The impact of strategic disclosure on returns and return volatility: Evidence from the ‘leverage effect’
Jonathan L. Rogers,€ Catherine M. Schrand, † and Robert E. Verrecchia *
July 2006
Abstract Strategic disclosure, which we define as the reporting of good news and the withholding of bad news, provides an explanation for predictable dynamic patterns in returns including the negative relation between return shocks and conditional return volatility, referred to as the leverage effect. With strategic reporting, positive share price responses in the event of good news result from news arrival. Negative share price responses, in contrast, are more likely due to an inference of bad news, which implies a smaller reduction in residual uncertainty. We document that the leverage effect is stronger in portfolios of individual stocks that are more likely to disclose strategically: The leverage effect is 1) stronger for firms in industries with lower private information, and 2) weaker for firms in industries with a high risk of shareholder litigation. The relationship between strategic disclosure and the leverage effect is greater for high-beta firms, for which patterns in total returns are more likely to reflect the idiosyncratic nature of news that firms choose to disclose strategically. Time-series and cross-sectional patterns in the leverage effect in market indices also are consistent with strategic disclosure as an explanation for it. These analyses are an important component of the study because they indicate that strategic disclosure decisions by individual firms are strong enough not only to create patterns in their own stock returns, but also that they might be powerful enough to explain market-wide patterns despite the covariance effects of aggregation of disclosure behavior over multiple firms.
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The University of Chicago Corresponding author: The Wharton School, University of Pennsylvania, 1300 SH-DH, Philadelphia, PA 191046365. e-mail
[email protected]. * The Wharton School of the University of Pennsylvania †
The authors thank Michael Brandt, Ron Kaniel, Christian Leuz, Russ Lundholm, Pat Hughes and seminar participants at Duke University, Indiana University, Insead, UCLA and the University of Utah Winter Conference for comments. We thank Joseph Gerakos for research assistance on model selection.
1. Introduction The broad goal of this paper is to explore the impact of endogenously determined information flow on dynamic return patterns. Researchers have long recognized the notion that firms’ disclosure decisions can be strategic. Value- maximizing firms with private information exercise discretion with regard to making the information public, and the firms’ choices anticipate the market’s rational response (e.g., Verrecchia, 1983). Only recently, however, has there been recognition that endogenous information flow might explain well-recognized dynamic patterns in returns. Shin (2003, 2004) suggests that information flow resulting from endogenous disclosure choices may explain post-earnings announcement drift (e.g., Bernard and Thomas, 1990), the short-run momentum effect (e.g., Jegadeesh and Titman, 2001), and long run reversals (e.g., DeBondt and Thaler, 1985). Earlier research had considered information-based explanations for such patterns with Bayesian learning by rational investors, but the information flow was exogenous (e.g., Lewellen and Shanken, 2002; Pástor and Veronesi, 2003). This paper examines the implications of endogenous information arrival for one specific dynamic pattern in retur ns – the leverage effect – which is the negative relation between returns and conditional return volatility. Black (1976) provided an early explanation for the phenomenon. As returns increase, market leverage decreases. As leverage decreases, the risk of the residual equity claims decreases. As equity risk decreases, return volatility decreases. In recognition of this explanation, the literature dubs the negative association between return shocks and conditional return volatility as the leverage effect. Subsequent empirical studies, however, document several patterns in the leverage effect that are inconsistent with changes in leverage as an explanation. 1 Nonetheless, for ease of exposition, we will refer to the negative relation
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For example, increases and decreases in return volatility are not associated with changes in leverage from issuing or retiring debt or shares (Figlewski and Wang, 2002); changes following a return shock die out earlier than the
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between returns and conditional return volatility as the leverage effect throughout the paper. An explanation for the leverage effect remains an open question (Figlewski and Wang, 2002). A disclosure strategy that predicts the leverage effect pattern in returns is for a firm to report “good” news and withho ld “bad” news, where good news is such that conditional firm value is above a threshold. For convenience, we define this threshold-style disclosure behavior as “strategic” disclosure. 2 The disclosure of good news leads to a positive share price response because the news is good, and also to a reduction in residual uncertainty because of news arrival. Alternatively, when managers do not disclose, the market rationally interprets withheld information as bad news. The inference of bad news leads to lower returns, but residual uncertainty is reduced less than in the event of a disclosure. Models based on a variety of assumptions result in this particular threshold-style disclosure equilibrium (e.g., Verrecchia, 1983; Jung and Kwon, 1988; Shin, 2003). It is an intuitively appealing equilibrium and it is supported by empirical evidence on firms’ disclosure decisions. Strategic disclosure as an explanation for the leverage effect is distinct from the volatility feedback explanation (e.g., French, Schwert, and Stambaugh, 1987; Campbell and Hentschel, 1992). The volatility feedback story (time-varying risk premium theory) assumes that investors believe conditional volatility is persistent. Thus, higher current-period volatility associated with a current-period return shock increases investor expectations of future volatility, which increases investors’ current-period required expected return. An increase in stock price associated with positive dividend news is partially offset by the decrease in stock price due to the higher required
effects of the leverage change (Engle and Lee, 1993; Figlewski and Wang, 2002); and, the relation between returns and return volatility is stronger for negative returns than for positive returns (e.g., Nelson, 1991; Engle and Lee, 1993). 2 Strategic reporting of this type can arise through a variety of modeling devices, such as the existence of an exogenous proprietary cost associated with an explicit disclosure (Verrecchia, 1983), or uncertainty as to whether the firm or manager is informed (Jung and Kwon, 1988; Shin, 2003). Models based on other stylized assumptions could lead to different optimal disclosure strategies.
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expected return. A decrease in stock price associated with negative dividend news is amplified by the price decrease caused by the higher required expected return. The assumption that conditional volatility is persistent is based on the empirical observation of autocorrelation in volatility; there is no economic rationale for why investors rationally expect persistence. Our empirical analysis documents that the leverage effect is stronger for portfolios of individual stocks that we identify as strategic disclosers. We measure the propensity for strategic disclosure based on proxies for ex ante incentives to behave strategically as opposed to ex post observation of disclosure behavior. An alternative research approach would be to identify individual firms as strategic disclosers based on ex post observed disclosure behavior. While such an approach may seem to provide more powerful tests, we emphasize that no single firm is a strategic discloser with respect to all sources of private information in all periods. Thus, from a practical standpoint, the portfolios that we define may be the lowest level at which we can aggregate individual stocks such that the across-portfolio variation in the propensity for firms to disclose strategically dominates the within-portfolio variation. Our research approach increases the probability of omitted correlated variables that are unrelated to strategic disclosure, and the most obvious candidate is systematic risk. The results are robust to controls for the potential correlation between systematic risk and the proxies for strategic disclosure. The first finding is that the leverage effect is stronger for firms that are less likely to have private information. When there is less private information, the threshold level above which firms disclose and below which firms withhold news rises. News arrival still reduces residual uncertainty, but less is inferred from a withheld disclosure. Thus, when there is less private information, the difference in the reduction of residual uncertainty associated with positive and negative returns is greater, which implies a greater asymmetric volatility reaction.
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The second finding is that the leverage effect is weaker for firms in industries in which there is a high risk of shareholder litigation. High-risk firms are less likely to engage in the type of strategic behavior that would induce the leverage effect. They are more likely to engage in a disclosure strategy that reduces their risk, which is to withhold favorable news and to announce bad news as soon as it is known. Throughout the analysis, we consider the effects of firm size. Our results indicate that larger firms have unconditionally greater asymmetry between the volatility reactions to positive and negative returns. This relation is expected if investors are more likely to anticipate announcements by large firms, which implies that their negative returns are more likely to represent an inference of bad news than the arrival of bad news. The supposition that larger firms have richer information environments, on average, and that investors are more likely to anticipate their announcements, also is reflected in greater conditional volatility responses to returns of either sign. Both positive and negative returns are more likely to represent an inference of news rather than news arrival. We recognize that size can be associated with many firm attributes that may also be associated with the leverage effect, and we do not view the associations as evidence that strategic disclosure explains the leverage effect. Nonetheless, the documented associations between size and the leverage effect are at least consistent with a strategic disclosure explanation for it. The stronger leverage effects for the individual stocks that we identify as strategic disclosers are amplified for high-beta firms. The nature of the private information that is revealed (or withheld) in the strategic disclosure models likely represents idiosyncratic news. Idiosyncratic shocks are expected to produce greater volatility asymmetry in total returns for high-beta firms (Braun, Nelson, and Sunier, 1995; Bekaert and Wu, 2000). The relation between
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the leverage effect and private information is not significant in the lowest four deciles of firms ranked on beta. The strength of the relation increases monotonically with beta across the remaining six deciles. The stronger leverage effect associated with lower shareholder litigation risk also increases with beta. Two patterns in leverage effects in market-wide return series also are consistent with strategic disclosure as an explanation. The market-wide leverage effect is stronger in the U.S. after the Private Securities Litigation Reform Act of 1995. The Act increased firms’ incentives to engage in strategic disclosure by lowering the expected litigation costs of making forwardlooking statements and of withholding bad news. The market-wide leverage effect also is stronger in Canada than in the U.S. The expected costs associated with the strategic disclosure of good news and with the strategic non-disclosure of bad news are lower in Canada because of its legal environment. Both of the tests of market-wide returns represent crude cuts of the data. These results are important, however, because the theoretical models that link strategic disclosure to the leverage effect are based on individual firm disclosures of presumably idiosyncratic information, while the observed leverage effect exists at the market level. Despite our ex ante concerns about the power of these tests given the necessary joint assumptions about the covariance structure of returns, we find the predicted cross-sectional and time-series variation in the market-wide leverage effect that is consistent with strategic disclosure as an explanation for it. The paper proceeds as follows. Section 2 provides an overview of our predictions about strategic disclosure and the leverage effect at the individual stock level. Section 3 describes the EGARCH model that we use to estimate the leverage effect and provides descriptive evidence on the parameter estimates that measure asymmetric volatility. Section 4 discusses the formation of
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the portfolios of strategic disclosers and presents the analysis of the leverage effect in individual stocks. Section 5 incorporates assumptions about conditional covariance effects and makes predictions about patterns in the market-wide leverage effect if strategic disclosure explains it. Section 6 concludes.
