Relation Between Stock Return Synchronicity and Information in Trades, and A Comparison of Stock Price Informativeness Measures

Transcription

1 Relation Between Stock Return Synchronicity and Information in Trades, and A Comparison of Stock Price Informativeness Measures Serhat Yildiz * University of Mississippi syildiz@bus.olemiss.edu Robert A. Van Ness University of Mississippi rvanness@bus.olemiss.edu Bonnie F. Van Ness University of Mississippi bvanness@bus.olemiss.edu January 11, 2016 Abstract We provide empirical evidence that stock return synchronicity is negatively associated and firmspecific return variation is positively associated with total information and private information incorporated into stock prices by trading. These findings support the view that the stock market is informationally efficient. Our results also show that trading-conveyed private information and total information are positively related to a stock s market risk. The impact of private information on the market risk of a stock is always greater than that of total information. These findings imply that private information induces a new form of systematics risk. We also find that low-frequency price informativeness measures cannot capture all information captured by the high-frequency measures. We find that Hasbrouck s VAR, weighted price contribution, variance ratios and the State Space Model (SSM) approach are capturing different facets of information. * Contact Author, School of Business Administration, University of Mississippi, University MS, 38677, syildiz@bus.olemiss.edu 1

2 Relation Between Stock Return Synchronicity and Information in Trades, and A Comparison of Stock Price Informativeness Measures 1. Introduction Roll (1988) proposes that low stock return synchronicity can be caused by either investors acting on their private information or noise unrelated to fundamental information. 1 If informed investors trading with private information lowers stock return synchronicity, then lower stock return synchronicity signals that stock prices closely follow fundamental value, and thus, lower stock return synchronicity reflects efficient markets (Durnev, Morck, Yeung, and Zarowin, 2003). If noise unrelated to fundamentals is the reason behind lower stock return synchronicity, then low return synchronicity signals that stock prices deviating from fundamental values (Durnev, Morck, Yeung, and Zarowin). Studies that center around the Roll s alternative explanations provide conflicting findings. 2 The conflicting findings about the firm-specific return movements and stock price informativeness are likely driven by the way in which firm-specific information is measured (Dang, Moshirian, and Zhang, 2015). Direct measures of firm-specific information are needed to test the relation between stock return synchronicity and firm-specific information (Dang, Moshirian, and Zhang). To this end, by employing market microstructure measures that capture information at trade level, we test how stock return synchronicity is related to the amount of private information incorporated into stock prices by trading. Our approach is based on findings that 1 Stock return synchronicity is measured by the R-square derived from the standard market model and a high R-square indicates a high degree of stock price synchronicity. Morck, Yeung, and Yu (2013) provide an excellent survey of the extensive literature on stock return synchronicity. 2 Morck, Yeung, and Yu (2000), Durnev, Morck, Yeung, and Zarowin (2003), Durnev, Morck, and Yeung (2004), and Dang, Moshirian, and Zhang (2015) find empirical evidence for a negative relation between stock price informativeness and stock return synchronicity. On the other hand, Chan and Chan (2014), Dasgupta, Gan, and Gao (2010), and Kelly (2014) provide empirical evidence for a positive relation between stock price informativeness and stock return synchronicity. In West s (1988) theoretical model firm-specific return variance is negatively associated with information. 2

3 trading incorporates speculators private information into stock prices, and microstructure models provide explicit estimates of this private information (Easley, Hvidkjaer, and O Hara, 2002). 3 Our analysis provides new empirical evidence regarding what stock return synchronicity reflects in terms of stock price informativeness. Another way to examine the relation between stock return synchronicity and stock price informativeness is to focus on investors information choices. For example, in Veldkamp s (2006a) theoretical model, when investors use a common signal to value an asset, return synchronicity increases. As investors use more signals (consume more firm-specific information) to value an asset, return synchronicity decreases. Based on Velkamp s theoretical prediction, we also examine the relation between firm-specific return movements and total information. Further, we provide a high-frequency examination of firm-specific and systematic return variations. Greater firm-specific return variation can increase portfolio risk of many investors who are not fully diversified, and causes investors to hold larger portfolios to diversify (Champbell, Lettau, Malkiel, and Xu, 2001). Since financial markets are becoming venues of high-frequency trading, 4 our examination of firm-specific and systematic return variations on intra-daily level can be especially beneficial for modern day portfolio management. Another contribution of our study is that we document the relations between highfrequency stock betas, total information and private information. While existing studies focus on variations in stock betas at monthly or quarterly frequencies (e.g., Lewellen and Nagel, 2006), examining stock betas at higher frequencies is critical to understanding the impact of information 3 In the following studies, trading incorporates speculators information into prices under different settings; Grossman and Stiglitz (1980), Glosten and Milgrom (1985), Kyle (1985), Dow and Gorton (1997), Leland (1992) and Easley, Kiefer, and O Hara (1997). 4 In the U.S. financial markets, high speed algorithmic traders generate a significant proportion of volume (Commodities Future Trading Commission, 2013). 3

