News-specific price discovery in credit default swap markets.
Of key interest to the finance profession is understanding how new information is incorporated into securities prices. One approach is the study of price discovery across markets. If new information is simultaneously priced into different markets, this is evidence of informational efficiency. Evidence of one market pricing information faster than another suggests market inefficiencies. Studies on price discovery often find that one market leads in price discovery. * (1)
In this paper, we explore the idea that inefficiencies in price discovery may be news-specific as traders in one market may have an advantage with respect to one type of information and not all information equally. In this case, price discovery would not unconditionally favor one market over another, but would depend upon the type of innovation. It would also suggest a more nuanced view regarding the informational efficiency of markets in that it may only hold conditional on specific information.
We focus our analysis on price discovery in equity and credit default swap (CDS) markets. The evidence concerning whether equity returns lead CDS price changes is mixed. Longstaff, Mithal, and Neis (2005) suggest that both markets move simultaneously (but that both lead the corporate bond market), while Norden and Weber (2009) and Hilscher, Pollet, and Wilson (2012) find that equity returns lead CDS price changes much more frequently than the other way around. (2) Acharya and Johnson (2007) demonstrate that under certain market conditions (typically bad news about the credit quality of specific firms), changes in CDS prices lead equity returns, a phenomenon they ascribe to insider trading by banks with access to nonpublic information about their customers.
We first analyze unconditional price discovery. We use daily panel data on US firms, larger in both cross-section and time series dimensions than typically examined previously, to study the lead-lag relationships between equity returns and CDS price changes. We find that equity returns robustly lead CDS price changes. There is very little support for the thesis that CDS price changes lead equity returns. This is strong evidence in favor of an unconditional informational advantage of equity markets, particularly since we have constructed our sample to include only the most liquid CDS entities thus effectively biasing the sample against finding an equity lead.
The key focus of our paper is to investigate more precisely the nature of the information that is priced faster in equity rather than CDS markets. Do equity prices lead CDS prices for all types of information or only in response to some information? We first ask whether common and firm-specific information are priced at different speeds. The evidence, based on alternative factor decompositions, is clear. The CDS market is slow to price common information, while it prices firm-specific news at about the same speed as equity markets. The dominant component of systematic information in equity returns that is priced slowly by the CDS market is, rather surprisingly, the (equity) market factor. One might have expected the (single) market factor to be more efficiently priced than news specific to individual firms.
In addition, we examine whether the lead-lag depends upon whether there is positive or negative news in the equity market. We find that positive and negative equity market returns appear to be priced at different speeds by the CDS market. Most of the lagged response of CDS prices is driven by slow CDS price changes in response to positive equity market returns. Our findings are complementary to Acharya and Johnson (2007). Acharya and Johnson (2007) argue that CDS markets can lead equities when there is bad news about a specific company, while our results suggest that CDS markets lag equities in pricing good news about the general economy.
What can account for the news-specific nature of price discovery? We bring forward an explanation based on the importance of different investor groups in the two markets. While a wide range of investors with very diverse trading interests are active in equity markets, participation in the CDS market is much more limited. Kapadia and Pu (2012) note that the CDS market is actively traded by sophisticated arbitrageurs, but a key reason for the development of CDS markets is institutional investors' demand (predominantly by banks) for an instrument capable of hedging credit risks. The significant presence of hedgers in CDS markets (together with the presence of barriers to arbitrage) can explain both the aggregate-idiosyncratic news and positive-negative news asymmetries. As these investors are likely to be well informed about news specific to the firms in their portfolio, CDS markets respond efficiently to such news. However, hedgers of firm risks are likely to focus less on macro-news. In response to positive equity market news, dealers in the CDS market can keep prices high and exploit their informational advantage. This dampens price adjustments in the CDS market and causes an equity-lead specific to positive macro news. Conversely, in the event of bad equity market news, CDS prices rise immediately as rapid adjustment is in the interest of dealers. (3)
If this explanation is correct, we would expect the lead-lag and its asymmetries to depend upon proxies for the hedging demand for a firm's debt. We consider three proxies for hedging demand on the firm level: (1) the amount of outstanding debt, (2) default risk, and (3) the variability default risk. We find that these proxies for hedging demand are positively and significantly related to observed lead-lag asymmetries, supporting the idea that the lead-lag relationship is driven by the hedging focus of investors in the CDS market.
A second implication for our explanation is that in periods of high informational asymmetry, the CDS market's lag should be longer as dealers then have greater pricing power vis-a-vis uninformed investors. We capture variations in levels of information asymmetry through the behavior of equity market bid-ask spreads and by examining major macroeconomic news announcements. We find that when information asymmetry is high, identified by either larger than usual bid-ask spreads or in days immediately preceding major macroeconomic news announcements, CDS returns are particularly sensitive to lagged positive equity returns.
This paper contributes to our understanding of the informational efficiency of markets by demonstrating that leads and lags in price discovery can differ depending upon the type of news. For a sample of stocks where equity markets lead CDS markets, we find that this effect is only associated with positive news shocks. Evidence using proxies for hedging and speculative demands in CDS markets supports the idea that asymmetries are connected to investor clienteles with different information sets operating in both markets.
The remainder of the paper is organized as follows: Section I describes the data. Section II contains the empirical analysis, while Section 1 provides our conclusions.
I. Data Sources and Descriptive Statistics
The CDS data used in our analysis come from Markit Group, a leading industry provider of credit derivatives pricing. Markit collects CDS quotes from over 30 contributing market makers each day and applies a screening process to remove outliers, stale prices, and other inconsistent data. Markit then computes the mean quoted price from those contributions that pass their data quality tests and releases a price when it has two or more contributors. We use daily five-year maturity single-name CDS quotes on US reference entities with publicly traded equity prices from January 1, 2004 to October 14, 2008. Since trades in the CDS market are relatively infrequent for all but a handful of reference entities, the use of quotes rather than transaction prices is advantageous. However, there is the risk that the quotes are not updated by inattentive traders. Markit's procedures attempt to control for stale quotes, but this may be imperfect. We return to this issue below.
Each reference entity is matched to a traded equity identifier (Bloomberg ticker) that we then translate into a Center for Research in Security Prices (CRSP) identifier (permno). Matched daily closing equity mid-market prices are extracted from CRSP. We use daily returns, calculated as changes in the log of these CDS and equity prices, as the key variables in our analysis.
Many of the reference entities' in CDS are very illiquid. These are flagged as such in the database (this indicator refers to liquidity at the point in time when the database was created). To concentrate our analysis on the most liquid firms, we retain only those reference entities flagged as liquid in the database and with nonzero daily CDS returns for at least 90% of the sample period analyzed. We also only retain entities with CDS (and equity) prices available for the full sample period and we exclude companies with significant merger and acquisition activities. The final data set is comprised of 193 reference entities, each with 1,208 daily return observations for both equities and CDS. The firms retained are detailed in Appendix B.
Table I reports some basic descriptive statistics. Univariate statistics suggest equity and CDS daily returns are broadly comparable, although the standard deviation of CDS returns is higher. CDS prices, on average, increased in the sample and the distribution of returns is positively skewed. Equity prices fell, on average, and the distribution of equity returns is negatively skewed. More important patterns emerge from the correlation statistics. Equity returns exhibit very low autocorrelations, while those for the CDS market are much larger in magnitude, especially at the first lag. Cross-autocorrelations also differ markedly. Lagged CDS returns are only weakly (negatively) correlated with equity returns, but the first lag of equity returns is strongly negatively correlated with the CDS returns. The magnitude of this correlation is similar to the magnitude of the contemporaneous correlation. The magnitude of the correlation with the second lag of equity returns is markedly smaller. Together, the significantly positive autocorrelation and significantly negative correlation with lagged equity returns are indicative of inefficiencies in the CDS market.
A. Equity-CDS Lead-Lag Relationships
Several papers have noted that, in general, equity returns lead CDS returns. There are occasions when the reverse appears to be true, but these are not long lasting periods of time or are they necessarily common for all entities. The first goal of this paper is to establish the robustness of the unconditional lead-lag relationship between equities and CDS for our panel. We emphasize that our data selection procedure produces a sample of reference entities with the most liquid CDS markets. As such, any evidence of a lag in the price discovery process for these firms would be suggestive of even more pronounced lags for less liquid entities.