2. Strategic disclosure and the leverage effect Our central prediction is that more strategic disclosure will be associated with a stronger (more negative) leverage effect. The intuition behind this prediction for an individual stock is as follows. Disclosure strategies in which a firm discloses when its conditional firm value is above a threshold (τ) and withhold s otherwise, have the feature that the firm’s disclosure is associated with a positive share price response because the news is “good.” When managers do not disclose, the market rationally interprets withheld information as bad news. The inference of bad news leads to lower returns, but residual uncertainty is reduced less than in the event of a disclosure. Thus, there is an asymmetric relation between a firm’s returns and its conditional return volatility. Three important assumptions underlie the basic intuition that endogenous disclosure can lead to the leverage effect pattern in the return series of an individual stock: 1) Disclosure is “strategic” in the sense that a firm is more likely to disclose good news and withhold bad news; 2) Residual uncertainty is reduced more when news arrive s than when it is inferred; and 3) Return volatility represents (or is correlated with) residual uncertainty. In this section, we discuss the ex ante validity of each assumption. The first assumption is that firms disclose news above a threshold and withhold news below. Numerous empirical studies document that firms engage in a threshold-style of strategic
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disclosure. 3 But numerous studies also document that firms voluntarily disclose bad news rather than good news in particular settings (e.g., Skinner, 1994; Kasznik and Lev, 1995) and that behavior represents the opposite extreme. These studies, however, acknowledge that the absolute frequency of voluntary bad-news disclosures is low. Survey evidence is mixed. Half of surveyed CFOs indicate no preference for revealing good news relative to bad news. Approximately 21% (27%) disclose good (bad) news faster (Graham, Harvey, and Rajgopal, 2005). We are aware of only one large sample study which suggests that strategic disclosure may characterize reporting practices on average (Kothari, Shu, and Wysocki, 2005). The raw numbers of good news and bad news disclosures, however, are only one part of the story. The stylized models characterize the firm as choosing whether to make a report, but the choice can be viewed as whether to make an informative report. Empirical evidence suggests that firms exhibit asymmetry in the informativeness of good news and bad news disclosures. For example, bad news forecasts tend to be more qualitative while good news forecasts tend to be more precise (Skinner, 1994). Surveyed CFOs also admit to “fuzziness” in bad news disclosures (Graham, Harvey, and Rajgopal, 2005). The strategy of making an uninformative bad news report presumably reduces expected litigation costs while maintaining the benefits of nondisclosure (Rogers, 2005). Thus, even if bad news is announced as (or more) frequently than good news, it may not reduce residual uncertainty as much as an announcement of good news.
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See reviews of the disclosure literature in Healy and Palepu (2001) and Core (2001). Anecdotal evidence also suggests that firms are more likely to disclose good news than bad news. A recent Wall Street Journal article (Hensley and Landers, 2004) indicates that drug companies announce positive results of research projects but failed projects are simply removed from the firm’s active project list. A study of R&D expenditure announcements supports this anecdotal evidence. Chan, Martin, and Kensinger (1990) find positive returns when firms announce increases in R&D expenditures, which suggests that firms, on average, self-select to disclose good news. The analysis is only for R&D expenditure increases because no firms made announcements about reductions in R&D expenditures. R&D spending is a particularly appealing example to consider because characteristics of this information – such as the probability that it is private and that there is likely uncertainty about whether the manager has it – parallel the assumptions that underlie the threshold-type disclosure models.
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The second necessary assumption to link strategic disclosure to the leverage effect is that residual uncertainty is reduced more in the case of news arrival than in the case of an inference of news. This assumption follows logically from the threshold models of strategic disclosure by individual firms. Empirical evidence on the reduction in residual uncertainty associated with news arrival relative to that associated with news inference, however, is sparse. While many papers examine the differences in stock return reactions to a variety of newsworthy events for samples of announcers and non-announcers, they do not examine differences in residual uncertainty. Several studies show that higher overall disclosure quality is associated with lower return volatility (see Kothari, 2000, for a summary). To the extent higher “quality” in these studies is associated with greater news flow, these results are consistent with greater return volatility reductions for news arrival relative to inferences. The third assumption that underlies the prediction that strategic disclosure leads to a leverage effect is that return volatility represents (or is correlated with) residual uncertainty. Shin (2003) shows explicitly that conditional return volatility is a decreasing function of priorperiod returns within the context of his strategic disclosure model. More generally, models that allow for learning (i.e., in the sense of Bayesian updating of beliefs about expected firm value) show that idiosyncratic return volatility increases with residual uncertainty about the distribution of the firm’s profitability (e.g., Pástor and Veronesi, 2003). Estimation risk models, in which uncertainty is priced, also lead to a prediction that residual uncertainty is correlated with return volatility (e.g., Barry and Brown, 1985). Empirical studies that use return volatility as a proxy for residual uncertainty (information asymmetry between a firm and its investors) include Bushee and Noe (2000) and Lang and Lundholm (1993).
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3. Estimating the return/return volatility relation 3.1 The EGARCH model We measure the relation between return shocks and conditional return volatility using an EGARCH – exponential generalized autoregressive conditional heteroskedasticity – model, which was first proposed by Nelson (1991):4 k
rt = a + ∑ bi rt− i + cht + ut
(3.1)
i =0
p
q
i =1
i =1
log( ht ) = ζ + ∑ δ i log(ht −i ) + ∑α i {[| vt −i | −E | vt −i |] + θ vt− i}
.
(3.2)
In equation 3.1, returns at time t ( rt ) are modeled as a function of prior-period returns. In equation 3.2, the first set of parameters ( δ i ) measures the association between lagged conditional volatility estimates and conditional volatility. The second set of parameters (α i and θ) relates unexpected return shocks to expected return volatility. The bracketed term {[| vt −i | − E | vt −i |] + θ vt −i } represents the lagged squared residual ( ut2− i ), where v t is the residual or return shock scaled by its expected standard deviation ( ut / ht ), and is distributed i.i.d., E( v t ) = 0, and E( vt2 ) = 1. The model allows 54 parameterizations. The returns equation (3.1) can include zero to two return lags (k), and it can be estimated with and without the “ARCH- in- mean” term (c), the coefficient on ht (Hamilton, 1994). The conditional return volatility equation (3.2) can include up to three lags of the conditional variance (p) and the unconditional residual variance or squared residuals (q).
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Nelson (1991) allows the intercept in the conditional variance equation to vary as a function of the nontrading days between t – 1 and t (i.e., his intercept in equation 3.2 is ζ t ). We use monthly rather than daily returns data and estimate only one intercept.
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The first parameter related to measuring the return/return volatility relation is αi (“the arch term”), which represents the average conditional volatility reaction to a return shock of either sign. If αi is positive, then the conditional return volatility following a return shock, whether positive or negative, is higher on average. The second parameter related to measuring the return/return volatility relation is θ, which we refer to as the leverage effect. θ measures the asymmetric reaction to return shocks based on their sign. A negative θ implies that the increase in unexpected volatility is lower for positive shocks (a positive ut / ht which equals v t ) than for negative shocks (a negative v t ). If θ is less than -1, the overall reaction to a positive return shock is a decrease in return volatility. For a given αi , as the leverage effect parameter (θ) becomes more negative, there is more of a distinction between the conditional return volatility reaction to positive and negative return shocks. Because θ is multiplied by αi in the EGARCH model, the impact of a given θ on conditional return volatility increases with αi . Each firm-specific regression has a maximum of 180 monthly return observations from January 1988 through December 2002. The starting values for the parameters in the returns model (equation 3.1) are OLS estimates, the starting values for the q autoregressive terms in equation 3.2 are the Yule-Walker estimates, and the starting values for the δ i parameters on the lagged conditional variance terms are 1.0-6 . The log likelihood of the EGARCH model is maximized assuming a generalized error distribution density function for v t normalized with mean zero, unit variance. There are two features of equations 3.1 and 3.2 that require further discussion. First, they model the unconditional variance of returns, whereas the strategic disclosure models predict a pattern in the conditional variance. As discussed by Braun, Nelson, and Sunier (1995), which
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uses a similar specification, this specification likely overstates the conditional variance of returns because prior empirical evidence suggests that time variation in expected returns explains a substantial part of the unconditional variance of returns. Braun et al. are able to conclude that the specification overstates the conditional variance in their portfolios by “as much as 20%.” The conditional variance in our sample of individual stocks also is overstated, although the magnitude of the overstatement is uncertain. Second, this specification effectively estimates the aggregate leverage effect across market-wide and idiosyncratic components, but Braun et al. document that leverage effects are strong for the market-wide component of conditional volatility, but weak (or nonexistent) for the idiosyncratic component. Ex ante this result is troubling because it suggests that strategic disclosure, which is likely associated with idiosyncratic shocks, may not be powerful enough to produce detectable leverage effects. We explicitly consider the impact of estimation error (or systematic bias) in the estimates of the leverage effect parameters when we test the hypotheses.