4 flows on a firm s market risk (Patton and Verardo, 2012). 5 Our findings about the relation between information flows and high-frequency betas should be of interest to a broad spectrum of empirical researchers, because understanding the covariance structure of securities is vital for hedging, trading, and measuring systematic risk (Patton and Verardo). Our measures of stock return synchronicity are based on market model R-square, and stock return s market-wide and firm-specific variations (as in Morck, Yeung, and Yu, 2000). We calculate total information and private information with Hasbrouck s (1991a-b) VAR-Model (as in Barclay and Hendershott, 2003; and Hendershott, Jones and Menkveld, 2011). We follow Patton and Verardo (2012) for high-frequency beta calculations, In the second section of the study, we determine the ability of low-frequency price informativeness measures to proxy for high-frequency price informational efficiency measures. We classify information measures that rely on intra-daily data as high-frequency measures and those that rely on daily data as low-frequency measures. Current price discovery and price informational efficiency studies rely mainly on high-frequency measures that are based on intradaily data. However, as pointed out by Goyenko, Holden, and Trzcinka (2009), U.S. markets transaction data are only available since 1983 and in many countries transaction data are not available at all. 6 Accordingly, when intra-daily data are unavailable, studying price informational efficiency and price discovery can be problematic. By identifying high-quality low-frequency measures that rely on daily data, our study aims to enable studying stock price informational efficiency and price discovery over long time periods, and across many markets. 5 Patton and Verardo (2012) explain in detail how data limitations and econometric difficulties limited studies of individual betas at higher frequencies and provide an excellent literature review of advances in econometric theory that enable studies of higher frequency betas. 6 Hasbrouck (2007, page 67) also emphasizes intra-daily data limitation; although we have good recent data on U.S. equity markets that allow us to infer quotes, this is not universally the case. In many data samples and markets, only trades prices are reported. 4

5 We examine the relation between low- and high-frequency metrics with the performance methods, similar to the ones applied by Goyenko, Holden, and Trzcinka (2009). 7 First, we examine the average cross-sectional correlations based on individual firms. Second, we compute time-series correlations based on an equally-weighted portfolio. High-frequency measures include: the cumulative impulse response from Hasbrouck (1991a), absolute trade informativeness measure from Hasbrouck (1991b), state space method (Menkveld, Koopman, and Lucas, 2007), three different specifications of intra-daily data based on the Llorente, Michaely, Saar, and Wang (2002) measure, weighted price contribution (Barclay and Warner, 1993) and variance ratios (as in Chordia, Roll, and Subrahmanyam, 2008). The low-frequency price informativeness measures include: six different specifications of a volume related information measure developed by Llorente, Michaely, Saar, and Wang (2002), Amihud s (2002) price impact ratio (as applied by Ferreira, Ferreira, and Raposo, 2011, and Fresard, 2012). We also include three different specifications of Roll s price impact to the low-frequency measures, because Goyenko, Holden, and Trzcinka (2009) find that Roll s price impact is highly correlated with Amihud s price impact measure. Finally, we provide an empirical comparison of Hasbrouck s VAR-model, weighted price contribution (WPC), variance ratio tests to the state space model approach. These measures are commonly used in price discovery and price informational efficiency studies, however, the measures employ different strategies, require different types of data and amount of computation time. 8 Moreover, Hendershott and Menkveld (2014) state several advantages of the state space 7 Goyenko, Holden, and Trzcinka (2009) examine the relation between high-frequency and low-frequency liquidity measures, and find that low-frequency liquidity measures can be good proxies for high-frequency liquidity measures. 8 Several papers use these measures. The state space model is used in Menkveld, Koopman, and Lucas (2007), Menkveld (2013), Brogaard, Hendershott, and Riordan (2014), Hendershott, Jones, and Menkveld (2013), and Hendershott and Menkveld (2014). Weighted price contribution is used in Barclay and Warner (1993), Cao, Ghysels, and Hatheway (2000), Barclay and Hendershott (2003), and Jiang, Likitapiwat, and McInish (2012). Hasbrouck s VAR-model is used in Hasbrouck (1991a-b), Barclay and Hendershott (2003), Jiang, Likitapiwat, and McInish (2012), 5

6 model to other methods. 9 Accordingly, by comparing Hasbrouck s VAR-model, weighted price contribution, and variance ratio tests to the state space model, we document the relation between these measures. Our empirical comparison should be helpful for researchers who want to assess possible costs and benefits of a particular high-frequency measure. Our main findings are as follows. Supporting Roll s (1988) private information explanation to low R-squares, we find that stocks with low return synchronicity and high firm-specific return variation contain more trading-incorporated private information. Supporting Veldkamp s (2006a) theoretical prediction, we document a negative relation between return synchronicity and the total amount of information incorporated into stock prices by trading. As opposed to West s (1988) theoretical prediction, we find that stocks with higher firm-specific variation reflect more private and total information. Thus, our findings support the informational efficiency view of the stock market. Our high-frequency beta examination provides supportive empirical evidence for Easley and O Hara s (2004) and O Hara s (2003) theoretical predictions that private information induces a new form of systematic risk. Specifically, we find that trading-conveyed private information and total information are positively related to a stock s market risk. However, the impact of private information on stock betas is always greater than that of total information. Thus, both types of trading-conveyed information matter for a stock s market risk. However, the effect of tradingconveyed private information on a stock s market risk is more important than that of tradingconveyed total information. and Hendershott, Jones, and Menkveld (2011). Variance ratio tests are used in French and Roll (1986), Barclay, Litzenberger, and Warner (1990) and Chordia, Roll, and Subrahmanyam (2008). 9 See section 2.4 for details. 6

