σ Ø 6 R - Fuqua School of Businessvmohan/bio/files/LRV010612.pdf · Mohan Venkatachalam...
Transcript of σ Ø 6 R - Fuqua School of Businessvmohan/bio/files/LRV010612.pdf · Mohan Venkatachalam...
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: [email protected]
Shivaram Rajgopal†
Schaefer Chaired Professor of Accounting Goizueta Business School
Emory University 1300 Clifton Road NE
Atlanta, GA 30322 Email: [email protected]
Mohan Venkatachalam
Professor, Fuqua School of Business Duke University 100 Fuqua Drive
Box 90120 Durham, NC 27708
Email: [email protected]
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.
1
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.
2
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.
3
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
4
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)
5
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
6
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.
7
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)
8
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
9
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).
10
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
11
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.
12
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
13
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.
14
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.
15
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
References
Aboody, D., Hughes, J., and Liu, J. 2005. Earnings quality, insider trading, and cost of capital. Journal of Accounting Research, 43(5): 651-673. Amihud, Y. 2002. Illiquidity and stock returns: cross-section and time series effects. Journal of Financial Markets 5, 31-56. Armstrong, C., K. Balakrishnan and D. Cohen. 2012. Corporate governance and the information environment: evidence from state antitakeover laws. Journal of Accounting and Economics, forthcoming. Ashbaugh-Skaife, H., J. Gassen, and R. LaFond. 2006. Does stock price synchronicity represent firm-specific information? The international evidence. Working paper. University of Wisconsin, Madison. Bakke, T., and T.M. Whited. 2006. Which firms follow the market? An analysis of corporate investment decisions. Working paper, University of Wisconsin, Madison. Bartram, S., G. Brown, and R. Stulz. 2011. Why are US stocks more volatile? Working paper, National Bureau of Economic Research. Bhattacharya, N., H. Desai, and K. Venkataraman. 2012a. Earnings quality and information asymmetry: evidence from trading costs. Contemporary Accounting Research, forthcoming. Bhattacharya, N., F. Ecker, P. Olsson, and K. Schipper. 2012b. Direct and mediated associations among earnings quality, information asymmetry and the cost of equity. The Accounting Review, forthcoming. Brockman, P., and X. Yan. 2009. Block ownership and firm-specific information. Journal of Banking and Finance 33: 308-316. Brown, N., and M. Kimbrough. 2011. Intangible investment and the importance of firm-specific factors in the determination of earnings. Review of Accounting Studies 16: 539-573. Brown, S., and S. Hillegeist. 2007. How disclosure quality affects the level of information asymmetry. Review of Accounting Studies 12 (2-3): 443-477. Campbell, J. Y., M. Lettau, B. G. Malkiel, and Y. Xu, 2001, Have individual stocks become more volatile? An empirical exploration of idiosyncratic risk, The Journal of Finance 56, 1-43. Chan, K., and A. Hameed. 2006. Stock price synchronicity and analyst coverage in emerging markets. Journal of Financial Economics 80, 115–147. Chen, Q., I. Goldstein, and W. Jiang. 2007. Price Informativeness and investment sensitivity to stock price. Review of Financial Studies 20: 619-650.
29
Chen, C., A. Huang and R. Jha. 2011. Idiosyncratic return volatility and the information quality underlying managerial discretion. Journal of Financial Quantitative Analysis (forthcoming). Chun, H., J. Kim, R. Morck, and B. Yeung. 2008. Creative destruction and firm-specific performance heterogeneity. Journal of Financial Economics 89: 109-135. Core, J., W. Guay, and R. Verdi, 2008. Is accruals quality a priced risk factor? Journal of Accounting and Economics 46, 2-22 Crawford, S., D. Roulstone and E. So. 2012. Analyst initiations of coverage and stock return synchronicity. The Accounting Review (forthcoming). Dechow, P., and I. Dichev. 2002. The quality of accruals and earnings: the role of accrual estimation errors. The Accounting Review 77 (Suppl.), 35–59. Durnev, A., R. Morck, B. Yeung, and P. Zarowin. 2003. Does greater firm-specific return variation mean more or less informed stock pricing? Journal of Accounting Research 41, 797-836. Durnev, A., R. Morck, and B. Yeung. 2004. Value-enhancing capital budgeting and firm- specific stock return variation. The Journal of Finance 59, 65-105. Easley D., S. Hvidkjaer and M. O'Hara. 2002. Is information risk a determinant of asset returns? Journal of Finance 47, 2185-2221. Fama, E., and K. French. 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3-56. Fama, E., and K. French. 1997. Industry costs of equity. Journal of Financial Economics, 43, 153-193. Fernandes, N., and M. Ferreira. 2008. Does international cross-listing improve the information environment. Journal of Financial Economics 88: 216-244. Ferreira, D., M. Ferreira, and C. Raposo. 2011. Board structure and price informativeness. Journal of Financial Economics 99: 523-545. Ferreira, M., and P. Laux. 2007. Corporate governance, idiosyncratic risk, and information flow. The Journal of Finance 2: 951-989. Francis, J., R. LaFond, P. Olsson, and K. Schipper. 2005. The market pricing of accruals quality. Journal of Accounting and Economics 39, 295-327. Griffin, J. M., P. J. Kelly, and F. Nardari, 2007, Measuring short-term international stock market efficiency, Working Paper, University of Texas at Austin.