3.2 Tests of model parameters In our subsequent cross-sectional analyses, we compare the average estimates of α 1 and θ across the 54 possible parameterizations of the model. A meaningful comparison of the first arch term (α 1 ) and the leverage effect (θ) requires that the estimates be from models with the same parameterization. There is, however, no accepted method to identify a single model ex ante. Various studies estimate an EGARCH (1, 1) because it is parsimonious. But, the (1, 1) parameterization is not necessarily appropriate in the context of the leverage effect (e.g., Chen and Kuan, 2002; Mitchell and McKenzie, 2003; Hansen and Lunde, 2005). An informationbased criterion like Schwarz’s Bayesian information Criterion (SBC) as an ex post diagnostic
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tool to identify a single model parameterization also is inappropriate in our setting. 5 A comparison of models in terms of out-of-sample forecast accuracy also is unacceptable because we have no economic context to specify a loss function (Diebold and Mariano, 1995). One drawback of analyzing the average of the estimates is that the average includes parameters from models that may have very poor fit. We take two steps to mitigate this drawback. We truncate the sample of estimated arch terms ( αˆ 1 s) and leverage effect parameters ( θˆ s) at the 5th and 95th percentiles of the estimate scaled by its standard error. We also analyze the robustness of the results to an alternative approach for aggregating the estimates that weights each observation by the rank of the model’s SBC. The weighted average θˆ for firm j across the 54 models (m) is:
RANK m, j ˆ WTDAVG θ j = c ∑ RANK m , j m=1
()
θˆ m, j
where RANK m, j is the rank of model m for firm j based on its SBC, and c is the number of models that converge for firm j. For example, the estimate of θ from the best (worst) model based on its SBC for a firm for which all 54 parameterizations converged would receive a weight of 3.6%, which is 54/1,485 (0.07%, which is 1/1,485). The same weighting procedure is applied SBC equals − 2 ln(l) + ln(n) g , where l is the value of the likelihood function, n is the number of observations in the firm-specific model, and g is the number of estimated parameters. Several factors influence the conclusion that it is inappropriate in this setting. First, the SBC favors fit of the return series, while the focus of the analysis is the volatility parameters (Pagan and Schwert, 1990). Second, studies using simulated returns data with known properties show that the SBC is an unreliable method to identify the “best” model (or model parameterization) with leverage effects (e.g., Gerakos, 2005; Mitchell and McKenzie, 2003). Third, non-statistical perusal of the SBCs for the 54 estimated models for our sample suggests that the SBCs are potentially unreliable to discriminate parameterizations. For example, the “best” model for the CRSP equal-weighted index has an SBC of -542.44; the SBC of the next best model is -542.40. These two models, however, are quite different in an economic sense. The second-best model has only one arch term instead of two and it includes an arch-in-mean term, in contrast to the best model. Certain variable parameterizations are consistently associated with better model ranks. The lowest rank 5
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to the αˆ 1 s. Results throughout the paper are virtually unchanged when using this alternative averaging approach and are not presented. In summary, a commitment to any single model parameterization would reflect our (unjustifiable) trade-off of one model flaw over another. We instead report averages and a reasonably parsimonious set of results from various parameterizations. We also provide illustrations of the estimates from all 54 parameterizations.
3.3 Summary of model parameter estimates Table I provides descriptive evidence of the EGARCH model estimates from the 54 model parameterizations. Although we use the return series of individual stocks to estimate the model for the primary analysis in the paper, for ease of exposition the descriptive statistics we present in Table I are for the monthly return on the CRSP equal-weighted index with dividends minus the one- month risk- free interest rate. We estimate the model from January 1988 through December 2002. 6 [Insert Table I here.]
The two parameters that are relevant for measuring the return/return volatility relation are the arch terms ( αi ) and θˆ . The median (mean) estimate of θ, which measures the asymmetric reaction to return shocks based on their sign is -0.4681 (-0.5101), consistent with the existence of an asymmetry between the volatility responses to positive and negative return shocks. The θˆ
values occur for models that include one return lag (k = 1), one lag of the variance term (p = 1), and one lag of the arch term (q = 1). The patterns, however, are not overwhelming. 6 See Braun, Nelson, and Sunier (1995) for justification of a preference for an equal-weighted index. We also estimate the models using a value-weighted index and a three-month risk-free interest rate; the results are qualitatively similar.
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term has a negative sign in 38 of the 44 parameterizations that converge; 7 two-thirds of the 38 are significant at the 10% level. A negative θˆ implies that the increase in unexpected volatility is lower for positive shocks (a positive ut / ht which equals v t ) than for negative shocks (a negative v t ). A θˆ less than -1 implies that the overall impact of a positive return in month t is a decrease in return volatility in month t+1. We focus the discussion of the arch term estimates on the first arch term ( αˆ 1 ). The median (mean) estimate of α 1 , which represents the average conditional volatility reaction to a return shock of either sign, is 0.3764 (0.3792). The αˆ 1 term has a positive sign in all 44 parameterizations that converge (98% are significant). Thus, on average, return volatility increases following a return shock, consistent with the results in the literature that report positive
αˆ 1 s for models of index returns (e.g., Braun, Nelson, and Sunier, 1995). The empirical observation that αˆ 1 is positive is not consistent with predictions from threshold-style strategic disclosure models (e.g., Verrecchia, 1983; Jung and Kwon, 1988; and Shin, 2003). Such models predict that both a disclosure of good news and an inference of bad news will increase the precision of investor’s estimates of firm value and lead to lower residual uncertainty. It is easy to imagine, however, assumptions about news arrival (or inferences) that would lead to an increase in residual uncertainty. For example, using a modeling framework following Kyle (1985), Kim and Verrecchia (1994) predict that residual uncertainty will increase following the dissemination of private information if market participants are heterogeneous with respect to their ability to process the disclosed information about firm value into private information. As another example, if there is asymmetric information about the support for the
7
We allow for a maximum of 100 iterations to attain convergence.
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unconditional distribution of the value-relevant information, or if the support is unbounded, the impact of news arrival on residual uncertainty is ambiguo us and could result in increasing uncertainty (Shin, 2003). A positive αˆ 1 , however, does not affect the implications of the disclosure models for predictions about the leverage effect. The existence of a threshold is the important feature of these models for linking the leverage effect to strategic disclosure behavior. A threshold implies that there is a difference in residual uncertainty following good news (which is correlated with positive returns) and bad news (which is correlated with negative returns) because one is revealed while the other is inferred. Table I also presents the estimates from the best model identified by Schwarz’s Bayesian information Criterion (SBC). The best model has one lagged return (k = 1) and no ARCH-inmean term in equation (3.1) and one lagged variance term (p = 1) and one arch term (q = 1) in equation (3.2). 8 The estimate of the arch term ( αˆ 1 ) is 0.1725, which is significantly greater than zero at the 5% level. The estimate of θ is -0.7964 (p-value = 0.107).
4. Cross-sectional patterns in the leverage effect for individual stocks This section proposes and tests two hypotheses about cross-sectional variation in the leverage effect in individual stocks. In section 4.1, we examine whether the leverage effect is stronger in industries about which there is less private information. In section 4.2, we examine whether the leverage effect is weaker when litigation risk reduces a firm’s incentives to strategically disclose. 8
The LM and q-statistic (see Engle, 1982) do not reject homoskedasticity at order 2, which is the parameterization for q in the best model identified by the SBC. Similar tests are conducted on the best models for which we report results throughout the paper, and the models that the SBC identifies as the best do not suffer from residual heteroskedasticity at order q based on these test statistics.
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4.1 Private information 4.1.1 Hypotheses and analysis The first hypothesis is that the leverage effect is stronger for firms about which there is less private information. Less private information (greater public information) increases the threshold level of disclosure (τ) because it ameliorates the adverse selection problem between firm managers and agents outside the firm, such as investors and creditors. Thus, investors’ expectations in the event of non-disclosure exert less pressure on managers to disclose. 9 As τ increases, the difference in the precision associated with a positive return, which represents good news, versus a negative return, which represents bad news, increases. As the difference increases, the leverage effect increases. As intuition for why an increase in the threshold level of disclosure implies a stronger leverage effect, consider the polar case where the threshold (τ) approaches its limit of negative infinity and there is full disclosure. Full disclosure implies no leverage effect because returns are always associated with news arrival; news is never inferred. As τ increases from its lower limit, less is inferred in the absence of news and residual uncertainty decreases less. 10 We analyze the leverage effect as a function of private information in a regression model. The dependent variables are the average firm-specific estimates of α 1 and θ over the 54 model parameterizations of equations 3.1 and 3.2. The sample includes all firms on CRSP, excluding
9
See, for example, Proposition 1 in Jung and Kwon (1988) and Corollary 2 in Verrecchia (1990). Disclosure models capture the concept of “private information” in different ways. Jung and Kwon (1988) operationalize the concept of less private information as a lower probability that the manager receives a private signal about the value of the firm at the interim reporting date. Verrecchia (1990) operationalizes the concept of less private information as greater precision of prior beliefs about the unconditional mean of firm value. 10 It is straightforward to demonstrate this result in the context of Jung and Kwon (1988) for well-behaved distributions of firm-value outcomes such as the uniform.
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firms in the financial services industry, with monthly data to estimate the EGARCH model. We separately regress the αˆ 1 s and θˆ s on a proxy for private information and a control for firm size. Our proxy for the extent to which a firm has private information is its return synchronicity with firms within its industry. We define industries at the 3-digit level, which provides a reasonable sample size and a reasonable level of homogeneity within each industry. The variable captures the extent to which information is likely not to be private, thus we refer to the variable as public information (PUBINFO). The computation of PUBINFO is analogous to that of a country- level measure of return synchronicity used by Li, Morck, Yang, and Yeung (2003). Define fIt as the average percentage of firms in the sample firm’s 3-digit industry that have monthly returns that move in the same direction:
f It ≡
max( n It > 0, n It < 0) n It > 0 + n It < 0
where n It is the number of firms in industry I during month t with non- zero returns. Firms with zero returns are excluded as they may be an indication of non-trading. PUBINFO is the average of the monthly percentages over all t periods for a given industry I. fIt is considered missing if the number of firms in the industry/month combination is less than five, and PUBINFO is considered missing if there are less than 20 monthly percentages for industry I. PUBINFO varies from 61.9% to 78.1%, with a mean of 67.7%. Given that a higher level of PUBINFO indicates greater return synchronicity and lower private information, we predict a negative association between PUBINFO and θˆ , which represents a stronger leverage effect for firms in industries characterized by less private information. The regression of the leverage effect parameters on PUBINFO includes firm size. We measure firm size (SIZE) as the log market value of the firm at December 31, 2002. Market
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value is the sum of the market value of common equity (COMPUSTAT data item 61 times item 14), plus the book value of long-term debt (items 51 plus 45). The average log market value of the sample firms is $5.07 million (4,802 firms) with a standard deviation of 2.17. We winsorize SIZE at the 1st and 99th percentile. 11 Firm size is a potentially important explanatory variable for two reasons, which predict opposite relations. Thus, the expected association between size and the leverage effect is ambiguous. The relation will be negative if firm size is associated with the likelihood that an announcement is anticipated. A key feature of models that generate a threshold disclosure strategy is that the market anticipates the possibility of an announcement. If the announcement is more likely to be anticipated, then negative returns are more likely an indication of an inference of bad news. Empirical evidence indicates that the degree to which investors update the unconditional expectation of firm value based on “no news” is a function of whether a news announcement was anticipated (Lev and Penman, 1990; Bagnoli, Kross, and Watts, 2002). Firm size will capture the extent to which news is anticipated if it is correlated with the richness of the firm’s information environment (e.g., Atiase, 1985; Freeman, 1987; Lang and Lundholm, 1993; Botosan, 1997). The relation between firm size and the leverage effect will be positive, however, if firm size is associated with litigation risk, which inclines larger firms to disclose less strategically. It is an empirical question which of these forces dominates. Table II, Panel A, reports the coefficient estimates and associated t-statistics from the regressions that measure the relation between αˆ 1 (and ?θˆ ) and PUBINFO and SIZE. There is a marginally significant positive association between the first arch term ( αˆ 1 ) and our proxy for 11
The winsorization does not affect the results. We also eliminate firms for which the average firm size is in the 1st or 99th percentile to assess the impact of extreme observations. The results are unchanged. Finally, we use three alternative specifications for SIZE: the log of average total assets at December 31, 2002, and the average firm market value and average assets over the 1992-2002 period. The results are similar.