7 Our results related to the correlations between low- and high-frequency measures are as follows. While the low-frequency information measures can have high correlations to Hasbrouck VAR model, they cannot completely capture the private information captured by Hasbrouck VAR model. A possible explanation is that quote updates may contain information that is not captured by stock returns and volume data. In addition, we find that information captured by WPC and variance ratios is not captured by low-frequency measures. The correlations of low-frequency measures to changes in and absolute value of SSM estimations are relatively high, but their correlations to the SSM estimation are low. The comparison of the high-frequency measures to the SSM estimations find that the direct impacts estimated by SSM are not highly correlated with any of the other measures. However, the change in and the absolute value of the SSM estimations are highly correlated to the other measures. Thus, using the change in the price rather than using the exact price when estimating SSM can increase the agreement between measures. In addition, using individual firm based estimation rather than a portfolio approach can also increase the agreement between the Hasbrouck VAR model and SSM estimation. Comparing Hasbrouck VAR, WPC and variance per hour to the SSM estimation, we find that each measure is capturing different facets of information. 2.0 Background and Hypotheses Development 2.1 Stock return synchronicity and private information Roll (1988) finds that market returns, industry returns, and public news explain around thirty percent of the changes in stock prices. Roll posits that lower stock return synchronicity can be attributed to private information. Studies find conflicting results regarding Roll s proposition for a negative relation between stock return synchronicity and private information. 7

8 A stream of literature provides supportive evidence for Roll s proposition. Morck, Yeung, and Yu (2000) find that stock prices move together less in developed economies than in emerging economies, and argue that stronger property rights promote informed arbitrage and reduce stock return synchronicity. 10 Consistently, Dang, Moshirian, and Zhang (2015) document a positive relation between news commonality and return synchronicity across 41 countries. Dang, Moshirian, and Zhang interpret their finding as supportive evidence for Roll s proposition. Durnev, Morck, Yeung, and Zarowin (2003) find that stock returns of firms and industries with lower stock return synchronicity contain more information about future earnings. Durnev, Morck, and Yeung (2004) find that industries with lower stock return synchronicity make more efficient investment decisions. Li, Morck, Yang, and Yeung (2004) find openness of each country s stock market to foreign investors is associated with higher firm-specific return variation and thus lower return synchronicity. Another stream of literature documents a positive relation between stock return synchronicity and price informational efficiency. In Dasgupta, Gan, and Gao s (2010) model high price informativeness leads to high return synchronicity. Dasgupta, Gan, and Gao provide empirical support for their predictions from seasoned equity offerings and listings of American Depositary Receipts. Chan and Chan (2014) find a negative relation between stock return synchronicity and seasoned equity offerings discounts, a proxy for information asymmetry. Kelly (2014) finds that smaller and younger firms with lower institutional ownership, lower analyst coverage, lower liquidity, and greater transactions costs have low return synchronicity. 10 As an alternative explanation to Morck, Yeung, and Yu s (2000) findings, Jin and Myers (2006) find that opaque information environments increase stock return synchronicity in 40 stock markets around the world. Consistent with Jin and Myers, Hutton and Tehranian (2009) find firm opacity is positively related with higher R-squares in U.S. markets. 8

9 We contribute to the literature on the relation between private information and stock return synchronicity by examining the relation between trading-conveyed private information and stock return synchronicity. Our reasoning is as follows: Roll (1988) points out that trades of speculators, who gather and possess private information, can move prices. Consistently, in several theoretical models, trading incorporates speculators private information into stock prices (e.g., Grossman and Stiglitz, 1980; Glosten and Milgrom, 1985; and Kyle, 1985). Thus, trades convey private information and can affect stock return synchronicity. Theoretically, Pasquariello s (2007) model predicts that heterogeneity in traders private information can lead to the propagation of a shock from one security or market to other securities and markets, and thus, lead to return comovement. In Veldkamp s (2006a) model, investors focus on information common to many firms. Due to this focus, prices exhibit higher synchronicity and less incorporation of private information about firms fundamentals. Thus, Veldkamp s model predicts a negative relation between return synchronicity and the amount of private information produced about a firm. 11 Based on prediction of Veldkamp s model we test the following hypothesis: Hypothesis 1: Stock return synchronicity is negatively related to the amount of private information incorporated into stock prices by trading. 2.2 Return synchronicity and total new information A stream of literature supports the view that trading is an important information source. Traders produce information about an individual firm s growth opportunities and incorporate their information into stock prices by trading (Dow and Gorton, 1997). Stock prices aggregate information from trades of agents who trade for informational and hedging motives (Dow and 11 Chen, Goldstein, and Jiang (2007) present a similar interpretation of Veldkamp s (2006a) model. 9

