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JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS Vol. 45, No. 3, June 2010, pp. 663–684COPYRIGHT 2010, MICHAEL G. FOSTER SCHOOL OF BUSINESS, UNIVERSITY OF WASHINGTON, SEATTLE, WA 98195doi:10.1017/S0022109010000232

A Reexamination of the Causes ofTime-Varying Stock Return Volatilities

Chu Zhang∗

Abstract

The decline of average stock return volatility in the 2001–2006 period provides an oppor-tunity to test various theories on why the average return volatility increased in the pre-2000period. This paper compares fundamentals-based theories with trading volume-based theo-ries. While both fundamentals-based and trading volume-based theories explain the upwardtrend in the average volatility in U.S. stocks from 1976 to 2000 and international stocksfrom 1990 to 2000, only the fundamentals-based theories explain the volatility pattern for2001–2006. Much of the variation in the stock return volatilities can be explained by thevariation in the earnings volatilities and proxies for growth options, but not by trading-related variables. Evidence also shows that the explanatory power of the fundamentalsvariables is time varying.

I. Introduction

Stock return volatility is at the center of asset pricing research. At the portfo-lio level, volatility is the simplest measure of investment risk. Campbell, Lettau,Malkiel, and Xu (2001) find that the average return volatility in the U.S. stockmarket increased during the period from 1962 to 1997. More importantly, it is theaverage idiosyncratic volatility that has been increasing, whereas the volatility ofthe value-weighted market portfolio does not follow an overall increasing pattern.This finding has prompted many studies on why the average return volatilitiesof individual stocks have increased. There are several possible causes, accord-ing to these studies, including increased stock ownership by financial institutions,deteriorating earnings, increasing earnings volatilities, increased earnings growth

∗Zhang, [email protected], Department of Finance, Hong Kong University of Science and Technol-ogy (HKUST), Clear Water Bay, Kowloon, Hong Kong. This paper was initially circulated under thetitle “The Fundamental Things Apply as Time Goes By: A Reexamination of the Causes of Time-Varying Stock Return Volatilities.” I thank Gang Li for his assistance in preparing the data, MungoWilson for related discussion, seminar participants at Fudan University and Tsinghua University, and,especially, Hendrik Bessembinder (the editor) and Tim Simin (the referee) for helpful comments onearlier versions of the paper. Financial support from the Hong Kong Research Grants Council (RGC)Competitive Earmarked Research Grant HKUST646007 is gratefully acknowledged. All remainingerrors are mine.

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options, changing profiles of the stocks listed in the exchanges, increased deriva-tive trading, etc. A consensus, however, has not been reached on identifying themain source of the observed increased stock return volatilities.

In this paper, time-varying stock return volatilities are reexamined. Whatmotivates this study is a recent change in the volatility pattern since the pub-lication of the paper by Campbell et al. (2001). During the 2001–2006 period,both the total volatilities and the idiosyncratic volatilities of individual stocksfell dramatically, reversing the increasing pattern that had lasted for about 40years. In the second half of 2007, stock return volatilities started to climb againand reached their all-time high in October 2008. There is no doubt that stockreturn volatilities will fluctuate in the future. These fluctuations offer an oppor-tunity to evaluate the various theories on the causes of time-varying volatilities.A good theory should predict the rise of the volatilities before 2000, the fall dur-ing the 2001–2006 period, and the rise again in 2008. There is evidence that thevolatility patterns differ across various economic sectors and industries. Thereis also evidence that a similar rise and fall pattern exists in average idiosyn-cratic volatilities across various international markets. A good theory should alsobe valid for the various sectors/industries in the U.S. and in markets of othercountries.

I compare two sets of theories on what causes stock return volatilities tochange. The first set of theories is based on fundamentals variables. Since a stock’sprice is the present value of all its future dividends paid from earnings, it is nat-ural to model return volatility as an increasing function of the uncertainty aboutcurrent and future earnings. According to this theory, stock returns become morevolatile simply because the fundamentals of the company, such as its earningsand sales, worsen, or the volatilities of the earnings and sales increase. The sec-ond set of theories has diverse sources, but they are all linked to return volatilitiesthrough trading volume. In the second half of the twentieth century, when theaverage stock return volatility increased, both institutional trading and derivativetrading dramatically increased. Also, during this period transaction costs fell sub-stantially and information about firm performance became more readily available,which induced more trading. It is natural to conjecture that increased stock returnvolatilities have something to do with institutional trading, derivative trading, andinformation-induced trading.

I examine the roles that fundamentals variables and trading volume-relatedvariables play in explaining time-varying return volatilities. The results for theentire U.S. market show that both fundamentals variables and trading volumevariables explain the upward trend in average volatilities up to 2000. However,trading volume variables lose their explanatory power for the period from 2001 to2006, while the explanatory power of the fundamentals variables remains strong.To a lesser extent, this is also confirmed by the averages of various sectors inthe U.S. and the averages of international markets. The evidence from the U.S.market also shows that the explanatory power of the fundamentals variables istime varying. Of the two fundamentals variables, the uncertainty about futureearnings growth appears to have better explanatory power than the uncertaintyabout the current earnings in explaining the idiosyncratic volatilities of the value-weighted averages of the U.S. market, especially when the market value peaked

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around 2000. However, the uncertainty about current earnings has a more robustrelationship with the return volatilities.

The rest of this paper is organized as follows. Section II briefly reviews theliterature that is directly relevant to volatility trends. Section III describes the data.Section IV presents the time-series regression results. The last section concludesthe paper.

II. A Brief Review of the Literature

The literature on stock return volatility is voluminous. The following is avery brief account of the various theories about why the average volatility has in-creased over time. Some theories are obvious and agreed upon among researchers,while others are more controversial. The theories that are based on traditional as-set pricing principles are called fundamentals-based theories, while the theoriesthat are related to the literature on microstructure and financial systems are calledtrading volume-based theories because the effects on stock return volatilities areall from the trading volume.

Theoretically, a stock’s price is the present value of its expected future divi-dends. It is not difficult to deduce that the volatility of stock returns is positivelyrelated to the conditional variance of future dividends under mild technical condi-tions. Vuolteenaho (2002) presents a model of this positive relationship. In empir-ical work, earnings data are often chosen to replace dividends because dividendsare generated at the managers’ discretion, which means that realized dividendscan be poor indicators of potential future dividends. Pastor and Veronesi (2003)use the sample variance of firm-level earnings to explain cross-sectional differ-ences in return volatilities, but not the time variation in return volatilities, becausethe earnings variances they construct are calculated with earnings across the en-tire sample period and have no time variation. Wei and Zhang (2006) constructearnings variances using firm-level earnings in the past 12 quarters and exam-ine their relation to return volatilities both cross sectionally and in time series.In both Pastor and Veronesi (2003) and Wei and Zhang (2006), realized earningsare used in addition to earnings variances because realized earnings also predictfuture earnings volatilities: A low or negative realized earnings number is typi-cally followed by greater uncertainty about future earnings than is a large, positiverealized earnings number. Wei and Zhang (2006) show that, cross sectionally, re-turn volatilities of individual stocks are negatively related to past earnings andpositively related to the sample variance of earnings. In a time-series analysis,the average earnings and earnings variance explain the trends in the average re-turn volatility. Irvine and Pontiff (2009) extend the work to consider the volatilityof cash flows and sales, allegedly due to increased market competition, and theyobtain similar results.

