《金融投资学》教学资源（英文文献）Have Individual Stocks Become More Volatile - An Empirical Exploration of Idiosyncratic Risk.

THE JOURNAL OF FINANCE.VOL.LVI,NO.1.FEBRUARY 2001 Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk JOHN Y.CAMPBELL,MARTIN LETTAU,BURTON G.MALKIEL, and YEXIAO XU* ABSTRACT This paper uses a disaggregated approach to study the volatility of common stocks at the market,industry,and firm levels.Over the period from 1962 to 1997 there has been a noticeable increase in firm-level volatility relative to market volatility. Accordingly,correlations among individual stocks and the explanatory power of the market model for a typical stock have declined,whereas the number of stocks needed to achieve a given level of diversification has increased.All the volatility measures move together countercyclically and help to predict GDP growth.Market volatility tends to lead the other volatility series.Factors that may be responsible for these findings are suggested. IT Is BY NOw A COMMONPLACE OBSERVATION that the volatility of the aggregate stock market is not constant,but changes over time.Economists have built increasingly sophisticated statistical models to capture this time variation in volatility.Simple filters such as the rolling standard deviation used by Officer (1973)have given way to parametric ARCH or stochastic-volatility models.Partial surveys of the enormous literature on these models are given by 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 risk and return,and it is the volatility experienced by holders of aggregate index funds.But the aggregate market return is only one component of the return to an individual stock.Industry-level and idiosyncratic firm-level shocks are also important components of individual stock returns.There are several reasons to be interested in the volatilities of these components. John Y.Campbell is at Harvard University,Department of Economics and NBER;Lettau is at the Federal Reserve Bank of New York and CEPR;Malkiel is at Princeton University;and Xu 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 Lettau (1994).We thank two anonymous referees and Rene Stulz for useful comments and Benjamin Zhang 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 reflect those of the Federal Reserve Bank of New York or the Federal Reserve System.Any errors and omissions are the responsibility of the authors

Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk JOHN Y. CAMPBELL, MARTIN LETTAU, BURTON G. MALKIEL, and YEXIAO XU* ABSTRACT This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period from 1962 to 1997 there has been a noticeable increase in firm-level volatility relative to market volatility. Accordingly, correlations among individual stocks and the explanatory power of the market model for a typical stock have declined, whereas the number of stocks needed to achieve a given level of diversification has increased. All the volatility measures move together countercyclically and help to predict GDP growth. Market volatility tends to lead the other volatility series. Factors that may be responsible for these findings are suggested. IT IS BY NOW A COMMONPLACE OBSERVATION that the volatility of the aggregate stock market is not constant, but changes over time. Economists have built increasingly sophisticated statistical models to capture this time variation in volatility. Simple filters such as the rolling standard deviation used by Officer ~1973! have given way to parametric ARCH or stochastic-volatility models. Partial surveys of the enormous literature on these models are given by 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 risk and return, and it is the volatility experienced by holders of aggregate index funds. But the aggregate market return is only one component of the return to an individual stock. Industry-level and idiosyncratic firm-level shocks are also important components of individual stock returns. There are several reasons to be interested in the volatilities of these components. * John Y. Campbell is at Harvard University, Department of Economics and NBER; Lettau is at the Federal Reserve Bank of New York and CEPR; Malkiel is at Princeton University; and Xu 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 Lettau ~1994!. We thank two anonymous referees and René Stulz for useful comments and Benjamin Zhang 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 reflect those of the Federal Reserve Bank of New York or the Federal Reserve System. Any errors and omissions are the responsibility of the authors. THE JOURNAL OF FINANCE • VOL. LVI, NO. 1 • FEBRUARY 2001 1

2 The Journal of Finance First,many investors have large holdings of individual stocks;they may fail to diversify in the manner recommended by financial theory,or their holdings may be restricted by corporate compensation policies.These inves- tors are affected by shifts in industry-level and idiosyncratic volatility,just as much as by shifts in market volatility.Second,some investors who do try to diversify do so by holding a portfolio of 20 or 30 stocks.Conventional wisdom holds that such a portfolio closely approximates a well-diversified portfolio in which all idiosyncratic risk is eliminated.However,the adequacy of this approximation depends on the level of idiosyncratic volatility in the stocks making up the portfolio.Third,arbitrageurs who trade to exploit the mispricing of an individual stock(as opposed to a pattern of mispricing across many stocks)face risks that are related to idiosyncratic return volatility,not aggregate market volatility.Larger pricing errors are possible when idiosyn- cratic firm-level volatility is high (Ingersoll (1987),Chapter 7,Shleifer and Vishny (1997)).Fourth,firm-level volatility is important in event studies. Events affect individual stocks,and the statistical significance of abnormal event-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 total volatility 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-level volatility 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 in the arrival rate of information about management quality may temporarily reduce output as resources are reallocated from low-quality to high-quality firms;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 of the industry or firm.A few papers use disaggregated data to study the "le- verage"effect,the tendency for volatility to rise following negative returns (Black (1976),Christie (1982),Duffee (1995)).Engle and Lee (1993)use a factor ARCH model to study the persistence properties of firm-level volatil- ity for a few large stocks.Some researchers have used stock market data to test macroeconomic models of reallocation across industries or firms(Loun- gani,Rush,and Tave(1990),Bernard and Steigerwald(1993),Brainard and Cutler (1993)),or to explore the firm-level relation between volatility and investment (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

