstcs of stocks n the low-β UNC and hghβ UNC portfolos, the predctve power of the uncertanty beta cannot be explaned by sze, book-tomarket, or dstress rsk. A notable pont n Table 2 s that stocks n the extreme decles (decles 1 and 10) have hgher past one year returns; that s, stocks n the low-β UNC and hgh-β UNC portfolos are momentum wnners compared to those n decles 2 to 9. Snce there s no monotoncally ncreasng or decreasng pattern n the past one year return of uncertanty beta portfolos, momentum cannot explan the predctve power of the uncertanty beta ether. 18
Interestngly, stocks n the extreme decles (decles 1 and 10) have hgher past one month returns as well, that s, stocks n the low-β UNC and hgh-β UNC portfolos are short-term wnners compared to those n decles 2 to 9. However, agan there s no monotoncally ncreasng or decreasng pattern n the past one month return of the uncertanty beta portfolos. Hence, short-term reversal cannot explan the hgh (low) returns on low uncertanty (hgh uncertanty) beta stocks. There are no sgnfcant dfferences n the lqudty, dosyncratc volatlty, analyst dsperson, and frm age of average stocks n the low-β UNC and hgh-β UNC portfolos, but consstent wth earler studes, small and lower-prced stocks n the low-β UNC and hgh-β UNC portfolos are somewhat more volatle, llqud, younger, and have a hgher analyst dsperson compared to those n decles 2 to 9. However, the dfferences n the lqudty, volatlty, dsperson, and age of stocks n decles 1 and 10 are so trval that smlar to our fndngs for sze, prce, value, leverage, momentum, and reversal effects, lqudty, volatlty, dsperson, and age cannot explan the return predctablty of the uncertanty beta. The only varable that seems to have a strong correlaton wth the uncertanty beta (at the portfolo level) s co-skewness. When movng from the low-β UNC to the hgh-β UNC portfolos, average coskewness ncreases monotoncally from 0.09 to 0.02. Harvey and Sddque (2000) fnd that stocks wth hgh co-skewness generate low returns. Hence, co-skewness may potentally explan the hgh (low) returns on low uncertanty (hgh uncertanty) beta stocks. We address ths potental concern n the followng two sectons. Although there are no strkng patterns n average portfolo characterstcs (wth the excepton of co-skewness), n the followng sectons, we provde dfferent ways of dealng wth the potental nteracton of the uncertanty beta wth the market beta, sze, book-to-market, momentum, short-term reversal, lqudty, co-skewness, dosyncratc volatlty, analyst dsperson, frm age, and leverage. Specfcally, we test whether the negatve relaton between the uncertanty beta and the cross-secton of expected returns stll holds once we control for the usual suspects usng bvarate portfolo sorts and Fama-MacBeth (1973) regressons. 4.3. Bvarate portfolo-level analyss Ths secton examnes the relaton between the uncertanty beta and future stock returns after controllng for well-known cross-sectonal return predctors. We perform bvarate portfolo sorts on the 19
uncertanty beta (β UNC ) n combnaton wth the market beta (BETA), the log market captalzaton (SIZE), the log book-to-market rato (BM), momentum (MOM), short-term reversal (REV), llqudty (ILLIQ), co-skewness (COSKEW), dosyncratc volatlty (IVOL), analyst dsperson (DISP), frm age (AGE), and leverage (LEV). Table 3 reports the value-weghted portfolo results of these condtonal bvarate sorts. We control for the market beta (BETA) by frst formng decle portfolos ranked based on BETA. Then, wthn each BETA decle, we sort stocks nto decle portfolos ranked based on the uncertanty beta (β UNC ) so that decle 1 (decle 10) contans stocks wth the lowest (hghest) β UNC values. The frst column of Table 3 averages value-weghted portfolo returns across the 10 BETA decles to produce decle portfolos wth dsperson n β UNC but that contan all the stocks market betas. Ths procedure creates a set of β UNC portfolos wth very smlar levels of market beta, and hence these β UNC portfolos control for dfferences n market beta. The row (Hgh Low) n the frst column of Table 3 shows that after controllng for the market beta, the average return dfference between the hgh-β UNC and lowβ UNC value-weghted portfolos s about 0.55% per month wth a Newey-West t-statstc of 3.46. The 10 1 dfference n the 4-factor alphas s 0.48% per month wth a t-statstc of 2.91. Thus, the market beta does not explan the hgh (low) returns on low uncertanty (hgh uncertanty) beta stocks. We control for market captalzaton (SIZE) smlarly, wth the results reported n the second column n Table 3. Agan the effect of the uncertanty beta s preserved after controllng for sze, wth an average raw return dfference between the hgh-β UNC and low-β UNC decles of 0.52% per month and a correspondng t-statstc of 2.49. The 10 1 dfference n the FFC alphas s also negatve, 0.45% per month, and hghly sgnfcant. Table 3 shows that after controllng for the other cross-sectonal return predctors (book-to-market, momentum, short-term reversal, llqudty, co-skewness, volatlty, analyst dsperson, age, and leverage), the average return dfferences between the hgh-β UNC and low-β UNC portfolos are n the range of 0.41% to 0.68% per month. These average raw return dfferences are both economcally and statstcally sgnfcant. The correspondng rsk-adjusted return dfferences are averaged n the range of 0.55% to 0.73%, and are also hghly sgnfcant. These results ndcate that well-known cross- 20