10 Rahi, 2003) and insiders trading incorporates information into stock prices (Leland, 1992). The order arrival process is informative for subsequent price moves (Easley, Lopez de Prado, and O'Hara, 2012) and the trading process carries information that is subsequently reflected in prices (Easley, Kiefer, and O Hara, 1997). Also, trading related market data, such as bids, asks, prices and volume of trades, are crucial updates to the public information set (Hasbrouck, 2007). We consider trading as a source of information and examine the role of total tradingconveyed information in firm-specific return synchronicity over an extended period. Veldkamp s (2006a) theory suggests that return synchronicity should be positively related to common information (information that is purchased and used many investors). In Veldkamp s model as the number of signals that investors use to value an asset increases, return synchronicity decreases. Based on Veldkamp s model, our second hypothesis is formalized as follows: Hypothesis 2: Stock return synchronicity is negatively related to the total amount of information incorporated into stock prices by trading. 2.3 Information flow and stock s beta The variations in a stock s beta at monthly or quarterly (low) frequencies are welldocumented. For example, Ferson and Harvey (1991) and Lewellen and Nagel (2006) find that stock betas vary significantly at monthly or quarterly frequencies. Shanken (1990) finds that beta (market risk) increases with the 1-month T-bill rate and decreases with the volatility of the 1-month T-bill rate, both of which are elements of public information sets. Ferson and Schadt (1996) find that variation in mutual funds betas at monthly frequencies are associated with public information variables (e.g., the market prices). Though, variations in a stock s beta at low frequencies are welldocumented, lack of data availability and econometrics difficulties blocked studies of beta at higher frequencies (Patton and Verardo, 2012). By building on recent econometrics advancements, 10

11 Patton and Verardo examine variations in beta around earnings announcements with intra-daily data. Patton and Verardo find that betas increase on the day of the earnings announcement and turn back to their regular levels in the following 2-5 days, and that earnings announcement with larger positive or negative surprises have greater positive impacts on betas. Extending the literature on variations of betas at high frequencies, we examine the impact of trading-conveyed information on betas over an extended time period. Instead of illustrating the variations in betas around earnings announcement as in Patton and Verardo (2012), our examination documents the continuous variation in betas due to different types of information in trades. Information moves prices (Veldkamp, 2006b) and firm-specific-information flow increases betas (Patton and Verardo). Accordingly, we expect trading-conveyed information to increase betas. Hypothesis 3: Total information incorporated into stock prices by trading is positively related to high-frequency stock betas. In Easley and O Hara s (2004) theoretical model, informed investors are over-weighted in stocks with good news, and under-weighted in stocks with bad news, and uninformed investors are under-weighted in stocks with good news, and over-weighted in stocks with bad news. Hence, private information induces a new form of systematic risk. O Hara (2003) provides a simplified version of Easley and O Hara s model and presents similar predictions. Based on Easley and O Hara s, and O Hara s theoretical models, we expect trading-conveyed private information to be positively related to betas (systematic risk measures). Hypothesis 4: Trading-conveyed private information is positively related to high-frequency stock betas (systematic risk). 2.4 Relation between low- and high-frequency measures 11

12 Studies of price discovery and price informational efficiency rely mainly on highfrequency measures such as weighted price contribution, Hasbrouck (1991a-b) VAR model, variance ratios, and the State Space Model approach. 12 However, intra-daily data availability can restrict conducting such studies over long time periods and across many countries. Identifying high quality information measures that rely on daily data rather than intra-daily data would enable studying stock price informational efficiency and price discovery over long time periods, and across many markets. To this end, we examine the relation between high-frequency measures and low-frequency measures. Goyenko, Holden, and Trzcinka (2009) find that low-frequency liquidity measures are high quality proxies for high-frequency liquidity measures. 13 Motivated with Goyenko, Holden, and Trzcinka s findings regarding liquidity, we focus on the relation between low- and high-frequency information measures. Both low- and high-frequency information measures aim to capture information incorporated into stock prices. Thus, we expect low-frequency information measures to be good proxies for high-frequency information measures. We test my hypothesis with methods similar to those of Goyenko, Holden, and Trzcinka (2009). Hypothesis 5: Low-frequency information measures are good proxies for high-frequency information measures. 2.5 Relations between high-frequency measures Finance research points out drawbacks of some of the high-frequency information measures. Specifically, variance ratio tests may be biased due to cross correlation (Ronen, 1997). One drawback of the Hasbrouck VAR model is that when estimating it, the econometrician must 12 The methodology section explains each measure in detail and cites studies that use each measure. 13 Goyenko, Holden, and Trzcinka (2009) define liquidity measures that are based on daily or weekly data as lowfrequency liquidity measures, and on intra-daily data as high-frequency liquidity measures. 12

13 truncate the lag structure (Menkveld, Koopman, and Lucas, 2007). WPC does not account for a temporary price-change component (Barclay and Warner, 1993). Hendershott and Menkveld (2014) state several advantages of the state space model over variance ratio tests, Hasbrouck VAR model, and WPC. First, the state space model estimation applies a maximum likelihood approach, which is asymptotically unbiased and efficient. Second, the state space model does not require a finite lag structure. Third, with the Kalman smoother, one can estimate at any point in time, the efficient price and transitory price change components using all observations (i.e., past prices, the current price, and future prices). The State Space Approach has aforementioned advantages over other models and captures the impact of trade innovation on the efficient stock price. Hasbrouck VAR also captures the permanent impact of trade innovation on the efficient price and considers the impact as private information. Since the State Space Approach is capturing the same impact as Hasbrouck VAR, we expect the State Space Approach to be closely related to Hasbrouck VAR model. High variance ratios are interpreted as proxies for private information incorporated into stock prices. Thus, we expect variance ratios to be highly correlated to the State Space Approach. WPC is designed to capture overall new information and does not distinguish between private and public information. If the impact public information cancels the impact of private information, then we expect WPC to have a low or negative correlation to the State Space Model. Hypothesis 6: The State Space Model estimation of the impact of trade innovation on the efficient price is positively correlated to the Hasbrouck s VAR model, variance ratios, but negatively related to WPC. 3. Data and Sample 13