We model the returns of equities and CDS in a standard bivariate vector autoregression (VAR) system of lag order k:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1a)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1b)
where the dependent variables are the returns (r) on the equity (e) or CDS (c) of firm i at time t. Lag lengths are chosen according to the Akaike information criterion (but our results are not sensitive to changes in lag lengths). Not surprisingly, given the autocorrelation patterns described in Table I, in the vast majority of cases, the criterion selects just one lag. CDS returns would be deemed to lag equity returns for firm i if the [[beta].sub.1] coefficients are jointly nonzero and equities would lag CDSs if the [[alpha].sub.2] coefficients are jointly nonzero.
Panel A of Table 11 summarizes the results of estimating VARs for each reference entity individually and for all entities pooled together. The dominant finding is that lagged equity returns contain information for current CDS price changes, while the reverse is rarely the case. Specifically, we find that of the 193 reference entities studied, lagged equity returns are significant in explaining current CDS returns in 149 cases at the 5% level. Lagged CDS returns explain equity returns for only 12 entities. The results of estimating the pooled VAR are fully consistent. The results in Panel A are based on regressions at the firm level. In Panel B, we determine that the same findings hold when we analyze returns from equally weighted equity and CDS portfolios.
In sum, unconditionally, equity returns lead CDS price changes. These results are very robust to alternative specifications of Equation (1) and to splitting the data in various ways (details are provided in Appendix A).
B. Asymmetric Response to Common and Firm-Specific Information
In this subsection, we further explore the nature of the information that is being incorporated more quickly into equity prices than CDS prices. The consistency of the firm and portfolio level lead-lag results detailed in Section II.A suggest that it is not just idiosyncratic information that is priced slowly in CDS markets and that there appears to be a systematic component. Thus, we use several techniques to split equity and CDS returns into common factor and idiosyncratic components to determine the contribution of each to the delay in CDS pricing.
We begin with a statistical decomposition of returns based on principal components (PC) analysis. Using the full sample of data, we extract p principal components for equity returns and q components for CDS returns. We then regress equity returns on the p equity principal components and collect, for each entity, a fitted series and a residual series. We view the fitted series as capturing the systematic or common component of each firm's equity returns, while the residual series is assumed to capture the firm-specific component. We do the same for each firm's CDS returns using the q CDS principal components.
We then perform a VAR analysis using these decomposed returns (we also perform regressions using common and idiosyncratic components of the CDS returns as dependent variables for completeness):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2a)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2b)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2c)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2d)
Significant values for [[beta].sub.11] [[[beta].sub.12]) would suggest that the common (idiosyncratic) component of firm z's lagged equity returns is important in explaining the common component of z's CDS returns. Similarly, significant values for [[beta].sub.21] ([[beta].sub.22]) would imply that the common (idiosyncratic) component of lagged equity returns is important in explaining the firm-specific CDS return for the firm.
The choice of how many principal components to retain is rather arbitrary and we do not take a firm stand on the issue. If too few components are retained, then components of the returns that are actually common are incorrectly labeled as idiosyncratic. If we retain too many components and the idiosyncratic elements of returns are incorrectly thought to be common. Thankfully, the tenor of our results is not sensitive to the exact number of components retained as long as the number of common components is at least one for both equities and CDS returns.
We report the results based on three retained components for both equity and CDS returns in Panel A of Table III. The results are quite stark. For 173 of the 193 companies, the lagged common component of equity returns significantly predicts the current common component of CDS returns. In contrast, the lagged common CDS component is never significant in predicting the common equity component.
In addition, there is some relatively weak evidence that lagged idiosyncratic equity returns predict idiosyncratic CDS returns (significant at the 5% level for 28 companies or 14.5% of the sample). The CDS market leads in the pricing of idiosyncratic information for 11.4% of the sample (22 companies). Moreover, and as we would expect, there is little evidence that idiosyncratic equity returns predict common CDS returns or that common equity returns predict idiosyncratic CDS returns.
The lead-lag relations between equity and CDS returns seen in the literature and confirmed in Section II.A are almost entirely driven by the equity market's ability to incorporate common information faster than the CDS market. To a much lesser extent, the equity market also appears able to incorporate firm-specific information faster, although there are also cases where the CDS market leads in pricing idiosyncratic information. This final point probably reflects the insider trading issues raised in the conditional analysis of Acharya and Johnson (2007).
To confirm the results using equity factors motivated by the literature, rather than statistically derived principal components, we repeat the analysis using the three Fama-French factors. Since there is no recognized factor model for CDS returns, we revert to using total CDS returns in the regressions. The results are reported in Panel B of Table III. Lagged fitted equity returns based on the three Fama-French factors are significant for CDS returns for 178 companies (92% of the sample), while the lagged residual equity returns not explained by these factors are significant for 40 firms (21% of the sample). We find almost exactly the same results if we use three principal components instead of the Fama-French factors. Lagged fitted returns are significant for 179 firms and lagged residual returns are significant for 18 firms. Correlation analysis between the largest principal components for equity returns and the Fama-French factors suggests that the first principal component is a very close proxy for the market. However, none of the other principal components correlate strongly with the Fama-French factors.
The similarity of the lead-lag results from PC and Fama-French-based analyses, combined with the fact that these two approaches only appear to share one common factor, suggest that the equity market return is behind the majority of the results. We proxy the equity market return in three ways: (1) the first principal component, (2) the return on an equally weighted portfolio of the equities in our sample, and (3) the market return from the Fama-French database. Panel C of Table III reports the results using lagged fitted values and lagged residuals from all three measures to explain CDS returns (with lagged CDS returns also included in the regressions). The results are quite consistent. Lagged equity market returns significantly explain CDS returns for a very large proportion of firms. Lagged idiosyncratic equity returns are much less frequently significant. It appears that the lead-lag relationship between equities and CDS is primarily driven by a single common equity component, the market return.
C. Asymmetric Response to Positive and Negative News
Thus far, we have imposed symmetrical responses of CDS returns to positive and negative lagged equity returns. We now relax this constraint and allow positive lagged equity returns to bear a different coefficient to negative returns. We regress the common component of CDS returns for each firm on lags of itself, lagged positive equity market returns, and lagged negative equity market returns. Market returns are proxied by the return on an equally weighted portfolio of the equities in our sample, but our results are not sensitive to alternative measures. Specifically, we use the following specification:
[r.sup.ccom.sub.i,t] = [[beta].sub.0] + [[beta].sub.1][r.sup.ccom.sub.i,t-1] + [[beta].sub.2][r.sup.epos.sub.i,t-1] + [[beta].sub.3][r.sup.eneg.sub.i,t-1] + [[epsilon].sup.ccom.sub.i,t], (3)
The results are reported in Table IV. For all 193 firms, the coefficient of common CDS returns on lagged positive equity market returns is negative and significantly different from zero. The cross-sectional mean of the coefficient on lagged positive equity returns is--0.5. The coefficient on lagged negative equity returns is also generally negative, averaging -0.16, but is significant for just 106 firms (55% of the sample). The restriction that the coefficients on positive and negative equity returns are equal is rejected in 56 cases (29% of the sample) although, in every case, the coefficient on lagged positive equity returns is larger in absolute terms than the coefficient on negative returns. We obtain very similar results if we use total CDS returns as the dependent variable. Coefficient values barely change and while the coefficient on positive equity returns is statistically significant, that of negative equity market returns is not.
The p-values reported in the first row of Table IV are from a test that the average coefficient value is zero. This test assumes independence across firms, which is unlikely to be valid. As an alternative, we pool the data and run a single regression for the entire sample with standard errors clustered by time (double clustering by time and firm or including firm fixed effects leave the results essentially unchanged). We report these results in the second row. The coefficient on lagged positive equity returns is larger in magnitude than that on lagged negative equity returns. The test of coefficient equality is not significant, but we note that by pooling the data, we impose the same coefficients on all firms. As we expand upon this later, we find there is important coefficient heterogeneity in the cross section. Thus, the clustered standard errors are likely to be too large.