First, many investors have large holdings of individual stocks; they may fail to diversify in the manner recommended by financial theory, or their holdings may be restricted by corporate compensation policies. These inves￾tors are affected by shifts in industry-level and idiosyncratic volatility, just as much as by shifts in market volatility. Second, some investors who do try to diversify do so by holding a portfolio of 20 or 30 stocks. Conventional wisdom holds that such a portfolio closely approximates a well-diversified portfolio in which all idiosyncratic risk is eliminated. However, the adequacy of this approximation depends on the level of idiosyncratic volatility in the stocks making up the portfolio. Third, arbitrageurs who trade to exploit the mispricing of an individual stock ~as opposed to a pattern of mispricing across many stocks! face risks that are related to idiosyncratic return volatility, not aggregate market volatility. Larger pricing errors are possible when idiosyn￾cratic firm-level volatility is high ~Ingersoll ~1987!, Chapter 7, Shleifer and Vishny ~1997!!. Fourth, firm-level volatility is important in event studies. Events affect individual stocks, and the statistical significance of abnormal event-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 total volatility 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-level volatility 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 in the arrival rate of information about management quality may temporarily reduce output as resources are reallocated from low-quality to high-quality firms; 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 of the industry or firm. A few papers use disaggregated data to study the “le￾verage” effect, the tendency for volatility to rise following negative returns ~Black ~1976!, Christie ~1982!, Duffee ~1995!!. Engle and Lee ~1993! use a factor ARCH model to study the persistence properties of firm-level volatil￾ity for a few large stocks. Some researchers have used stock market data to test macroeconomic models of reallocation across industries or firms ~Loun￾gani, Rush, and Tave ~1990!, Bernard and Steigerwald ~1993!, Brainard and Cutler ~1993!!, or to explore the firm-level relation between volatility and investment ~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. 2 The Journal of Finance

Have Individual Stocks Become More Volatile? 3 The purpose of this paper is to provide a simple summary of historical movements in market,industry,and firm-level volatility.We provide a de- composition of volatility that does not require the estimation of covariances or betas for industries or firms.In the interest of simplicity we follow Mer- ton(1980),Poterba and Summers(1986),French,Schwert,and Stambaugh (1987),Schwert (1989),and Schwert and Seguin(1990)and use daily data within each month to construct sample variances for that month,without imposing any parametric model to describe the evolution of variances over time.Multivariate volatility models are notoriously complicated and diffi- cult to estimate.Furthermore,although the choice of a parametric model may be essential for volatility forecasting,it is less important for describing historical movements in volatility,because all models tend to produce his- torical fitted volatilities that move closely together.The reason for this was first given by Merton (1980)and was elaborated by Nelson (1992):with sufficiently 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 Schwert's(1989)finding that market vola- tility has no significant trend using monthly data from 1926 to 1997.We next estimate market,industry,and firm-level variances using daily CRSP data ranging from 1962 to 1997.We find that market and industry vari- ances have been fairly stable in that sample period also.However,firm-level variance displays a large and significant positive trend,more than doubling between 1962 and 1997.This finding is robust to plausible variations in our methodology,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 on the level of individual firms has increased substantially over a 35-year pe- riod.Consistent with this observation,we find declines over time in the correlations among individual stocks and in the explanatory power of the market 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 with each other as well as autocorrelated.Granger-causality tests suggest that market volatility tends to lead the other volatility series.All three volatility measures increase substantially in economic downturns and tend to lead recessions.The volatility measures-particularly industry-level volatility- help 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,we provide alternative indirect evidence of increased idiosyncratic volatility.Here we study correlations across individual stocks,the explanatory power of the market model for individual stocks,and the number of stocks needed to