An obvious reason for the average stock return volatility to change over timeis the changing profile of the listed stocks, from which the average return volatil-ity is taken. That newly listed stocks have characteristics prone to higher volatilityis also observed by Fama and French (2004) and Schwert (2002). Wei and Zhang(2006) document that the number of firms included in the Center for Research in


Security Prices (CRSP) database substantially increased up to 1998, especially inthe 1980s with the inclusion of NASDAQ stocks. About one-third of the increas-ing trend in the average volatility can be attributed to newly listed companies,which tend to be smaller, younger, more high-tech oriented, and, above all, tohave lower earnings and higher earnings volatilities. Brown and Kapadia (2007)further examine the issue and find more evidence that newly listed companiescontribute to increasing stock return volatilities.

Schwert (2002) suggests that the unusually high return volatility during thelate 1990s could be attributed to technology firms and hints that the increasingvolatility is due to the increasing value of growth options associated with tech-nology advances. The idea that links volatility to growth options also belongs tothe fundamentals-based theories. While current earnings capture returns on as-sets in place, the present value of growth opportunities is an indispensable com-ponent of stock prices, especially for technology-oriented firms. It has becomecommon in finance textbooks to state that stock prices are determined as the sumof the present value of earnings at the current level and growth opportunities.In a recent paper, Cao, Simin, and Zhao (2008) use the market-to-book ratio ofassets (MABA), the market-to-book ratio of equity, and their variations as proxiesfor growth options and find that the value-weighted average idiosyncratic volatil-ity can be explained by these proxies. In addition, they report that an empiri-cal model using a proxy for growth options outperforms models using earningsvolatility.

The trading-based theories about volatility originate from various startingpoints. They share a common thread that their effects on stock return volatilityare caused by trading volume. Volatility is widely believed to be related to tradingvolume. Schwert (2002) proposes to study the relation between the upward trendin stock return volatilities and trading volume, citing the ever-declining tradingcosts as one reason that trading volume has increased over time. Another rea-son for the increasing trading volume is the information at the firm level thathas become more readily available due to improved regulations, better account-ing standards, and more coverage by analysts. Early empirical studies on therelationship between volume and volatility are summarized by Karpoff (1987).Karpoff’s evidence, however, is mixed. More recent studies report a positive re-lationship between return volatilities and trading volumes. A notable example byGallant, Rossi, and Tauchen (1992) is the most relevant to the work presented inthis paper.

The second half of the twentieth century saw a tremendous increase in in-stitutional trading. Thanks to the propagation of the idea of diversification, moreindividuals now invest in stocks through mutual funds and pension funds. Institu-tional trading allegedly causes higher volatility because of the large trading sizes,which may cause stock prices to move more easily. Xu and Malkiel (2003) analyzethe relationship between stock return volatility and institutional ownership and re-port a significantly positive association between the two. Bennett, Sias, and Starks(2003) report an increase over time in institutional holdings of smaller and riskierstocks that are known to be more volatile. This can potentially explain why theaverage stock return volatility has increased. It should be noted that institutionalownership is only used as a proxy for institutional trading because, obviously,

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ownership per se will not affect volatility. The result, however, is challenged ina recent paper by Brandt, Brav, Graham, and Kumar (2010). They confirm Xuand Malkiel’s (2003) result for high-priced stocks. But they contend that high-priced stocks are not responsible for the increased average return volatility. Low-priced stocks, which are responsible for the increased average return volatility, aremostly held and traded by retail investors. The relationship between return volatil-ity and institutional holdings is negative for low-priced stocks. As such, whetheror not institutional trading of stocks causes return volatility remains an unsettledquestion.

As in this paper, Brandt et al. (2010) question whether there is a sustainedtrend in idiosyncratic volatility. The difference between the two papers is that,while Brandt et al. (2010) document evidence of irrational trading behavior by re-tail investors during the late 1990s that allegedly caused a speculative bubble, thispaper investigates the extent to which changes in the volatility trend can be ex-plained by changes in the fundamentals. Another paper by Bekaert, Hodrick, andZhang (2008) also questions whether there is a continued trend in idiosyncraticvolatility in international markets. They focus on econometric modeling issues,however, rather than on the causes of the changing volatility.

III. Data

The U.S. data I use in this paper are from CRSP at the University of Chicago,Compustat, Datastream, and Thomson Financial. Daily return data for stockslisted on NYSE/AMEX/NASDAQ and monthly data on trading volume are fromCRSP. Quarterly accounting data are from Compustat. I use January 1976 as thestarting point and December 2006 as the ending point of the sample period be-cause before 1976 the number of firms with available earnings data and trad-ing volume data is small. Thomson Financial’s CDA/Spectrum database containsinstitutional holdings data (S34), which is the amount of a stock’s outstandingshares held by all financial institutions that are required to file reports to the Se-curities and Exchange Commission (SEC). The institutional holdings data areavailable from March 1980. I also use international data from Datastream as arobustness check.

A. Average Volatility: The U.S.

While in most related studies, researchers have followed the lead of Campbellet al. (2001) in defining volatility as the variance of returns, the term volatility inthis paper refers to the standard deviation of returns, which is more consistent withthe current market practice. This change makes no material difference. Volatilityas the conditional standard deviation is not directly observed. The early literature,such as that by Schwert (1989), uses the absolute value of unexpected monthlyreturns according to certain models of expected returns as the realized monthlyreturn volatility. More recent literature, however, has adopted the method of us-ing the sum of the squared daily returns within a month as the realized monthlyvolatility.


The definition of idiosyncratic volatility depends on the specification of thesystematic factors in the return-generating process. Let ritd be the return on stocki on trading day d in month t and let ftd be the daily observations of the factors onday d in month t, and assume that the returns are generated by

ritd = ait + b′it ftd + εitd,(1)

where the coefficients ait and bit are constant within a month but may changeacross months. The idiosyncratic volatility for stock i in month t is defined as

IVit =

(12

Dt∑d=1

ε2itd

)1/2

,(2)

where Dt is the number of trading days in month t and εitd is evaluated at theordinary least squares (OLS) estimates of ait and bit. Two sets of factors are con-sidered in this paper. The first set is the excess returns on the market portfolio,MKT. The second set consists of the three well-known factors, MKT, SMB, andHML, of Fama and French (1993). The two sets of idiosyncratic volatilities cor-responding to the two sets of factors are very similar, so only the one correspond-ing to the Fama-French factors is reported. I focus on value-weighted averagesin this paper and denote them as IVt. The IVt calculated from all the stocks islabeled as IV and is plotted in Graph A of Figure 1. The upward trend of thevalue-weighted average idiosyncratic volatility of all stocks, which is influencedmainly by large stocks, is not obvious until the late 1990s. The average volatil-ities declined sharply after 2000, with a brief surge in 2002. The level of value-weighted average idiosyncratic volatility at the end of 2006 is about the same asthat in the 1970s. Besides a spike in October 1987, the most volatile period inthe sample is the 5 years around 2000 when the stock prices were known to bevery high.

