R2 and Idiosyncratic Risk are not Inter-Changeable

Bin Li Fuqua School of Business

Duke University 100 Fuqua Drive

Box 90120 Durham, NC 27708

Email: bin.li2@duke.edu

Shivaram Rajgopal†

Schaefer Chaired Professor of Accounting Goizueta Business School

Emory University 1300 Clifton Road NE

Atlanta, GA 30322 Email: shivaram.rajgopal@emory.edu

Mohan Venkatachalam

Professor, Fuqua School of Business Duke University 100 Fuqua Drive

Box 90120 Durham, NC 27708

Email: vmohan@duke.edu

June 1, 2012 Abstract: A burgeoning literature investigates the association between firm-specific stock return variation (the dependent variable) and several aspects of firms’ information and governance structures. However, some papers in this literature use the variance of residual returns from a market model (σ ) as the measure of firm-specific return variation whereas others use return synchronicity, or R2. Although, at first blush, these two variables appear equivalent, we show that the specific dependent variable used, σ or R2, can lead to contradictory inferences depending on the degree of correlation between systematic risk (the complement of idiosyncratic return volatility) and the variable of interest, e.g., earnings quality or governance quality. Therefore, we caution researchers to not view σ or R2 as inter-changeable measures. _________________________ †Corresponding Author. We are grateful for financial support from the Fuqua School of Business, Duke University and the Goizueta Business School, Emory University. We thank Stephen Brown and Søren Hvidkjær for generously providing us with data on PIN measures. We appreciate helpful comments from Scott Dyreng, Frank Ecker, Henock Louis, Ken Merkley, Craig Nichols and workshop participants at National University of Singapore and Syracuse University.

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R2 and Idiosyncratic Risk are not Inter-changeable

1. Introduction

There is a growing literature in both finance and accounting on the association between

firm-specific variation in stock returns and several aspects of the firm’s information or

governance environment. We found 18 papers in top-tier finance and accounting journals (see

appendix A for a list) and at least 75 working papers on the Social Sciences Research Network

(SSRN)1 which rely on one of two proxies for firm-specific return variation as the dependent

variable: (i) idiosyncratic risk, often measured as the variance of the residual (σ from a

regression of firm’s stock return on the market return; and (ii) synchronous movement of a firm’s

stock return with the market’s stock return, often operationalized as R2 from the market model.

These studies treat lower σ as equivalent to higher R2 and vice versa. The objective of this

paper is to demonstrate that such presumed equivalence between these seemingly similar

dependent variables is incorrect. We show that these two proxies for firm-specific return

variation can yield diametrically opposite inferences due to econometric considerations alone.

A firm’s return synchronicity, or R2 from a market model, is simply 1 minus the ratio of

idiosyncratic risk to total risk, where total risk is the sum of idiosyncratic risk σ and

systematic risk. That is, R2 is a relative (scaled) measure of idiosyncratic volatility. Therefore,

similar inferences obtain when using R2 and σ as the dependent variable if and only if the

correlation between the independent variable of interest and systematic risk (i.e., the scalar in R2)

is zero.

To illustrate this point, we consider a set of papers that correlate firm-specific return

variation and earnings quality but find contradictory results. In particular, Rajgopal and

1 We use the key word ‘return synchronicity’ as the search term in www.ssrn.com to compile the list of working papers that use some variant of R2 or idiosyncratic return volatility to represent firm-specific news or noise.

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Venkatachalam (2010) (RV hereafter) and Chen, Huang and Jha (2011) document that poor

earnings quality is related to greater idiosyncratic risk. Contrary to these papers, at least three

studies (Durnev, Morck, Yeung and Zarowin 2003, Ferreira and Laux 2007 and Hutton, Marcus

and Tehranian 2009) conclude that poor earnings quality is associated with lower firm-specific

return variation, measured as higher R2. Yet other research (Fernandes and Ferreira 2008; Gul,

Ng and Srinidhi 2011) reports an insignificant association between earnings quality and R2.

For parsimony, we focus on two of these studies that rely on either R2 (or a

transformation thereof) or idiosyncratic risk σ as the dependent variable, but draw different

conclusions. In particular, we select (i) Hutton et al. (2009) (hereafter, HMT) as a representative

study in the class of papers that use R2 as the dependent variable; and (ii) Rajgopal and

Venkatachalam (2010) (hereafter, RV) for studies that use σ . Specifically, while RV use σ ,

HMT use the inverse of R2 or the inverse synchronicity measure, ‘Φ’ (where Φ = ln [(1-R2)/R2]),

to capture firm-specific return variation. These two dependent variables,σ , and Φ, are prima

facie, isomorphic. Both these studies use two commonly used measures of earnings quality -

absolute abnormal accruals and volatility of Dechow-Dichev (2002) residuals - as the

independent variable. Hence, the divergent results are solely attributable to the dependent

variable, namely σ or Φ.

Using a simple econometric model, we demonstrate that the relation betweenσ and

earnings quality may be similar to or different from the association between Φ and earnings

quality, depending on the correlation between earnings quality and systematic risk. In particular,

we show that when the association between systematic risk and earnings quality is greater

(smaller) than the association between σ and earnings quality, using the two dependent

variables will lead to different (similar) inferences.

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To demonstrate this insight empirically, we first run simulations using data over a period

covering 1964-2008 and show that the association between earnings quality and firm-specific

return variation differs depending on the variable used to proxy for firm-specific return variation,

σ or Φ. In addition, as predicted by the econometric model, we show that the association

between Φ and earnings quality is the same as or different from the association between σ and

earnings quality depending on the correlation between systematic risk and earnings quality.

While the simulation provides broad empirical support for the predictions from the

econometric model, it is unclear whether those predictions will hold after including different

covariates of interest or when different time periods are considered. Therefore, we replicate RV

and HMT that consider data from different time periods and use different sets of covariates.

While for the time period considered by RV, the inference is unchanged regardless of whether

we use σ or Φ; for HMT, the inference depends crucially on the dependent variable used. In

particular, while the relation between earnings quality and Φ is negative, consistent with results

reported in HMT, the relation between earnings quality and σ is positive, consistent with the

results in RV. The negative relationship documented in HMT occurs because during the time

period studied by HMT, the association between earnings quality and systematic risk is greater

than the association between earnings quality and idiosyncratic risk. In sum, the replications of

RV and HMT suggest that (i) the association between earnings quality and σ is insensitive to

the covariates as well as the time period; but (ii) the association between earnings quality and Φ

is sensitive to both time period and covariates.

The issue of whether inverse return synchronicity (Φ) or idiosyncratic risk σ ) is a more

appropriate proxy for firm-specific return variation is related to a larger debate on whether

greater firm-specific return variation captures value-relevant information or noise. Several

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papers such as Morck, Yeung and Yu (2000), Wurgler (2000), Durnev et al. (2003), Durnev et al.

(2004), Piotroski and Roulstone (2004), Jin and Myers (2006) and Bakke and Whited (2006),

Ferreira and Laux (2007) and HMT, follow Roll (1988) and assume that lower R2, or greater

firm-specific return variation, captures stock prices with more information and less noise. In

contrast, the following papers assume, argue or find that more firm-specific return variation

captures noise: Xu and Malkiel (2003), Hou et al. (2005), Kelly (2007), Mashruwala et al.

(2006), Pontiff (2006), Ashbaugh-Skaife, Gassen, and LaFond (2006), Chan and Hameed (2006),

Griffin, Kelly, and Nadari (2007), and Teoh, Yang and Zhang (2008). Campbell et al. (2001)

and Bartram, Brown and Stulz (2011) entertain the possibility that greater firm-specific return

variation can capture noise in some contexts and information in other situations.

Thus, a researcher interested in evaluating the relevance of an independent variable of

interest (e.g., earnings quality, governance characteristic) for firm-specific return variation can

easily provide evidence to support either a noise or an information hypothesis by choosing σ or

Φ as the dependent variable. What should a researcher do when confronted with a situation

where differing conclusions obtain from relying on apparently equivalent proxies of firm-

specific return variation? We suggest that only if the results using bothσ and Φ are consistent

can the researcher confidently assert that (i) firm-specific return variation is related to a variable

of interest; and (ii) idiosyncratic volatility or R2 captures either value-relevant information or

noise. Therefore, it is important for a researcher to (i) justify the use of return synchronicity

(R2)/ inverse return synchronicity (Φ) or residual return variance σ ) as the more appropriate

dependent variable in their context; (ii) carefully examine whether the correlation between their

treatment variable of interest and systematic risk dominates or is dominated by the correlation

between their treatment variable and idiosyncratic risk, if they use R2 or variants thereof; (iii)

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consider controlling for systematic risk in the empirical specification to isolate the effect of the

treatment variable on firm-specific return variation; and (iv) explore the robustness of findings to

alternate dependent variables that capture the relevant construct (information versus noise).