We also run a version of this equation using equally weighted portfolio returns. We regress portfolio CDS returns on a lagged dependent variable and a lagged positive and negative portfolio equity returns series:
[r.sup.c.sub.m,t] = [[beta].sub.0] + [[beta].sub.1] [r.sup.c.sub.m-t] + [[beta].sub.2] [r.sup.epos.sub.m,t-1] + [[beta].sub.3][r.sup.eneg.sub.m,t-1] + [[epsilon].sup.c.sub.m,t]. (4)
The coefficients on both positive and negative equity returns are significantly negative, though only marginally so in the case of negative returns (see the third row of Table IV). The absolute value of the coefficient is much larger for positive returns than negative returns (-0.49 compared with -0.17) and the equality of these coefficients is rejected. Partitioning lagged CDS returns into positive and negative components also has no effect on our results since they bear effectively the same coefficient.
In the following sections, we will put forward our hypothesis that the asymmetric lead-lag relationship we have documented is driven by dealers exploiting an informational advantage by deliberately not adjusting CDS prices sufficiently following positive equity market news. An alternative explanation might be that CDS dealers are inattentive following positive news, perhaps due to less trading demand from clients. Bad news, conversely, leads to raised activity levels in the default risk-oriented CDS market. As such, dealers tend to be attentive and adjust prices rapidly. We address this by first selecting observations where the Day t - 1 portfolio CDS return is in the upper or lower 25% tails of the distribution (effectively this means Day t - 1 CDS price change is greater than 0.006% in the absolute value). In doing so, we identify days when CDS prices have already changed by more than usual. These are likely to be days when dealers were paying attention. We then repeat Regression (4) reporting the results in the final row of Table IV. The results are essentially unchanged from those generated by the full sample. Even though lagged CDS price changes were large, today's CDS price change is still significantly predicted by lagged equity returns, and today's CDS price change is larger for positive equity market news than for negative equity market news. We obtain the same findings if we move further into the tails of the CDS price change distribution, or if we only use data when both the lagged equity and CDS price changes lie in the extreme tails of their respective distributions.
D. The Lead-Lag Relationship, Hedging Demand, and Informational Asymmetries
Thus far, we have established three robust sets of results: (1) the equity markets leads the CDS market in price discovery, but this lead is specific to (2) common news, and, (3) positive news.
The presence of lead-lag relationships across markets documented in Sections II.A-II.C is at odds with market efficiency. Moreover, the news-specific nature of the lead-lags demonstrated in Sections II.B-II.C rules out standard explanations, such as arbitrage risk or transaction costs, since these would be expected to apply regardless as to the type of news. Hilscher et al. (2012), for example, argue that the CDS lag reflects a separating equilibrium where informed traders only trade in equities due to high bid-ask spreads in the CDS markets. This explanation is not consistent with our findings that firm-specific and negative equity market news is priced approximately equally rapidly by both markets. (4)
While relatively unexplored in the finance literature, asymmetric adjustment of prices to changes in fundamentals is a frequent phenomenon in goods markets, termed "rockets and feathers" (Bacon, 1991). In a study of 242 goods markets, Peltzman (2000) finds that in two-thirds of the markets, the upward adjustment of prices in response to a positive (cost) shock is faster than the downward response of prices to a negative shock of similar magnitude. Prices rise like rockets, but fall like feathers. While smacking of collusive actions by intermediaries, such price setting behavior is consistent with the profit-maximizing behavior of imperfectly competitive intermediaries who face customers that are rational, but only partially informed (Tappata, 2009). In most goods markets, the intermediary buys in wholesale markets against well informed participants, but sells in retail markets to consumers that are less informed about the nature of costs in the market. Since search costs prevent consumers from locating the lowest available price for the good, intermediaries can set relatively high prices following cost reductions, exploiting their market power and extracting rent. Conversely, when costs rise, they immediately pass these increases on to consumers. As such, prices rise accordingly.
This behavior has also recently been documented in the finance literature. Green et al. (2010) find that there is an asymmetric response by US municipal bond yields to Treasury bond yield shocks. They determine that muni bond prices rise rapidly when Treasury bonds prices increase, yet they fall very slowly following a drop in T-bond prices. Green et al. (2010) argue that asymmetries in the clientele in muni bonds, with the buy side dominated by retail customers, while the sell side includes both retail and institutional sellers, are behind these results. They translate the search costs faced by retail consumers in goods markets into information asymmetries in asset markets such that the sell side is, on average, better informed than the buy side due to the presence of informed institutions in the former.
As we have demonstrated, the CDS market displays similar pricing behavior. In the remainder of the paper, we explore whether the rockets and feathers hypothesis can explain our results. The hypothesis relies on there being an asymmetry in the clientele faced by dealers on different sides of the market, with one side likely to be less informed than the dealer and the participants on the other side of the market. We argue that while the CDS market is dominated by informed institutional traders, there is a class of customers present predominantly on the protection buying side of the market, credit risk hedgers, who may be less focused on the consequences of some types of news.
Following this, we test two implications of the rockets and feathers hypothesis. First, the larger the market share of the relatively uninformed participants, the longer the CDS market lag as dealers can exploit their market power to a greater extent. Since we argue that the relatively uninformed are likely to be credit risk hedgers, we relate the magnitude of the CDS market's lag in the cross-section to several proxies for hedging demand. In addition, if information asymmetries are behind the lead-lag relationships, then longer CDS market lags should be observed when information asymmetries are high. To examine this prediction, we analyze the impact of variations in two types of information asymmetries across time on the lead-lag.
1. The Lead-Lag Relation, Limits to Arbitrage, and the Demand for Hedging Credit Risks
A key difference between equity and CDS markets arises from different motivations for trading in these markets and (ultimately related) the types of investors that are active in them. Equity markets are characterized by a wide group of investors including private investors and most types of institutional investors, and their motives for trading are diverse. Furthermore, investors are, on average, equally active on both the buy and sell side of the equity market. There is no pronounced asymmetry in clientele in equity markets.
Credit derivatives markets are much more limited in scope. Participants in this market are almost exclusively institutional investors, with banks forming the largest group. Sixty percent of CDS protection in 2006 (the mid-year in our sample) was purchased by banks, 28% by hedge funds, and 6% by insurance companies (BBA, 2006). A key motive for banks taking CDS positions is to hedge (about one-third of their credit derivatives positions are held in the loan book). This hedging demand is largely passive as it is determined by the lending business of banks, which is governed by medium to long-term considerations. The importance of the hedging motive in CDS markets creates a natural asymmetry.
We hypothesize that the speculative trading desks of banks, hedge funds, and other potentially well informed participants both buy and sell credit protection through CDS contracts. However, the credit risk management (CRM) desks of banks concentrate their trading on just one side of the market, buying credit protection. Due to the information generated by their banks' lending activities, they may be well informed about firm-specific news (as discussed by Acharya and Johnson, 2007), but we argue that they may be relatively uninformed with respect to the credit risk implications of market-wide information. One explanation for the CRM desk's lack of focus on market-wide information may be that it considers its bank to be (independently) hedged against broad market movements, leaving the desk free to concentrate on managing firm-specific risks.
The presence of a large group of uninformed participants in a market should not have important efficiency implications if dealers are competitive. However, CDS dealers have market power for at least two reasons. First, the CDS market is a bilateral over-the-counter market with no centralized quote disclosure mechanism. Since there is no central counterparty system, counterparties need to enter into an ISDA Master Agreement before they can trade against each other. It is unlikely that hedgers enter into agreements with all dealers. As such, they are limited in who they can trade against at any point in time. In addition, protection purchased on Firm X from Bank A is different from protection purchased on Firm X from Bank B since the probability of the joint default of Firm X and the protection writing bank differs. Therefore, there is a degree of product differentiation across dealers. Product differentiation has been identified as a contributory factor to asymmetric price adjustment in goods markets.
The consequences of information asymmetry across participants and less than fully competitive dealer networks are as follows. When firm-specific news arrives, all participants in the CDS market are well informed. They cannot be exploited by market makers, resulting in efficient pricing in the CDS market. When macro news occurs, hedgers tend to be relatively less well informed. CDS prices will still be efficient in the case of bad news, as in this case it is in the interest of market makers to pass on the higher cost of protection to the hedgers. However, in the case of good economic news, market makers can exploit their informational advantage vis-a-vis hedgers and delay lowering the cost of protection. Pricing in the CDS market then becomes inefficient.