18
non-private information (coefficient estimate of 0.3215, p-value = 0.12). This result indicates that investors infer more about firms in an industry in which there is less private information, either good or bad. There is a negative association between firm size and αˆ 1 . On average, the increase in return volatility following a return shock of either sign is less positive for larger firms. A smaller reaction in the arch term for large firms is consistent with the notion that returns of either sign are more likely to represent an inference of news, which is consistent with large firms having a richer information environment on average.
[Insert Table II here.]
There is a negative and significant association between the leverage effect ( θˆ ) and nonprivate information (coefficient estimate of -1.5263, p-value = 0.09). The results are consistent with the predicted stronger leverage effect (more negative θˆ s) for firms about which there is more public (less private) information. The relation between firm size and θˆ is also negative. 12 Thus, the difference between conditional return volatility reactions to positive and negative return shocks is greater for larger firms. The stronger leverage effect for large firms is consistent with the notion that investors anticipate announcements for larger firms with richer information environments and thus are more likely to infer bad news in the event of non-disclosure. A second model specification includes nine interaction terms equal to the product of PUBINFO and indicator variables (SIZE_n) that equal one if the firm’s size is in the nth decile of all sample firms and equal zero otherwise. Table II, Panel B, reports the results. The positive relation between PUBINFO and the first arch term ( αˆ 1 ) is significant only for firms in the three 12
The relation between size and the leverage effect for our sample is opposite the univariate results in Cheung and Ng (1992), who show a positive correlation between firm size and θˆ for a sample of 251 of the largest firms on
19
smallest deciles, as measured by the significance of the sum of the coefficient estimate on PUBINFO and the interaction variable. The sum is not significantly different from zero for firms in the top seven deciles. The negative relation between PUBINFO and θˆ is significant only for firms in the highest three deciles of firms. This combination of results suggests that, for small firms, the PUBINFO proxy explains more of the cross-sectional variation in the overall information environment of firms in an industry than in the likelihood that the firms are strategic disclosers. For small firms, it is more likely that return shocks of either sign represent inferred information rather than news arrival. For large firms, however, the public information proxy explains cross-sectional variation in strategic disclosure that can explain the leverage effect. Figure 1 shows the coefficient estimates on PUBINFO and the associated t-statistics from 54 OLS regressions of firm-specific θˆ s (one from each model parameterization) on an intercept, PUBINFO, and SIZE. The models are labeled “kpqc” where k equals the number of return lags, p and q equal the number of lags of the conditional variance and squared residual, and c equals one if the model includes an ARCH- in- mean term and zero otherwise. The models are in ascending order on the horizontal axis based on return lags, p lags, and q lags. Of the 54 estimates, 44 (81.5%) have the predicted negative relation between θˆ and PUBINFO; seven of the 44 are significant (p-value < 10%). None of the positively signed estimates are significant. The average of the 54 coefficient estimates is -0.80 with a standard deviation of 1.15.
4.1.2 The impact of systematic risk
CRSP with non-missing data from 1962-1989. Our results appear to reflect the greater cross-sectional variation in firm size of our sample.
20
As discussed in Section 3.1, the model estimates the leverage effect in the total return of the individual stock, which includes its market-wide and idiosyncratic components. In this specification, estimates of leverage effects associated with idiosyncratic shocks will appear amplified if idiosyncratic shocks also increase the firm’s conditional covariance with the market (Bekaert and Wu, 2000; Braun, Nelson, and Sunier, 1995). 13 Recognition of this issue leads to two additional analyses, both of which involve consideration of a firm’s systematic risk. Thus, before describing the analyses, we first describe our firm- specific measures of systematic risk. We estimate systematic risk for each sample firm using monthly returns data in a single factor market model over the period January 1988 through December 2002. We compute systematic risk relative to the CRSP equal-weighted index ( βˆ ew ) and the value-weighted index ( βˆ vw ). Systematic risk shows little univariate correlation with αˆ 1 or θˆ . βˆ ew is positively and significantly correlated with the arch term (8.6%), but not significantly correlated with θˆ . βˆ vw is not significantly correlated with either measure. The first analysis includes systematic risk as a control variable in the four models in Table II. The classification of individual stocks as strategic disclosers based on PUBINFO, which is constructed at the 3-digit SIC level, is deliberately broad. It reduces noise inherent in measuring the strategic reporting behavior of individual firms over extended time periods. The broad classification, however, introduces the potential for omitted variables that are correlated with the partitioning variable (PUBINFO) to explain the results. The results in Bekaert and Wu and Braun et al. suggest that systematic risk is a potential omitted variable because PUBINFO
13
Braun, Nelson, and Sunier (1995) develop a bivariate EGARCH model of returns that allows for leverage effects. Bekaert and Wu (2000) also model returns and conditional volatility in a way that allows for leverage effects, but with the specific purpose of distinguishing two competing hypotheses for the observed phenomenon: leverage and volatility feedback. Both models assume information arrival is exogenous, and both separately consider the effects of market-wide news and firm-level news.
21
could be correlated with the degree to which the market component of returns, rather than the idiosyncratic component, drives total returns. Consistent with this possibility, PUBINFO is negative ly correlated with firm-specific return variation (RETVAR). 14 Univariate analys is does not indicate an economically significant correlation between systematic risk and the partitioning variable, PUBINFO. Both βˆ ew and βˆ vw are negatively correlated with PUBINFO, but the correlations are low (-14.0% and -8.3%, respectively). βˆ ew and βˆ vw are negatively (-22.1%) and positively (6.9%) correlated with SIZE, respectively. Spearman correlations generally exhibit similar trends. There is enough controversy, however, to merit further investigation.
[Insert Table III here.]
Panel A of Table III presents results of the analysis when βˆ vw is included in the regression models. The upshot is that conditional betas do not explain the results from Panel A of Table II. The market beta is not associated with the arch term ( αˆ 1 ) or the leverage effect ( θˆ ). Including βˆ vw (or βˆ ew ) in the model does not change the magnitude of the other coefficient estimates or their significance. Including systematic risk as a control variable in the models that include the size interaction terms (in Panel B of Table II) also does not affect the magnitude or significance of the coefficient estimates on PUBINFO and SIZE (results untabulated). The second analysis examines cross-sectional patterns in the leverage effect as a function of systematic risk. Bekaert and Wu (2000) and Braun et al. (1995) both predict that leverage
14
RETVAR is the residual sum of squares from a market-model regression of monthly returns regressed on a market index. The correlations between PUBINFO and the mean and median industry values of RETVAR are negative 31.3% and 26.7%, respectively, both significant at less than the 1% level.
22
effects in individual stocks will be stronger for firms with high systematic risk. Although their models assume that idiosyncratic shocks are exogenous, not strategic, this prediction holds as long as idiosyncratic shocks increase conditional covariances with the market. 15 Given that the nature of the news about which firms are strategic is likely to be idiosyncratic, support for this prediction is further evidence that supports (or at least is not in conflict with) a strategic disclosure explanation for the leverage effect. Table III Panel B presents results of the analysis. We rank the firms on the basis of beta and create nine interaction terms equal to the product of PUBINFO and indicator variables (BETA_n) that equal one if the firm’s βˆ vw is in the nth decile of all sample firms and equal zero otherwise. The results from the expanded model are consistent with the prediction of a stronger relation between PUBINFO and the leverage effect in the high-beta portfolios. The coefficient on PUBINFO is almost monotonically decreasing (as predicted) across the beta portfolios. It becomes significant only in the fifth beta portfolio. Although the trend of a more negative coefficient continues across beta portfolios nine and ten, the sum loses statistical significance (pvalue = 0.15 for both estimates) due to high standard errors.