In particular, we advocate that the researcher triangulate his/her findings using settings

where stock prices are likely to be uninformative such as in the presence of greater information

asymmetry, greater insider trading, greater illiquidity or higher liquidity risk. In supplementary

analyses, we find that σ is higher and R2 is lower in firms with poorer information

environments, characterized by higher PIN scores (probability of informed trading as per Easley

et al. 2002), greater levels of illiquidity, more zero return days and higher bid-ask spreads. These

findings are inconsistent with the common interpretation in studies (such as HMT, following

Roll 1988) that lower R2 captures firms whose stock prices contain more information and less

noise.

The contribution of this study is to focus the academic community on the divergent and

unreliable empirical results that can stem from the seemingly innocuous choice of using

idiosyncratic risk or R2 as the proxy for firm-specific return variation. Although our paper

considers the relation between firm-specific return variation and one specific covariate of interest

- earnings quality - the spirit of our comments applies to the broader literature that is interested in

the relation between firm-specific return variation and other variables of interest such as

governance structure, audit quality and more generally, the information environment (see

appendix A for a list).

The remainder of the paper is organized as follows. Section 2 discusses the background

behind the R2 and the idiosyncratic risk measures and derives a simple econometric model which

highlights the tenuous, sample-dependent nature of the inferences when R2 is the dependent

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variable. Section 3 discusses the data and the measurement of the dependent and independent

variables used in the analyses. Section 4 reports the results from simulations and replications of

RV and HMT, and section 5 offers some recommendations for researchers. Section 6

summarizes and concludes.

2. Background and Proof

2.1 R2 and idiosyncratic volatility

R2, or the synchronicity measure, owes its origins to Roll (1988) who argues that the

extent to which stocks move together depends on the relative magnitudes of firm-level and

market-level information capitalized into stock prices. The measure was later popularized by

Morck, Yeung and Yu (2000) and Jin and Myers (2006) in a cross-country context. Morck et al.

(2000) find that R2 is higher in countries with less developed financial systems and weaker

corporate governance. Jin and Myers (2006) document positive associations between R2 and

several measures of opacity for a cross-section of countries. This line of work generally

concludes that stock prices move together more (R2 is higher) when the quality of institutions in

that country is low. Durnev et al. (2003), Ferreira and Laux (2007), and HMT find results

similar to Jin and Myers (2006) in the U.S. context. That is, when earnings opacity is higher,

firm-specific information is lower (i.e., R2 is higher).

Along these lines, a recent paper by Bartram, Brown and Stulz (2011) shows that firms

from developed countries have lower R2s than firms from emerging markets, but U.S. firms have

significantly lower R2s than both groups. In other words, Bartram et al. (2011) find that the U.S.

has higher idiosyncratic return volatility when compared to several emerging markets. Contrary

to Jin and Myers (2006), but consistent with RV and Chen et al. (2011), Bartram et al. (2011)

show that greater idiosyncratic risk (or lower R2) is related to lower corporate disclosure quality.

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Thus, a collective reading of the literature suggests that association between firm-specific return

variation and opacity is ambiguous. One potential reason for such ambiguity is that R2 captures

the aggregate effect of both systematic risk and idiosyncratic risk. Thus, the correlation between

earnings quality and systematic risk can influence the correlation between earnings quality and

R2. We demonstrate this point using a simple econometric model discussed below.

2.2 Econometric model

Consider the standard market model. For stock i,

ri = αi + βi rm + ei (1)

with E(ei) = 0. In equation (1), ri is the return on stock i, and rm is the return on a market index.

Thus βi = Cov (ri, rm)/ Var(rm). From this relation, idiosyncratic risk is measured as the variance

of the error term in (1), σ , and total risk is the variance of the dependent variable in (1) or σ .

Note that R2 or the synchronicity measure from (1) is

(1 - σ /σ ) (2)

For ease of exposition, without any loss in generality, consider the dependent variable (Φ) used

in HMT, i.e., ln [(1-R2)/R2], where ln is the natural logarithm. This variable captures the inverse

of R2 (also known as the “inverse synchronicity measure”). Substituting (2) into the term ln [(1-

R2)/R2] yields the following expression:

Φ = ln [(1-R2)/R2] = ln [σ / σ - σ )] (3)

Recall from (1) that σ = ( β ∗ σ + σ ). Hence, σ - σ ) can be rewritten as

β ∗ σ . (4)

Substituting (4) into (3) yields expression (5):

Φ = ln [(1-R2)/R2] = ln [σ / β ∗ σ )] = ln [σ ] – ln β ∗ σ ] (5)

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Now, consider two versions of the same econometric model where the independent variable is a

proxy for earnings quality, labeled as EQ, and the dependent variable is either idiosyncratic risk

(ln [σ ]) or the systematic risk component of R2, i.e., ln β ∗ σ ].2 That is,

ln [σ ] = α0 + α1 EQi + ε1 (6)

ln β ∗ σ ] = λ0 + λ1 EQi + ε2 (7)

Consistent with the measurement of the two proxies of earnings quality – absolute value of

abnormal accruals and variance of Dechow-Dichev residuals considered here – higher EQ

implies poorer earnings quality.

Subtracting (7) from (6) yields the following expression where the dependent variable is

the one used by HMT:

Φ = ln [σ ] – ln β ∗ σ ] = δ0 + δ1 EQi + ε3 (8)

where δ0 = α0 - λ0 and δ1 = α1- λ1. Let’s compare regression (6) estimated by RV and Chen et al.

(2011) with regression (8) estimated by HMT. It is obvious from the comparison that the

coefficients on EQ in both models (α1 in 6 and δ1 in 8) would not be equal unless λ1 = 0, where

coefficient λ1 from (7) is the association between systematic risk and EQ. Thus, the

specifications used by the two papers studied here will yield similar coefficients on EQ only if

the correlation between systematic risk and EQ is zero.

Moreover, a comparison of (6) and (8) suggests that the following relations will hold: α1

> δ1 if λ1 > 0 and α1 < δ1 if λ1 < 0. However, λ1 < 0 is unlikely to obtain in the data as we do not

expect systematic risk and EQ to be negatively correlated.3 The more interesting case is when α1

2 Although the traditional measure of systematic risk is β, we measure systematic risk differently for expositional convenience, but without loss of generality. 3 There are both conceptual and empirical reasons for why λ1 may be positive, i.e., earnings quality is positively associated with systematic risk. Lambert, Leuz and Verrecchia (2007) use the capital asset pricing model to analytically show that earnings quality (more broadly, information quality) affects a firm’s equity cost of capital through its effect on systematic risk. Consistent with this model’s predictions, Francis, LaFond, Olsson, and

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exceeds λ1, or vice versa. When α1 exceeds λ1, we expect to find a positive association between

idiosyncratic risk and EQ and between inverse return synchronicity and EQ. When α1 is smaller

than λ1, however, we will find a positive association between idiosyncratic risk and EQ but a

negative and hence contradictory association between inverse return synchronicity and EQ. If α1

= λ1, we will find no association between inverse return synchronicity and EQ (i.e., δ1 = 0)

despite a positive association between idiosyncratic risk and EQ.

In sum, because Φ is a relative measure of idiosyncratic risk to systematic risk, the

relation between Φ and EQ relative to the relation between idiosyncratic risk (σ ) and EQ will

depend on the exact nature of correlation between systematic risk, β ∗ σ , and EQ in the

sample considered by the researcher. Hence, based on equation (8), one can plausibly conjecture

that HMT find a negative coefficient on EQ because λ1 > α1 in their sample. That is, the

divergent findings in HMT, relative to RV, arise because the correlation between systematic risk

and EQ dominates the correlation between idiosyncratic risk and EQ in their sample. In the

following section we empirically demonstrate that this is indeed the case. The other key

motivation for taking this analytical result to the data is (i) to test whether this analytical result,

derived in a univariate context, is robust to the presence of empirically added covariates; and (ii)

to highlight the empirical sample dependent nature of the inferences drawn.

3. Data and Variables

3.1 Sample

In order to generate data for the papers we replicate, we first combine stock return data

from the CRSP database with annual financial data obtained from the Compustat database for the

Schipper (2005) document that systematic risk (beta) increases monotonically across accrual quality quintiles. Moreover, Bhattacharya, Ecker, Olsson and Schipper (2012) directly test the Lambert, et al. (2007) model and show that the relation between earnings quality and cost of capital is mediated by the relation between earnings quality and beta. However, the association between earnings quality and systematic risk is controversial (e.g., Core, Guay and Verdi 2008).

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two different time periods, 1964-2001 and 1991-2005, covered in RV and HMT respectively.

We need to retain both samples to highlight the sample dependent nature of the findings in this

literature. We obtain analyst forecast data from the I/B/E/S database and institutional ownership

data from Thomson’s institutional ownership database compiled from Form 13F filings. Stock

returns are assigned to each firm’s fiscal year to match the time period of its reported financial

data.4 We exclude firm fiscal-years with fewer than 12 months of stock return data, observations

with fewer than 10 trading days each month, financial service firms and utilities (SIC 6000-6999

and 4900-4999), resulting in a sample of 60,205 firm-year observations for the RV paper and

53,185 firm-year observations for the HMT study.5 For all sample firms, we construct measures

of stock return volatility, financial reporting quality, and control variables.