If our explanation has any bearing, we would expect the CDS lag in the presence of good news to depend upon the importance of uninformed hedgers. In particular, if there is no hedging demand for a specific firm, the response of CDS prices to good and bad news should be equivalent. The greater the demand by hedgers, the slower the response when good news occurs. However, there should not be much cross-sectional variation in the response to bad news. Thus, we next examine whether various proxies of hedging can explain cross-sectional variations in the lead-lag to equity market news. (5)
We consider three determinants of hedging demand on the firm level:
(a) Outstanding debt. The greater the debt of the firm, the higher the demand for hedging (Oehmke and Zawadowski, 2014). We measure debt by the log of the average total outstanding long-term debt of a firm, which we extract from Compustat at a quarterly frequency.
(b) Default risk. Qiu and Yu (2012) posit a nonlinear relation between hedging demand and the level of default risk. Briefly, their argument is as follows. Top quality credits face little hedging demand since insurance is deemed unnecessary, but as credit quality falls, hedgers obtain greater credit protection. Once assets fall below investment grade, however, the cost of insurance becomes excessive. In addition, many investors have already been forced to sell their assets due to mandates and the remaining investors are likely to bear the risk of further deterioration. We use the numerical long-term S&P credit rating variable as a proxy for firm risk (whereby an AAA rating translates to 1, AA to 2, etc.). (6) We compute a time-weighted average rating level for each firm in the cross section. We allow for nonlinearity in the relationship by including a quadratic term.
(c) Default risk volatility. A firm whose default risk varies substantially tends to require more frequent adjustments in hedging positions. Hedging-motivated trading should be more important for such a firm. We proxy this effect by the (log of the) standard deviation of CDS returns in the sample.
It should be pointed out that any importance of passive hedgers for price formation requires limits to arbitrage across the two markets. However, Kapadia and Pu (2012) find significant short-term pricing discrepancies across equity and CDS markets and ascribe these discrepancies to limited arbitrage capital flows between the two. In our analysis, we include two proxies for arbitrage costs as controls for limits to arbitrage, and a third variable that proxies for speculative demand:
(a) Transactions costs. Illiquidity constrains the actions of an arbitrageur since entering into or unwinding a position in a timely manner will impact price and make arbitrage costly. Thus, a lower level of liquidity is expected to reduce arbitrage activity. We use the average bid-ask spread on the equity of the firm as a simple measure of illiquidity.
(b) Idiosyncratic risk. Shleifer and Vishny (1997) and Pontiff (2006) argue that exposure to idiosyncratic risk deters arbitrage. In the case of CDS equity arbitrage, Kapadia and Pu (2012) note that an imperfect hedge caused by an incorrect or out of date hedge ratio leaves the arbitrageur with an unhedged position in the firm. As such, arbitrage flows are less likely for firms with high idiosyncratic risk. We measure idiosyncratic risk as the (log of the) standard deviation of the residuals from a regression of daily equity returns on the market return.
Since higher limits to arbitrage should lead to more pronounced efficiencies, we expect the arbitrage cost proxies to be positively associated with cross-market lead-lags. More importantly, the significance of the limit to arbitrage proxies also provides an explanation as to why dealers are able to exploit informational asymmetries across markets.
Following Oehmke and Zawadowski (2014), we include a measure of equity analyst forecast disagreement as a proxy for speculative trading. The greater the disagreement about earnings prospects, the higher the likelihood of speculative trading in the CDS market since default probabilities should be related to earnings. Specifically, we compute the average value of the earnings-per-share forecast dispersion for a firm divided by the firm's share price. (7) We expect that greater disagreement is related to more speculative demand and with smaller lags in the CDS market.
We examine the cross-sectional relation between a firm's CDS lag and hedging demand by running the following regression:
LagCoef [f.sub.i] = [alpha] + [[gamma].sub.1] [H.sub.i] + [[gamma].sub.2][A.sub.i] + [[gamma].sub.3][C.sub.i] + [[epsilon].sub.i]. (5)
The dependent variable (the CDS lag) is one or more of the coefficients obtained from firm-by-firm estimation of Equation (4). The explanatory variables fall into three categories: (1) H refers to the set of hedging proxies, (2) A refers to a set of arbitrage costs and speculative demand, and (3) C refers to the general control variables. As a control, we first use the (log of) average equity market capitalization to capture size effects. In addition, we include the average level of the CDS price. This variable may proxy for various factors, such as the market's attention to a specific firm (higher attention is expected for firms with a higher CDS price) or the extent to which a firm is subject to informational asymmetries (for a firm with a low CDS price, there is limited potential to gain from information acquisition and, as such, asymmetries are expected to be low).
The first column of Table V reports the regression results where the CDS lag is the estimated coefficient on lagged positive equity market returns from Equation (4) ([[beta].sub.2i]). Since the dependent variable in Equation (5) is an estimated coefficient, we use weighted least squares for the estimation (with weights inversely proportional to the variance of the coefficient estimates in the first stage regression).
The hedging proxies are all significant and have the expected signs. In particular, long-term debt enters negatively indicating that greater hedging demand due to higher debt exposure increases inefficiencies in the CDS market. The rating variable is significantly negative, while the rating squared is significantly positive. Thus, as firm quality declines, the CDS lag initially becomes more pronounced, but at a sufficiently high degree of default risk, the relationship reverses. Interestingly, the coefficients imply that this happens at a single-A rating. This nonlinear relation is consistent with the argument put forward in Qiu and Yu (2012) that hedging demand is maximized near the boundary between investment grade and noninvestment grade. Finally, the standard deviation of CDS returns has the expected negative sign indicating that more frequent adjustments in hedging behavior lead to a more pronounced CDS lag.
Among the proxies for arbitrage costs, illiquidity in the equity market is associated with a larger CDS lag, consistent with higher inefficiencies when arbitrage becomes more costly although significance here is only weak (p-val is 0.138). The second arbitrage limit proxy, idiosyncratic volatility, however, does not significantly affect the CDS lag. Forecast disagreement, proxying for speculative demand, is significant at the 10% level and enters with the expected positive sign. Greater disagreement, which is assumed to be related to more speculative trading, reduces the CDS lag.
Turning to the general control variables, we note that market capitalization (the size proxy) significantly reduces the CDS lag. This is consistent with the notion that asset markets for larger firms are generally more efficient. The average CDS price is negatively associated with the CDS lag. The negative sign may reflect the notion that the scope for informational asymmetries is larger for firms that have higher CDS prices.
One potential concern is that the hedging results may be driven by multicollinearity between the hedging and arbitrage cost proxies. However, the correlation among these groups of proxies is modest. The highest correlation arises between the rating variable and equity illiquidity and is -0.20. We also ran a regression excluding the arbitrage cost proxies (unreported). The results do not change in any important way. Finally, it should be noted that the explanatory power coming from the hedging variables is substantial. While the [R.sup.2] in Column 1 is 0.401, the [R.sup.2] drops to 0.004 when the hedging variables are excluded.
The results from this regression are supportive of the rockets and feathers hypothesis as they confirm that the CDS market's slow incorporation of positive equity market news is related to hedging demand. However, we can exploit this setting further. The hypothesis suggests that while the lag with respect to positive stock market news should be related to hedging proxies, the lag following negative news should not. This provides us with an important placebo test. The second column in Table V reports the results when the dependent variable is the coefficient on the CDS response to lagged negative equity news. We find that there is no longer significance for any of the hedging proxies (only the squared rating variable enters with marginal significance).
Finally, the third column in Table V presents results where the dependent variable is the difference between positive and negative equity market news [[[beta].sub.2i] - [[beta].sub.3i] from Equation (5)]. The results are largely unchanged from those reported in the first column. In particular, the hedging proxies are all significant and signed as expected.
Taken together, the results in this section corroborate the idea that the asymmetry in the lead-lag relationship is driven by the presence of passive hedgers that allow CDS dealers to maintain high protection prices in the advent of positive news.