4.2 Litigation risk 4.2.1 Hypotheses and analysis The second hypothesis is that the magnitude of the leverage effect is lower for firms that ex ante are exposed to greater shareho lder litigation risk. Disclosure-related regulations in Section 10b of the 1934 Securities Exchange Act have an asymmetric impact on good news and bad news disclosure incentives. It is unlawful for firms to make untrue statements, which 15
We recognize that this is a partial equilibrium analysis. Their model does not contemplate whether strategic
23
decreases incentives to disclose favorable news before it is realized. It also is unlawful to omit reporting material information, which increases incentives to disclose bad news. In the extreme, litigation risk could reverse a firm’s optimal disclosure strategy such tha t it withholds news above a threshold τ (good news) and discloses news below τ (bad news). Hence, litigation risk increases the expected cost of strategic disclosure, and we assume that it therefore decreases the probability that strategic disclosure characterizes the disclosures, on average, of high-risk firms. Empirical evidence on the implications of shareholder litigation risk for firms’ disclosure strategies is mixed. Firms preannounce earnings to avoid large negative earnings surprises (Skinner, 1994) presumably to reduce expected litigation costs (Soffer, Thiagarajan, and Walther, 2000; Kasznik and Lev, 1995). Skinner (1997) finds greater voluntary disclosure in quarters that result in shareholder suits, which he conjectures is driven by pre-emptive disclosures of bad news. Firms subject to shareholder suits, however, are not more likely to have omitted material negative information or to have reported optimistic information (Francis, Philbrick, and Schipper, 1994). A comprehensive review of securities class action suits indicates that the vast majority of securities litigation is disclosure-related, and the majority of the disclosure-related cases are for making misleading statements rather than for failing to make statements (Bajaj, Mazumdar, and Sarin, 2000). The power of our tests is reduced if litigation risk does not create incentives for the disclosure of bad news and for the withholding of good news, as assumed. We analyze the impact of litigation risk on the leverage effect in a regression model. We measure ex ante exposure to litigation risk following Francis et al. (1994). Firms are considered
disclosure would be optimal if such covariance effects are taken into account.
24
high-risk if they operate in the biotechnology, computing, electronics, and retailing industries. 16 These industries have a high incidence of securities litigation during the period 1988-1992. We regress the average firm-specific estimates of α 1 and θ over the 54 model parameterizations on an indicator variable equal to one for firms in high-risk industries (HIRISK) and SIZE. We estimate a second specification of the regression that includes an interaction term between the continuous measure of firm size (SIZE) and the high-risk indicator variable.
[Insert Table IV here.]
Table IV Panel A shows no association between exposure to shareholder litigation risk and conditional volatility reactions to return shocks of either sign ( αˆ 1 s). The coefficient estimate on the HIRISK indicator variable is insignificant in both model specifications. Litigation risk, however, has a positive relation with the leverage effect ( θˆ ), as predicted. The positive coefficient estimate on HIRISK indicates that the leverage effect is weaker (i.e., less negative) for firms in high- risk industries. This result is consistent with our prediction that firms in these industries are less likely to strategically disclose given the higher expected costs of doing so, and thus their returns series are less likely to exhibit the leverage effect. As in Table II, the results indicate a strong negative relation between firm size and both
αˆ 1 (Panel A) and θˆ (Panel B). The interaction terms between SIZE and the high-risk indicator, however, do not explain either variable. Thus, strategic disclosure incentives associated with litigation risk firm are sufficient to explain cross-sectional variation in the parameter estimates. SIZE, which could proxy for the richness of the firms information environment and mitigate the relation, or which could proxy for litigation risk and attenuate the rela tion, does not further 16
Results based on the Kasznik and Lev (1995) definition of high-risk industries, which includes high-tech firms
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explain the results. Low-risk firms are more strategic regardless of firm size. The resulting information flow is rationally interpreted by markets and generates a stronger leverage effect. Figure 2 shows the coefficient estimates on HIRISK for 54 OLS regressions of firmspecific θˆ s (one from each model parameterization) on an intercept, HIRISK, and SIZE. Of the 54 estimates, 48 have the predicted positive sign; 25 of these (52%) are significant (p- value < 10%). None of the negatively signed estimates are significant. The average value of the 54 coefficient estimates is 0.0678 with a standard deviation of 0.0814.
4.2.2 The impact of systematic risk As in the previous section, we consider whether correlation between systematic risk and the partitioning variable – securities litigation risk – explains the results. Univariate analysis (untabulated) indicates that both βˆ ew and βˆ vw are positively correlated with the HIRISK indicator variable (33.8% and 30.5%, respectively). Spearman correlations are similar. The results are robust to controlling for correlation between HIRISK and systematic risk. The first two columns of Table V show that including βˆ ew or βˆ vw in the basic model from Table IV has little impact on the magnitudes of the reported coefficient estimates for the variables in the model. The results for the model that includes an interaction term between SIZE and HIRISK (from Panel B of Table IV) also results in economically and statistically similar coefficient estimates when βˆ vw is included as a regressor (results untabulated).
[Insert Table V here.]
and excludes retailing, are similar.
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The last two columns of Table V provide evidence about whether the stronger leverage effects associated with low shareholder litigation risk are stronger for high-beta firms. The models estimate the main effects of HIRISK, βˆ vw , and an interaction term on αˆ 1 and θˆ . In the model of θˆ , the sum of the main effect and the interaction term is significantly greater than zero; the stronger leverage effect for low-risk firms increases with beta. This result is consistent with the models of Bekaert and Wu (2000) and Braun et al. (1995) which predict that leverage effects in individual stocks will be stronger for firms with high systematic risk.
5. Patterns in the leverage effect for market-wide stock return indices We test for two predictable patterns in the leverage effect in market-wide stock indices as a function of variation in strategic disclosure probability. Section 5.1 investigates if the leverage effect increased after the Private Securities Litigation Reform Act of 1995. Section 5.2 investigates if the leverage effect in Canadian stocks is stronger than in U.S. stocks. Equations 3.1 and 3.2 model total returns, whereas strategic disclosure models are typically couched in terms of firms exercising discretion over firm-specific information. If firmspecific information is diversifiable in portfolios of firms, then strategic disclosure would not predict a leverage effect in market-wide indices. Recent work demonstrates, however, that firmspecific information is not diversifiable in the covariance of returns, and thus not diversifiable in general (Lambert, et al., 2006). 17 Thus, a strategic disclosure explanation for the leverage effect at the firm level should extend naturally to a market-wide index. This having been said, strategic disclosure is mute on why the leverage effect is amplified in a market-wide index versus individual stocks. As Bekaert and Wu (2000) and Braun et al.
17
See specifically Proposition 2 of Lambert, et al., 2006.
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(1995) demonstrate, amplification can occur when the covariance of returns has a specific structure. Thus, a test of the validity of strategic disclosure as an explanation of the amplification of the leverage effect in a market-wide index is a joint test of strategic disclosure and the covariance of returns having a specific structure along the lines discussed by Bekaert and Wu (2000) and Braun et al. (1995). Hence, a salient aspect of our analysis is whether differences in regimes – before and after the Private Securities Litigation Reform Act or between the U.S. and Canada – are correlated wit h differences in the covariance of returns. We attempt to create matched regimes that mitigate the potential for confounding effects of differences in the covariance of returns to limit interpretation of the results. Differences in the covariance of returns, however, remain an alternative explanation.
5.1 Private Securities Litigation Reform Act of 1995 We predict that the leverage effect is stronger after the Private Securities Litigation Reform Act of 1995 (the Act). 18 The Act lowered expected litigation costs associated with both disclosing good news and withholding bad news. The Act provides safe- harbor provisions for good news disclosures (i.e., forward-looking statements). The Act also includes a variety of provisions that were intended to decrease “nuisance” securities class action suits. Whether the Act increased strategic behavior, however, is an empirical question. Two sets of facts help provide an ex post assessment of the likelihood that strategic disclosure increased after the Act. First, a comparison of disclosure practices before and after the Act provides direct, but not overwhelming, evidence that strategic disclosure increased (Johnson, Kasznik, and Nelson, 2001). The incidence of “good news” long- horizon forecasts
28
increased after the Act for a sample of high technology firms, while bad news forecasts did not increase. But, firms also provided more frequent short- horizon forecasts of both good and bad news. And, earlier studies had suggested that firms were hesitant even after the Act to make forward-looking statements (SEC, 1997). Second, comparisons of disclosure-related litigation before and after the Act suggests that the expected cost of strategic disclosure declined, which provides indirect evidence that firms would increase strategic disclosure. Cases containing accounting and insider trading allegations, which studies define as “meritorious,” increased while cases that allege false forward- looking statements, which studies define as “frivolous,” decreased (Grundfest and Perino, 1997; Johnson, Nelson, and Pritchard, 2002). Conditional on surviving a motion to dismiss, however, the average settlement is higher in the post-Act period (Johnson et al., 2002) and has been increasing (Simmons and Ryan, 2003). Bajaj, Mazumdar, and Sarin, (2000) show that the higher post-Act settlement amounts, on average, reflect the relative increase in more costly cases related to improper accounting practice and revenue recognition and the relative decrease in less costly disclosure-related cases. Under the maintained assumption that strategic disclosure increased after the Act, we predict that the leverage effect will be stronger in the post-Act period. We estimate equations 3.1 and 3.2 for market-wide return indices separately over the pre-Act and post-Act periods using the CRSP equal- weighted index (including distributions) less the one month risk- free rate. The Act was introduced into Congress on January 4, 1995 and became law on December 22, 1995 when Congress overrode President Clinton’s veto. Thus, the pre-Act period is through December 1994 and the post-Act period begins January 1996 (see Johnson, Kasznik, and Nelson, 2001).
18
See Johnson, Kasznik and Nelson (2001) for a thorough discussion of the provisions of the Act.
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[Insert Table VI here.]
Table VI compares the leverage effect in the pre- and post-Act periods. Panel A reports that the median (average) estimate of θ is 0.1148 (1.2289) in the pre-Act period and -0.5648 (0.6290) in the post-Act period. Forty percent of the θˆ s are negative in the pre-Act period; all are negative in the post-Act period. Pane l B reports that the estimates of θ from the best models are lower in the post-Act period (-0.7794 and -1.1851) than in the pre-Act period (0.9100 and 0.1287) for the corresponding model parameterization. The difference in the estimates based on the best pre-Act model is significant. 19 Figure 3 shows that the θˆ s in the post-Act period are less than the θˆ s in the pre-Act period for the corresponding model parameterization (i.e., the difference is negative) for approximately 90% of the parameterizations that converge in both periods. Of the negative differences, however, only 17% are significantly less than zero based on a χ 2 test, one-sided significance level of 10%. A comparison of the first arch terms ( αˆ 1 s) across periods suggests that conditional return volatility has a stronger reaction to return shocks of either sign after the Act. The average estimate reported in Panel A is higher in the post-Act period (0.3049) than in the pre-Act period (0.1530). Over two-thirds of the post-Act estimates are greater than the pre-Act estimates, and 38.5% of the positive differences are significant at the 10% level. The post-Act αˆ 1 is significantly greater than the pre-Act estimate in best pre-Act model.