In addition to examining the average idiosyncratic volatility of all stocks,I also analyze the average idiosyncratic volatility of stocks in various sectors. I di-vide stocks into sectors according to the exchange on which they are traded, theirage (defined as the number of years they have been listed), and the industry theybelong to. More specifically, stocks are classified into three exchanges: NYSE,AMEX, and NASDAQ; and two age groups: YOUNG firms that have been listed7 or fewer years and MATURE firms that have been listed more than 7 years.1

These six averages, ALL, NYSE, AMEX, NASDAQ, YOUNG, and MATURE,are classified as U.S. aggregates. I also study 10 industries: consumer nondurables(food, tobacco, textiles, apparel, leather, and toys), consumer durables (cars, TVs,furniture, and household appliances), manufacturing (machinery, trucks, planes,chemicals, office furniture, paper, and commercial printing), energy (oil, gas, andcoal extraction and processing), high-tech business equipment (computers, soft-ware, and electronic equipment), telecom (telephone and television transmission),shops (wholesale, retail, etc.), health (health care, medical equipment, and drugs),utilities, and others (mines, construction, construction materials, transportation,

1The median of firm age for all firm/month observations is slightly less than 7.

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FIGURE 1

Value-Weighted Average IV, VROE, MABA, VOLD, and INST

Figure 1 plots the time series of the value-weighted average of idiosyncratic volatilities (IV) with respect to the three Fama-French factors, the sample volatility of return on equity (VROE), the market-to-book ratio of assets (MABA), the logarithmof trading volume in dollars (VOLD), and the holdings in percentage by institutions (INST).

Graph A. IV, VROE, and MABA

Graph B. VOLD and INST

hotels, bus services, entertainment, and finance). These 10 averages are classifiedas U.S. industries.

B. Fundamentals Variables: The U.S.

I consider two fundamentals variables: the volatility of return on equity(VROE) and the MABA. The return on equity for stock i in month t is the stock’smost recent quarterly earnings (annualized by a multiplier of 4), divided by themost recent book value of equity. Since financial statements are typically avail-able with a 3-month delay, I assume a 3-month delay for determining when theearnings data are available. Most observations of the annualized return on equityfall in the interval of (−3, 3). However, some extreme values lie outside the inter-val. To avoid spurious inferences from these extreme values, they are winsorizedat −3 and 3. The VROE used in this study, VROEit for stock i in month t, is thesquare root of the sample variance of the annualized quarterly return on equityover the last 12 quarters. The value-weighted average of VROEits in month t isdenoted as VROEt. Its time series is plotted in Figure 1 with the average idiosyn-cratic volatility. The value-weighted VROEt moves roughly with the trend of thevalue-weighted average total volatility. The time series of the average VROEt is


much smoother than the volatility series, partially because it is calculated as a12-quarter average.2

The market-to-book ratio of the assets of firm i in month t, denoted MABAit,is constructed as the market value of equity plus the book value of debt as themarket value of assets at the end of month t divided by the most recent book valueof assets at t using the 3-month delay assumption. The value-weighted average ofMABAit is denoted as MABAt. MABAt is used as a proxy for growth options.Cao et al. (2008) also use the book-to-market ratio of equity, the ratio of capitalexpenditure to fixed assets, the ratio of debt to equity, and another proxy for thepresent value of growth options. Since they report that all these proxies give ro-bust results, for brevity, these additional proxies are not analyzed in this paper.3

In Graph A of Figure 1, the value-weighted average MABA moves very closelywith the value-weighted average return volatility.

C. Trading Volume-Related Variables: The U.S.

Let VOLDit denote the trading volume for stock i in month t measured inthousands of dollars. Denote VOLDt as the logarithm of the value-weighted av-erage VOLDit. The plot in Graph B of Figure 1 shows that it increased over timewith the average idiosyncratic volatility before 2000. However, while the aver-age idiosyncratic volatility reduces after 2000, the value-weighted trading volumestays high. This observation casts doubt on the robustness of trading volume inexplaining volatility trends.

Let INSTit be the fraction of stock i held in month t by the so-called 13F fi-nancial institutions (mutual funds, pension funds, banks, insurance companies,university endowments, and numerous other professional investment advisers)that are required to file Form 13F with the SEC. Denote INSTt as the value-weighted average of INSTit. Graph B of Figure 1 plots its time series. The value-weighted average institutional holding increases from about 40% to above 60%during March 1980–December 2006 (1980.03–2006.12). The speed of the in-crease is fairly steady.

D. International Markets

Datastream includes data on both returns and accounting information ofinternational markets. Due to data constraints, I examine the average returnvolatilities in Australia, Canada, France, Germany, Italy, the U.K., Japan, HongKong, and Singapore during the period 1990.02–2006.12. Figure 2 plots thevalue-weighted average idiosyncratic volatilities with respect to the marketportfolios of the respective countries. The plots reveal that there is a pattern

2Wei and Zhang (2006) also use return on equity in their study because it tends to be negativelycorrelated with future VROE for most stocks. For large stocks in the second half of the sample period,this is no longer the case, as first noted by Wei and Zhang (2006) in their footnote 9. In studyingvalue-weighted average volatility in this paper, I do not use return on equity for the U.S. market.

3Cao et al. (2008) also use the sample variance of MABA as an additional explanatory variable.The variation in MABA, however, comes mostly from the market value, which is to be explained,rather than explanatory. It is well known that return volatilities are highly autocorrelated. The autore-gressive models of volatilities may fit the data well, but they do not answer questions about the causesof volatility trends. I avoid using the sample variances of MABA in this paper.

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similar to that in the U.S. in all these countries to various degrees. The volatilitiesincrease slowly before 2000 and decrease roughly after 2000. The turning pointvaries, however. The only exception is Japan, which had a stock market bubbleand burst around 1990, and the return volatility is unusually high at that time.

FIGURE 2

Value-Weighted Average Volatilities in International Markets

Figure 2 plots the time series of the value-weighted average idiosyncratic return volatility in Australia, Canada, France,Germany, Italy, the UK, Japan, Hong Kong, and Singapore.

Graph A. Australia, Canada, and France

Graph B. Germany, Italy, and the UK

Graph C. Japan, Hong Kong, and Singapore

The accounting data available from Datastream are on an annual basis. There-fore, VROE cannot be meaningfully constructed. I opt for using return on equityitself, denoted as ROE. Trading volume data are not available until 1990 for manycountries. Data on institutional holdings are not available either. The analysis be-low is conducted under these constraints. To conserve space, I skip the plots forthe fundamentals variables and the volume variables.