2. The Lead-Lag Relation and Information Asymmetries
The rockets and feathers hypothesis relies on participants on one side of the market being, on average, less informed about the true value of the asset than the dealers and the participants on the other side. We have established that variation in proxies for hedging demand are correlated with the magnitude of the CDS market's lag in the face of good equity market news. In this section, we determine whether the lag is also related to informational asymmetries, exploiting time-series variations.
Chordia, Sarkar, and Subrahmanyam (2011) argue that an important economic announcement should resolve uncertainty. Thus, information asymmetries should be high immediately prior to this news announcement, and lead-lags should be relatively large. Our previous results suggest that macroeconomic, rather than firm-specific, information is important in explaining the equity lead over the CDS market. Consequently, we focus on three key US macroeconomics announcements: (1) the release of advanced gross domestic product (GDP) estimates, (2) the employment situation announcement (which includes nonfarm payroll figures), and (3) the producer price index release. (8) We construct two indicator variables. PRE takes a value of one on the day immediately prior to an announcement (and zero otherwise). POST takes a value of one on the day immediately after an announcement (and is zero otherwise). (9) Since the previous results suggest that good news is critical to understanding the lagged response of the CDS market, we interact these two indicators with the lagged positive component of the return on an equally weighted portfolio of equity returns. We include the positive component of equity returns that captures the "normal" effect of lagged positive equity news. The interaction terms capture the modification of this effect when information asymmetries are highest (PRE) or lowest (POST). The lagged negative component of equity returns is included, but is not interacted with the indicator variables. We run the following regression:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)
If information asymmetries are important in explaining the magnitude of the CDS market's lag behind the equity market, then we would expect [[alpha].sub.1] < 0 < [[alpha].sub.2] since the coefficient on lagged good equity market performance should be more negative than usual on days immediately preceding announcements, and less negative than usual on days immediately after the announcement.
Coefficient point estimates reported in the first column of Table VI are supportive of the hypothesized relationship in that the coefficient signs are correct for the interaction variables. However, the test of equality between the two coefficients cannot be rejected at conventional significance levels as the standard errors on these coefficients are relatively large. To increase the power of the test, we pool data on individual firms and rerun the regression. The results are reported in the second column of the table. Again, the coefficient estimates are supportive of the hypothesis and the p-value of the equality of coefficients restriction is just 0.016. We interpret these results as (weakly) confirming that information asymmetries are behind the CDS market's lag relative to the equity market.
Our second time series-based test is also derived from Chordia et al. (2011). They reason that increased information asymmetry will result in widening bid-ask spreads and decreased liquidity in the lead market, equities in our case. Increases in the bid-ask spreads for equities then predict slower adjustment of CDS returns to (positive) stock market returns. We measure stock-level illiquidity using the daily proportional bid-ask spread on each firm in our sample (sourced from CRSP) and construct a daily equally weighted average spread across stocks (denoted SP). We interact [SP.sub.t] with positive and negative components of equity market returns and include these interactions as additional regressors in portfolio-level regressions:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)
The results are reported in Table VII for portfolio CDS returns and for pooled individual returns. The coefficients on the interaction of spreads with positive equity market movements are negative and statistically significant, supporting the idea that information leading to widening equity spreads and a rising equity market is incorporated into CDS prices with a relatively long lag. More importantly, the results suggest that it is not the direction of the news per se that drives the asymmetry as restricting the coefficients on lagged positive and negative equity markets to be equal is not rejected and barely alters the goodness of fit. Rather it is the direction of news, combined with high levels of asymmetric information that drive the asymmetry in the lead-lag relationship. Conversely, the coefficients on the interaction of spreads with negative equity news are significantly positive, although the coefficient magnitude is much smaller than for positive news. This suggests that bad news actually reduces the lag of the CDS market.
This subsection has focused on demonstrating that information asymmetries lie behind the equity market's lead over the CDS market. In line with the rockets and feathers hypothesis, we find that at times of high information asymmetry, such as immediately prior to important macroeconomic announcements or when market-wide equity bid-ask spreads are high and the news is positive, the equity market's lead is maximized. Conversely, when asymmetries are low, the lead is small.
E. Effect of the Global Financial Crisis
Our analysis thus far has spans January 1, 2004 to October 14, 2008. That is, our sample ends at the start of the global financial crisis as Lehman Brothers filed for bankruptcy on September 15, 2008, Troubled Asset Relief Program (TARP) was announced on October 3, and $250bn is injected into the US banking system on October 14, with many of the main banks who were active in the CDS market receiving public money.
In this section, we extend our sample over the financial crisis and focus on our key result, the asymmetric response of CDS prices to lagged equity market information. Unfortunately, we do not have access to Markit CDS data for this period. Instead we use data from credit market analytics (CMA) as this source provides CDS quotes sourced from a panel of 30 leading financial institutions until September 30, 2010. (10) We match 153 of our original 193 firms. As such, our new sample is longer, but narrower.
Our explanation for the asymmetric response of CDS prices to lagged equity market returns rests on three key components: (1) passive hedgers, concentrated on the credit protection buying side of the CDS market, are less informed about the credit risk implications of market-wide information (though they are probably very well informed about the implications of firm-specific news), (2) dealers have market power, at least in part through product differentiation, and (3) there are limits to arbitrage preventing speculators from exploiting any mispricing by dealers. Once the financial crisis hits, there are good reasons to assume that the first two components are substantially weakened. While at the start of the crisis problems might arguably have been interpreted as specific to certain firms or financial institutions, by October 2008, it was clear this was a market-wide and, indeed, global crisis. Hedgers then had good reason to become informed about the credit risk implications of macro news, as well as firm-specific news. The ability of dealers to claim product differentiation is also arguably weaker when the probability of the joint default of reference entities and all protection writers are high and rising. Implications of the crisis for the third component, binding limits to arbitrage, are less clear. Risk capital dried up during the crisis suggesting less arbitrage. However, the CDS market was one of the few markets that remained active during the crisis. Once the focus shifted to the European debt markets, the (sovereign) CDS market was at the heart of the crisis. As such, a larger proportion of total arbitrage capital might have been attracted to the CDS market. Vause (2010) reports continued strong growth in trading volumes across the financial crisis.
As a result of these effects, we expect that the asymmetry between good and bad equity market returns should diminish in the crisis. In Table VIII, we report the results of pooled regressions (analogous to the second row of Table IV) over various sample periods. The first row indicates that our key result of asymmetric responses to positive and negative lagged equity returns is present for the pre-crisis period in the CMA data. The second row reports that the asymmetry is present, though weaker, if we focus on the post January 1, 2007 period. Crucially, the third row indicates that the asymmetry completely disappears during the crisis (defined to run from October 1, 2008 to July 31, 2009). This is not just due to a lack of power when considering this shorter time interval since the coefficient estimates also alter substantially. In fact, over this period, the point estimates suggest the effect of lagged bad equity market news is greater than that of good news. There is, however, no statistically significant difference in these responses. Finally, the fourth row demonstrates that the asymmetry is strong if we look at the post January 1,2007 period, but with the crisis window excluded.
In sum, our key results are robust across two leading CDS databases and are strong in noncrisis periods. However, as expected, the asymmetric response disappears during the crisis due to a weakening of some, if not all, of the necessary conditions.
This paper has analyzed lead-lag patterns in the equity and CDS markets. Using a large data set, we find a strong and robust advantage for the equity market over the CDS market in pricing new information. We also confirm that this advantage is primarily due to the pricing of aggregate and positive information in the equity market. One potential explanation for this is the presence of institutional investors with hedging demands in the CDS market. While these investors may be well informed about news specific to the firms in their portfolio, they may behave relatively passively in the advent of macro news. Dealers can exploit their local market power following good equity market news and maintain relatively high CDS prices when hedgers are not fully informed about the fall in the true price of protection. Conversely, after bad equity market news, CDS prices rise much more rapidly since it is in the dealers' best interest to raise prices for protection buyers.