5.2 U.S. versus Canada
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We predict that the leverage effect is greater for Canadian stocks than for U.S. stocks because Canadian firms are more likely to engage in strategic reporting behavior than U.S. firms. The expected costs associated with the strategic disclosure of good news are lower in Canada because of greater statutory safe harbor protection. 20 The expected costs associated with strategic withholding of bad news are also lower in Canada because of differences between the U.S. and Canadian legal environments. In Canada, but not the U.S.: 1) unsuccessful plaintiffs pay court costs of successful defendants; 2) “unemotional” judges (instead of juries) hear many technical cases; 3) discovery rules are more limited; 4) contingent fees are generally not allowed and when allowed, not used frequently; 5) it is more difficult to bring class action suits and they remain rare; and 6) the “fraud on the market theory” is not allowed as a substitute for showing that the plaintiff relied on a misrepresentation. 21 Consistent with the assertion that the expected costs of strategic disclosure are lower in Canada than the U.S., Canadian firms are more likely to issue management forecasts when earnings are increasing, while U.S. firms have a tendency to issue forecasts in periods of declining earnings (Baginski, Hassell, and Kimbrough, 2002). Several other empirical studies indicate that Canadian firms strategically disclose favorable news and withhold unfavorable news (e.g., Clarkson, Kao and Richardson, 1994; Scott, 1994; Boone, Luther and Raman, 1998). We analyze leverage effects in various return series for U.S. and Canadian firms. We first estimate equations 3.1 and 3.2 for five established market indices, two Canadian and three U.S. The Canadian indices are the S&P/TSX Composite and the TSE 100. The U.S. indices are 19
The best post-Act model has the second highest SBC. The best model for the post-Act period did not converge in the pre-Act period. 20 The major U.S. and Canadian exchanges have similar rules about disclosure of material information. In short, the exchanges require timely dissemination of materia l information. Both the NYSE and the TSE may require firms to release a statement if unusual trading activity indicates that some investors have gained access to confidential information or are trading on speculation.
31
the S&P 500, which is value-weighted, and the CRSP equal and value-weighted indices including all distributions. Canadian returns are converted to U.S. dollar equivalents. The onemonth interest rate is subtracted from the Canadian and U.S. indices. Table VII reports descriptive statistics for the parameter estimates for the five indices across the 54 model parameterizations. 22 The arch terms ( αˆ 1 s) for the Canadian indices are lower than for the U.S. indices. Thus, conditional return volatility has a weaker reaction to return shocks of either sign in Canada. The most comparable U.S. index arch terms are for the S&P 500 index. This result is consistent with the negative correlation between SIZE and the first arch term documented in the previous analyses. In addition, the median (average) estimates of θ for the Canadian indices are -0.9889 and -0.8489 (-2.0627 and -9.2521), which are stronger than the median (average ) estimates for the U.S. indices, which range from 0.1705 to -0.6823. These results are consistent with the prediction that the leverage effect is stronger in Canada, but the y should be viewed with caution. The Canadian θ estimates have high standard deviations (2.9446 and 21.7138), and are infrequently significant. The U.S. estimates for the CRSP indices, by comparison, have lower coefficients of variation (mean relative to standard deviation) and are significant in 51% to 71% of the models.
[Insert Table VII here.]
We also create our own index of Canadian firms and an index for a matched sample of U.S. firms. This matched pair of indices resolves two issues with the established indices, which
21
This list is from Baginski, Hassell, and Kimbrough (2002), which provides an excellent description of the differences in the legal environments between Canada and the U.S., and from Clarkson and Simunic (1994). 22 The reported results for the equal-weighted index differ from those presented in Table 1 because the samples used in the regression analysis are truncated as described in the text.
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are convenient to use but not tailored to testing our hypotheses. First, we can limit the firms in the index to only liquid stocks. A significant criticism of the TSE 100 was that it contained illiquid stocks. It was eventually replaced by the TSE 60. The TSE 35 was introduced subsequent to the TSE 60, again to improve liquidity. It was criticized because it had significant industry concentration in seven stocks (financial services). Dow Jones marketed an index of 40 Canadian stocks as a competitor to the TSE 60 with improved liquidity in mind. Our concern about differences in liquidity is supported by the unreasonable estimates for certain parameterizations in the established Canadian indices reported above. Return series for established, but more liquid Canadian indices, howeve r, are not available over a sufficient time period to estimate the model, thus we create our own. Second, we can match the firms in the more liquid Canadian index to U.S. firms on the basis of firm size and industry. Industry composition and firm size are significantly different in the broad established indices discussed previously. Clearly, there are additional differences between the U.S. and Canadian equity markets, but these two are important because both can affect information flow, and in particular, the extent to which idiosyncratic and market news affects returns. The Canadian index is constructed to include the thirty largest stocks (based on December market value of equity) traded on the Toronto Stock Exchange that have suitable U.S. matches in CRSP. 23 We require the matched firms to share the same 4-digit Global Industry Classification Standard (GICS) code and also require the market value of equity for the matched U.S. firms to be within 25% of the FX-adjusted market value of equity for the Canadian firms. The Canadian returns are converted to U.S. dollar terms prior to calculating the equal-weighted
23
The choice to include 30 firms in the index was guided by the competition across index sponsors described previously that has resulted in indices of 35 and 40 stocks. We also created Canadian indices with 50 and 60 stocks.
33
returns for each index. Individual securities are held for one calendar year; therefore, the specific firms in each index are allowed to vary from year to year. Table VII reports descriptive statistics of estimates for the matched sample indices. Restricting the firms in the Canadian index to more liquid stocks produces minor changes in the Canadian index estimates relative to those for the established indices. Estimates for the U.S. matched index, however, are considerably different from those for the established U.S. indices, reflecting the smaller number of firms, greater industry concentration and lower variation in firm size within the portfolio. The tenor of the results, however, is the same. The median (average)
θˆ for the Canadian index is -5.21 (-8.49) compared to -1.78 (-2.18) for the U.S. index. As with the established indices, while these patterns are consistent with the predictions, there are large standard errors on the estimates for both indices. If we restrict the analysis to the estimates from models that converge in both countries (18 models), all of the θˆ s are more negative in Canada (results not presented). The best model for the Canadian index and for the matched U.S. index is the same: No lagged returns and no ARCH- in-mean term in the returns equation (3.1) and one lagged variance term (p = 1) and one arch term (q = 1) in the cond itional variance equation (3.2). The θˆ from the best model for the Canadian index is -6.89 compared to an estimate of -1.73 for the U.S. index (results not tabulated). Finally, we estimate the leverage effects at the individual stock level for 31 individual stocks that are in the Canadian index and 28 individual stocks that are in the matched sample of U.S. firms. 24 A limitation of the analysis done at the index level is that differences in the impact
24
The 31 Canadian firms and 28 U.S. firms were chosen based on natural breakpoints in the data. There are (90) 144 individual stocks that appear in the (Canadian) U.S. index in at least one year. Of the Canadian firms, 31 appear in five or more years, eight appear in four years, and 51 appear in three or fewer years. We included individual
34
of idiosyncratic news on conditio nal covariances across the countries will confound the analysis. The ana lysis of the individual stocks mitigates this limitation. The results are mixed. The average estimate of the leverage effect across all models for the 31 Canadian firms is -0.6167, which is stronger than for the 28 individual U.S. stocks (-0.3772). The median observations, however, suggest a weaker leverage effect for the individual Canadian stocks.
6. Conclusions The idea that information flow is strategic and that strategic dis closure could affect the dynamics of equity returns is intuitive, and studies of the impact of information on returns have acknowledged this notion informally (e.g., Mitchell and Mulherin, 1994). The voluntary disclosure literature also has recognized the importance of strategic disclosure to equity market inferences. Empirical predictions of voluntary disclosure models, however, extend to instantaneous changes in prices or other equity-market dimensions (e.g., bid-ask spreads). Formal modeling of the implications of endogenously determined information flow for dynamic return patterns is fairly recent (e.g., Shin, 2003 and 2004). This study contributes empirical evidence about whether strategic disclosure represents a viable explanation for dynamic return patterns. We show that the leverage effect in individual stock returns is stronger when it is more likely that the firm strategically discloses good news and withholds bad news. We identify firms as likely strategic disclosers when there is more public information available about the firm and when the firm faces lower risk of securities litigation associated with a disclosure policy of reporting good news and withholding bad news. We also document that the leverage effect in market-wide indices is greater when strategic disclosure, on
Canadian stocks that appear in five or more years in the analysis. Of the U.S. firms, 28 appear in three or more years; 86 appear in one year and 30 appear in two years.
35
average, within the entire market is more likely to characterize disclosure behavior. The leverage effect is stronger after the Private Securities Litigation Reform Act of 1995, which lowered the expected costs of disclosure-related securities litigation and hence increased the likelihood that strategic disclosure characterized information arrival. The leverage effect also is stronger for indices of Canadian firms than for indices of U.S. firms. Canadian firms face lower expected litigation costs associated with strategic disclosure than U.S. firms. Our results represent one piece of evidence related to the larger questions of the extent to which information arrival is strategic, how and whether markets anticipate it, and the implications for return patterns in individual stocks and markets. Our broad analysis jointly tests of all of these questions. A small sample study that examines the leverage effect for individually identified firms that consistently follow a strategic disclosure strategy could provide important complementary evidence. It cannot, however, provide evidence about whether strategic disclosure is an economically important (and statistically detectable) explanation for information arrival and thus for dynamic return patterns that are observed in large cross-sections of firms. The broad results suggest that variation in the leverage effect for individual stocks are consistent with strategic revelation of idiosyncratic news, and can be aggregated and generalized to explain what is predominantly a market-wide phenomenon.