14 My analysis focuses on S&P 500 firms as in Todorov and Bollerslev (2010), Jiang, Likitapiwat, and McInish, (2012), and Patton and Verardo (2012). The sample period is the year We obtain accounting data and S&P 500 index constituents from the Compustat database, stock price related data from the Center for Research in Security Prices (CRSP), national best bid and offer (NBBO) and intra-daily trade data from the NYSE TAQ database. In our intra-daily return calculations, we divide the trading day into 26 fifteen-minute intervals and also consider the time between date t s close and date t + 1 s open as an interval, as in O Hara and Ye (2011). We consider quote midpoints as my main price variable. Using quote based prices rather than trade prices has several advantages. For example, NBBO based returns are free from bid-ask bounce (Chordia, Roll, and Subrahmanyam, 2008) and almost all data errors that are common in high-frequency prices are identified during the construction of the NBBO (Patton and Verardo, 2012). We classify trades as buys or sells following the Lee and Ready (1991) algorithm. Specifically, we classify a trade as a buy (sell) when it is closer to the ask (bid) of the prevailing quote. When the trade is exactly at the midpoint of the prevailing quote, we look at the last price change prior to the trade. If the last price change prior to the trade is positive (negative) the trade is classified as a buy (sell). 14 Table 1 shows price, market capitalization and volume information of the full sample and volume subsamples. Volume is the average number of shares traded per day (in thousands). The average market capitalization of my sample is around $36.36 billion and average stock price is approximately $82. The average market capitalization decreases from $66.52 billion to $16.31 billion as we move from the high-volume sample to the low volume sample. 14 My implementation of the Lee and Ready algorithm is similar to that of Chordia, Roll, and Subrahmanyam (2008). 14

15 {Insert Table 1 here} 4. Measure calculations 4.1 Intra-daily R-squared Similar to Morck, Yeung, and Yu (2000) and Li, Morck, Yan, and Yeung (2004), we calculate our measure of stock return synchronicity using the following linear regression: r it = i + β i r mt + ε it, (1) where r it is stock i s return during time period t, and r mt is a market index return during time t. A high R 2 in such a regression indicates a high degree of stock price synchronicity. Since R 2 is bounded to the interval of [0, 1], I apply a logistic transformation: φ j = log (R 2 j (1 R 2 j )). 4.2 Systematic and firm-specific variations Similar to Morck, Yeung, and Yu (2000) and Li, Morck, Yan, and Yeung (2004), we also employ a variance decomposition approach to calculate stock returns market-wide variation and firm-specific variation. We estimate the model in equation (1) on a stock-day-by-stock-day basis. On a given day τ, the sum of squared variation (total variation), s iτ 2, in stock i s return can be expressed as the sum of the squared variation explained by the market model in equation (1), s iτ 2 m, 2 and the residual (firm-specific) variation, ε s iτ. Dividing the sum of squared variations by number of observations minus one, we calculate market-wide and firm-specific variations. Market-wide and firm-specific variation in stock i during day τ is calculated as σ iτ 2 = 1 σ iτ 2 = 1 N i 1 2 ε ε s iτ 4.3 High-frequency betas 15 2 m s N i 1 iτ m and, respectively. N i is the number of return observations for stock i during day τ. Following Patton and Verardo (2012), we estimate realized the beta of stock i on a given day as follows: Rβ i,t (S) (S) RCov i,m,t RV (S) S S 2 m,t = k=1 r i,t,k r m,t,k k=1 r m,t,k, where r i,t,k = logp i,t,k logp i,t,k 1 is the return on asset i during the k th intraday period on day t, and S is the number of intra-daily

16 periods. As in Todorov and Bollerslev (2010) and Patton and Verardo (2012), we use the exchange-traded fund tracking the S&P 500 index (SPDR, traded on Amex with ticker SPY, and available in the TAQ database) to measure the market return. 4.4 Hasbrouck VAR model Hasbrouck (1991a) models the interaction of trade and quote revisions in a vector autoregressive (VAR) system to measure private information. Building on Hasbrouck s (1991a) VAR model, Hasbrouck (1991b) decomposes information into its public and private components (Barclay and Hendershott, 2003). Hasbrouck s (1991a-b) VAR model is commonly used in the finance literature. Employing Hasbrouck s (1991a-b) VAR-approach, Hendershott, Jones, and Menkveld (2011) find that algorithmic trading increases quote informativeness, and Barclay and Hendershott (2003) and Jiang, Likitapiwat, and McInish (2012) find that significant private information is revealed during after-hours trading. Goldstein and Yang (2014) recommend using Hasbrouck s VAR-approach to test the empirical predictions of their model about information complementarity in financial markets. We estimate the VAR model in transaction time and consider the midpoint of the quotes as the primary price variable, as in Hasbrouck (1991a-b). The VAR model of trades and changes in quotes is defined as follows: 10 r t = a i r t i + i=1 10 i=0 b i x t i + υ 1,t (2a) 10 x t = c i r t i + i=1 10 i=1 d i x t i + υ 2,t (2b) 16