3.2 Stock return volatility measures

The empirical work that follows relies on an expanded version of the market model, i.e.,

the three-factor Fama and French (1993) model. However, the intuition developed in section 2.2

with the market model ought to hold for a multi-factor Fama-French model as well. We compute

five measures of stock return volatility (firm subscripts suppressed for ease of exposition): (i)

σ (idiosyncratic volatility); (ii) σ (systematic risk measure that parallels the β ∗ σ ]

discussed in section 2.2); (iii) Φ (inverse synchronicity measure, i.e., ln[(1 – R2)/ R2] or ln

[σ /σ ); (iv) ln [σ (logarithm of idiosyncratic volatility), and (v) ln [σ (logarithm of

systematic risk).6 σ is computed as the average monthly variance of excess returns adjusted for

4 We define the end of each year as the month of annual earnings announcement. If the month of earnings announcement is missing in Compustat quarterly database, we define it as the second month after the fiscal year end. 5 Note that the sample sizes for both HMT and RV are influenced by the measurement of the two different measures of earnings quality. The OPAQUE measure in HMT requires far fewer variables to estimate than the DD measure used in RV. 6 Note that the model that we use here is different from that described in section 2.2. Specifically, we augment the market model with Fama-French factors as the Fama-French model is more descriptive of the variation in returns than the market model. As such, the systematic risk measure we compute is the difference between the total risk (σ minus idiosyncratic risk (σ ). Nonetheless, the intuition underlying the econometric arguments in section 2.2

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the three-factor expected returns of Fama and French (1993) model, and σ is the average

monthly variance of the three-factor expected returns from the Fama and French (1993) model.

Specifically, we measure excess returns as the residual from a regression of a firm’s daily stock

returns on SMB, HML, and market beta factors. Φ is the inverse return synchronicity variable

that measures the ratio of idiosyncratic volatility to systematic volatility, i.e., Φ = ln [σ - ln

[σ . Φ is also measured as the average of ln [σ /σ calculated on a monthly basis.

3.3 Earnings quality measures

We consider two measures of earnings quality (DD and OPAQUE). Our first measure of

earnings quality, DD, used as the main variable of interest in RV (2010), is based on an approach

proposed by Dechow and Dichev (2002) and Francis et al. (2005). The principal idea behind

Dechow and Dichev (2002) is to determine the extent of measurement error in the mapping of

accruals to current, past and future operating cash flows. The standard deviation of this

measurement error (DD) can be viewed as an inverse measure of earnings quality, i.e., higher

DD implies poorer earnings quality. We employ the modified Dechow and Dichev model to

calculate the measurement error in earnings (McNichols, 2002; Francis et al., 2005).

TCAit = φ0 + φ1CFOit-1 + φ2CFOit + φ3CFOit+1 + φ4(ΔREVit -ΔARit) + φ5PPEit + νit (9)

where TCA is the total current accruals calculated as ΔCA – ΔCL – ΔCash + ΔSTDEBT for

observations before fiscal year 1988 and calculated as IBEX – CFO after fiscal year 1988. ΔCA

is the change in current assets (Compustat ACT), ΔCL is the change in current liabilities

(Compustat LCT), ΔCash is the change in cash (Compustat CHE), ΔSTDEBT is the change in

debt in current liabilities (Compustat DLC). IBEX is the net income before extraordinary items

(Compustat IB), CFO is the cash flow from operations (Compustat OANCF) for fiscal years after

about the relation between systematic risk and earnings quality ought to hold for the augmented Fama-French model as well. For completeness, we rerun the regression specifications using idiosyncratic risk and Φ estimated based on the market model. Results (not tabled) form this analyses leave our inferences unchanged.

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1988. For fiscal years prior to 1988, CFO is computed as IBEX – TCA + DEPN where DEPN is

the depreciation and amortization expense (Compustat DP). Subscripts i and t are the firm and

time subscripts, respectively. We estimate equation (9) for each of Fama and French (1997) 49

industry groups with at least 20 firms in year t (all variables are scaled by lagged assets).

In equation (9), higher accrual quality implies that accruals capture most of the variation

in current, past, and future operating cash flows. As a consequence, the firm-specific residual,

νit, from equation (9), forms the basis of the earnings quality proxy used in the study.

Specifically, the earnings quality (DDit) metric is computed as the standard deviation of firm i’s

residuals calculated over years t-4 through t, i.e., DDit = σ(νit-4,t). We treat larger standard

deviations of residuals as an indication of poor accruals and earnings quality.

Our second measure of earnings quality, OPAQUE, is based on the variable of interest in

HMT. This measure relies on the idea that changes in a firm’s accruals are primarily determined

by changes in the firm fundamentals, proxied as changes in revenues and changes in property,

plant and equipment. If a firm’s accruals deviate significantly from the level determined by

changes in firm fundamentals, then such deviation is deemed abnormal, which are, in turn,

assumed to reduce the quality of accruals and earnings.

To determine abnormal accruals, we apply the modified Jones (1991) model and estimate

the following regression for each of Fama and French (1997) 49 industry groups with at least 20

firms in year t (all variables are scaled by lagged total assets).

TAit = δ0 + δ1(ΔREVit -ΔARit) + δ2PPEit + δ3ROAit + ηit (10)

where TA is the firm i’s total accruals, computed as TCA – DEPN, and ΔAR is the change in

accounts receivable (Compustat RECT). Kothari, Leone and Wasley (2005) show that firm

performance is an important determinant of abnormal levels of accruals. Therefore, we include

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return on assets (ROA) as an additional variable in equation (10). ROA is IBEX divided by

lagged total assets (Compustat AT). All the other variables have been previously defined.

Consistent with HMT, we treat the firm-specific residual, ηit , as abnormal accruals and

use the three-year moving average of the absolute value of the residual as our second proxy for

earnings quality, i.e., OPAQUE = { | ηit-2 | + | ηit-1 | + | ηit | }/3. The intuition behind this measure

is that firms with consistently large absolute values of discretionary accruals are more likely to

have managed reported earnings.

3.4 Control variables

Consistent with the controls employed in the replicated papers of interest, we consider the

following variables: firm size (SIZE), market-to-book ratio (M/B), leverage (LEV), operating

cash flows scaled by lagged total assets (CFO), standard deviation of operating cash flows

(VCFO), return on equity (ROE), volatility of return on equity (VROE), and annual buy-and-

hold stock return (RET).

We include analyst following (NANAL), squared analyst forecast revision (FREV2), and

institutional ownership (INST) as additional control variables in the replication of RV to be

consistent with that paper. In replicating HMT, we also include the variance of the two-digit SIC

industry return (VAR (industry)) and the kurtosis and the skewness of firm-specific returns as

control variables. See Appendix B for detailed definitions of variables.

3.5 Descriptive statistics

Descriptive statistics on the variables used in the replication of the two studies (RV and

HMT) are reported in Table 1. We report descriptive statistics for the two sample periods 1964-

2001 and 1991-2005 used in the respective studies.7 The mean and median of idiosyncratic

7 We replicated the analysis for an expanded sample period covering 1964-2008 and the tenor of our conclusions is unaltered.

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volatility and inverse synchronicity presented in Panels A and B of Table 1 are similar to those

reported in the two studies of interest (RV and HMT).

More relevant are the cross-sectional correlations reported in Table 2. In Panel A, we

find that consistent with the evidence in RV, the Pearson correlation between idiosyncratic

volatility (measured in logarithm) and DD measure of earnings quality is positive (ρ = 0.447).

The correlation between the inverse synchronicity measure Φ, measured as ln[(1 – R2)/ R2] or ln

[σ /σ used in HMT and DD is also positive (ρ = 0.177), suggesting that regardless of whether

we use an unscaled measure of idiosyncratic return volatility or a scaled measure, the relation

between earnings quality and idiosyncratic risk is positive.8 In Panel B, we report the

correlations for the variables in the HMT sample. It is noteworthy that the earnings quality

measure, OPAQUE, is positively related to inverse synchronicity (Pearson ρ = 0.090) as well as

to un-scaled idiosyncratic risk measure (Pearson ρ = 0.362).

The weak positive association between inverse synchronicity (Φ) and OPAQUE in the

HMT sample relative to the RV sample period (ρ = 0.090 versus 0.177) suggests that the

negative association documented by HMT between these two variables is likely attributable to

the influence of covariate variables, most notably size. In particular, size is highly correlated

with both Φ and with σ for both samples suggesting that controlling for size is important.

The Pearson correlation between idiosyncratic component of return volatility (ln[σ ) and

systematic component of return volatility (ln[σ ) is strongly positive (ρ = 0.862, 0.872 in panels

A and B respectively). Furthermore, earnings quality measures are positively correlated with the

systematic component of return volatility (ρ = 0.388, 0.354 in Panels A and B respectively).

