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Have Individual Stocks Become More Volatile?An Empirical Exploration of Idiosyncratic RiskJOHN Y.CAMPBELL,MARTIN LETTAU,BURTON G.MALKIEL,and YEXIAO XU*ABSTRACTThis paper uses a disaggregated approach to study the volatility of common stocksat the market,industry,and firm levels.Over the period from 1962 to 1997 therehas been a noticeable increase in firm-level volatility relative to market volatility.Accordingly,correlations among individual stocks and the explanatory power of themarket model for a typical stock have declined,whereas the number of stocksneeded to achieve a given level of diversification has increased.All the volatilitymeasures move together countercyclically and help to predict GDP growth.Marketvolatility tends to lead the other volatility series.Factors that may be responsiblefor these findings are suggested.IT IS BY NOW A COMMONPLACE OBSERVATIONthat the volatility of the aggregatestock market is not constant,but changes over time.Economists have builtincreasingly sophisticated statistical models to capture this time variationin volatility.Simple filters such as the rolling standard deviation used byOfficer 1973!have given way to parametric ARCH or stochastic-volatilitymodels.Partial surveys of the enormous literature on these models are givenby Bollerslev,Chou,and Kroner 1992!,Hentschel 1995!,Ghysels,Harvey,and Renault 1996!,and Campbell,Lo,and MacKinlay 1997,Chapter 12!.Aggregate volatility is,of course,important in almost any theory of riskand return,and it is the volatility experienced by holders of aggregate indexfunds.But the aggregate market return is only one component of the returnto an individual stock.Industry-level and idiosyncratic firm-level shocks arealso important components of individual stock returns.There are severalreasons to be interested in the volatilities of these components.*John Y.Campbell is at Harvard University,Department of Economics and NBER;Lettau isat the Federal Reserve Bank of New York and CEPR;Malkiel is at Princeton University;andXu is at the University of Texas at Dallas.This paper merges two independent projects,Camp-bell and Lettau 1999!and Malkiel and Xu 1999!.Campbell and Lettau are grateful to Sang-joon Kim for his contributions to the first version of their paper,Campbell,Kim,and Lettau1994!.We thank two anonymous referees and Ren Stulz for useful comments and BenjaminZhang for pointing out an error in a previous draft.Jung-Wook Kim and Matt Van Vlack pro-vided able research assistance.The views are those of the authors and do not necessarily reflectthose of the Federal Reserve Bank of New York or the Federal Reserve System.Any errors andomissions are the responsibility of the authors.THE JOURNAL OF FINANCE VOL.LVI,NO.1 FEBRUARY 20011First,many investors have large holdings of individual stocks;they mayfail to diversify in the manner recommended by financial theory,or theirholdings may be restricted by corporate compensation policies.These inves-tors are affected by shifts in industry-level and idiosyncratic volatility,justas much as by shifts in market volatility.Second,some investors who do tryto diversify do so by holding a portfolio of 20 or 30 stocks.Conventionalwisdom holds that such a portfolio closely approximates a well-diversifiedportfolio in which all idiosyncratic risk is eliminated.However,the adequacyof this approximation depends on the level of idiosyncratic volatility in thestocks making up the portfolio.Third,arbitrageurs who trade to exploit themispricing of an individual stock as opposed to a pattern of mispricing acrossmany stocks!face risks that are related to idiosyncratic return volatility,notaggregate market volatility.Larger pricing errors are possible when idiosyn-cratic firm-level volatility is high Ingersoll 1987!,Chapter 7,Shleifer andVishny 1997!.Fourth,firm-level volatility is important in event studies.Events affect individual stocks,and the statistical significance of abnormalevent-related returns is determined by the volatility of individual stock re-turns relative to the market or industry Campbell et al.1997!,Chapter 4!.Finally,the price of an option on an individual stock depends on the totalvolatility of the stock return,including industry-level and idiosyncratic vol-atility as well as market volatility.Disaggregated volatility measures also have important relations with ag-gregate output in some macroeconomic models.Models of sectoral realloca-tion,following Lilien 1982!,imply that an increase in the industry-levelvolatility of productivity growth may reduce output as resources are di-verted from production to costly reallocation across sectors.Models of“cleans-ing recessions”Caballero and Hammour 1994!,Eden and Jovanovic 1994!emphasize similar effects at the level of the firm.An exogenous increase inthe arrival rate of information about management quality may temporarilyreduce output as resources are reallocated from low-quality to high-qualityfirms;alternatively,a