36
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40
Rogers, Jonathan, 2005, Disclosure quality and manage ment trading incentives, Ph.D. Dissertation, University of Pennsylvania. Scott, Thomas W., 1994, Incentives and disincentives for financial disclosure: Voluntary disclosure of defined benefit pension plan information by Canadian firms, The Accounting Review 69 (1): 26-43. Securities and Exchange Commission (SEC), 1997, Report to the President and the Congress on the first year of practice under the Private Securities Litigation Act of 1995. Shin, Hyun Song, 2003, Disclosures and asset returns, Econometrica 71 (1): 105-133. Shin, Hyun Song, 2004, Endogenous disclosures and the post-earnings announcement drift, Working paper, London School of Economics. Simmons, Laura E. and Ellen M. Ryan, 2003, Post-Reform Act securities lawsuits: Settlements reported through December 2002, Cornerstone Research. Skinner, Douglas, 1994, Why firms voluntarily disclose bad news, Journal of Accounting Research 32 (1): 38-60. Skinner, Douglas J., 1997, Earnings disclosures and stockholder lawsuits, Journal of Accounting and Economics 23 (3): 249-282. Soffer, Leonard C., S. Ramu Thiagarajan, and Beverly R. Walther, 2000, Earnings preannouncement strategies, Review of Accounting Studies 5 (1): 5-26. Verrecchia, Robert E., 1983, Discretionary disclosure, Journal of Accounting and Economics 5 (3): 179-194. Verrecchia, Robert E., 1990, Information quality and discretionary disclosure, Journal of Accounting and Economics 12 (4): 365-380.
41
Table I Summary of coefficient estimates of the EGARCH model Descriptive statistics for the coefficient estimates from the 44 model parameterizations of equations 3.1 and 3.2 that converge and from the best model identified by Schwarz’s Bayesian information Criterion (SBC). The return series is the monthly return on the CRSP equal-weighted index including all distributions less the onemonth risk-free interest rate. The best model for that return series has one lagged return (k) and no ARCH-in -mean term in the returns equation (3.1) and one lagged variance term (p) and one arch term (q) in the conditional variance equation (3.2). k
rt = a + ∑ bi rt− i + cht + ut
(3.1)
i =1
p
q
i =1
i =1
log( ht ) = ζ + ∑ δ i log(ht −i ) + ∑α i {[| vt −i | −E | vt −i |] + θ vt− i}
(3.2)
--------------------------------------Across 54 model parameterizations-------------------------------------Parameters: a b1 b2 c
n 44 26 11 21
Median -0.0345 -0.3349 0.0598 -2.5549
Mean -0.0329 -0.3415 0.0085 -2.4537
Std Dev 0.0102 0.0360 0.0851 4.6453
Minimum -0.0478 -0.4385 -0.1453 -11.3124
Maximum -0.0039 -0.2738 0.0776 4.1694
ζ δ1 δ2 δ3 α1 α2 α3 θ
44 44 26 10 44 29 15 44
-1.4514 0.2501 0.3984 0.6148 0.3764 0.2599 0.3916 -0.4681
-2.3995 0.4196 0.1520 0.3908 0.3792 0.1664 0.3186 -0.5101
2.4068 0.4995 0.7300 0.5887 0.1216 0.2426 0.2245 0.3957
-9.6254 -0.7221 -1.3743 -0.6679 0.1725 -0.2696 -0.2966 -1.2939
-0.0666 1.4650 0.9620 0.8971 0.8833 0.6010 0.5597 0.1273
SBC
44
-526.700
-527.459
7.593
-541.907
42
-513.966
Best model -0.0376 -0.3194
-0.2700 0.9538
0.1725
-0.7964 -541.907
Table II Private information and the return/return volatility relation Panel A reports coefficient estimates and t-values from OLS regressions of average firm-specific estimates of α1 and θ on a proxy for non-private information (PUBINFO) and firm size (SIZE). PUBINFO is the average of the max( n It > 0, n It < 0) monthly percentages of f It ≡ , where nIt is the number of firms in industry I during month t n It > 0 + n It < 0 with non-zero returns. SIZE is the log of firm market value at December 31, 2002. Panel B reports coefficient estimates from a model that includes interaction terms equal to the product of PUBINFO and indicator variables (SIZE_n) that equal one if the firm’s size is in the nth decile of all sample firms and equal zero otherwise. * (**) {***} indicates significance at the 10% (5%) {1%} level. † (†† ) {††† } indicates that the sum of the coefficient estimates on PUBINFO and the interaction term is significant at the 10% (5%) {1%} level. Dependent variable is the average firm-specific: arch term (α1 ) estimate theta (θ) estimate Panel A: Model includes SIZE Intercept
0.0892
0.67
0.8876
1.55
PUBINFO
0.3215
1.56
-1.5263
-1.72*
-0.0266
-11.36***
-0.0300
-2.99***
SIZE N Adjusted-R2
4,278 2.89%
4,459 0.27%
Panel B: Model includes SIZE interacted with PUBINFO Intercept -0.0812
-0.52
PUBINFO
0.5737
2.55***
SIZE
0.0039
0.29
PUBINFO * SIZE_2 SIZE_3 SIZE_4 SIZE_5 SIZE_6 SIZE_7 SIZE_8 SIZE_9 SIZE_10 N Adjusted-R2
-2.36** †† -3.40***† -3.70*** -3.47*** -3.09*** -3.15*** -3.01*** -2.83*** -2.06**
-0.0986 -0.1831 -0.2406 -0.2635 -0.2701 -0.3124 -0.3389 -0.3671 -0.3311 4,272 3.78%
0.4836
0.71
-1.2000
-1.22
0.0189
0.32
0.0561 0.0341 -0.0539 0.1657 0.0444 -0.0678 -0.3533 -0.3943 -0.6180
0.31 0.15 -0.19 0.50 0.12 -0.16 -0.72† -0.70† -0.88†
4,462 0.52%
43
Figure 1 Coefficient estimates on the non-private information proxy for the 54 model parameterizations Coefficient estimates on the proxy for non-private information (PUBINFO) from 54 separate OLS regressions (one for each model parameterization) of firmmax( n It > 0, n It < 0) specific ? estimates on an intercept, PUBINFO, and SIZE. PUBINFO is the average of the monthly percentages of f It ≡ , where nIt is the n It > 0 + n It < 0 number of firms in industry I during month t with non-zero returns. Estimate
t-value
2
1
0
-1
-2
-3
-4
-5
01 10 01 1 01 1 2 01 0 2 01 1 3 01 0 3 02 1 1 02 0 11 02 2 02 0 21 02 3 02 0 3 03 1 1 03 0 11 03 2 03 0 21 03 3 03 0 3 11 1 1 11 0 11 11 2 11 0 2 11 1 30 11 3 12 1 1 12 0 1 12 1 20 12 2 12 1 3 12 0 31 13 1 13 0 1 13 1 20 13 2 13 1 3 13 0 31 21 1 21 0 1 21 1 20 21 2 21 1 3 21 0 31 22 1 22 0 1 22 1 2 22 0 21 22 3 22 0 3 23 1 1 23 0 1 23 1 2 23 0 21 23 3 23 0 31
-6
Model
44
Table III Private information and the return/return volatility relation as a function of systematic risk Coefficient estimates and t-values from OLS regressions of average firm-specific estimates of α1 and θ on a proxy for non-private information (PUBINFO) and firm size (SIZE). PUBINFO is the average of the monthly percentages max( n It > 0, n It < 0) of f It ≡ , where nIt is the number of firms in industry I during month t with non-zero returns. n It > 0 + n It < 0 SIZE is the log of firm market value at December 31, 2002. The model in Panel A includes a continuous measure of systematic risk ( βˆ ), which is estimated using monthly returns data in a single-factor market model including the vw
CRSP value-weighted index over the period January 1988 through December 2002. Panel B includes the firm’s rank based on βˆ and interaction terms equal to the product of PUBINFO and indicator variables (BETA_n) that vw
equal one if the firm’s βˆ vw is in the nth decile of all sample firms and equal zero otherwise. * (**) {***} indicates significance at the 10% (5%) {1%} level. † (†† ) {††† } indicates that the sum of the coefficient estimates on PUBINFO and the interaction term is significant at the 10% (5%) {1%} level. Dependent variable is the average firm-specific: arch term (α1 ) estimate theta (θ) estimate Panel A: Model includes systematic risk Intercept
0.1067
0.79
0.8779
1.52
PUBINFO
0.3062
1.48
-1.5168
-1.70*
SIZE
-0.0264
-11.27***
-0.0300
-3.00***
βˆ vw
-0.0081
N Adjusted-R2
-1.20
4,278 2.89%
0.0034
0.12
4,459 0.25%
Panel B: Model includes βˆ vw interacted with PUBINFO Intercept
0.4421
PUBINFO
-0.1542
SIZE
-0.0250
Rank of βˆ vw
-0.0800
PUBINFO * BETA_2 BETA_3 BETA_4 BETA_5 BETA_6 BETA_7 BETA_8 BETA_9 BETA_10
0.0944 0.1326 0.2676 0.3987 0.5441 0.6216 0.7605 0.9298 1.0011
N Adjusted-R2
1.82* -0.42 -10.53*** -1.54
1.09 0.82 1.11 1.25 1.37† 1.30† 1.36† 1.46†† 1.39†
4,273 3.19%
0.2988
0.29
-0.5664
-0.36
-0.0266
-2.62***
0.1575
0.71
-0.2759 -0.6457 -0.9457 -1.1646 -1.1178 -1.5931 -1.8419 -1.8064 -2.2975
-0.74 -0.93 -0.92 -0.85† -0.66† -0.78† -0.77† -0.66 -0.75
4,458 0.33%
45
Table IV Shareholder litigation risk and the return/return volatility relation Coefficient estimates and t-values from OLS regressions of average firm-specific α1 estimates (Panel A) and θ estimates (Panel B) on an indicator variable (HIRISK) equal to one if the firm has a high risk of shareholder litigation and zero otherwise. High-risk firms are those that operate in the biotechnology, computing, electronics, and retailing industries, following Francis et al. (1994). The models include firm size (SIZE) and an interaction term between SIZE and HIRISK. SIZE is the log of firm market value at December 31, 2002. * (**) {***} indicates significance at the 10% (5% ) {1%} level. Panel A: Dependent variable is the average firm-specific arch term (α1 ) estimate Intercept
0.3050
HIRISK
-0.0101
SIZE
-0.0263
21.75***
0.2887
-0.28
0.0244
-11.15***
SIZE*HIRISK N Adjusted-R2
4,557 2.93%
18.51*** 0.95
-0.0236
-8.51***
-0.0064
-1.35
4,557 2.83%
Panel B: Dependent variable is the average firm-specific theta (θ) estimate Intercept
-0.1237
-2.23**
-0.1607
-2.43**
HIRISK
0.0733
1.69*
0.1747
1.62*
-0.0240
-2.04**
SIZE
-0.0312
-3.28***
SIZE*HIRISK N Adjusted-R2
-0.0205 4,750 0.26%
4,750 0.27%
46
1.03
Figure 2 Coefficient estimates on the litigation risk indicator variable for the 54 model parameterizations Coefficient estimates on the high-risk indicator variable (HIRISK) for 54 separate OLS regressions of firm-specific ? estimates on an intercept, HIRISK, and SIZE. HIRISK is an indicator variable equal to one if the firm is in an industry subject to high-litigation risk and equal to zero otherwise.