Consistent with this hypothesis, we have demonstrated that the lead-lag is stronger for firms where there is greater hedging demand. We have also presented evidence to support the notion that the pricing advantage of the equity market is related to informational asymmetries, as the equity lead is more pronounced in times of higher macroeconomic uncertainty (as measured by days prior to macroeconomic announcements and high bid-ask spreads). In contrast, our evidence does not lend support to alternative explanations of the lead-lag that are consistent with efficient markets.
Our paper strikes a negative note regarding the efficiency of CDS markets. CDS markets are widely considered to be the most efficient means of pricing credit risk. As such, one would expect them to do also relatively well when compared to equity markets. However, our results indicate that this is not the case as we find a strong lead for equity markets. Perhaps most disturbingly, this lead arises from supposedly easy-to-price economy-wide information, such as the equity market factor. We should also reiterate that we have centred our sample on those firms with the most liquid CDS contracts, thus effectively biasing us against finding inefficiencies in the CDS market.
The empirical patterns reported in this paper are consistent with attributing the inefficiency of the CDS market to the presence of institutional investors with a passive demand for hedging. This would suggest that the composition of investors in a market may have important implications for pricing inefficiencies, especially when some classes of investors are informed (or uninformed) about certain types of news. More research in this area seems warranted. In particular, an understanding as to whether the pricing properties of other markets and assets (for example, CDS vs. bond markets or large vs. small firm stocks) can also be linked to the presence (or lack) of certain investor groups.
Appendix A: Robustness of Unconditional Equity Lead-CDS Lag Result
Table II in the text summarizes the results of estimating VARs of equity and CDS returns. The dominant finding is that lagged equity returns contain information for current CDS price changes, while the reverse is rarely the case. This appendix demonstrates the robustness of these findings.
The VAR as specified in Equations (la) and (lb) does not control for contemporary CDS or equity returns, respectively. The delayed diffusion of information from equity to CDS markets suggested by our results may simply be due to the omission of contemporaneous equity returns from Equation (1 b). We test for this by incorporating the relevant contemporaneous return in each equation for each reference entity individually and for all entities pooled together. The results are reported in Panel A of Table Al. Our key finding, that CDS returns lag equity returns, is robust to the inclusion of contemporaneous equity returns.
Panel B of Table Al summarizes the results when we pool the companies, but split the sample according to the credit rating and equity market capitalization of the firms. Irrespective as to whether the companies are rated AAA-A versus BBB-B, or whether they are in the smallest quartile or the middle 50% by market capitalization, lagged equity returns are significant in explaining current CDS returns. Lagged equity returns are not significant in pooled regressions for firms in the largest quartile, but this is driven by a small number of firms since lagged equity returns are significant for the largest quintile (coefficient = -0.29, p-val = 0.000). Conversely, but irrespective as to how we separate the firms, lagged CDS returns are not significant in the equity returns regressions with the sole exception of the smaller firms. Even in this case, however, the magnitude of the coefficient is very small and the goodness of fit very low indicating statistical, but not economic significance.
Panel C of Table A1 pools the companies, but splits the sample into pre-crisis and crisis periods. The pre-crisis period runs from the beginning of the sample through the end of June 2007, while the crisis period runs from the beginning of August 2007 to the end of the sample period. Observations for July 2007 are dropped from the analysis. Again, there is a strong lag of the CDS market in both periods. It is interesting to note that CDS predictability is higher in the crisis period (the coefficient on lagged equity returns is -0.349 compared to -0.226 prior to the crisis). There is some evidence of information in lagged CDS returns for the equity market prior to the crisis, but this is statistically, but not economically significant and it completely disappears during the crisis interval.
Table A1. Bivariate VAR Results The table reports the results of a bivariate vector autoregression of daily equity and CDS returns with one lag. The relevant dependent variable is given in the first column of each row. The first two rows report the average results (coefficient values and [R.sup.2] values) across the 193 individual firms together with a count of the number of firms with coefficients significant at the 5% level. The latter is also expressed as a percentage of the total sample of 193 firms. The p-val figure is the result of a test where the average coefficient value is zero. The remaining rows report pooled regression results. OLS results use standard errors robust to unspecified heteroskedasticity and serial correlation. Pooled regressions report--values based on standard errors robust to unspecified heteroskedasticity and double clustered by day and by firm. The full sample runs from January 1, 2004 to October 14, 2008 (1,208 observations per firm). In Panel A, the equity (CDS) equation in the VAR is augmented with contemporaneous CDS (equity) returns. In Panel C, the pre-crisis period runs from January 1, 2004 through the end of June 2007 (877 observations per firm), while the crisis period runs from the beginning of August 2007 to the end of the sample (308 observations per firm). Lagged Equity Returns Coefficient Count (p-val) Significant (% signif.) Panel A. Individual Firms with Contemporaneous "Other Asset" Returns Equity returns -0.051 43 (0.392) (22.3%) CDS returns -0.208 154 (0.023) (79.8%) Pooled Firms with Contemporaneous "Other Asset" Returns Equity returns 0.000 (0.998) CDS returns -0.160 (0.000) Panel B. Credit rating AAA-A Equity returns 0.002 -0.003 (0.946) CDS returns -0.240 0.150 (0.000) (0.000) BBB-B Equity returns -0.008 -0.004 (0.677) (0.785) CDS returns -0.162 0.228 (0.000) (0.000) Size Largest 25% Equity returns 0.111 -0.014 (0.398) (0.587) CDS returns -0.140 (0.193) Middle 50% Equity returns -0.015 (0.510) CDS returns -0.189 (0.000) Smallest 25% Equity returns 0.002 (0.885) CDS returns -0.150 (0.000) Panel C. Precrisis Equity returns 0.006 (0.590) CDS returns -0.147 (0.000) Crisis period Equity returns 0.027 (0.573) CDS returns -0.166 \(0.002) * Lagged CDS Returns Coefficient Count [R.sup.2] (p-val) Significant (% signif.) Panel A. Individual Firms with Contemporaneous "Other Asset" Returns Equity returns 0.029 47 0.054 (0.424) (24.4%) CDS returns 0.196 157 0.118 (0.001) (81.3%) Pooled Firms with Contemporaneous "Other Asset" Returns Equity returns 0.018 0.036 (0.161) CDS returns 0.190 0.091 (0.000) Panel B. Credit rating AAA-A Equity returns 0.000 (0.829) CDS returns 0.050 BBB-B Equity returns 0.000 CDS returns 0.077 Size Largest 25% Equity returns 0.014 CDS returns 0.158 0.037 (0.000) Middle 50% Equity returns -0.000 0.002 (0.974) CDS returns 0.200 0.064 (0.000) Smallest 25% Equity returns -0.014 0.003 (0.263) CDS returns 0.222 0.077 (0.000) Panel C. Precrisis Equity returns -0.004 0.000 (0.388) CDS returns 0.166 0.037 (0.000) Crisis period Equity returns -0.00 0.001 (0.837) CDS returns 0.210 0.075 (0.000)
Appendix B: List of Firms Analyzed
E I Du Pont De Nemours
Black & Decker
Coca Cola Ents.
Cooper Tire & Rub.
D R Horton
Jones Apparel Group
Starwood Htls. & Rsts.
Capital One Finl.
Goldman Sachs Gp.
Marsh & Mclennan
Wells Fargo & Co
Bristol Myers Squibb
Merck & Co.
United Parcel Ser.
Oil & Gas
Kinder Morgan En.Ptns.
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(1) For example, Chan (1992) finds that equity index futures tend to lead the cash index. Hou (2007) and Chordia, Sarkar, and Subrahmanyam (2011), along with many others, examine lead-lag effects between large and small cap equities, while Hotchkiss and Ronen (2002) consider lead-lags between corporate bonds and equities.
(2) There is solid evidence that with very few exceptions, CDS markets price information faster than corporate bond markets, although arbitrage relationships tie credit spreads and CDS prices together in the long run (Blanco, Brennan, and Marsh, 2005). There is also evidence that the corporate bond market lags the stock market (Kwan, 1996; Downing, Underwood, and Xing, 2009).
(3) Asymmetric responses to positive and negative price shocks are widespread in goods markets (Bacon, 1991) where the phenomenon is driven by consumers facing search costs that afford intermediaries a degree of market power. Recently, Green, Li, and Schurhoff (2010), interpreting search costs as informational asymmetries, find that such asymmetries can also occur in financial markets (municipal bond markets).