IV. Volatility Trends

To investigate the volatility trends, I begin with the following regressions:

IVt = a1D1t + a2D2t + (bt1D1t + bt2D2t)t + εt,(3)

IVt = a + btt + ε′t ,(4)


where D1t is the dummy variable for 1976.01–2000.12 and Dt2 is the dummyvariable for 2001.01–2006.12. The slope coefficients, bt1 and bt2, measure themonthly increment of the idiosyncratic volatility during the two subperiods, re-spectively. The hypothesis that the average volatility is described by a simplelinear trend for the entire sample period can be tested through the linear hypoth-esis (a1, bt1) = (a2, bt2), which is represented by regression model (4). Table 1reports the estimated slope coefficients using the U.S. aggregate data. LR(OLS) isthe likelihood ratio test of the linear hypothesis, known as the Chow test for test-ing the existence of a structural break, under the assumption that the error termis independent and identically distributed (i.i.d.) and the distribution is normal.LR(GMM) is the likelihood ratio test of the linear hypothesis with the generalizedmethod of moments (GMM) estimation under the assumption that the error term isautocorrelated with heteroskedasticity, as proposed by Newey and West (1987a).The numbers in the parentheses under the coefficient estimates are Newey andWest (1987b) t-ratios adjusted for autocorrelation and heteroskedasticity with alag of 24 months. It should be noted that regression models (3)–(4) are not meantto be good descriptive models for average idiosyncratic volatilities. They play therole of a simple structure to test the null hypothesis that there is a common trendin the volatilities in the entire sample period.

TABLE 1

Trends of Average Volatilities: U.S. Aggregates

Table 1 presents the results of regressions of the form

(3) IVt = a1D1t + a2D2t + (bt1D1t + bt2D2t )t + εt ,

(4) IVt = a + bt t + ε′t ,

where IV is the value-weighted average idiosyncratic volatility of ALL stocks; NYSE-, AMEX-, and NASDAQ-listed stocks;YOUNG firm stocks; and MATURE firm stocks. Here, D1t equals 1 for t from 1976.01 to 2000.12 and 0 from 2001.01 to2006.12, and D2t = 1 − D1t . The reported estimates of b1t , b2t , and bt are multiplied by 100. LR(OLS) is the likelihoodratio test of the constraint under the assumption that the error term is independent and identically distributed (i.i.d.) andnormally distributed, following the F(T − 4, 2) distribution, where T is the number of observations for the entire sampleperiod. LR(GMM) is the likelihood ratio test of the constraint under the assumption that the error term is autocorrelatedwith conditional heteroskedasticity, following the χ2

2 distribution asymptotically. The numbers in parentheses below the bestimates are t-statistics adjusted for autocorrelation and heteroskedasticity using the Newey-West (1987b) method (witha lag of 24 months). The numbers below the likelihood test statistics are their right-tail p-values.

Stocks bt1 bt2 bt LR(OLS) LR(GMM)

ALL 0.53 –3.00 0.23 100.16 45.33(2.91) (–5.73) (1.39) (0.00) (0.00)

NYSE 0.38 –2.52 0.14 84.05 46.41(2.42) (–6.25) (1.01) (0.00) (0.00)

AMEX 0.30 –2.97 –0.13 97.45 52.07(1.63) (–5.90) (–0.70) (0.00) (0.00)

NASDAQ 0.94 –4.75 0.31 264.70 62.71(6.41) (–4.58) (1.17) (0.00) (0.00)

YOUNG 0.97 –5.10 0.44 139.41 53.07(3.79) (–5.68) (1.63) (0.00) (0.00)

MATURE 0.41 –2.66 0.18 82.87 44.07(2.57) (–5.98) (1.27) (0.00) (0.00)

Except for the aggregate volatility of the stocks traded on AMEX, all thevolatility series have a significantly positive trend in the 1976–2000 subperiodand a significantly negative trend in the 2001–2006 subperiod. None of them havea significant trend over the entire sample period, however, as evidenced by the

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insignificant estimates, bts. For the six aggregate volatility series, the hypothesisthat they have the same structure during the two subperiods is strongly rejectedby the very low p-values of the likelihood ratio tests. During the two subperiods,it is the NASDAQ stocks and YOUNG firm stocks that have the largest rises andfalls in their idiosyncratic volatility.

Table 2 reports the same trend analysis for the 10 industries. Among the10 industries, consumer durables, manufacturing companies, high-tech compa-nies, telecom companies, shops, and health companies exhibit significant increasesin the value-weighted average idiosyncratic volatility, while others do not exhibitvery significant increases in 1976–2000. Except for the energy industry, all theindustries have significant declines in their idiosyncratic volatility. Over the en-tire sample period, all the industries have insignificant trend slopes except forthe consumer durables industry. The hypothesis that they have the same structureduring the two subperiods is also strongly rejected by the very low p-values of thelikelihood ratio tests.

TABLE 2

Trends of Average Volatilities: U.S. Industries

Table 2 presents the results of trend regressions for U.S. industries. The notation is the same as in Table 1.

U.S. Industries bt1 bt2 bt LR(OLS) LR(GMM)

Nondurables 0.20 –2.26 –0.02 70.21 61.05(1.40) (–7.55) (–0.18) (0.00) (0.00)

Durables 0.47 –1.44 0.32 30.28 15.16(3.43) (–3.08) (2.99) (0.00) (0.00)

Manufacturing 0.38 –2.20 0.13 64.19 23.91(2.25) (–4.04) (0.94) (0.00) (0.00)

Energy 0.21 –1.09 0.06 18.65 6.84(1.26) (–1.86) (0.49) (0.00) (0.03)

High-Tech 1.00 –4.65 0.54 191.50 48.96(6.05) (–5.58) (2.35) (0.00) (0.00)

Telecom 0.93 –4.09 0.60 122.87 77.39(4.50) (–7.60) (2.98) (0.00) (0.00)

Shops 0.48 –2.54 0.14 112.55 50.12(3.26) (–5.70) (0.94) (0.00) (0.00)

Health 0.56 –2.51 0.27 87.19 128.35(3.82) (–8.55) (1.91) (0.00) (0.00)

Utilities 0.09 –3.41 0.10 66.91 40.24(0.66) (–6.04) (0.85) (0.00) (0.00)

Others 0.31 –2.28 –0.00 105.96 55.82(2.14) (–5.86) (–0.02) (0.00) (0.00)

Table 3 reports the results of the trend analysis for the international mar-kets. Except for Japan, all the countries have significant increases in idiosyncraticvolatility during 1990.02–2000.12. All the countries have significant decreasesin idiosyncratic volatility during 2001.01–2006.12. Over the entire sample of1990.02–2006.12, no country has a significantly positive trend in idiosyncraticvolatility. The hypothesis of equal coefficients of the regression model for the twosubperiods is strongly rejected for all the countries.

The results presented in this section clearly indicate that there are rises andfalls in the idiosyncratic volatility in all the sectors/industries of the U.S. market


TABLE 3

Trends of Average Volatilities: International Markets

Table 3 presents the results of trend regressions for the international markets. The notation is the same as in Table 1, exceptfor the beginning of the first subperiod, which is 1990.02.