The purpose of this paper is to provide a simple summary of historical movements in market, industry, and firm-level volatility. We provide a de￾composition of volatility that does not require the estimation of covariances or betas for industries or firms. In the interest of simplicity we follow Mer￾ton ~1980!, Poterba and Summers ~1986!, French, Schwert, and Stambaugh ~1987!, Schwert ~1989!, and Schwert and Seguin ~1990! and use daily data within each month to construct sample variances for that month, without imposing any parametric model to describe the evolution of variances over time. Multivariate volatility models are notoriously complicated and diffi￾cult to estimate. Furthermore, although the choice of a parametric model may be essential for volatility forecasting, it is less important for describing historical movements in volatility, because all models tend to produce his￾torical fitted volatilities that move closely together. The reason for this was first given by Merton ~1980! and was elaborated by Nelson ~1992!: with sufficiently 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 Schwert’s ~1989! finding that market vola￾tility has no significant trend using monthly data from 1926 to 1997. We next estimate market, industry, and firm-level variances using daily CRSP data ranging from 1962 to 1997. We find that market and industry vari￾ances have been fairly stable in that sample period also. However, firm-level variance displays a large and significant positive trend, more than doubling between 1962 and 1997. This finding is robust to plausible variations in our methodology, 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 on the level of individual firms has increased substantially over a 35-year pe￾riod. Consistent with this observation, we find declines over time in the correlations among individual stocks and in the explanatory power of the market 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 with each other as well as autocorrelated. Granger-causality tests suggest that market volatility tends to lead the other volatility series. All three volatility measures increase substantially in economic downturns and tend to lead recessions. The volatility measures—particularly industry-level volatility— help 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, we provide alternative indirect evidence of increased idiosyncratic volatility. Here we study correlations across individual stocks, the explanatory power of the market model for individual stocks, and the number of stocks needed to Have Individual Stocks Become More Volatile? 3

4 The Journal of Finance achieve a given level of diversification.Section IV studies the lead-lag rela- tions among our volatility measures as well as their cyclical properties.In Section V,we suggest some factors that may have influenced the apparent increase in idiosyncratic volatility.Section VI presents concluding comments. I.Estimation of Volatility Components A.Volatility Decomposition We decompose the return on a "typical"stock into three components:the market-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 define volatility measures that sum to the total return volatility of a typical firm, without having to keep track of covariances and without having to estimate betas for firms or industries.In this subsection,we discuss how we can achieve such a representation of volatility.The next subsection presents the estimation procedure and some details of the data sample. Industries are denoted by an i subscript and individual firms are indexed by j.The simple excess return of firm j that belongs to industry i in period t is denoted as Rit.This excess return,like all others in the paper,is mea- sured as an excess return over the Treasury bill rate.Let wiit be the weight of firm j in industry i.Our methodology is valid for any arbitrary weighting scheme 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 Ri=jewRIndustries are aggregated correspondingly.The weight of industry i in the total market is denoted by wit,and the excess market return is Rmt=iwit Rit. The next step is the decomposition of firm and industry returns into the three components.We first write down a decomposition based on the CAPM, and we then modify it for empirical implementation.The CAPM implies that we can set intercepts to zero in the following equations: Rit =Bim Rmt Eit (1) for industry returns and Rm=B:Rt+可m =B元Bim Rmt+B元et+it (2) for individual firm returns.1 In equation (1)Bim denotes the beta for indus- try i with respect to the market return,and e is the industry-specific re- sidual.Similarly,in equation(2)B is the beta of firmjin industry i with We could work with the market model,not imposing the mean restrictions of the CAPM, and allow free intercepts a;and a in equations (1)and (2).However our goal is to avoid estimating firm-specific parameters;despite the well-known empirical deficiencies of the CAPM, we feel that the zero-intercept restriction is reasonable in this context

achieve a given level of diversification. Section IV studies the lead-lag rela￾tions among our volatility measures as well as their cyclical properties. In Section V, we suggest some factors that may have influenced the apparent increase in idiosyncratic volatility. Section VI presents concluding comments. I. Estimation of Volatility Components A. Volatility Decomposition We decompose the return on a “typical” stock into three components: the market-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 define volatility measures that sum to the total return volatility of a typical firm, without having to keep track of covariances and without having to estimate betas for firms or industries. In this subsection, we discuss how we can achieve such a representation of volatility. The next subsection presents the estimation procedure and some details of the data sample. Industries are denoted by an i subscript and individual firms are indexed by j. The simple excess return of firm j that belongs to industry i in period t 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 wjit be the weight of firm j in industry i. Our methodology is valid for any arbitrary weighting scheme 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 Rit 5 (j[i wjit Rjit . Industries are aggregated correspondingly. The weight of industry i in the total market is denoted by wit, and the excess market return is Rmt 5 (i wit Rit . The next step is the decomposition of firm and industry returns into the three components. We first write down a decomposition based on the CAPM, and we then modify it for empirical implementation. The CAPM implies that we can set intercepts to zero in the following equations: Rit 5 bim Rmt 1 eI it ~1! for industry returns and Rjit 5 bji Rit 1 hI jit 5 bji bim Rmt 1 bji eI it 1 hI jit ~2! for individual firm returns.1 In equation ~1! bim denotes the beta for indus￾try i with respect to the market return, and eI it is the industry-specific re￾sidual. Similarly, in equation ~2! bji is the beta of firm j in industry i with 1 We could work with the market model, not imposing the mean restrictions of the CAPM, and allow free intercepts ai and aji in equations ~1! and ~2!. However our goal is to avoid estimating firm-specific parameters; despite the well-known empirical deficiencies of the CAPM, we feel that the zero-intercept restriction is reasonable in this context. 4 The Journal of Finance