recession that occurs for some other reason may re-veal information about management quality and increase the pace of real-location across firms.There is surprisingly little empirical research on volatility at the level ofthe industry or firm.A few papers use disaggregated data to study the“le-verage”effect,the tendency for volatility to rise following negative returnsBlack 1976!,Christie 1982!,Duffee 1995!.Engle and Lee 1993!use afactor ARCH model to study the persistence properties of firm-level volatil-ity for a few large stocks.Some researchers have used stock market data totest macroeconomic models of reallocation across industries or firms Loun-gani,Rush,and Tave 1990!,Bernard and Steigerwald 1993!,Brainard andCutler 1993!,or to explore the firm-level relation between volatility andinvestment Leahy and Whited 1996!.Roll 1992!and Heston and Rouwen-horst 1994!decompose world market volatility into industry and country-specific effects and study the implications for international diversification.Bekaert and Harvey 1997!construct a measure of individual firm disper-sion to study the volatility in emerging markets.2The Journal of FinanceThe purpose of this paper is to provide a simple summary of historicalmovements in market,industry,and firm-level volatility.We provide a de-composition of volatility that does not require the estimation of covariancesor betas for industries or firms.In the interest of simplicity we follow Mer-ton 1980!,Poterba and Summers 1986!,French,Schwert,and Stambaugh1987!,Schwert 1989!,and Schwert and Seguin 1990!and use daily datawithin each month to construct sample variances for that month,withoutimposing any parametric model to describe the evolution of variances overtime.Multivariate volatility models are notoriously complicated and diffi-cult to estimate.Furthermore,although the choice of a parametric modelmay be essential for volatility forecasting,it is less important for describinghistorical movements in volatility,because all models tend to produce his-torical fitted volatilities that move closely together.The reason for this wasfirst given by Merton 1980!and was elaborated by Nelson 1992!:withsufficiently high-frequency data,volatility can be estimated arbitrarily ac-curately over an arbitrarily short time interval.Recently Andersen et al.1999!have used a similar approach to produce daily volatilities from intra-daily data on the prices of large individual stocks.We first confirm and update Schwerts 1989!finding that market vola-tility has no significant trend using monthly data from 1926 to 1997.Wenext estimate market,industry,and firm-level variances using daily CRSPdata ranging from 1962 to 1997.We find that market and industry vari-ances have been fairly stable in that sample period also.However,firm-levelvariance displays a large and significant positive trend,more than doublingbetween 1962 and 1997.This finding is robust to plausible variations in ourmethodology,for example,downweighting the influence of the 1987 crash,fixing the number of firms in the sample,or using weekly or monthly re-turns instead of daily returns to estimate volatility.We conclude that,al-though the market as a whole has not become more volatile,uncertainty onthe level of individual firms has increased substantially over a 35-year pe-riod.Consistent with this observation,we find declines over time in thecorrelations among individual stocks and in the explanatory power of themarket model for a typical stock.We also study the variations of the volatility measures around their long-term trends.The three volatility measures are positively correlated witheach other as well as autocorrelated.Granger-causality tests suggest thatmarket volatility tends to lead the other volatility series.All three volatilitymeasures increase substantially in economic downturns and tend to leadrecessions.The volatility measuresparticularly industry-level volatilityhelp to forecast economic activity and reduce the significance of other com-monly used forecasting variables.The paper is organized as follows.In Section I we present the basic de-composition of volatility into market,industry,and idiosyncratic compo-nents.Section II directly measures trends in volatility.In Section III,weprovide alternative indirect evidence of increased idiosyncratic volatility.Herewe study correlations across individual stocks,the explanatory power of themarket model for individual stocks,and the number of stocks needed toHave Individual Stocks Become More Volatile?3achieve a given level of diversification.Section IV studies the lead-lag rela-tions among our volatility measures as well as their cyclical properties.InSection V,we suggest some factors that may have influenced the apparentincrease in idiosyncratic volatility.Section VI presents concluding comments.I.Estimation of Volatility ComponentsA.Volatility DecompositionWe decompose the return on a“typical”stock into three components:themarket-wide return,an industry-specific residual,and a firm-specific