Markets by Country bt1 bt2 bt LR(OLS) LR(GMM)

Australia 0.66 –0.84 0.15 33.84 12.49(3.53) (–2.05) (1.19) (0.00) (0.00)

Canada 1.41 –1.48 0.35 75.80 36.02(4.09) (–4.11) (1.64) (0.00) (0.00)

France 1.29 –3.08 0.00 93.06 64.01(3.84) (–6.83) (0.01) (0.00) (0.00)

Germany 1.62 –2.40 0.44 88.38 66.76(3.87) (–6.34) (1.41) (0.00) (0.00)

Italy 1.03 –2.04 –0.12 64.07 66.19(5.02) (–6.02) (–0.43) (0.00) (0.00)

UK 1.49 –2.62 0.27 76.68 63.51(3.06) (–6.88) (0.90) (0.00) (0.00)

Japan 1.19 –2.29 0.02 37.38 26.28(1.81) (–4.97) (0.06) (0.00) (0.00)

Hong Kong 1.47 –1.10 0.37 46.05 50.99(4.99) (–3.03) (1.76) (0.00) (0.00)

Singapore 2.09 –2.09 0.47 86.42 42.10(5.29) (–3.37) (1.46) (0.00) (0.00)

and various international markets. Overall, there is no sustained upward lineartrend in the U.S. sectors, industries, or international markets.

V. Fundamentals- versus Trading Volume-BasedExplanations

In this section, I present time-series regression results that compare the per-formance of the fundamentals-based theories with the trading volume-based the-ories in explaining the pattern of the idiosyncratic volatility of stock returns.Strictly speaking, since volatility is positive, a positive function is required to de-scribe its relationship with other variables. It turns out that the qualitative resultsare the same whether volatility or log volatility is used as the dependent variable.I report the results of the former because they can be compared more easily withthe results in the literature.

A. U.S. Aggregates

I begin with a reexamination of each of the explanatory variables individ-ually. I estimate the slope coefficients in the univariate regressions of IVt onVROEt−1, MABAt−1, VOLDt−1, and INSTt−1. The univariate regression takesthe form

IVt = (ax1D1t + ax2D2t) + (bx1D1t + bx2D2t)xt−1 + εt,(5)

where x is VROE, MABA, VOLD, or INST; D1t equals 1 for t in 1976.01–2000.12(1980.03–2000.12 for INST) and 0 in 2001.01–2006.12; and D2t = 1 − D1t.

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In addition, I run regressions in which the coefficients in the two subperiods areconstrained to be the same,

IVt = ax + bxxt−1 + ηt,(6)

and I run a regression of the estimated residual on the time trends,

ηt = (at1D1t + at2D2t) + (bt1D1t + bt2D2t)t + ξt.(7)

Like those in the trend analysis, LR(OLS) and LR(GMM) are the likelihood ratiotests of the hypothesis (ax1, bx1)=(ax2, bx2). As a legitimate explanatory variable,the sign of the coefficients, bx1 and bx2, will not change across the two subperiodseven when the trend in the idiosyncratic return volatility reverses. If the relation-ship between the idiosyncratic volatility and the explanatory variable is stable,the magnitudes of the coefficients for the two subperiods will not be too differenteither. In addition, if the variable is adequate in explaining the return volatility byitself, the residual, ηt, will not contain trend components.

The estimated slope coefficients for the U.S. aggregates are reported inTable 4. The results in Panel A show that the slope coefficients of VROE are sig-nificantly positive in both subperiods for U.S. aggregate averages except AMEX.The hypothesis of no structural break is rejected, however. The estimated slopecoefficient for the entire period under the constraint of no structural break is lesssignificant than is the estimated slope coefficient for the first subperiod in mostcases. More importantly, the residual from the regression under the constraint ofno structural break still has a positive trend in the first subperiod and a negativetrend in the second subperiod in all cases, although it is not always significant.

The results in Panel B of Table 4 indicate that the slope coefficients of MABAare significantly positive in both subperiods for all U.S. aggregate averages exceptAMEX, for which the slope coefficient in the second subperiod is significantlynegative. The hypothesis of no structural break is rejected at the 0.01 level for allthe cases except NYSE after adjustments for autocorrelation and heteroskedastic-ity. The estimated slope coefficient under the constraint of no structural break issignificantly positive for all cases, including NYSE, whose value is very small.The residuals under the constraint of no structural break contain a significantlypositive trend in the first subperiod for ALL, NASDAQ, and YOUNG firm stocks.

Panel C of Table 4 reports the estimated slope coefficients of VOLD. Theyare all significantly positive for the first subperiod, but mixed for the second sub-period. The slope coefficient for the entire sample is insignificant except for NAS-DAQ, which is positive and marginally significant. Under the constraint of nostructural break, the residuals of all aggregates contain a significantly positivetrend in the first subperiod and a negative, though not significant, trend in thesecond subperiod.4

Panel D of Table 4 reports the estimated slope coefficients of INST.As anticipated from Figure 1, they are positive for the first subperiod, negative

4It is worth noting that the other volume variable, volume in shares, is even worse as an explanatoryvariable for the time-varying return volatility. While VOLD declined as the stock prices declined after2000, the volume in shares continued to soar. If volume in shares is used, the slope coefficients in thesecond subperiods are significantly negative for all U.S. aggregates.


for the second subperiod, and insignificant for the entire sample period under theconstraint of no structural break. The hypothesis of no structural break is stronglyrejected, and the residuals estimated from the constraint of no structural breakexhibit a significant, positive trend in the first subperiod and a not-so-significant,negative trend in the second subperiod.

The results of univariate regressions clearly indicate that the fundamentalsvariables do a much better job than the trading volume variables in explainingthe variation in the return volatilities. Between the two fundamentals variables,

TABLE 4

Univariate Regressions: U.S. Aggregates

Table 4 presents estimates of slope coefficients in univariate regressions of value-weighted average idiosyncratic volatilitieson various explanatory variables,

(5) IVt = (ax1D1t + ax2D2t ) + (bx1D1t + bx2D2t )xt−1 + εt ,

where IV is the value-weighted average idiosyncratic volatility; x is the value-weighted average volatility of return on equity(VROE), market-to-book assets (MABA), the logarithm of trading volume in dollars (VOLD), or the holding percentage byinstitutions (INST); D1t equals 1 for t from 1976.01 (1980.03 for INST) to 2000.12 and 0 from 2001.01 to 2006.12; andD2t = 1− D1t . The table also reports estimate of slope estimate of the constrained regressions,

(6) IVt = ax + bx xt−1 + ηt ,

(7) ηt = (at1D1t + at2D2t ) + (bt1D1t + bt2D2t )t + ξt .

LR(OLS) is the likelihood ratio test of the hypothesis (ax1, bx1)=(ax2, bx2) under the assumption that the error term is i.i.d.and normally distributed, following the F(T− 4, 2) distribution where T is the number of observations for the entire sampleperiod. LR(GMM) is the likelihood ratio test of the constraint under the assumption that the error term is autocorrelatedwith conditional heteroskedasticity, following the χ2

2 distribution asymptotically. The reported estimates of b1t and b2t aremultiplied by 100. The numbers in parentheses below the b estimates are t-statistics adjusted for autocorrelation andheteroskedasticity using the Newey-West (1987b) method (with a lag of 24 months). The numbers below the likelihood teststatistics are their right-tail p-values.