17 In the model, x t is the direction of trade and equals one for buys and negative one for sells, and r t is the log return based on the quote midpoint of a stock from trade t 1 to trade t. 15 We employ 10 lags in the VAR estimation as in Hendershott, Jones, and Menkveld (2011). Once estimated, under an assumption of invertibility, the VAR model can be inverted into a vector moving average (VMA) following Hasbrouck (1991b): 16 r t = (υ 1,t + a i υ 1,t i ) + i=1 x t = c i υ 1,t i + ( i=1 i=0 b i υ 2,t i υ 2,t + d i υ 2,t i ) i=1 (3a) (3b) Hasbrouck (1991b) decomposes the quote midpoint, q t, into two unobservable components: a random walk component, m t and a stationary component, s t. Specifically, q t = m t + s t, (4) where m t = m t 1 + w t, w t ~N(0, σ w 2 ) and Ew t w s = 0 for t s. The random walk component is referred to as the permanent component of the price, and the stationary component is referred to as the transitory component of the price. Hasbrouck (1991b) shows that the variance of the random walk component, σ w 2, can be decomposed into price changes caused by the arrival of public information and price changes caused by the arrival of private information through trades: σ w 2 = ( i=0 a i ) 2 σ 2 υ1 + ( b i ) 2 σ υ2 i=0 2, (5) where σ 2 2 υ1 = Eυ 1,t and σ 2 υ2 = Eυ 2 2,t. From an economic view, the first term of the right hand-side of the equation reflects the impact of public nontrade information and the second term represents the component of price discovery attributable to private information revealed through trades. The VMA approach allows us to identify these components. 15 It is assumed that innovations have zero means and are jointly and serially uncorrelated, specifically: Eυ 1,t = Eυ 2,t = 0 and Eυ 1,t υ 1,s = Eυ 2,t υ 2,s = Eυ 1,t υ 2,s = 0, for s t. 16 I use the SAS code provided by Joel Hasbrouck from his website for this analysis. 17

18 By focusing on the variance of the random walk component of the efficient price, Hasbrouck (1991b) develops four statistics to capture trade-conveyed information. The first statistics is called impulse, b i, and it reflects private information conveyed by trade innovation. Hasbrouck shows that a 1-unit trade innovation leads to a persistent change in the quote midpoint by a magnitude of impulse. The second measure is variance of trade innovations, σ x 2, which is a measure of trade intensity. The third measure is an absolute trade informativeness measure, which captures the comprehensive contribution of trades of all sizes to the efficient price variance. The absolute trade informativeness measure is defined as σ 2 w,x =( b i ) 2 σ 2 υ2. The fourth measure is the relative trade informativeness measure, Rw. Rw is the percent of the variance of efficient price changes that is attributable to trades. 4.5 Weighted price contribution (WPC) Barclay and Warner (1993) develop WPC to examine which trades move prices. 17 Our WPC calculation is similar to that of Cao, Ghysels, and Hatheway (2000). Specifically, weighted price contribution of period i to daily price change is determined as: T WPC i = ( ΔP t T ) ΔP t t=1 t=1 i=0 ( ΔP i,t ΔP t ), (6) where ΔP i,t is the total price change (log-return) for period i on day t, and ΔP t is the price change from day t 1 close to day t close. The first term in equation (6) is the weighting factor for each day, the second term is the relative contribution of the price change for period i on day t relative to the price change on day t. 4.6 State space model approach 17 Using WPC, Barclay and Warner (1993) find informed traders prefer medium size trades. Barclay and Hendershott (2003) and Jiang, Likitapiwat, and McInish (2012), employing WPC, find that after-hours trading generates significant price discovery. Cao, Ghysels, and Hatheway (2000) employ WPC to examine the role of price signaling in price discovery, and find that there is price leadership among market makers. 18

19 Menkveld, Koopman, and Lucas (2007) develop a state space approach (SSM) to study the price discovery process in a multiple market setting. 18 They model the (unobserved) efficient price as an unobservable state variable and mid-quotes as observations of this variable with measurement error. According to Menkveld, Koopman, and Lucas the observed stock price can be decomposed into two components: a permanent component and a transitory component: p i,t = m i,t + s i,t (7) where p i,t is the log quote of the midpoint at time t for stock i, m i,t is the permanent (efficient) component, and s i,t is the transitory (pricing error) component. Equation (7) is the observation equation and the two right hand side variables are the unobservable (latent) state processes. As in Brogaard, Hendershott, and Riordan (2014), we model m i,t the efficient component, as a martingale: m i,t = m i,t 1 + w i,t (8) The permanent process describes the information arrival and w i,t represents permanent price innovations (as in Brogaard, Hendershott, and Riordan, 2014). Including trading variables that incorporate trading-based private information into the w i,t specification is important for identification (Hendershott, Li, Menkveld, and Seasholes, 2014). To capture the impact of highfrequency traders on permanent price component, Brogaard, Hendershott, and Riordan specify w i,t as: w i,t = К i, HFT i,t + μ i,t, (9) 18 Menkveld (2013), Brogaard, Hendershott, and Riordan (2014), and Hendershott, Li, Menkveld, and Seasholes (2014) implement different SSM specifications. Main findings of these three studies that employ SSM approach are as follows. Brogaard, Hendershott, and Riordan (2014) find that HFTs have a significant impact on the permanent and transitory component of prices. Menkveld (2013) finds that a high-frequency trader contributed to the success of Chi- X and, in return, benefited from low fees. Hendershott, Li, Menkveld, and Seasholes (2014) find that transitory price changes are associated with eight percent of stock s daily return variance and twenty-five percent of its monthly return variance. 19