Estimate
t-value
5
4
3
2
1
0
-1
01 1 01 0 11 01 2 01 0 2 01 1 30 01 3 02 1 1 02 0 1 02 1 2 02 0 2 02 1 3 02 0 3 03 1 1 03 0 1 03 1 2 03 0 2 03 1 30 03 3 11 1 1 11 0 1 11 1 20 11 2 11 1 3 11 0 3 12 1 10 12 1 12 1 2 12 0 2 12 1 3 12 0 3 13 1 1 13 0 1 13 1 2 13 0 2 13 1 3 13 0 3 21 1 10 21 1 21 1 2 21 0 2 21 1 30 21 3 22 1 1 22 0 1 22 1 20 22 2 22 1 3 22 0 3 23 1 10 23 1 23 1 2 23 0 2 23 1 3 23 0 31
-2
Model
47
Table V Shareholder litigation risk and the return/return volatility relation as a function of systematic risk Coefficient estimates and t-values from OLS regressions of average firm-specific α1 estimates (Panel A) and θ estimates (Panel B) on an indicator variable (HIRISK) equal to one if the firm has a high risk of shareholder litigation and zero otherwise. High-risk firms are those that operate in the biotechnology, computing, electronics, and retailing industries, following Francis et al. (1994). The models include firm size (SIZE), systematic risk ( βˆ ), and an interaction term between βˆ and HIRISK. SIZE is the log of firm market value at December 31, vw
vw
2002. Systematic risk ( βˆ vw ) is estimated using monthly returns data in a single factor market model over the period January 1988 through December 2002. * (**) {***} indicates significance at the 10% (5%) {1%} level. ††† indicates that the sum of the coefficient estimates on HIRISK and the interaction term is significant at the 1% level. Panel A: Dependent variable is the average firm-specific arch term (α1 ) estimate Intercept
0.3115
HIRISK
-0.0061
SIZE
-0.0261
βˆ vw βˆ *HIRISK
-0.0093
21.86***
0.2959
-0.56
0.0285
-11.69*** -1.34
vw
N Adjusted-R2
4,555 2.93%
17.88*** 1.10
-0.0235
-8.52***
-0.0062
-1.33
-0.0091
-1.31
4,556 2.84%
Panel B: Dependent variable is the average firm-specific theta (θ) estimate Intercept
-0.1236
HIRISK
0.0733
-2.06** 1.60
-0.1605 0.1749
-2.30** 1.61
SIZE
-0.0312
-3.28***
-0.0241
-2.04**
βˆ vw βˆ *HIRISK
-0.0001
-0.00
-0.0205
-1.03
-0.0003
-0.01†
vw
N Adjusted-R2
4,750 0.24%
4,750 0.24%
48
Table VI The return/return volatility relation before and after the Private Securities Litigation Reform Act of 1995 Panel A presents descriptive statistics for αˆ 1 and θˆ across the multiple parameterizations of equations 3.1 and 3.2 estimated separately over the pre-Act period (January 1988 – December 1994) and the post-Act period (January 1996 – December 2002). The return series is the monthly return on the CRSP equal-weighted index including all distributions less the one-month risk-free interest rate. Panel B presents parameter estimates and standard errors (in parentheses) of αˆ 1 and θˆ from the best model specification based on the SBC criterion. The best model in the preAct period (January 1988 – December 1994) has one return lag (k=1) and no ARCH-in-mean term and one lag of the conditional variance (p=1) and two lags of the squared residual (q=2). The best model in the post-Act period (January 1996 – December 2002) has no lagged returns (k=0) and no ARCH-in-mean term, and one lag of the conditional variance (p=1) and the squared residual (q=1). The Wald statistic is distributed χ 2 (1). * (**) {***} indicates significance at the 10% (5%) {1%} level. Panel A: Average estimates across all models Pre-Act (n = 30) ˆ arch1 estimates ( α1 ) Median 0.1322 Mean 0.1530 Standard deviation 0.2673 Minimum -0.5288 Maximum 0.7926 % positive/{significant} 90.0%/{23.3%} theta estimates ( θˆ ) Median Mean Standard deviation Minimum Maximum % negative/{significant}
0.1148 1.2289 3.3600 -1.4847 11.7937 40.0%/{10.0%}
Panel B: Estimates from the best model based on the SBC Pre-Act From best pre-Act model: -0.2298*** arch1 ( αˆ 1 ) (0.0764) ˆ 0.9100*** theta ( θ ) (0.2740) From best post-Act model: 0.7926*** arch1 ( αˆ 1 ) (0.3009) 0.1287 theta ( θˆ ) (0.2363)
49
Post-Act (n = 32) 0.3380 0.3049 0.1243 0.1127 0.7162 100.0%/{18.8%}
-0.5648 -0.6290 0.2945 -1.1850 -0.0478 100%/{0%}
Post-Act
Wald Stat
0.2882 (0.2684) -0.7794 (0.8037)
3.4455*
0.3405 (0.2911) -1.1851 (1.0131)
1.1666
3.9581**
1.5948
Figure 3 Differences between pre-Act and post-Act θ estimates for 54 model parameterizations Differences between θˆ s for the post- and pre-Act periods and the associated Wald statistic to test the significance of the difference from zero. A negative amount indicates that the post-Act θˆ is lower than the pre-Act θˆ . The Wald statistics are signed to match the difference. Wald statistics and differences greater than |10| are winsorized to preserve perspective in the figure. The return series is the monthly return on the CRSP equal-weighted index including all distributions less the one-month risk-free interest rate. The model specifications are reported below the x-axis. A model with return lags (k = 1), conditional variance terms (p = 3), residual variance terms (q = 2), and no ARCH-in-mean term (c = 0) is labeled 1320 (kpqc). Difference
Wald Stat
2
0
-2
-4
-6
-8
-10
01 10 01 11 01 20 01 21 01 30 01 31 02 10 02 11 02 20 02 21 02 30 02 31 03 10 03 11 03 20 03 21 03 30 03 31 11 10 11 11 11 20 11 21 11 30 11 31 12 10 12 11 12 20 12 21 12 30 12 31 13 10 13 11 13 20 13 21 13 30 13 31 21 10 21 11 21 20 21 21 21 30 21 31 22 10 22 11 22 20 22 21 22 30 22 31 23 10 23 11 23 20 23 21 23 30 23 31
-12
Model
50
Table VII The return/return volatility relation in Canada and the U.S. Descriptive statistics for αˆ 1 and θˆ across the mult iple parameterizations of equations 3.1 and 3.2 estimated separately for various Canadian and U.S. return series. The Canadian indices are the S&P/TSX Composite index, the TSE 100, and our matched index of 30 firms . The U.S. indices are the S&P 500, the CRSP equal and value-weighted indices including all distributions, and our matched index of 30 firms . Descriptive statistics are also presented for portfolios of individual Canadian and U.S. stocks. The one-month interest rate is subtracted from each inde x return or individual stock return. arch1 estimates ( αˆ 1 )
N
Median
Indices
Composite TSE100 S&P500 EW VW
35 33 39 45 41
0.1149 0.1808 0.1066 0.3186 0.4440
0.1409 0.1981 0.1171 0.3125 0.4136
0.0837 0.1954 0.1131 0.1034 0.1002
Matched
Canada U.S.
21 39
0.0535 0.1825
0.0628 0.2152
Portfolios
Canada U.S.
956 939
0.3922 0.2389
0.3738 0.2550
theta estimates ( θˆ ) Indices Composite TSE100 S&P500 EW VW
Mean
Std Dev
Min
Max
% pos (sig)
0.0030 0.0009 -0.0689 0.1175 0.2466
0.2616 0.7100 0.4928 0.5069 0.6078
100% 100% 85% 100% 100%
0.0424 0.1073
0.0115 0.0146
0.1453 0.4127
100% (0%) 100% (23%)
0.3548 0.2342
-1.4922 -0.3337
1.4474 0.8899
89% (65%) 84% (56%)
(26%) (36%) (33%) (62%) (100%)
% neg (sig) 35 33 39 45 41
-0.9889 -0.8489 -0.0314 -0.4331 -0.6823
-2.0627 -9.2521 0.1705 -0.5410 -0.5967
2.9446 21.7138 1.0901 0.2368 0.2828
-14.5045 -106.7927 -0.7885 -1.1221 -0.9503
0.6667 -0.0179 3.7961 -0.2416 -0.1117
94% 100% 56% 100% 100%
100% (0%) 100% (3%)
Matched
Canada U.S.
21 39
-5.2054 -1.7840
-8.4937 -2.1787
8.5679 2.7449
-36.0863 -17.6973
-1.6914 -0.3605
Portfolios
Canada U.S.
956 939
-0.2037 -0.2865
-0.6167 -0.3772
3.0750 3.9894
-32.3218 -40.2876
40.5374 30.3238
51
(11%) (30%) (0%) (51%) (71%)
73% (20%) 70% (28%)