Panel A. VROE

Stocks bVROE1 bVROE2 bVROE LR(OLS) LR(GMM) bt1 bt2

ALL 1.42 2.21 0.98 47.24 36.63 0.14 –2.29(3.04) (3.94) (2.18) (0.00) (0.00) (2.21) (–1.28)

NYSE 1.07 1.85 0.73 33.61 34.02 0.11 –2.09(2.44) (4.34) (1.78) (0.00) (0.00) (2.23) (–1.36)

AMEX 0.45 0.80 0.75 34.23 9.42 0.02 –2.92(1.22) (1.20) (1.90) (0.00) (0.01) (0.47) (–1.28)

NASDAQ 1.42 2.37 1.01 95.98 52.80 0.38 –3.29(4.64) (3.14) (2.90) (0.00) (0.00) (2.43) (–1.09)

YOUNG 1.17 2.00 1.15 26.15 19.03 0.03 –3.10(4.84) (3.70) (4.37) (0.00) (0.00) (0.73) (–1.43)

MATURE 1.20 1.87 0.76 33.58 26.09 0.15 –2.16(2.47) (4.42) (1.85) (0.00) (0.00) (2.45) (–1.39)

Panel B. MABA

Stocks bMABA1 bMABA2 bMABA LR(OLS) LR(GMM) bt1 bt2

ALL 0.03 0.07 0.03 23.53 102.87 0.05 –2.35(19.49) (8.62) (18.55) (0.00) (0.00) (2.38) (–1.65)

NYSE 0.05 0.08 0.05 24.95 7.49 –0.04 –1.50(5.90) (6.50) (5.44) (0.00) (0.02) (–1.41) (–1.33)

AMEX 0.00 –0.03 0.00 63.12 186.86 0.16 –3.03(4.20) (–2.42) (4.53) (0.00) (0.00) (1.86) (–1.16)

NASDAQ 0.01 0.06 0.01 38.22 116.05 0.38 –4.21(8.05) (10.43) (8.18) (0.00) (0.00) (2.70) (–1.60)

YOUNG 0.01 0.04 0.01 8.34 192.52 0.46 –4.78(10.67) (15.63) (10.19) (0.00) (0.00) (2.77) (–1.70)

MATURE 0.03 0.07 0.04 19.53 48.31 –0.02 –1.85(10.99) (6.88) (8.99) (0.00) (0.00) (–1.28) (–1.56)

(continued on next page)

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TABLE 4 (continued)

Univariate Regressions: U.S. Aggregates

Panel C. VOLD

Stocks bVOLD1 bVOLD2 bVOLD LR(OLS) LR(GMM) bt1 bt2

ALL 0.04 0.13 0.02 77.87 11.77 0.19 –2.99(4.04) (1.49) (1.90) (0.00) (0.00) (2.35) (–1.37)

NYSE 0.03 0.00 0.01 54.01 7.69 0.17 –2.56(3.21) (0.06) (1.43) (0.00) (0.02) (2.45) (–1.41)

AMEX 0.02 –0.09 –0.00 131.25 173.68 0.39 –2.83(2.47) (–6.86) (–0.56) (0.00) (0.00) (2.62) (–1.26)

NASDAQ 0.03 0.28 0.01 176.07 56.95 0.43 –4.61(6.17) (3.49) (2.04) (0.00) (0.00) (2.47) (–1.27)

YOUNG 0.05 –0.07 0.03 86.66 46.69 0.40 –5.70(4.87) (–2.58) (1.86) (0.00) (0.00) (2.54) (–1.47)

MATURE 0.03 0.15 0.02 62.85 11.83 0.13 –2.62(3.58) (2.50) (1.84) (0.00) (0.00) (2.27) (–1.42)

Panel D. INST

Stocks bINST1 bINST2 bINST LR(OLS) LR(GMM) bt1 bt2

ALL 0.49 –1.22 0.05 63.78 131.36 0.50 –3.10(1.89) (–6.01) (0.30) (0.00) (0.00) (2.54) (–1.62)

NYSE 0.35 –1.18 0.01 53.85 233.49 0.35 –2.54(1.52) (–6.42) (0.08) (0.00) (0.00) (2.52) (–1.61)

AMEX 0.27 –0.67 –0.16 74.20 291.82 0.56 –2.38(1.64) (–10.92) (–1.90) (0.00) (0.00) (2.52) (–1.48)

NASDAQ 0.53 –1.25 –0.01 178.58 63.61 0.90 –4.73(4.52) (–4.01) (–0.04) (0.00) (0.00) (2.50) (–1.50)

YOUNG 0.46 –1.54 0.09 73.63 64.59 0.85 –5.35(2.35) (–4.99) (0.56) (0.00) (0.00) (2.53) (–1.61)

MATURE 0.35 –1.12 0.02 49.91 152.89 0.37 –2.71(1.44) (–6.37) (0.17) (0.00) (0.00) (2.54) (–1.65)

MABA appears to have stronger explanatory power than VROE in terms of thet-ratio when both are used alone. Figure 3 presents scatter plots of IV in relationto VROE and IV in relation to MABA for the average of ALL stocks and revealscertain differences between the two fundamentals variables. The relationship be-tween IV and VROE does not appear to be very tight, indicating that VROE aloneleaves much variation in IV unexplained. The relationship also appears slightlynonlinear. On the other hand, the relationship between IV and MABA is mainlydriven by a small number of influential points, defined as observations whoseMABA value is more than three standard deviations away from the mean. In arobust regression (not reported here) that removes these influential points, mostlythe observations around year 2000, the explanatory power of MABA is much re-duced. For example, the t-ratio of bMABA for ALL stocks in Panel B of Table 4drops from 18.55 to 2.91 if observations that are three standard deviations awayfrom the mean of the remaining sample are removed. In fact, about half of theslope estimates of MABA in Tables 4–6 become insignificant with their t-ratiosless than 2 when influential points are removed. On the other hand, the coefficientsof VROE are robust.

I now examine the explanatory power of various variables in multiple regres-sions. Instead of reporting results on all the variables and various combinations,I report in Table 5 the results of the regression of IV on VROE and MABA and


FIGURE 3

Scatter Plots of IV versus VROE and IV versus MABA

Figure 3 presents scatter plots of the value-weighted average idiosyncratic return volatility in relation to the value-weightedaverage VROE and in relation to the value-weighted average MABA (1976.01–2006.12).

Graph A. IV in Relation to VROE

Graph B. IV in Relation to MABA

of the regression of its residual on VOLD and INST separately. The results showthat MABA is the most useful explanatory variable for all the U.S. aggregate av-erage volatilities. For ALL, NYSE, and MATURE stocks, VROE is edged out byMABA, while for NASDAQ, YOUNG, and, to a lesser extent, AMEX, VROEremains useful in explaining the variation in return volatility. Cao et al. (2008)report that MABA outperforms VROE in explaining the value-weighted averageof ALL stocks volatilities. Conditioned on VROE and MABA, VOLD does nothave additional explanatory power. While INST has a significant slope coefficientin most cases, the sign of the estimated coefficient is wrong, contrary to the ex-planation given by its proponents.