Have Individual Stocks Become More Volatile? 5 respect to its industry,and is the firm-specific residual.is orthogonal by construction to the industry return Rit;we assume that it is also orthog- onal to the components R and In other words,we assume that the beta of firm jwith respect to the market,Bim,satisfies Bim=BBim The weighted sums of the different betas equal unity: ∑0aBm=1,∑0m月a=1 (3) The CAPM decomposition (1)and (2)guarantees that the different com- ponents of a firm's return are orthogonal to one another.Hence it permits a simple variance decomposition in which all covariance terms are zero: Var(Rit)=Bin Var(Rmt)+Var(it), (4) Var(Rt)-β院mVar(Rmt)+B院Var(et)+Var(m): (5) The problem with this decomposition,however,is that it requires knowledge of firm-specific betas that are difficult to estimate and may well be unstable over time.Therefore we work with a simplified model that does not require any information about betas.We show that this model permits a variance decomposition similar to equations (4)and(5)on an appropriate aggregate level. First,consider the following simplified industry return decomposition that drops the industry beta coefficient Bim from equation (1): Rit Rmt eit. (6) Equation (6)defines eit as the difference between the industry return Rit and the market return Rm.Campbell et al.(1997,Chapter 4,p.156)refer to equation (6)as a "market-adjusted-return model"in contrast to the mar- ket model of equation (1). Comparing equations (1)and(6),we have t=et+（Bm-1)Rmt. (7) The market-adjusted-return residual eit equals the CAPM residual of equa- tion(4)only if the industry beta Bim=1 or the market return Rmt=0. The apparent drawback of the decomposition(6)is that Rmt and eit are not orthogonal,and so one cannot ignore the covariance between them.Com- puting the variance of the industry return yields Var(Rit)=Var(Rmt)+Var(Eit)+2 Cov(Rmt,Eit) Var(Rmt)+Var(Eit)+2(Bim -1)Var(Rmt), (8)

respect to its industry, and hI jit is the firm-specific residual. hI jit is orthogonal by construction to the industry return Rit; we assume that it is also orthog￾onal to the components Rmt and eI it. In other words, we assume that the beta of firm j with respect to the market, bjm, satisfies bjm 5 bjibim. The weighted sums of the different betas equal unity: ( i wit bim 5 1, ( j[i wjit bji 5 1. ~3! The CAPM decomposition ~1! and ~2! guarantees that the different com￾ponents of a firm’s return are orthogonal to one another. Hence it permits a simple variance decomposition in which all covariance terms are zero: Var~Rit ! 5 bim 2 Var~Rmt ! 1 Var~eI it !, ~4! Var~Rjit ! 5 bjm 2 Var~Rmt ! 1 bji 2 Var~eI it ! 1 Var~hI jit !. ~5! The problem with this decomposition, however, is that it requires knowledge of firm-specific betas that are difficult to estimate and may well be unstable over time. Therefore we work with a simplified model that does not require any information about betas. We show that this model permits a variance decomposition similar to equations ~4! and ~5! on an appropriate aggregate level. First, consider the following simplified industry return decomposition that drops the industry beta coefficient bim from equation ~1!: Rit 5 Rmt 1 eit . ~6! Equation ~6! defines eit as the difference between the industry return Rit and the market return Rmt. Campbell et al. ~1997, Chapter 4, p. 156! refer to equation ~6! as a “market-adjusted-return model” in contrast to the mar￾ket model of equation ~1!. Comparing equations ~1! and ~6!, we have eit 5 eI it 1 ~ bim 2 1!Rmt . ~7! The market-adjusted-return residual eit equals the CAPM residual of equa￾tion ~4! only if the industry beta bim 5 1 or the market return Rmt 5 0. The apparent drawback of the decomposition ~6! is that Rmt and eit are not orthogonal, and so one cannot ignore the covariance between them. Com￾puting the variance of the industry return yields Var~Rit ! 5 Var~Rmt ! 1 Var~eit ! 1 2 Cov~Rmt , eit ! 5 Var~Rmt ! 1 Var~eit ! 1 2~ bim 2 1!Var~Rmt !, ~8! Have Individual Stocks Become More Volatile? 5