Based on the model discussed in section 2.2, these statistics suggest that using a scaled version of

8 Note that RV consider both DD and absolute value of abnormal accruals from Jones (1991) model as measures of earnings quality. In unreported results, we find that repeating the entire analyses using absolute value of abnormal accruals as the earnings quality measure does not alter our inferences.

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idiosyncratic risk (Φ) can lead to unstable inferences relative to using the unscaled volatility

measure (ln σ .

4. Simulation and Replications

4.1 Simulation

In this section we run simulations to test the predictions from the econometric model

described in section 2.2. In particular, we begin by constructing 1,000 random samples of 100

observations each, obtained with replacement. We draw random samples from data over a

broader time period covering 1964-2008. Subsequently, we relax this assumption when we

consider the replications of RV and HMT. We estimate equations (6), (7) and (8) for each of

these 1,000 samples.

Results presented in Panel A and B of Table 3 rely on DD and OPAQUE as the measure

of earnings quality, respectively. In Panel A, we find that, of the 1,000 samples, the coefficient

on DD (α1) is positive and statistically significant at the 10% level 994 times when ln σ is the

dependent variable. Also, when ln σ is the dependent variable, 975 of coefficients on DD (λ1)

are positive and statistically significant. In either case, none of the samples report negatively

significant coefficients. This suggests strong support for a positive relation between earnings

quality and idiosyncratic volatility as well as between earnings quality and systematic volatility.

However, when Φ is the dependent variable, the number of positive coefficients on DD (δ1) is

much smaller (478 cases). In all of the 478 cases, the coefficient of ln σ on DD (α1) is greater

than the coefficient of ln σ on DD (λ1), consistent with the prediction in section 2.2. There are

5 instances where δ1 is negative and in each of those cases, α1 < λ1, as predicted. Interestingly,

the coefficient on DD (δ1) is insignificant in 517 of the 1,000 estimations. The insignificant

16

coefficients for δ1 are due to the positive correlations between idiosyncratic risk and DD

potentially offsetting the positive correlations between systematic risk and DD.

Our results are very similar when we consider OPAQUE as the earnings quality metric

(see Panel B). The predictions from the econometric model continue to hold. However, the

number of insignificant coefficients on OPAQUE when Φ is the dependent variable is much

higher (766 relative to 517 in panel A). Taken together, the simulation evidence serves to

demonstrate that the relation between earnings quality and firm-specific return variation is (i)

unaffected by the particular earnings quality measure used, (ii) dependent on the specific

measure of firm-specific return variation used (Φ or ln σ ) and (iii) different, when Φ is the

dependent variable, depending on the relation between earnings quality and systematic risk.

We now turn to the replication of the two papers (RV and HMT) that use different time

periods, for a more detailed examination of the econometric and economic issues surrounding the

determinants of firm-specific return variation. Apart from the influence of time-period, these

replications will shed light on the impact of the covariates used in these papers.

4.2 Replication of Rajgopal and Venkatachalam (2010)

Panel A of Table 4 presents results from a replication of RV for the same time period

(1964-2001) examined in that paper. The estimation procedure and the control variables are

identical to the ones used in RV.9 In our replication reported in column (1) of Table 4, panel A

we find, consistent with RV, a strong positive cross-sectional association between idiosyncratic

volatility and the Dechow-Dichev measure (coefficient on DD is 0.185, t-statistic = 67.86)

obtains. The coefficient magnitude is similar to that reported in Panel B, Table 2 of RV. Based

on this analysis we can conclude, similar to RV, that poor earnings quality, or a higher DD

measure, is associated with greater idiosyncratic risk. 9 In unreported results we find that our inferences are unchanged if we cluster the standard errors by firm and year.

17

Column (2) of Table 4 estimates the same regression as column (1) with one important

difference. The dependent variable is the inverse return synchronicity measure (Φ), or scaled

idiosyncratic risk measure, used by HMT. The coefficient on DD is again significantly positive

(coefficient = 0.859, t-statistic = 26.81) suggesting that higher the inverse return synchronicity or

higher the inverse synchronicity, the greater the DD measure and the poorer the earnings quality.

This result, although consistent with RV, contradicts the findings in HMT who find a negative

association between Φ and earnings quality.

There are two possible explanations for this. First, as suggested by the simulation results

reported in section 4.1, the inconsistent results may be a manifestation of the different time

periods considered by RV and HMT. However, in un-tabulated results, we have confirmed that

when the column (2) specification is estimated for the HMT sample period, the coefficient on

DD is indeed negative. Hence, differing time-periods are not the first order reason for this

puzzling result. Second, the inconsistent findings may stem from the use of different earnings

quality measure (DD versus OPAQUE) employed in the two studies. However, in un-tabulated

results, we replaced OPAQUE instead of DD in the specifications reported in Table 4 and find

that our inferences do not change. That is, we find that the association between Φ and OPAQUE

is also positive in the RV sample period (1964-2001). Thus, different EQ proxies are not

responsible for this contradictory result either and the reasons for the result lie elsewhere.

To further explore why we obtain a positive relation between Φ and earnings quality, we

decompose the two components of Φ, i.e., ln [σ and ln [σ and report the results with these

two variables as dependent variables in columns (3) and (4). We find the coefficient on DD in

both regressions to be positive. But, the coefficient of 6.087 on DD in the regression of ln [σ

on DD (reported in column 3) exceeds the coefficient of 5.072 on DD in the regression of ln [σ

18

on DD (reported in column 4). Thus, the association between idiosyncratic risk and DD

dominates the association between systematic risk and DD. It is precisely in these situations, as

per the model in section 2.2, that we would expect to observe a positive coefficient on DD, when

Φ is the dependent variable. We show next that when a similar analysis is conducted for the time

period used by HMT, the association between Φ and EQ becomes negative.

4.3 Replication of Hutton et al. (2009)

In Table 5 we report results of replicating the main findings in HMT. Again, the

estimation procedure and the control variables are identical to that used in HMT. The main

finding of the HMT paper is that financial reporting opacity, captured by OPAQUE, is positively

associated with R2, i.e., they document a negative association between OPAQUE and the inverse

return synchronicity measure (Φ).

When we replicate HMT’s (2009) model 3 reported in their Table 7, Panel A, the

coefficient on OPAQUE is negative (coefficient = -0.313, t-statistic = -4.33 in column 2 of Table

5 of this paper). This is comparable to the coefficient of -0.402 reported by HMT (see model 3,

Table 7 on page 49 of HMT). When we use the idiosyncratic return volatility measure instead of

inverse synchronicity (Φ) as the dependent variable, we find results that are diametrically

opposite to that reported by HMT. That is, the coefficient on OPAQUE is positive regardless of

whether we use σ (coefficient = 0.141, t-statistic = 18.09) or ln [σ (coefficient = 6.337, t-

statistic = 44.58) as the dependent variable (see columns 1 and 3).

The negative coefficient obtained for OPAQUE in column (2) stems from the greater

association of OPAQUE and DD with systematic risk (ln [σ ) relative to their association with

idiosyncratic risk (ln [σ ). That is, the coefficient of 6.337 in column (3) when ln [σ is the

dependent variable is smaller than the coefficient of 6.583 when ln [σ is the dependent

19

variable. Had the association between idiosyncratic risk and earnings quality dominated the

correlation between systematic risk and earnings quality as in the RV sample, the coefficient on

earnings quality in HMT analysis would have become positive. Our findings (not tabled) are

similar when DD, instead of OPAQUE, is used as the earnings quality variable.

5. What should a researcher do?

A natural question stemming from the above analysis relates to what a researcher ought

to do when the results obtained by using σ and Φ (or R2) are not convergent. An easy solution

is to control for systematic risk in the empirical specification. We re-estimate the regressions

reported in columns (2) and (3) of Table 5 after including ln [σ to investigate whether the

relationship between earnings quality and return volatility measure changes. The results reported

in Table 6 show that the relation between earnings quality and Φ now turns positive (coefficient

= 0.899, t-statistic = 13.29; column (1)), consistent with RV. Although one might think that this

is a mechanical re-estimation of the regression with ln [σ as the dependent variable, note that

the coefficient on ln [σ is not -1 due to the inclusion of other covariates.10 More important, the

relation between earnings quality and idiosyncratic risk continues to be positive, despite the

strong positive relation between systematic risk and idiosyncratic risk (see column (2)).

Another way to break the deadlock is to focus on the conceptual differences underlying

the interpretation of the findings. Whereas RV argue that poorer financial reporting quality

results in greater noise in the information environment resulting in greater return variation, HMT

argue that earnings opacity results in firm-specific news not being incorporated in stock prices

leading to lower return variation. Thus, the fundamental issue is whether higher σ and Φ, or

equivalently lower R2, reflects noise or information in stock prices.