From the previous analysis, it is clear that, although fundamentals variableshave better explanatory power across the two subperiods, the hypothesis of nostructural break is strongly rejected. To investigate the change in their absoluteand relative explanatory power over time, I calculate the following quantities:At the end of each month from 1985.12 to 2006.12, I regress IV on VROE usingthe data of the past 10 years. The R2 is denoted as R2

VROE. I then regress the resid-ual on MABA and denote the partial R2 as R2

MABA|VROE. The analysis is repeated,

switching the roles of VROE and MABA. The resulting R2 and partial R2 are

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TABLE 5

Multiple Regressions: U.S. Aggregates

Table 5 presents estimated slope coefficients of regressions

IVt = a + b∗VROEVROEt−1 + b∗MABAMABAt−1 + ηt

and their R2s. It also presents the estimated slope coefficients of regressions of the residual in the above regression, ηt ,on VOLDt−1 and INSTt−1 separately,

ηt = a + b∗∗VOLDVOLDt−1 + εt ,

ηt = a + b∗∗INSTINSTt−1 + ε′t .

The numbers in parentheses are t-statistics adjusted for autocorrelation and heteroskedasticity using the Newey-West(1987b) method (with a lag of 24 months). The sample period is 1976.01–2006.12 except for that involving INST, which is1980.03–2006.12.

Stocks b∗VROE b∗MABA R2 b∗∗VOLD b∗∗INST

ALL –0.00 0.03 0.62 –0.00 –0.15(–0.01) (9.16) (–0.09) (–2.11)

NYSE –0.63 0.07 0.49 –0.00 –0.16(–1.97) (6.53) (–0.29) (–2.53)

AMEX 0.65 0.00 0.17 –0.01 –0.15(1.78) (4.44) (–1.40) (–2.25)

NASDAQ 0.57 0.01 0.50 –0.00 –0.20(2.26) (6.40) (–0.67) (–2.31)

YOUNG 0.74 0.01 0.67 –0.00 –0.10(4.03) (5.00) (–0.54) (–1.24)

MATURE –0.33 0.04 0.54 –0.00 –0.17(–1.10) (10.05) (–0.10) (–2.73)

denoted R2MABA and R2

VROE|MABA, respectively. The time series of the four R2s forvalue-weighted average ALL stocks are plotted in Graph A of Figure 4

The plot shows that in the early part of the sample period while the idiosyn-cratic volatility is low, the proportion that can be explained is also low, less than20%. As VROE and MABA are highly correlated in the early part, the addi-tional explanatory power of either VROE or MABA, conditioned on the othervariable, is near 0. It is not until the late 1990s, when the idiosyncratic volatil-ity shoots up, that the proportion explained by the two fundamentals variablesstarts to increase. These proportions peak for the 10 years ending around 2001.The additional contribution from VROE remains near 0, while the additionalcontribution from MABA becomes higher. As the return volatility declines af-ter 2000, so do the R2s. By the end of 2006, the explanatory power of VROEdeclines to around 25%, while that of MABA remains above 60%. The par-tial R2 of VROE conditioned on MABA, R2

VROE|MABA, remains low all the time.

The partial R2 of MABA conditioned on VROE fluctuates in relation to R2VROE

after 2000.The plots of the R2s for NYSE, AMEX, and MATURE stocks are very

much the same as those for ALL stocks. The plots for NASDAQ are also sim-ilar to a lesser degree. They are not presented here. The plots for YOUNG stocks,however, appear to be quite different and are plotted in Graph B of Figure 4.The difference is that the proportion of the idiosyncratic volatility explained byfundamentals variables is relatively much higher in the early part of the sam-ple period. Another important difference is that, toward the end of the sample


FIGURE 4

R2s of Regressions of Moving Windows

Figure 4 plots the time series of the R2VROE (R2

MABA) of the average idiosyncratic volatility of ALL and YOUNG stocksexplained by the average VROE (MABA) and partial R2

VROE|MABA (R2MABA|VROE) by VROE (MABA) conditioned on MABA

(VROE) in each month using the data from the past 10 years.

Graph A. ALL Stocks

Graph B. YOUNG Stocks

period, the explanatory power of VROE increases, unlike the counterparts forother aggregates.

B. U.S. Industries and International Markets

In this subsection, I examine the U.S. industries and international markets.The purpose is to check how robust the major findings on the U.S. aggregate aver-ages are. I focus on the comparison between the fundamentals-based variables andtrading volume-based variables. Table 6 reports univariate and multiple regres-sions of the value-weighted average idiosyncratic volatility on value-weightedaverage ROE, MABA, VOLD, and INST over the entire sample period. For cer-tain industries, such as nondurables, energy, and utilities, none of the variables isuseful. These industries tend to be the ones that do not have large fluctuations inidiosyncratic volatility, as seen from Table 2. Other than these industries, eitherVROE or MABA is useful. For some industries, both are useful when used alone.VOLD is useful for durables, high-tech, telecom, and health industries when usedalone. INST is not useful at all. For those industries that do have large variationsin idiosyncratic volatility, MABA is the most useful in multiple regressions, andVROE remains useful for durables and high-tech industries. The residuals from

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multiple regressions of IV on VROE and MABA cannot be further explainedby VOLD. While INST is significant for the residuals, the sign is wrong. Thesepatterns are very similar to those found for the U.S. aggregate averages.

TABLE 6

Univariate and Multiple Regressions: U.S. Industries

Table 6 presents estimated slope coefficients of univariate and multiple regressions of IVt on VROEt−1, MABAt−1,VOLDt−1, and INSTt−1, for various industries. From the multiple regressions

IVt = a + b∗VROEVROEt−1 + b∗MABAMABAt−1 + ηt ,

the residual, ηt , is regressed on VOLDt−1 and INSTt−1 separately,

ηt = a + b∗∗VOLDVOLDt−1 + εt ,

ηt = a + b∗∗INSTINSTt−1 + ε′t .

The numbers in parentheses are t-statistics adjusted for autocorrelation and heteroskedasticity using the Newey-West(1987b) method (with a lag of 24 months). The sample period is 1976.01–2006.12 except for that involving INST, which is1980.03–2006.12.

Univariate Multiple ηRegressions Regressions Regressions

U.S. Industries bVROE bMABA bVOLD bINST b∗VROE b∗MABA R2 b∗∗VOLD b∗∗INST

Nondurables 0.30 0.01 0.00 –0.14 0.25 0.00 0.07 –0.01 –0.27(1.08) (1.33) (0.12) (–1.01) (0.63) (0.30) (–1.13) (–2.50)

Durables 0.40 0.04 0.03 0.11 0.42 –0.01 0.15 0.01 0.02(2.55) (1.53) (2.96) (1.59) (2.38) (–0.33) (1.48) (0.26)

Manufacturing 0.23 0.05 0.01 0.02 –0.85 0.08 0.39 0.00 –0.11(0.75) (2.59) (1.36) (0.22) (–2.84) (6.21) (0.23) (–1.96)

Energy 0.03 0.04 0.01 –0.05 –0.40 0.05 0.10 –0.00 –0.14(0.08) (1.41) (0.87) (–0.68) (–1.53) (1.84) (–0.00) (–2.02)

High-Tech 1.47 0.02 0.04 0.10 0.98 0.01 0.67 –0.00 –0.35(4.59) (9.33) (2.93) (0.33) (4.28) (7.98) (–0.47) (–3.29)