(4) The relatively good ability of the CDS market in pricing negative (equity) news may arise from short selling constraints in the equity market. However, short selling constraints cannot explain the differential response to common and idiosyncratic news and are also inconsistent with evidence provided later in this section.
(5) There may also be variations in hedging demand over time. In particular, we would expect higher hedging demand during times of crises. This is consistent with our findings in Section II. I that the equity-CDS lead-lag is higher during the crisis of 2007-2008.
(6) It might be argued that risk increases demand for trading in the CDS of a firm generally (and regardless as to whether it is for speculative or hedging purposes). However, in this case, we would expect the lead-lag and the asymmetries to decrease in firm risk as additional trading should increase the efficiency of the CDS market.
(7) We use the standard deviation of I/B/E/S (Institutional Brokers' Estimate System) EPS (earnings per share) forecasts of one-year earnings to calculate our measure of disagreement.
(8) In some months, the consumer price index was announced before the producer price index. In these months, we use the day of the consumer price index release.
(9) In the few instances where announcements occur on successive days, PRE takes a value of one only on the day prior to the first announcement.
(10) We do not use CMA as our main source since many observations are flagged as being model-derived prices rather than being based on market quotes or trades. For some of our previous analysis, a complete dataset is important. Mayordomo, Pena, and Schwartz (2013) suggest that CMA data led the price discovery process, ahead of Markit data using the Gonzalo Granger metric based on a sample of 43 US firms. However, for our shorter, but much broader panel, we instead find that Markit data makes the largest contribution to price discovery (68% using all observations until mid-October 2008).
The authors gratefully acknowledge financial support from NCCR Trade Regulation. We would like to thank Ana-Maria Fuertes, Aneel Keswani, Chensheng Lu, Richard Payne, Asani Sarkar, seminar participants at Aberdeen University and Cass Business School for constructive discussions, and an anonymous hedge fund for providing some of the data used in the project. The paper has benefitted from the comments of an anonymous referee and Marc Lipson (Editor). Excellent research assistance from Norman Niemer is gratefully acknowledged.
Ian W. Marsh, Wolf Wagner *
* Ian W. Marsh is a Professor in the Department of Finance at the Cass Business School in London, UK. Wolf Wagner is a Professor of Finance at the Rotterdam School of Management at Erasmus University in The Netherlands.
Table I. Descriptive Statistics This table provides summary statistics of the key returns series used in the paper. The sample runs from January 1, 2004 to October 14, 2008 (1,208 observations per firm), and there are 193 firms in the data set. Figures in rows denoted Autocorrelation 1, 2, and 3 provide autocorrelations with one, two, and three lags. Figures in rows denoted cross-autocorrelation 1, 2, and 3 report correlations between the time t-dated returns of the asset in that column and returns of the other asset at times t - 1, t - 2, and t - 3. Statistics are calculated from the pooled data set. Equity Returns CDS Returns Mean -0.0003 0.001 25th percentile -0.009 -0.010 75th percentile 0.009 0.010 Standard deviation 0.024 0.035 Skew -6.131 2.430 Autocorrelation 1 0.024 0.214 Autocorrelation 2 -0.053 0.111 Autocorrelation 3 -0.009 0.038 Cross-correlation -0.189 -0.189 Cross-autocorrelation 1 -0.015 -0.149 Cross-autocorrelation 2 -0.024 -0.026 Cross-autocorrelation 3 -0.009 -0.031 Table II. Bivariate VAR Results The table reports the results of a bivariate vector autoregression of daily equity and CDS returns with one lag. The relevant dependent variable is given in the first column of each row. The first two rows of Panel A report average OLS results (coefficient values and [R.sup.2] values) across the 193 individual firms together with a count of the number of firms with coefficients significant at the 5% level. The latter is also expressed as a percentage of the total sample of 193 firms. The p-val figure is the result of a test where the average coefficient value is zero. The second two rows of Panel A report pooled regression results. Panel B presents the results of a bivariate vector autoregression of daily equity and CDS equally weighted portfolio returns with one lag. OLS results use standard errors robust to unspecified heteroskedasticity and serial correlation. Pooled regressions provide p-values based on standard errors robust to unspecified heteroskedasticity and double clustered by day and by firm. The full sample runs from January 1, 2004 to October 14, 2008 (1,208 observations per firm). Lagged Equity Returns Coefficient Count Significant (p-val) (% signif.) Panel A. Individual firms Equity returns -0.025 20 (0.648) (10.4%) CDS returns -0.201 149 (0.011) (77.2%) Pooled firms Equity returns 0.021 (0.517) CDS returns -0.166 (0.000) Panel B. Equity port returns -0.027 (0.599) CDSP port returns -0.306 (0.000) Lagged CDS Returns Coefficient Count Significant (p-val) (% signif.) [R.sup.2] Panel A. Individual firms Equity returns -0.001 12 0.008 (0.977) (6.2%) CDS returns 0.197 157 0.076 (0.001) (81.3%) Pooled firms Equity returns -0.007 0.001 (0.582) CDS returns 0.191 0.057 (0.000) Panel B. Equity port returns 0.024 0.003 (0.612) CDSP port returns 0.408 0.279 (0.000) Table III. Factor VAR Results The table reports the results of vector autoregressions of daily factor decomposed equity and CDS returns with one lag. The table reports average results (coefficient values and [R.sup.2] values) across the 193 individual firms together with a count of the number of firms with coefficients significant at the 5% level. The latter is also expressed as a percentage of the total sample of 193 firms. The p-val figure is the result of a test where the average coefficient value is zero. In Panel A, firm-level equity and CDS returns are decomposed into common and idiosyncratic components based on principal components analysis. Specifically, the first three principal components are extracted from the equity returns of the 193 firms. The equity returns of each firm are then regressed on these three principal components, fitted values are saved as the common component of equity returns, and residuals are saved as the idiosyncratic component. A similar approach is taken for CDS returns. These four components form the VAR. The relevant dependent variable is given in the first column and the explanatory variables are identified by the column headings. In Panel B, a similar decomposition is performed for equity returns using three Fama-French factors. CDS returns are not decomposed and the trivariate VAR is composed of the common equity return component, the idiosyncratic equity component, and the total CDS return. In Panel C, the equity decomposition is performed using just one factor, alternately the first principal component, the equally weighted average return from the 193 equities, and the Fama-French market factor. Each row in Panel C reports the results of regressions with the total CDS return as the dependent variable. All VAR estimates are computed using OLS with standard errors robust to unspecified heteroskedasticity and serial correlation. The full sample runs from January 1, 2004 to October 14, 2008 (1,208 observations per firm). Lagged Equity Returns Common Returns Coefficient Count Signif. (p-val) (% signif.) Panel A. PCA factors Equity common -0.026 0 (0.632) (0.0%) Equity 0.004 30 idiosyncratic (0.954) (15.5%) CDS common -0.279 173 (0.000) (89.6%) CDS -0.009 19 idiosyncratic (0.922) (9.8%) Lagged Equity Returns Idiosyncratic Returns Coefficient Count Signif. (p-val) (% signif.) Panel A. PCA factors Equity common 0.001 14 (0.989) (7.3%) Equity -0.020 31 idiosyncratic (0.677) (16.1%) CDS common -0.012 17 (0.816) (8.8%) CDS -0.058 28 idiosyncratic (0.459) (14.5%) Lagged CDS Returns Common Returns Coefficient Count Signif. (p-val) (% signif.) Panel A. PCA factors Equity common 0.027 0 (0.553) (0.0%) Equity -0.005 20 idiosyncratic (0.896) (10.4%) CDS common 0.451 193 (0.000) (100.0%) CDS 0.005 21 idiosyncratic (0.940) (10.9%) Lagged CDS Returns Idiosyncratic Returns Coefficient Count Signif. [R.sup.2] (p-val) (% signif.) Panel A. PCA factors Equity common -0.001 12 0.009 (0.947) (6.2%) Equity -0.012 22 0.017 idiosyncratic (0.603) (11.4%) CDS common -0.002 30 