30
Gul, F., J., Kim, and A. Qiu. 2010. Ownership concentration, foreign shareholding, audit quality, and stock price synchronicity: Evidence from China. Journal of Financial Economics 95: 425-442. Gul, F., Ng, A., Srinidhi, B., 2011. Does board gender diversity improve the informativeness of stock prices? Journal of Accounting and Economics 51(3): 314-338. Hou, K., L. Peng, and W. Xiong. 2005. R2 and momentum. Working paper. Ohio State University. Hutton, A., A. Marcus, and H. Tehranian. 2009. Opaque financial reports, R2, and crash risk. Journal of Financial Economics 94: 67-86. Jin, L. and S.Myers. 2006. R-squared around the world: New theory and new tests. Journal of Financial Economics 79(2), 257-292. Jones, J. 1991. Earnings management during import relief investigations. Journal of Accounting Research 29: 193-228. Kelly, P. 2007. Information efficiency and firm-specific return variation, unpublished working paper, University of South Florida. Khanna, T., and C. Thomas. 2009. Synchronicity and firm interlocks in an emerging market. Journal of Financial Economics 92: 182-204. Kim, Y., H. Li, and S. Li. 2011. Does eliminating the Form 20-F reconciliation from IFRS to U.S. GAAP have capital market consequences? Journal of Accounting and Economics, forthcoming. Kim, J., and S. Shi. 2012. IFRS reporting, firm-specific information flows and institutional environment: International evidence. Review of Accounting Studies (forthcoming). Kothari, S. P., A. Leone, C. Wasley. 2005. Performance matched discretionary accrual measures. Journal of Accounting and Economics, 39: 163-197. Lambert, R., C. Leuz, and R. Verrecchia. 2007. Accounting information, disclosure, and the cost of capital. Journal of Accounting Research 45: 385-420. Lang, M., and M. Maffett. 2011. Transparency and liquidity uncertainty in crisis periods.Journal of Accounting and Economics 52: 101-125. Mashruwala, C., S. Rajgopal, and T. Shevlin. 2006. Why is the accrual anomaly not arbitraged away? The role of idiosyncratic risk and transaction costs. Journal of Accounting and Economics 2006, 42 (1-2), 3-33.
31
McNichols, M. 2002. Discussion of ‘The quality of accruals and earnings: the role of accrual estimation errors.’. The Accounting Review 77 (Suppl.), 61–69. Morck, R., B. Yeung, and W.Yu. 2000. The information content of stock markets: Why do emerging markets have synchronous stock price movements? Journal of Financial Economics 58, 215-260. Ng, J. 2011. The effect of information quality on liquidity risk. Journal of Accounting and Economics, 52 (2-3): 126-143. Pontiff, J, 2006. Costly arbitrage and the myth of idiosyncratic risk. Journal of Accounting and Economics 42 (12), 35-52. Piotroski, J.D., and D. T. Roulstone, 2004. The influence of analysis, institutional investors, and insiders on the incorporation of market, industry, and firm-specific information into stock prices. The Accounting Review 79, 1119-1151. Rajgopal, S., and M. Ventatachalam. 2010. Financial reporting quality and idiosyncratic return volatility. Journal of Accounting and Economics 51, 1-20. Roll, R. 1988. R2. The Journal of Finance 43, 541-566. Teoh, S.H., Y. Yang, and Y. Zhang. 2008. R-square: Noise of firm-specific information?, unpublished paper, University of California, Irvine. Welker, M. 1995. Disclosure policy, information asymmetry and liquidity in equity markets. Contemporary Accounting Research 11 (2): 801-828. Wurgler, J., 2000. Financial markets and the allocation of capital. Journal of Financial Economics, 58, 187-214. Xu, Y. and B., Malkiel, 2003. Investigating the behavior of idiosyncratic volatility. Journal of Business, 76(4), 613-644.
32
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)