10 Our inferences are similar if we use σ as the measure of systematic risk.

20

One way to shed light on this problem is to focus on settings where stock prices are more

likely to be uninformative and to investigate whether the return variation is higher or lower in

poorer information environments such as in the presence of greater information asymmetry,

greater insider trading, lower liquidity levels and higher liquidity risk. To provide some

exploratory empirical support, we evaluate the association between both measures of return

variation and (i) Amihud (2002) liquidity measure (LIQ); (ii) volatility of Amihud (2002)

liquidity measure (LIQVOL) used in Lang and Maffett (2011); (iii) PIN scores (probability of

informed trading as per Easley et al. 2002); (iv) zero return days (ZRDAYS); and (v) bid-ask

spread (SPREAD). For a detailed description of the measurement of each of these variables see

Appendix B. We standardize the measurement of each variable such that a higher number

represents less informative stock prices or more noise. For example, a higher Amihud (2002)

liquidity measure or bid-ask spread implies higher levels of information asymmetry and hence,

less informative stock prices.

If the interpretation that greater Φ and greater σ indicate more informative stock prices

is valid (as assumed in HMT, and consistent with Roll 1988), we ought to find that firms with

greater Φ (and σ ) should be systematically characterized by lower PIN scores, lower illiquidity

(LIQ), lower volatility in liquidity (LIQVOL), lower zero return days (ZRDAYS) and lower bid-

ask spread (SPREAD). In contrast, if greater Φ and greater σ indicate more noise in stock

prices, as assumed in RV, we should find the opposite. To shed some empirical light on this

theoretical conflict, we form quintile portfolios sorted on both Φ and σ and investigate whether

the characteristics of liquidity and other information environment proxies in the extreme

portfolios behave in a manner consistent with noise or news.11 For the purpose of this analysis

11 The analysis conducted in this section is similar in the spirit of Kelly (2007) who forms decile portfolios based on R2 and shows that firms in the low R2 portfolio have greater degree of information asymmetry relative to firms in the

21

we consider the sample period in HMT (1991-2005) because the contradictory findings when

using Φ and σ occur during this sample period.12

Results presented in Table 7 Panels A and B for portfolios formed on σ or Φ

respectively, are consistent with a noise story, rather than an information story. In particular, we

find that regardless of the sort, Φ or σ , firms in the highest quintile portfolio display greater

levels of LIQ, LIQVOL, PIN, ZRDAYS, and SPREAD relative to the lowest quintile portfolio.

In fact, each of the information variables increases monotonically across the quintile portfolios of

idiosyncratic volatility. This is strong evidence that higher levels of Φ are more symptomatic of

noise in returns rather than firm-specific information being incorporated in stock prices.

Because size is significantly correlated with R2 (Roll 1988), we need to ensure that the

relation between idiosyncratic volatility and various information variables is not spurious.

Therefore, we examine whether the findings in Panels A and B of Table 7 are stable across

various size quintiles. To do this we form five size quintiles within each of the idiosyncratic

volatility quintile portfolios formed based on Φ and σ . We then examine whether the firm-

specific information variables behave similarly across each of the size quintiles. Results reported

in Panels C and D suggest that our previous findings are robust to controlling for size. Across

each of the size quintiles the higher levels of Φ and σ exhibit poorer liquidity, higher PIN

scores, greater bid-ask spread and more zero return days.

In addition to the evidence presented here, the literature, by and large, suggests that firms

with poorer earnings quality are associated with environments of relatively uninformative prices

in expectation. In particular, Aboody, Hughes and Liu (2005) find that insiders are able to

highest decile portfolio. Although the time period considered by Kelly (2007) is different (1983-2003), our conclusions are the same. 12 For completeness, we repeat the analysis, subject to data availability, for the period considered by RV (1964-2001) as well as for an expanded sample period covering 1964-2008. Our inferences are similar.

22

execute more (less) profitable trades in firms with worse (better) earnings quality. Bhattacharya

et al. (2012a, 2012b) document that poor earnings quality, proxied as the Dechow-Dichev

residuals, is associated with higher adverse selection risk, greater bid-ask spreads and greater

PIN scores. Welker (1995) and Brown and Hillegeist (2007) document associations between a

more opaque disclosure policy, as proxied by AIMR scores, and two measures of information

asymmetry, higher bid-ask spreads and PIN scores. Ng (2011) finds that better earnings quality,

proxied as the Dechow-Dichev residuals, earnings precision and the level of analyst’s consensus

in earnings forecasts, is associated with lower liquidity risk, after controlling the levels of

liquidity. This literature is inconsistent with a negative association between Φ and OPAQUE

found by HMT which presumes that higher levels of Φ represents stock prices that are more

informative.

Thus, a combined reading of the evidence suggests that researchers ought be cautious

before accepting the claim that lower R2 (following Roll 1988) denotes an environment where

stock prices are more informative. Our recommendation is that supplementary tests confirming

this claim are essential to ensure robust inferences.

6. Conclusions

In this paper, we attempt to reconcile the incongruent findings of papers that relate firm-

specific return variation and earnings quality. The lack of congruence arises primarily because

of the different measures that researchers use to measure firm-specific return variation, in

particular, residual return volatility or R2 from a model of firm returns on systematic risk factors.

We rely on a simple econometric model to demonstrate that these two measures will result in

different research outcomes, unless the variable of interest is uncorrelated or negatively

correlated with systematic risk in stock returns.

23

Our empirical findings are consistent with this prediction. We replicate two published

papers on the association between firm-specific return variation and earnings quality and show

that inferences that rely on R2 are often inconsistent with inferences that rely on idiosyncratic

return volatility, particularly because of the strength of the association between systematic risk

and earnings quality. Therefore, we caution researchers interested in exploring associations

between firm-specific return variation and a treatment variable of interest to be mindful of the

particular proxy they use to capture firm-specific return variation.

What should a researcher do when confronted with incongruent findings as a result of

using the two alternate measures of return variation? We advocate that future researchers (i)

motivate why a scaled measure such as R2 or an unscaled residual return volatility measure is the

best proxy for firm-specific variation in their research setting; (ii) control for systematic

volatility in the empirical specification; and (iii) examine the robustness of the findings,

especially those that rely on R2 as the primary variable, by considering alternative dependent

variables that capture firm-specific information or noise inherent in returns. In particular, the

researcher would be well served by triangulating their findings by exploring the relation in

settings where stock prices are more likely to be uninformative, e.g., settings characterized by the

presence of greater insider trading, greater information asymmetry, higher illiquidity and

liquidity risk.

24

Appendix A

List of published papers that rely on stock return synchronicity

There is a large literature that investigates the impact of several corporate finance and accounting

variables on stock return synchronicity. We have restricted this list to published papers in top-

tier finance and accounting journals (apart from the replicated papers).

1) Papers that relate return synchronicity to disclosure quality and information environment:

a) Morck, Yeung and Yu (2000, JFE) show that R2 is higher in countries with less developed financial systems and poorer corporate governance.

b) Piotroski and Roulstone (2004, TAR) investigate the extent to which trading by informed stakeholders affects stock return synchronicity.

c) Chan and Hameed (2006, JFE) consider the association between analyst coverage and return synchronicity in emerging markets.

d) Jin and Myers (2006, JFE) document that control rights and lack of transparency in disclosure impact R2.

e) Fernandes and Ferreira (2008, JFE) examine the impact of international cross-listing on return synchronicity.

f) Crawford, Roulstone and So (2012, TAR) examine the impact of the initiation of analyst coverage on return synchronicity.

2) Papers that relate return synchronicity to audit quality and IFRS adoption

a) Gul et al. (2010, JFE) investigate the effects of largest-shareholder ownership concentration, foreign ownership, and audit quality on stock price synchronicity of Chinese-listed firms over the 1996–2003 period.

b) Kim, Li and Li (2011, JAE) consider the impact of eliminating 20-F reconciliation filings with the SEC on return synchronicity.

c) Kim and Shi (2012, RAST) find that firms with lower return synchronicity (lower R2) are more likely to adopt IFRS.

3) Papers that relate return synchronicity to corporate investments:

a) Durnev, Morck and Yeung (2004, JF) examine the association between the economic efficiency of investment and return synchronicity.

b) Chun, Kim, Morck and Yeung (2008, JFE) show that traditional U.S. industries with higher firm-specific stock return (lower return synchronicity) use information technology more intensively and post faster productivity growth in the late 20th century.

c) Brown and Kimbrough (2011, RAST) relate the level of intangible investments to return synchronicity.

25

d) Chen, Goldstein and Jiang (2007, RFS) investigate the association between return non-synchronicity and the sensitivity of corporate investments to stock price.

4) Papers that relate return synchronicity and governance quality

a) Armstrong, Balakrishnan and Cohen (2012, JAE) examine how changes in antitakeover protection (an element of firms’ governance structures) influence firms’ information environments.

b) Khanna and Thomas (2009, JFE) investigate the association between different kinds of firm interlocks, control groups, and synchronicity in Chile.

c) Brockman and Yan (2009, JBF) examine the association between block holders and return synchronicity.

d) Ferreira, Ferreira and Raposo (2011, JFE) investigate how stock price informativeness (return synchronicity) affects the composition of boards.

e) Gul et al. (2011, JAE) find that firms that have low return synchronicity are more likely to have a higher proportion of women on their boards.