0.293 (0.947) (15.5%) CDS 0.078 81 0.029 idiosyncratic (0.171) (42.0%) Table IV. Asymmetric Responses to Positive and Negative Equity Market News This table reports the results of regressions of CDS returns on lagged equity market returns partitioned into positive and negative components. Lagged CDS returns are also included in the regressions. The first row of the table summarizes the results using common components of firm CDS returns as dependent variables. The common components were extracted using the first three principal components of the CDS returns. This row reports the average results (coefficient values and [R.sup.2] values) across the 193 individual firms together with a count of the number of firms with coefficients or test statistics significant at the 5% level. The latter is also expressed as a percentage of the total sample of 193 firms. The p-val figure is the result of a test where the average coefficient value is zero. The second row provides results from the equivalent pooled regressions. The third row presents the regression results using equally weighted portfolio CDS returns. Equity market returns are computed as the equally weighted equity market return for our sample of stocks. The final row repeats this regression using observations when lagged CDS returns are in one of the 25% of the tails of the distribution. All estimates are computed using OLS with standard errors robust to unspecified heteroskedasticity and serial correlation. The pooled regression results report robust double clustered (firm and time) standard errors. The sample runs from January 1, 2004 to October 14, 200B (1,208 observations per firm). Lagged Positive Equity Market Returns Coefficient Count Signif. (p-val) (% signif.) Individual common -0.497 193 CDS returns (0.000) (100.0%) Pooled regression -0.572 (0.000) Portfolio CDS returns -0.489 (0.000) Portfolio CDS returns -0.505 (large) (0.002) Lagged Negative Equity Market Returns Coefficient Count Signif. (p-val) (% signif.) Individual common -0.159 106 CDS returns (0.092) (54.9%) Pooled regression -0.347 (0.000) Portfolio CDS returns -0.168 (0.058) Portfolio CDS returns -0.217 (large) (0.035) Coefficient Equality Test p-val (% signif.) [R.sup.2] Individual common 0.121 0.299 CDS returns (29.0%) Pooled regression 0.148 0.069 Portfolio CDS returns 0.043 0.286 Portfolio CDS returns 0.000 0.304 (large) Table V. Cross-Sectional Variation in Responses to Good and Bad News The first column of this table reports the results of cross-sectional regressions of estimated coefficients from Row 2 of Table IV on firm-specific variables. Specifically, the dependent variable is the estimated coefficient on lagged positive equity market returns from regressions of CDS returns on lags of itself, lagged positive equity market returns, and lagged negative equity market returns. The second column uses the coefficient on lagged negative equity market returns from the same regression. In the third column, we use Difference, defined as the coefficient on positive news minus the coefficient on negative news, as a dependent variable. All estimates are computed using weighted least squares with robust standard errors. Weights are inversely proportional to the variance of the estimated coefficients from the first stage regression. Coefficient estimates are reported with associated p-values in parentheses. Positive Negative Coefficient Coefficient Difference Long-term debt -0.081 0.005 -0.090 (0.000) (0.804) (0.018) Rating -0.199 0.108 -0.274 (0.014) (0.272) (0.051) Rating squared 0.031 -0.016 0.045 (0.007) (0.241) (0.020) CDS volatility -0.633 0.127 -0.747 (0.000) (0.078) (0.000) Equity illiquidity -6.767 2.245 -9.548 (0.138) (0.494) (0.151) Idiosyncratic volatility -0.055 -0.053 -0.003 (0.284) (0.144) (0.973) Forecast disagreement 0.008 0.006 0.004 (0.068) (0.165) (0.618) Market capitalization 0.087 -0.021 0.109 (0.006) (0.317) (0.017) Average CDS level -0.0004 0.0003 -0.001 (0.068) (0.352) (0.108) [R.sup.2] 0.401 0.091 0.311 Table VI. Information Asymmetries and News Announcements The table reports the results of regressions of CDS returns on lagged positive equity market returns interacted with three indicator variables. PRE takes a value of one on the two days immediately prior to important macroeconomic announcements (and zero otherwise), and POST takes a value of one if both of the other indicator variables equal zero (and zero otherwise). Equity market returns are computed as the equally weighted equity market returns for our sample of stocks. Lagged CDS returns and lagged negative equity market returns are also included in the regressions. The results are reported for equally weighted portfolio CDS returns and for pooled individual CDS returns. The final row presents the test statistics and p-values of the test where the coefficients on the two interacted variables are equal. All estimates are computed using OLS with standard errors robust to unspecified heteroskedasticity and serial correlation. The sample runs from January 1, 2004 to October 14, 2008 (1,208 observations per firm). Portfolio Pooled Individual CDS Returns CDS Returns Coefficient (p-val) Coefficient (p-val) Lagged positive equity -0.209 (0.238) -0.126 (0.040) market returns x PRE Lagged positive equity 0.016 (0.925) 0.010 (0.733) market returns x POST Lagged positive equity -0.433 (0.003) -0.539 (0.000) market returns Lagged negative equity -0.171 (0.055) -0.349 (0.000) market returns Lagged CDS returns 0.421 (0.000) 0.182 (0.000) [R.sup.2] 0.287 0.069 Coefficient equality test 1.84 (0.175) 3.89 (0.049) Table VII. Information Asymmetries and Illiquidity This table reports the results of a regression of equally weighted portfolio CDS returns on the variables listed in the first column. The main innovation in this set of regressions is the inclusion of lagged equity market returns interacted with the lagged average equity market bid-ask spreads. Equity market returns are computed as the equally weighted equity market returns for our sample of stocks. Estimates are computed using OLS with standard errors robust to unspecified heteroskedasticity and serial correlation. Coefficient estimates are reported with associated p-values in parentheses. The final row reports the test statistic and p-value of the test where the sum of the coefficients on the two interacted variables is equal to zero. The sample runs from January 1, 2004 to October 14, 2008 (1 x 208 observations). Portfolio CDS Returns Coefficient (p-val) Lagged positive equity market -0.247 (0.044) returns Lagged negative equity market -0.277 (0.007) returns Lagged positive equity market -1.244 (0.026) returns x lagged spreads Lagged negative equity market 0.334 (0.004) returns x lagged spreads Lagged CDS returns 0.420 (0.000) [R.sup.2] 0.290 Coefficient equality test 5.98 (0.003) Pooled Individual CDS Returns Coefficient (p-val) Lagged positive equity market -0.387 (0.000) returns Lagged negative equity market -0.477 (0.000) returns Lagged positive equity market -0.908 (0.001) returns x lagged spreads Lagged negative equity market 0.428 (0.000) returns x lagged spreads Lagged CDS returns 0.182 (0.000) [R.sup.2] 0.070 Coefficient equality test 4.99 (0.000) Table VIII. Asymmetric Responses to Positive and Negative Equity Market News This table reports the results of regressions of CDS returns on lagged equity market returns partitioned into positive and negative components. Lagged CDS returns are also included in the regressions. This table uses CMA CDS data and there are 152 firms in the cross section. Market returns are calculated as the cross-section average of these firm returns. Coefficient estimates are reported with associated p-values in parentheses. Significance levels are based upon robust double clustered (firm and time) standard errors. Lagged Lagged Positive Equity Negative Equity Market Returns Market Returns Coefficient Coefficient (p-val) (p-val) Precrisis sample -0.698 -0.345 (1/01/04-9/30/08) (0.000) (0.010) Post 2006 period -0.402 -0.246 (1/1/07-9/30/10) (0.000) (0.002) Crisis period -0.242 -0.369 (10/1/08-7/31/09) (0.051) (0.004) Post '06 excl. crisis -0.606 -0.175 (1/1/07-9/30/08 & (0.000) (0.180) 8/1/09-9/30/10) Coefficient Equality Test p-val (% signif.) [R.sup.2] Precrisis sample 0.092 0.034 (1/01/04-9/30/08) Post 2006 period 0.210 0.056 (1/1/07-9/30/10) Crisis period 0.538 0.081 (10/1/08-7/31/09) Post '06 excl. crisis 0.044 0.048 (1/1/07-9/30/08 & 8/1/09-9/30/10)
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|Author:||Marsh, Ian W.; Wagner, Wolf|
|Date:||Jun 22, 2016|
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