resid-ual.Based on this return decomposition,we construct time series of volatil-ity measures of the three components for a typical firm.Our goal is to definevolatility measures that sum to the total return volatility of a typical firm,without having to keep track of covariances and without having to estimatebetas for firms or industries.In this subsection,we discuss how we canachieve such a representation of volatility.The next subsection presents theestimation procedure and some details of the data sample.Industries are denoted by an i subscript and individual firms are indexedby j.The simple excess return of firm j that belongs to industry i in periodt is denoted as Rjit.This excess return,like all others in the paper,is mea-sured as an excess return over the Treasury bill rate.Let wjitbe the weightof firm j in industry i.Our methodology is valid for any arbitrary weightingscheme provided that we compute the market return using the same weights;in this application we use market value weights.The excess return of in-dustry i in period t is given by Rit5(jiwjitRjit.Industries are aggregatedcorrespondingly.The weight of industry i in the total market is denoted bywit,and the excess market return is Rmt5(iwitRit.The next step is the decomposition of firm and industry returns into thethree components.We first write down a decomposition based on the CAPM,and we then modify it for empirical implementation.The CAPM implies thatwe can set intercepts to zero in the following equations:Rit5 bimRmt1 I eit1!for industry returns andRjit5 bjiRit1 I hjit5 bjibimRmt1 bjiI eit1 I hjit2!for individual firm returns.1In equation 1!bimdenotes the beta for indus-try i with respect to the market return,and I eitis the industry-specific re-sidual.Similarly,in equation 2!bjiis the beta of firm j in industry i with1We could work with the market model,not imposing the mean restrictions of the CAPM,and allow free intercepts aiand ajiin equations 1!and 2!.However our goal is to avoidestimating firm-specific parameters;despite the well-known empirical deficiencies of the CAPM,we feel that the zero-intercept restriction is reasonable in this context.4The Journal of Financerespect to its industry,and I hjitis the firm-specific residual.I hjitis orthogonalby construction to the industry return Rit;we assume that it is also orthog-onal to the components Rmtand I eit.In other words,we assume that the betaof firm j with respect to the market,bjm,satisfies bjm5 bjibim.The weightedsums of the different betas equal unity:(iwitbim5 1,(jiwjitbji5 1.3!The CAPM decomposition 1!and 2!guarantees that the different com-ponents of a firms return are orthogonal to one another.Hence it permits asimple variance decomposition in which all covariance terms are zero:VarRit!5 bim2VarRmt!1 Var I eit!,4!VarRjit!5 bjm2VarRmt!1 bji2Var I eit!1 Var I hjit!.5!The problem with this decomposition,however,is that it requires knowledgeof firm-specific betas that are difficult to estimate and may well be unstableover time.Therefore we work with a simplified model that does not requireany information about betas.We show that this model permits a variancedecomposition similar to equations 4!and 5!on an appropriate aggregatelevel.First,consider the following simplified industry return decomposition thatdrops the industry beta coefficient bimfrom equation 1!:Rit5 Rmt1 eit.6!Equation 6!defines eitas the difference between the industry return Ritand the market return Rmt.Campbell et al.1997,Chapter 4,p.156!referto equation 6!as a“market-adjusted-return model”in contrast to the mar-ket model of equation 1!.Comparing equations 1!and 6!,we haveeit5 I eit1 bim2 1!Rmt.7!The market-adjusted-return residual eitequals the CAPM residual of equa-tion 4!only if the industry beta bim5 1 or the market return Rmt5 0.The apparent drawback of the decomposition 6!is that Rmtand eitare notorthogonal,and so one cannot ignore the covariance between them.Com-puting the variance of the industry return yieldsVarRit!5 VarRmt!1 Vareit!1 2 CovRmt,eit!5 VarRmt!1 Vareit!1 2bim2 1!VarRmt!,8!Have Individual Stocks Become More Volatile?5where taking account of the covariance term once again introduces the in-dustry beta into the variance decomposition.Note,however,that although the variance of an individual industry re-turn contains covariance terms,the weighted average of variances acrossindustries is free of the individual covariances:(iwitVarRit!5 VarRmt!1(iwitVareit!5 smt21 set2,9!where smt2 VarRmt!and set2(iwitVareit!.The terms involving betasaggregate out because from equation 3!