26

Appendix B Definition of Variables

Variable

Definition Reference

Panel A: Stock Return Volatility Variables (Firm-level)

Idiosyncratic Volatility σe2 Average monthly variance of excess returns adjusted for the three-factor expected returns of

Fama and French (1993) model. Rajgopal and Venkatachalam (2010)

Systematic Volatility σS2 Average monthly variance of expected returns of Fama and French (1993) model.

Inverse Synchronicity Φ ln(1-R2)/R2 , R2 is the mean of monthly R2s from Fama and French (1993) model. Hutton et al. (2009)

Log Idiosyncratic Volatility ln [σe2] Logistic transformed idiosyncratic volatility estimated from Fama and French (1993) model.

Log Systematic Volatility ln [σS2] Logistic transformed systematic volatility estimated from Fama and French (1993) model.

Panel B: Financial Reporting Quality Variables (Firm-level)

Accruals Quality DD Standard deviation of abnormal accruals estimated from modified Dechow and Dichev (2002) model over years t-4 throught t. TCAit = φ0 + φ1CFOit-1 + φ2CFOit + φ3CFOit+1 + φ4(ΔREVit -ΔARit) + φ5PPEit + νit

Rajgopal and Venkatachalam (2010)

Average of Absolute Value of Abnormal Accruals

OPAQUE Three-year moving average of the absoluate value of abnormal accruals from modified Jones (1991) model. TAit = δ0 + δ1(ΔREVit -ΔARit) + δ2PPEit + δ3ROAit + ηit

Hutton et al. (2009)

Panel D: Firm-level Control Variables

Firm Size SIZE Log market capitalization (market value of equity = PRCC_F х CSHO). Rajgopal and Venkatachalam (2010); Hutton et al. (2009)

Book-to-market Ratio B/M Fiscal-year-end book value of equity over fiscal-year-end market value of equity = (CEQ+TXDB)/(PRCC_F х CSHO). Rajgopal and Venkatachalam (2010); Hutton et al. (2009)

Leverage LEV The ratio of long-term debt to total assets = (DLTT+DLC)/AT. Rajgopal and Venkatachalam (2010); Hutton et al. (2009)

Operating Cash Flows CFO [earnings before extra ordinary iterms (IB) - total accruals (balance-sheet method)]/total assets (AT), before fiscal year 1988; [OANCF (income-statement method)]/total assets (AT), after 1988.

Rajgopal and Venkatachalam (2010)

Cash Flow Volatility VCFO Standard deviation of operating cash flows scaled by total assets over the trailing five years window. Rajgopal and Venkatachalam (2010)

Stock Return Performance RET Contemporaneous buy-and-hold returns. Rajgopal and Venkatachalam (2010)

Analyst Following NANAL Number of analysts determining the consensus forecast subsequent to the fiscal year. When analyst following is not available for the pre-IBES time period we set it to zero.

Rajgopal and Venkatachalam (2010)

Analyst Revision FREV2 Squared forecast revision computed as the the first available median consensus one-year-ahead earnings forecast following three months after the fiscal year end minus the two-year-ahead earnings forecast available following three months after the previous fiscal year end. When analyst data is not available for the pre-IBES time period we set the variable to zero.

Rajgopal and Venkatachalam (2010)

Institutional Holding INST Average percentage of institutional ownership during the fiscal year. For years prior to 1980 when data on institutional ownership is not available, we set INST to zero.

Rajgopal and Venkatachalam (2010)

Return-on-equity ROE Return-on equity = IB scaled by lagged book value of equity. Hutton et al. (2009);

Skewness Skewness Skewness of firm-specific daily returns Hutton et al. (2009)

Kurtosis Kurtosis Kurtosis of firm-specific daily returns Hutton et al. (2009)

Variance of industry index Var(Industry) Average monthly variance of the 2-digit SIC industry returns during the firm's fiscal year. Hutton et al. (2009)

27

Appendix B (continued) Definition of Variables

Variable Definition Reference

Panel A: Stock Return Volatility Variables (Firm-level)

Liquidity Measure LIQ Average daily price impact of trade measured as |Ri|/Pi*Voli,where R is the daily return, P is the stock price, Vol is the daily

trading volume. Amihud (2002)

Volatility of Liquidity LIQVOL Annual standard deviation of the daily LIQ measure. Lang and Maffett (2011))

PIN PIN Probability of informed trading as measured in Easley et al. (2002).

Bid-ask spread SPREAD Average daily bid-ask spread in a fiscal year.

Zero return days ZRDAYS The ratio of zero return days to total trading days in a fiscal year.

28

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Table 1 Descriptive Statistics

Descriptive statistics of the variables used for the replication of Rajgopal and Venkatachalam (2010) and Hutton et al. (2009) in panels A and B respectively. All variables are winsorized at the bottom and top 1% levels. All variables are defined in the Appendix B. Panel A: Descriptive statistics for variables used in replicating Rajgopal and Venkatachalam (2010)

Variable Mean Std. Dev.

Q1 Median Q3 Min Max

Volatility measures (N=60205)

Idiosyncratic volatility σe2 0.025 0.039 0.005 0.011 0.026 0.001 0.284

Systematic volatility σS2 0.006 0.008 0.002 0.004 0.007 0.000 0.062

Inverse synchronicity Φ 1.281 0.492 0.975 1.337 1.635 -0.234 2.249

Earnings quality measure

Earnings quality DD 0.055 0.058 0.021 0.037 0.066 0.006 0.456

Control variables

Market-to-book ratio M/B 2.010 2.659 0.800 1.331 2.297 -5.632 21.554

Firm size (in log) SIZE 4.621 2.147 3.012 4.429 6.106 0.242 10.323

Leverage LEV 0.237 0.176 0.095 0.222 0.344 0.000 0.826

Operating cash flows CFO 0.073 0.136 0.024 0.084 0.140 -0.827 0.431

Cash flow volatility VCFO 0.015 0.054 0.001 0.004 0.010 0.000 0.647

Institutional Ownership INST 0.119 0.211 0.000 0.000 0.160 0.000 1.000

Number of Analysts NANAL 4.015 6.721 0.000 0.000 5.000 0.000 31.000

Forecast Revision2 FREV2 0.281 2.062 0.000 0.000 0.026 0.000 25.000

Return2 RET2 0.351 1.078 0.014 0.069 0.231 0.000 9.507 Panel B: Descriptive statistics for variables used in replicating Hutton et al. (2009)

Variable Mean Std. Dev.

Q1 Median Q3 Min Max

Volatility measures (N=53185)

Idiosyncratic volatility σe2 0.040 0.055 0.008 0.020 0.047 0.001 0.284

Systematic volatility σS2 0.010 0.012 0.003 0.006 0.011 0.000 0.062

Inverse synchronicity Φ 1.313 0.534 0.990 1.411 1.704 -0.234 2.249

Earnings quality measure

Earnings quality OPAQUE 0.085 0.072 0.037 0.063 0.106 0.009 0.387

Control variables Variance of Industry Index

Var(Industry) 0.004 0.005 0.001 0.003 0.005 0.000 0.381

Firm size (in log) SIZE 5.124 2.206 3.494 4.988 6.631 0.242 10.323

Market-to-book ratio M/B 2.840 3.716 1.048 1.821 3.318 -5.632 21.554

Leverage LEV 0.221 0.202 0.032 0.188 0.346 0.000 0.826

Return on Equity ROE -0.031 0.535 -0.081 0.072 0.169 -2.793 1.472

Skewness in returns Skewness 0.273 0.302 0.079 0.262 0.460 -0.807 1.148

Kurtosis in returns Kurtosiss 1.438 1.250 0.665 1.214 1.920 -0.188 12.021

33

Table 2 Correlation Coefficients

This table reports the correlation coefficients for both Rajgopal and Venkatachalam (2010) and Hutton et al. (2011) samples. Pearson correlations are below the diagonal; Spearman correlations are above the diagonal. p-values are shown in the parentheses. See Appendix B for variable definitions. Panel A: Correlation matrix for Rajgopal and Venkatachalam (2010) sample

Variable Φ ln(σe2) ln(σS

2) DD FREV2 RET2 NANAL INST CFO VCFO RET SIZE M/B LEV

Φ 0.390 -0.060 0.254 -0.311 -0.018 -0.397 -0.063 -0.177 0.185 -0.075 -0.550 -0.206 -0.003

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.412)

ln(σe2) 0.393 0.853 0.519 -0.191 0.246 -0.294 -0.066 -0.291 0.425 -0.147 -0.497 -0.013 0.053

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.000)

ln(σS2) -0.087 0.862 0.425 -0.069 0.274 -0.128 -0.045 -0.224 0.356 -0.126 -0.265 0.084 0.057