Telecom 1.18 0.12 0.06 0.19 0.64 0.08 0.58 0.01 0.00(3.99) (5.95) (4.07) (1.01) (1.83) (2.27) (0.96) (0.02)

Shops 1.21 0.04 0.01 –0.00 0.08 0.04 0.34 –0.01 –0.15(2.55) (4.59) (1.21) (–0.03) (0.26) (4.03) (–0.98) (–1.91)

Health 0.39 0.03 0.02 0.02 –0.04 0.03 0.47 –0.00 –0.20(1.98) (6.15) (2.43) (0.10) (–0.29) (5.09) (–0.28) (–3.42)

Utilities 0.23 0.02 0.01 0.06 0.18 0.02 0.02 0.01 0.03(0.46) (0.92) (1.10) (0.56) (0.38) (0.83) (0.62) (0.26)

Others 0.77 0.04 0.00 –0.15 0.28 0.03 0.25 –0.01 –0.27(1.97) (5.93) (0.39) (–1.16) (0.84) (3.35) (–1.27) (–3.30)

Table 7 reports the slope coefficients of the univariate and multiple regres-sions of the value-weighted average idiosyncratic volatility in international mar-kets on their ROE, MABA, and VOLD. As VROE is not available, ROE is used tocapture the uncertainty in the current earnings. Except for Singapore, ROE is notuseful in explaining the value-weighted average idiosyncratic volatility, as in theU.S. data. The coefficients of MABA for value-weighted average idiosyncraticvolatilities are significant for most countries in the univariate regressions. Thevolume variable is useful to explain volatility in Canada, Hong Kong, and Singa-pore. The results of the multiple regressions of the volatility on ROE and MABAare similar to those of the univariate regressions. Volume is useful conditionedon ROE and MABA only for Singapore. Overall, while the usefulness of thesevariables is mixed for different countries, the patterns that can be identified aresimilar to those found in the U.S.


TABLE 7

Univariate and Multiple Regressions: International Markets

Table 7 presents estimated slope coefficients of univariate and multiple regressions of IVt on ROEt−1, MABAt−1, andVOLDt−1 for international markets. From the multiple regressions

IVt = a + b∗ROEROEt−1 + b∗MABAMABAt−1 + ηt ,

the residual, ηt , is regressed on VOLDt−1,

ηt = a + b∗∗VOLDVOLDt−1 + εt .

The numbers in parentheses are t-statistics adjusted for autocorrelation and heteroskedasticity using the Newey-West(1987b) method (with a lag of 24 months). The sample period is 1990.02–2006.12.

Univariate Multiple ηRegressions Regressions Regressions

Markets by Country bROE bMABA bVOLD b∗ROE b∗MABA R2 b∗∗VOLD

Australia 0.17 0.04 0.11 0.01 0.04 0.09 0.01(1.46) (1.72) (1.80) (0.09) (1.70) (0.21)

Canada 0.38 0.07 0.26 0.24 0.06 0.17 0.10(1.82) (2.31) (2.50) (1.54) (2.07) (0.93)

France 0.10 0.09 0.34 –0.06 0.09 0.28 0.01(0.33) (7.37) (1.95) (–0.29) (6.93) (0.07)

Germany 1.49 0.20 –0.04 0.77 0.15 0.48 0.03(4.13) (5.08) (–0.84) (2.66) (3.27) (0.69)

Italy –0.06 0.04 0.03 –0.45 0.07 0.12 0.00(–0.26) (2.82) (0.59) (–1.90) (3.84) (0.05)

UK 0.11 0.12 0.37 –0.40 0.14 0.42 0.09(0.24) (4.43) (1.46) (–1.21) (7.49) (0.58)

Japan –0.29 0.07 –0.04 –0.69 0.08 0.30 –0.11(–0.44) (2.80) (–0.45) (–1.35) (3.86) (–2.51)

Hong Kong –0.40 0.07 0.32 –0.61 0.07 0.26 0.19(–1.18) (3.00) (3.08) (–1.50) (3.18) (1.62)

Singapore –0.87 0.01 0.26 –0.93 0.02 0.07 0.22(–2.19) (0.24) (4.16) (–2.65) (0.55) (3.98)

VI. Conclusions

Recent changes in volatility trends provide an opportunity to test various the-ories on what causes stock return volatilities to vary. I first present evidence thatthere is no common linear trend in the entire sample period of 1976–2006, basedon the aggregate index of all U.S. stocks, stocks in various sectors and indus-tries in the U.S., and stocks in international markets. I examine two broad sets oftheories on the causes of time-varying stock return volatilities, the fundamentals-based theories and the trading volume-based theories. Both types of theories canexplain the upward trend in the return volatilities for U.S. stocks from 1976 tothe late 1990s. However, the fundamentals-based theories remain valid, while thetrading volume-based theories cannot explain trends in the 2001–2006 period.To a lesser degree, some international markets exhibit the same pattern. The ex-planatory power of the two fundamentals variables varies over time. The market-to-book ratio of assets as a proxy for growth options is found to be capable ofexplaining the volatility patterns better than the current earnings volatility doesfor large and mature firms, especially in the second half of the sample periodfrom 1976 to 2006. However, the relationship between the return volatility andthe market-to-book ratio is not very robust. The volatility of current earnings,on the other hand, remains useful in explaining the return volatility for smaller

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and younger firms. The relationship between the return volatility and the earningsvolatility is robust.

While the results of this paper are based on data in the sample period 1976–2006, it is likely that the subsequent increase in the stock return volatilities in2007 and the turmoil in the autumn of 2008 provide further evidence to supportthe fundamentals-based theories, especially the theory based on earnings volatil-ity. The rise of return volatilities in 2007 was largely caused by increasing en-ergy costs, which ate into corporate earnings and created uncertainty about futureearnings. The surge in return volatilities in 2008, on the other hand, was triggeredby problems with the fundamentals of the financial services industry, which hadbeen badly damaged by the credit squeeze from the failure of subprime loans inthe property market.

The results in this paper have implications for many asset pricing and cor-porate finance issues. First, the concern for investors who cannot fully diversifytheir investments that investment performance would continually deteriorate, trig-gered by the Campbell et al. (2001) finding, is unwarranted. According to thefundamentals-based theory, investment risk can be reduced for such investorsby avoiding stocks that have high volatilities in their fundamentals. Second, forlarge investors, such as mutual funds and pension funds, diversification gains ex-ist mostly in stocks that have high earnings volatilities and high market-to-bookratios, which, to some extent, are predictable and therefore can be taken into con-sideration in forming dynamically optimal portfolios. Third, the empirical factsdocumented in this paper should help to resolve the theoretical and empiricalissues on the cross-sectional relationship between expected returns and idiosyn-cratic volatilities. The results in this paper are also useful to corporate managersand investors who need to calculate the cost of equity in various applications thatrequire decomposing the total return risk into systematic risk and idiosyncraticrisk. This is particularly relevant to determining the cost of capital of initial pub-lic offerings, for which historical return data are not available, while past earn-ings data can be used to determine the cost of equity, as well as expected futureearnings.

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