(iwitbim5 1.Therefore we can usethe residual eitin equation 6!to construct a measure of average industry-level volatility that does not require any estimation of betas.The weightedaverage(iwitVarRit!can be interpreted as the expected volatility of a ran-domly drawn industry with the probability of drawing industry i equal to itsweight wit!.We can proceed in the same fashion for individual firm returns.Considera firm return decomposition that drops bjifrom equation 2!:Rjit5 Rit1 hjit,10!where hjitis defined ashjit5 I hjit1 bji2 1!Rit.11!The variance of the firm return isVarRjit!5 VarRit!1 Varhjit!1 2 CovRit,hjit!5 VarRit!1 Varhjit!1 2bji2 1!VarRit!.12!The weighted average of firm variances in industry i is therefore(jiwjitVarRjit!5 VarRit!1 shit2,13!where shit2(jiwjitVarhjit!is the weighted average of firm-level volatilityin industry i.Computing the weighted average across industries,using equa-tion 9!,yields again a beta-free variance decomposition:(iwit(jiwjitVarRjit!5(iwitVarRit!1(iwit(jiwjitVarhjit!5 VarRmt!1(iwitVareit!1(iwitshit25 smt21 set21 sht2,14!6The Journal of Financewhere sht2(iwitshit25(iwit(jiwjitVarhjit!is the weighted average offirm-level volatility across all firms.As in the case of industry returns,thesimplified decomposition of firm returns 10!yields a measure of averagefirm-level volatility that does not require estimation of betas.We can gain further insight into the relation between our volatility de-composition and that based on the CAPM if we aggregate the latter equa-tions 4!and 5!across industries and firms.When we do this we find thatset25 I set21 CSVtbim!smt2,15!whereI set2(iwitVar I eit!is the average variance of the CAPM industryshock I eit,and CSVtbim!(iwitbim2 1!2is the cross-sectional variance ofindustry betas across industries.Similarly,sht25 I sht21 CSVtbjm!smt21 CSVtbji!I set2,16!where I sht2(iwit(jiwjitVar I hjit!,CSVtbjm!(iwit(jwjitbjm2 1!2isthe cross-sectional variance of firm betas on the market across all firms inall industries,and CSVtbji!(iwit(jwjitbji2 1!2is the cross-sectionalvariance of firm betas on industry shocks across all firms in all industries.Equations 15!and 16!show that cross-sectional variation in betas canproduce common movements in our variance components smt2,set2,and sht2,even if the CAPM variance components I set2and I sht2do not move at all withthe market variance smt2.We return to this issue in Section IV.A,where weshow that realistic cross-sectional variation in betas has only small effectson the time-series movements of our volatility components.B.EstimationWe use firm-level return data in the CRSP data set,including firms tradedon the NYSE,the AMEX,and the Nasdaq,to estimate the volatility compo-nents in equation 14!based on the return decomposition 6!and 10!.Weaggregate individual firms into 49 industries according to the classificationscheme in Fama and French 1997!.2We refer to their paper for the SICclassification.Our sample period runs from July 1962 to December 1997.Obviously,the composition of firms in individual industries has changeddramatically over the sample period.The total number of firms covered bythe CRSP data set increased from 2,047 in July 1962 to 8,927 in December1997.The industry with the most firms on average over the sample is Fi-nancial Services with 628 increasing from 43 to 1,525 over the sample!,andthe industry with the fewest firms is Defense with 8 increasing from 3 to 12over the sample!.Based on average market capitalization,the three largest2They actually use 48 industries,but we group the firms that are not covered in theirscheme in an additional industry.Have Individual Stocks Become More Volatile?7industries on average over the sample are Petroleum0Gas 11 percent!,Fi-nancial Services 7.8 percent!and Utilities 7.4 percent!.Table 4 includes alist of the 10 largest industries.To get daily excess return,we subtract the30-day T-bill return divided by the number of trading days in a month.We use the following procedure to estimate the three volatility compo-nents in equation 14!.Let s denote the interval at which returns are mea-sured.We will use daily returns for most estimates but also consider weeklyand monthly returns to check the sensitivity of our results with respect tothe return interval.Using returns of interval s,we construct volatility esti-mates at intervals t.Unless otherwise noted,t refers to months.To estimatethe variance components in equation 14!we use time-series variation of theindividual return components within each period t.The sample volatility ofthe market return in period t,which we denote from now on as MKTt,iscomputed asMKTt5 smt25(stRms2 mm!2,17!where mmis defined as the mean of the market return Rmsover the sample.3To be consistent with the methodology presented above,we construct themarket returns as the weighted average using all firms in the sample in agiven period.The weights are based on market capitalization.Although thismarket index differs slightly from the value-weighted index provided in theCRSP data set,the correlation is almost perfect at 0.997.For weights inperiod t we use the market capitalization of a firm in period t 2 1 and takethe weights as constant within period t.For volatility in industry i,we sum the squares of the industry-specificresidual in equation 6!within a period t:seit25(steis2.18!As shown above,we have to average over industries to ensure that the co-variances of individual industries cancel out.T