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

DDt 0.177 0.447 0.388 -0.002 0.184 -0.067 0.108 -0.158 0.550 -0.078 -0.234 0.198 -0.074

(0.000) (0.000) (0.000) (0.556) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

FREV2t-1 -0.042 0.029 0.052 0.046 -0.011 0.887 0.349 0.161 -0.143 -0.005 0.587 0.243 -0.017

(0.000) (0.000) (0.000) (0.000) (0.004) (0.000) (0.000) (0.000) (0.000) (0.153) (0.000) (0.000) (0.000)

RET2t-1 -0.052 0.162 0.200 0.157 0.016 -0.047 -0.025 -0.019 0.182 -0.038 -0.098 0.127 0.008

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.030)

NANALt-1 -0.460 -0.312 -0.107 -0.109 0.073 -0.049 0.383 0.240 -0.211 0.034 0.695 0.292 -0.042

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

INSTt-1 -0.178 -0.144 -0.067 -0.010 -0.003 -0.023 0.429 0.113 -0.087 0.006 0.297 0.162 -0.058

(0.000) (0.000) (0.000) (0.012) (0.405) (0.000) (0.000) (0.000) (0.000) (0.142) (0.000) (0.000) (0.000)

CFOt-1 -0.147 -0.290 -0.237 -0.279 -0.061 -0.019 0.191 0.125 -0.180 0.095 0.288 0.172 -0.218

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

VCFOt-1 0.075 0.212 0.189 0.414 0.046 0.085 -0.088 -0.066 -0.290 -0.075 -0.370 0.087 -0.086

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

RETt -0.029 0.008 0.017 0.006 -0.033 -0.033 -0.013 -0.020 0.040 -0.017 -0.029 -0.132 -0.013

(0.000) (0.049) (0.000) (0.116) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001)

34

Table 2 (continued)

Variable Φ ln(σe2) ln(σS

2) DD FREV2 RET2 NANAL INST CFO VCFO RET SIZE M/B LEV

SIZE -0.567 -0.489 -0.240 -0.164 0.066 -0.037 0.689 0.398 0.225 -0.110 -0.098 0.422 -0.064

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

M/B -0.118 0.094 0.160 0.258 0.027 0.205 0.125 0.077 -0.092 0.198 -0.078 0.229 -0.185

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

LEV 0.028 0.092 0.085 -0.040 0.034 -0.024 -0.040 -0.053 -0.150 -0.013 0.001 -0.075 -0.107

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.705) (0.000) (0.000)

Panel B: Correlation matrix for Hutton et al. (2009) sample

Variable Φ ln(σe2) ln(σS

2) OPAQUE SIZE M/B LEV ROE Var

(Industry) Skewness Kurtosis

Φ 0.448 0.018 0.123 -0.674 -0.265 0.028 -0.204 -0.185 0.139 0.114

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

ln(σe2) 0.443 0.868 0.413 -0.664 -0.090 -0.075 -0.402 0.215 0.312 0.173

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

ln(σS2) -0.019 0.872 0.389 -0.403 0.023 -0.093 -0.344 0.349 0.276 0.096

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

OPAQUE 0.090 0.362 0.354 -0.261 0.183 -0.185 -0.134 0.155 0.159 0.110

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

SIZE -0.654 -0.657 -0.391 -0.205 0.363 0.034 0.282 0.063 -0.246 -0.183

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

M/B -0.142 0.040 0.117 0.245 0.188 -0.194 0.163 -0.004 -0.052 -0.037

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.306) (0.000) (0.000)

LEV 0.047 -0.016 -0.039 -0.116 0.003 -0.122 0.038 -0.034 -0.021 -0.041

(0.000) (0.000) (0.000) (0.000) (0.539) (0.000) (0.000) (0.000) (0.000) (0.000)

ROE -0.120 -0.312 -0.280 -0.234 0.184 -0.238 -0.002 -0.070 -0.139 -0.119

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) 0.729 (0.000) (0.000) (0.000)

Var(industry) -0.143 0.191 0.295 0.158 0.045 0.065 -0.052 -0.051 0.055 0.092

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

Skewness 0.142 0.323 0.288 0.159 -0.236 0.021 -0.002 -0.142 0.049 0.280

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.625) (0.000) (0.000) (0.000)

Kurtosis 0.157 0.154 0.070 0.077 -0.248 -0.019 -0.005 -0.080 0.006 0.169

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.216) (0.000) (0.178) (0.000)

35

Table 3 Simulation of the econometric models with alternative measures of firm-specific return variation

This table reports number of significant coefficients from estimaing equations (6), (7) and (8) for 1000 random sample of 100 observations each drawn from the time period 1964-2008.

ln [σ ] = α0 + α1 EQi + ε1 (6) ln σ = λ0 + λ1 EQi + ε2 (7) Φ = δ0 + δ1 EQi + ε3 (8)

where ln[σe2] is logistic transformed idiosyncratic volatility, ln[σS

2] is logistic transformed systematic volatility and Φ is relative volatlity. EQ is either DD calculated from the modified Dechow and Dichev (2002) model or OPAQUE calculated using the modified Jones (1991) model. Positive (Negative) represents number of coefficients that are statistically significant at the 10% level.

Panel A: DD

Variable α1 λ1 δ1 α1 > λ1 α1 < λ1

Positively significant 994 975 478 478

Negatively significant 5 5

Insignificant 6 25 517 454 63

Total 1000 1000 1000 932 68

Panel B: OPAQUE

Variable α1 λ1 δ1 α1 > λ1 α1 < λ1

Positively significant 967 927 230 230

Negatively significant 4 4

Insignificant 33 73 766 319 447

Total 1000 1000 1000 549 451

36

Table 4 Replication of Rajgopal and Venkatachalam (2010)

This table reports estimation of Eq. (3) in Rajgopal and Venkatachalam (2010). VARit = α0 + α1DDi,t-1 + α2FREV2

i,t-1 + α3RET2i,t-1 + α4NANALi,t-1 + α5INSTi,t-1 + α6CFOi,t+1 + α7CFOi,t-1

+ α8VCFOi,t-1 + α9M/Bi,t-1 + α10SIZEi,t-1 + α11LEVi,t-1 + α1RETi,t + ζit

where VAR represents idiosyncratic volatility (σe

2), logistic transformed idiosyncratic volatility (ln[σe2]),

relative volatlity (Φ), or logistic transformed systematic volatiltiy (ln[σS2]); DD is a measure of earnings

quality calculated from the modified Dechow and Dichev (2002) model; all other variables are defined in Appendix B. The sample period is from 1964 to 2001 and all variables are winsorized at the bottom and top 1% levels. t-statistics are presented in parentheses. ***, **, and * indicate statistical significance at .001, .01, and .05 levels, respectively.

Variable

(1) (2) (3) (4) σe

2 Φ ln[σe2] ln[σS

2]

DDt-1 0.185*** 0.859*** 6.087*** 5.072*** (67.86) (26.81) (88.45) (69.56)

FREV2t-1 0.000 -0.001 0.013*** 0.014***

(1.20) (-0.99) (7.85) (7.81) RET2

t-1 0.001*** -0.041*** 0.080*** 0.124*** (9.07) (-27.23) (24.56) (35.74)

NANALt-1 0.001*** -0.011*** 0.009*** 0.020*** (20.34) (-33.48) (11.91) (26.11)

INSTt-1 -0.002* 0.186*** 0.196*** -0.008 (-2.12) (22.02) (10.80) (-0.43)

CFOt+1 -0.022*** 0.004 -0.465*** -0.442*** (-18.51) (0.27) (-15.57) (-13.96)

CFOt-1 -0.020*** 0.016 -0.455*** -0.484*** (-17.07) (1.15) (-15.11) (-15.17)

VCFOt-1 -0.029*** -0.212*** -0.768*** -0.536*** (-10.13) (-6.35) (-10.73) (-7.07)

M/Bt-1 0.001*** 0.002** 0.042*** 0.040*** (13.59) (2.61) (29.32) (26.63)

SIZEt-1 -0.007*** -0.115*** -0.260*** -0.136*** (-73.73) (-103.94) (-109.72) (-54.25)

LEVt-1 0.010*** -0.026** 0.499*** 0.528*** (12.17) (-2.79) (25.06) (25.00)

RETt -0.001*** -0.071*** -0.038*** 0.029*** (-3.38) (-24.68) (-6.19) (4.38)

Intercept 0.044*** 1.819*** -3.729*** -5.530*** (90.95) (323.39) (-308.73) (-432.20)

Adj. R2 26.7% 37.0% 42.9% 24.5%

N 60,205 60,205 60,205 60,205

37

Table 5

Replication of Hutton et al. (2009)

This table reports estimation of Model 3 in Table 6 in Hutton et al. (2009) VARit = β0 + β1OPAQUEi,t + β2Var(Industry)i,t + β3SIZEi,t-1 + β4M/Bi,t-1 + β5LEVi,t-1 + β6ROEi,t

+ β7Skewnessi,t + β8Kurtosisi,t + β9OPAQUE2i,t + νit

where VAR represents idiosyncratic volatility (σe2), logistic transformed idiosyncratic volatility (ln[σe

2]), relative volatlity (Φ), or logistic transformed systematic volatiltiy (ln[σS

2]); OPAQUE is a measure of earnings quality calculated using the modified Jones (1991) model; all variables are defined in Appendix B. The sample period is from 1991 to 2005 and all variables are winsorized at the bottom and top 1% levels. t-statistics are presented in parentheses. ***, **, and * indicate statistical significance at .001, .01, and .05 levels, respectively.