20 where HFT i,t is the surprise innovation in HFT trades, which is obtained as residuals of an autoregressive model. The trading variable, HFT i,t, is designed to capture informed trading, and the impact of informed trading on the permanent component of prices (Brogaard, Hendershott, and Riordan). Similar to Brogaard, Hendershott, and Riordan, we aim to capture information included in trading. However, instead of a specific type of traders, we are interested in overall trading activity. Thus, we focus on innovations in overall trades and modify equation (9) accordingly. Consistent with our approach, aforementioned SSM studies modify SSM to examine the impact of different factors, such as market maker s inventory (as in Hendershott and Menkveld, 2014) on the permanent price component. In addition, Hendershott, Jones, and Menkveld (2013) state that the SSM estimation can incorporate enormous amounts of data including all trades, orders, and news. We define w i,t as: w i,t = К i, Trade i,t + μ i,t, (10) where Trade i,t is the surprise innovation in overall trades, which is obtained the residual of an autoregressive model. 19 Similar to Brogaard, Hendershott, and Riordan, we expect equation (10) to capture trading-conveyed information and its impact on the efficient component of price. Brogaard, Hendershott, and Riordan (2014) model transitory component of prices, s i,t, as a stationary AR(1) process, and specify s i,t as: s i,t = s i,t 1 + ψ i HFT i,t + υ i,t, (11) where HFT i,t is overall trading variable and reflects the impact of HFT trading on the transitory price component. To identify the stationary pricing error component of prices, we follow a similar approach and define transitory price movements as: 19 I choose lag length 20, which minimizes the Akaike information criterion (AIC) as in Brogaard, Hendershott, and Riordan (2014). 20

21 s i,t = s i,t 1 + ψ i Trade i,t + υ i,t, (12) where Trade i,t is overall trading variable and ψ i captures the role of overall trading activity on pricing error component. 20 Noise in observed midquote prices and in longer-lived private information is captured by the pricing error component (Brogaard, Hendershott, and Riordan, 2014). 4.7 Open-close to close-open return variance ratios Market microstructure research considers informational efficiency, the extent of private information reflected by prices, as a market quality metric (Chordia, Roll, and Subrahmanyam, 2008). Higher ratios of open-to-close return variances to close-to-open return variances, with decreasing autocorrelation, is associated with higher private information incorporation into prices and, thus, higher informational efficiency (French and Roll, 1986; and Chordia, Roll, and Subrahmanyam). 21 To calculate the ratio of per hour open-to-close return variance to per hour close-to-open return variance, we follow a method similar to Chordia, Roll, and Subrahmanyam. We calculate open-to-close return variances and close-to-open return variances based on quote midpoint returns. Then, we divide each variance by the number of calendar hours over the subsample period. 4.8 Llorente, Michaely, Saar, and Wang (2002) private information measures In Llorente, Michaely, Saar, and Wang s (2002) model, returns generated by hedging trades tend to reverse, while returns generated by speculative trades tend to continue. By focusing on the opposite impacts of hedging and speculative trading on return autocorrelation, Llorente, 20 As in the literature, I assume error terms in equations (10) and (12) are uncorrelated: Cov(μ t, υ t ) = By comparing trading and non-trading hours variance ratios, French and Roll (1986) find that informed traders trading on their private information is the main factor behind high trading-time variance. Barclay, Litzenberger, and Warner (1990) document a positive impact of private information on return variance and volume on the Tokyo Stock Exchange. Employing variance ratio tests, Chordia, Roll, and Subrahmanyam (2008) find that reduced tick sizes enhance stock price informational efficiency by encouraging trading on private information. 21

22 Michaely, Saar, and Wang develop a private information trading measure. Llorente, Michaely, Saar, and Wang (2002) present different specifications of the private information measure. The most commonly used specification in the literature is as follows: 22 r i,t+1 = C0 i + C1 i r i,t + C2 i V i r it + error it+1 where r i,t is the firm i s daily returns and V i,t is the logarithm of firm i s daily turnover, detrended by subtracting a 200-days moving average. The coefficient C2 i gives the amount of informationbased trading and higher C2 i values indicate more information-based trading (as opposed to noise or liquidity trading) (Llorente, Michaely, Saar, and Wang). While the literature mainly uses the aforementioned specification, Llorente, Michaely, Saar, and Wang (2002) state that in the theoretical model, volume and return have a non-linear relation, and it is the squared volume that affects the subsequent period s returns (page 1036). Accordingly, their theory predicts that the relation between volume and return must be specified as: r i,t+1 = C0 i + C1 i r i,t + C2 i V 2 it r it + error it+1, where all variables are defined as the variables in first specification. In Llorente, Michaely, Saar, and Wang s (2002) model, it is the firm-specific private information and hedging needs that generate trading. Thus, in the following specification they eliminate the market-wide component of volume and return, and then capture the impact of information-based trading as follows: ResR i,t+1 = C0 i + C1 i ResR i,t + C2 i ResV it ResR it + error it+1, where residual volume (ResV ) and return (ResR i,t i,t ) are obtained from market models of volume and market return. Following, Llorente, Michaely, Saar, and Wang, we consider S&P 500 daily 22 Studies such as Fernandes and Ferreira (2008) and Fernandes and Ferreira (2009) employ this measure to examine stock price informativeness under different settings. Fernandes and Ferreira (2008) find that while cross-listing increases stock price informativeness in developed countries, it decreases stock price informativeness in emerging markets. Using the same measure, Fernandes and Ferreira (2009) find that enforcement of insider trading laws increases stock price informativeness in developed countries but does not affect stock price informativeness in emerging markets. 22