Variable

(1) (2) (3) (4) σe

2 Φ ln[σe2] ln[σS

2]

OPAQUEt 0.141*** -0.313*** 6.337*** 6.583*** (18.09) (-4.33) (44.58) (42.53)

VAR(Industry)t 1.184*** -10.742*** 38.961*** 51.846*** (33.38) (-32.71) (60.38) (73.78)

SIZEt-1 -0.011*** -0.158*** -0.319*** -0.157*** (-113.67) (-177.13) (-181.78) (-82.04)

M/Bt-1 0.000*** -0.001 0.022*** 0.023*** (5.66) (-0.98) (21.92) (20.98)

LEVt-1 0.014*** 0.104*** 0.159*** 0.067*** (14.63) (11.97) (9.32) (3.62)

ROEt -0.016*** -0.012*** -0.285*** -0.262*** (-43.48) (-3.34) (-41.68) (-35.21)

Skewnesst 0.031*** -0.008 0.532*** 0.560*** (48.61) (-1.29) (45.21) (43.72)

Kurtosist -0.001*** -0.001 -0.038*** -0.055*** (-5.81) (-0.71) (-13.32) (-17.94)

OPAQUE2t -0.207*** 0.448* -11.983*** -12.317***

(-9.30) (2.17) (-29.54) (-27.88) Intercept 0.070*** 2.172*** -3.014*** -5.183***

(84.14) (280.11) (-197.92) (-312.52)

Adj. R2 37.9% 44.3% 57.0% 36.7% N 53,185 53,185 53,185 53,185

38

Table 6 Replication of Hutton et al. (2009) using systematic risk as a control variable

This table reports estimation of Model 3 in Table 6 in Hutton et al. (2009) VARit = β0 + β1OPAQUEi,t + β2Var(Industry)i,t + β3SIZEi,t-1 + β4M/Bi,t-1 + β5LEVi,t-1 + β6ROEi,t

+ β7Skewnessi,t + β8Kurtosisi,t + β9OPAQUE2i,t + β10 ln[σS

2]i,t + νit

where VAR represents logistic transformed idiosyncratic volatility (ln[σe2]) or relative volatlity (Φ);

OPAQUE is a measure of earnings quality calculated using the modified Jones (1991) model; all variables are defined in Appendix B. The sample period is from 1991 to 2005 and all variables are winsorized at the bottom and top 1% levels. t-statistics are presented in parentheses. ***, **, and * indicate statistical significance at .001, .01, and .05 levels, respectively.

Variable (1) (2) Φ ln[σe

2]

OPAQUEt 0.899*** 1.187*** (13.29) (15.67)

VAR(Industry)t -1.196*** -1.597*** (-3.77) (-4.50)

SIZEt-1 -0.187*** -0.196*** (-214.69) (-201.28)

M/Bt-1 0.004*** 0.004*** (7.89) (7.69)

LEVt-1 0.116*** 0.106*** (14.58) (11.91)

ROEt -0.060*** -0.080*** (-18.51) (-22.05)

Skewnesst 0.095*** 0.094*** (17.03) (14.94)

Kurtosist -0.011*** 0.006*** (-8.44) (3.73)

OPAQUE2t -1.820*** -2.347***

(-9.52) (-10.97) ln[σs

2] -0.184*** 0.782*** (-98.83) (375.08)

Intercept 1.217*** 1.040*** (101.41) (77.44)

Adj. R2 52.9% 88.2% N 53,185 53,185

39

Table 7 Information Variables Across Quintiles of Idiosyncratic Volatility Proxies

Panels A and B report the averages for each of the information variable in quintile portfolios formed on return volatility covering the period 1991-2005. Quintile portfolios are formed each fiscal year separately for the two measures of return volatility(σe

2 and Φ). For Panels C and D we provide the mean difference in Quintile 5 – Quintile 1 portfolios for each of the information variable across different size quintiles. t-statistics are reported in paranthesis. Panel A: Mean of information variables across quintiles of idiosyncratic volatility (σe

2)

Variable

Quintiles based on σe2 Mean

(1) (2) (3) (4) (5) (5) – (1)

LIQ 0.028 0.080 0.184 0.515 2.951 2.923 (63.23)

LIQVOL 0.039 0.134 0.347 1.069 6.738 6.699 (69.98)

SPREAD 0.010 0.015 0.020 0.028 0.045 0.034 (76.49)

PIN 0.172 0.193 0.212 0.228 0.251 0.079 (42.14)

ZRDAYS 0.105 0.129 0.146 0.172 0.225 0.120 (63.27)

Panel B: Mean of information variables across quintiles of relative volatlity (Φ)

Variable

Quintiles based on Φ Mean

(1) (2) (3) (4) (5) (5) – (1)

LIQ 0.023 0.191 0.573 1.148 1.820 1.797 (49.95)

LIQVOL 0.042 0.424 1.252 2.566 4.044 4.002 (52.61)

SPREAD 0.011 0.019 0.025 0.031 0.033 0.022 (55.27)

PIN 0.143 0.174 0.206 0.252 0.283 0.140 (82.01)

ZRDAYS 0.068 0.119 0.161 0.198 0.230 0.162 (98.15)

40

Table 7 (continued) Panel C: Mean of information variables for Quintile 5 and Quintile 1 portfolios of idiosyncratic volatility (σe

2) by size quintile

Variable Quintile

Based on σe2

Size Quintile (1) (2) (3) (4) (5)

LIQ 1 0.112 0.014 0.006 0.007 0.002

5 6.367 4.042 2.432 1.423 0.600 Diff 6.255 4.028 2.426 1.417 0.598

(t-stat) (45.71) (36.72) (28.10) (21.63) (14.60)

LIQVOL 1 0.158 0.021 0.009 0.010 0.003 5 13.948 9.396 5.727 3.454 1.408

Diff 13.791 9.375 5.718 3.444 1.404 (t-stat) (50.62) (40.93) (31.08) (23.44) (15.19)

SPREAD 1 0.012 0.013 0.011 0.009 0.007 5 0.037 0.047 0.051 0.048 0.039

Diff 0.025 0.034 0.040 0.039 0.032 (t-stat) (20.20) (23.61) (43.98) (45.10) (38.34)

PIN 1 0.272 0.191 0.153 0.134 0.109 5 0.293 0.276 0.256 0.233 0.200

Diff 0.021 0.085 0.103 0.100 0.091 (t-stat) (4.24) (21.47) (30.39) (31.50) (29.57)

ZRDAYS 1 0.215 0.113 0.083 0.066 0.048 5 0.289 0.250 0.223 0.199 0.165

Diff 0.074 0.137 0.140 0.133 0.117 (t-stat) (13.34) (34.99) (41.38) (41.50) (36.79)

Panel D: Mean difference in information variables between Quintile 5 and Quintile 1 portfolios of relative volatlity (Φ) reported for each size quintile.

Variable Quintile

Based on Φ Size Quintile (1) (2) (3) (4) (5)

LIQ 1 0.112 0.003 0.001 0.001 0.000

5 5.068 2.344 1.118 0.461 0.230 Diff 4.956 2.341 1.117 0.460 0.229

(t-stat)

(39.98) (29.25) (22.26) (15.65) (9.71)

LIQVOL 1 0.203 0.005 0.001 0.001 0.001 5 11.041 5.338 2.574 1.061 0.463

Diff 10.838 5.332 2.573 1.060 0.462 (t-stat) (43.19) (30.70) (22.70) (15.77) (10.06)

SPREAD 1 0.018 0.013 0.010 0.008 0.007 5 0.032 0.039 0.038 0.034 0.023

Diff 0.014 0.026 0.028 0.025 0.016 (t-stat) (11.70) (26.64) (34.16) (37.43) (29.68)

PIN 1 0.191 0.165 0.146 0.127 0.104 5 0.307 0.302 0.293 0.273 0.247

Diff 0.117 0.137 0.147 0.145 0.143 (t-stat) (25.14) (26.64) (42.04) (47.07) (40.28)

ZRDAYS 1 0.107 0.076 0.062 0.053 0.042 5 0.296 0.256 0.228 0.204 0.165

Diff 0.189 0.180 0.165 0.151 0.123 (t-stat) (39.24) (39.24) (52.78) (52.48) (45.43)