23 return as the market return, and value-weighted daily volume of S&P 500 firms as the daily market volume. We regress volume and returns of individual stocks on market volume and returns, and obtain residual volume and returns. We use these residuals to capture firm-specific private information. In addition to the three main specifications summarized above, Llorente, Michaely, Saar, and Wang (2002) extend the first specification by including market return, number of trades, and replacing detrended turnover in the first specification with daily turnover of a stock without detrending. We also examine these three extended specifications in my analysis. 4.9 Amihud (2002) price impact measure We calculate Amihud s (2002) price impact measure as the ratio of daily absolute stock returns to dollar volume (as in Goyenko, Holden, and Trzcinka, 2009). Specifically, we define Amihud s price impact ratio as: Average( r t Volume t ), where r t is the stock return on day t and Volume t is the dollar volume on day t. Since the ratio is undefined for zero volume days, it is calculated only for non-zero volume days. Studies, such as Ferreira, Ferreira, and Raposo (2011) and Fresard (2012), employ Amihud price impact measure in stock price informativeness examinations Roll price impact Goyenko, Holden, and Trzcinka (2009), extending Roll s spread measure, develop a Roll price impact measure and show that Amihud s price impact and Roll s price impact are highly correlated. Thus, we also examine Roll s price impact as a low-frequency price impact measure and define it as follows: 23 Ferreira, Ferreira, and Raposo (2011), employing Amihud s illiquidity measure, find a negative relation between stock price informativeness and board independence. Fresard (2012) also utilizes this measure and finds that stock price informativeness affects managers saving decisions. 23

24 where P t is the last observed price on day t. where i is the time interval. 5.0 Empirical analyses and results Roll = { 2 Cov( P t, P t 1 ) if Cov( P t, P t 1 ) < 0 0 if Cov( P t, P t 1 ) 0 Roll impact i = Roll i, Average daily volume i 5.1 Return synchronicity and trading-conveyed information analysis Our first objective is to determine the relation between firm-specific return synchronicity measures (the R-squared, firm-specific variation, and systematic variation) and stock price informativeness measures (Hasbrouck s (1991a-b) information measures). To this end, we adopt a similar empirical approach to those of Durnev, Morck, Yeung, and Zarowin (2003) and Chan and Chan (2014). Particularly, we regress informativeness measures on return synchronicity measures. We hypothesize that, after controlling for appropriate factors, stocks with higher synchronicity should reflect less private and total information. Thus, we expect stock return synchronicity to have a negative coefficient in my regressions. Specifically, we estimate the following regression: Y i,t = β 0 + β 1 X i,t + β j Control j,t + ε i,t where dependent variables (Y i,t ) are total information and private information measures. My variables of interest (X i,t ) include the natural logarithms of firm-specific variation, market-wide variation, and R-squared measures. All models include firm and day of week fixed effects. Standard errors used to compute t-statistics, shown in parentheses, are adjusted for 24

25 heteroscedasticity and within firm clustering. To enable easy interpretation of our findings, we normalize all variables with their means and standard deviations following Wooldridge (2012). 24 Our control variables include market capitalization, volume, market volatility, price and adjusted bid ask spread (ASPR). We control for volume because volume provides information about the quality of traders information (Blume, Easley and O Hara, 1994). Since size can be a proxy for information asymmetry (Llorente, Michaely, Saar, and Wang, 2002), we control for market capitalization. Increased volatility may be associated with higher information incorporation into stock prices (Chordia, Roll, and Subrahmanyam, 2008), thus we control for volatility. Changes in liquidity can affect information incorporation into stock prices (Chordia, Roll, and Subrahmanyam), hence we control for liquidity (ASPR). We calculate ASPR as in Patton and Verardo (2012). We divide the trading day into five minute intervals and calculate the difference between bid and ask quotes as a proportion of the midquote in percent. We adjust spreads for time trends by regressing daily spread on the day of week dummies. The residuals of this regression are the adjusted proportional quoted spreads (ASPR) Descriptive statistics for return synchronicity and price informativeness analysis Table 2 presents the descriptive statistics of variables that are employed in the tradingconveyed information and return synchronicity relation examination. The mean R-squared, around 30%, indicates that only 30% of intra-daily return variation is explained by the market returns and 70% of intra-daily return variation is firm-specific. It is interesting that my mean R-squared is very close to that of Roll (1988). Even at an intra-daily level, market returns do not explain a significant portion of the stock return variations. However, R-squared values at 5 th and 95 th percentile show 24 Foucault and Fresard (2014) employ a similar approach. Due to normalization, I do not report the constant term, see Wooldridge (2012) for details. 25