2. Literature Review and Hypothesis Development
2.4 Simultaneity of the Equity Spread and Firm’s Disclosure Practice
Several past studies, including theoretical and empirical ones, have indicated that simultaneity may exist in the determination of bid-ask spread and firm’s disclosure policy.
Dye (1985) designs a theoretical model in which the information asymmetry between managers and investors can influence firms’ disclosure policies. Lang and Lundholm (1993) analyzes the determinants of voluntary disclosure policy and argues that there is simultaneity in the determination of bid-ask spread and disclosure practice. Welker (1995) suggests that disclosure policy choice may be influenced by the level of information asymmetry between management and uninformed investors as well as other determinants of bid-ask spreads.
Hence, we follow these works and develop our second hypothesis as follows,
Hypothesis.2: The determination of the spread and firm’s disclosure practice is simultaneous.
If the simultaneity indeed exists, employing the OLS procedure for estimation will generate inconsistent estimates, and the inferences are invalid. Accordingly, we utilize the determinants of the disclosure practice and the spread as instrumental variables to construct a system of simultaneous equations, and employ three-stage least squares (3SLS) method to estimate and test the coefficients in our simultaneous equations. Furthermore, we also use a more robust estimation method, the general method of moments (GMM), to estimate and test the simultaneous equations. If the coefficient of our liquidity measure (the quoted spread, effective spread, or information asymmetry component) did not reveal strongly explanatory ability to the disclosure practice, we will argue that there might be no simultaneity existing in the determination of the spread and disclosure practice.
3. Estimating the Measures of Equity Liquidity and the Information Asymmetry Component
3.1 The Model
In this section, we introduce the model of liquidity measures and information asymmetry component of the spread used in this study.
The first two measures of equity liquidity are the quoted half-spread and the proportional quoted half-spread suggested by Stoll (1978a, 1978b, 1989, 2000), Welker (1995)5, and others. The proportional quoted half-spread (PSP) is defined as the quoted half-spread divided by the quote midpoint. The quoted half-spread (QSP) and quote midpoint (Q) are defined as proportional quoted half-spread (PSP) can be written as
(3).
The other two measures of market liquidity are the effective spread and the relative effective spread, and the information asymmetry component is decomposed from the effective spread. We follow the model suggested by Huang and Stoll (1994), Lin (1992), Stoll (1989) and Lin, Sanger, and Booth (1995):
5 Welker (1995) uses the proportional quoted bid-ask spread instead of the proportional quoted half-spread as his liquidity measure. The only difference of these two liquidity measures is that the former uses the bid-ask spread as numerator and the latter uses the half of bid-ask spread.
(4),
is the one-half signed effective spread, defined as the transaction price minus the prevailing quote midpoint, with zi,t <0 for a sell order and zi,t >0 for a buy order. Van Ness et al. (2001) indicate that the idea of this model is that both bid and ask quotes at time t+1 will have quote revisions of λ to reflect possible adverse information revealed by the trade at time t. Since z λ reflects the quote revision in response to a trade as a fraction of the effective spread, it can be viewed as the information asymmetry component of the effective spread. The effective spread is defined as the absolute value of the one-half signed effective spread:
(6), midpoint for the transaction at time t of firm i. In addition, we define the relative effective spread (RESP) as the effective spread divided by the prevailing quote midpoint:
(7).
To estimate our measures of equity liquidity and the information asymmetry component of the effective spread, we obtain the intraday transaction and quote data from the Trade and Quote (TAQ) database which contains intraday data of every trades and quotes for all securities listed on the New York Stock Exchange (NYSE) and American Stock Exchange (AMEX), as well as Nasdaq National Market System (NMS) and SmallCap issues.
For each security in our sample, we use intraday quotes to calculate the quoted half-spread (QSP) and the proportional quoted half-spread (PSP). We first compute the quoted half-spread and the proportional quoted half-spread by each quote during the normal transaction time of a day and then calculate daily averages of these two measures. After obtaining the daily averages, we then use them to calculate annual averages of the quoted half-spread and the proportional quoted half-spread for every security in our sample.
To estimate the model of the effective spread and the information asymmetry component, we additionally need intraday transaction data besides quote data. Following the procedure of Lin, Sanger, and Booth (1995), the transaction time, the trade price, and the prevailing bid and ask prices are identified for each transaction6. After obtained the transaction data with prevailing quotes, we estimate Equation (4) by OLS to obtain the daily estimate of the information asymmetry component,λˆ, for each equity in our sample by using all transaction data with prevailing quotes in each day, and then calculate the annual average information asymmetry component of each firm7. To obtain the real cost of information asymmetric risk induced by informed trading, we multiply each stock’s annual average information asymmetry component by annual average of its effective spread, so our measure of information asymmetry cost of the effective spread is defined as follows,
(8).
The effective spreads and relative effective spreads are calculated from the transaction
6 Lin, Sanger, and Booth (1995) follow the suggestion of Ready (1991) to identify the prevailing quotes for each transaction as the quotes that are in effect five seconds earlier and are eligible for inclusion in the National Market System and NASD best bid and offer calculation. After identifying the prevailing quotes for each trade and deleting the transaction data without prevailing quotes, there are 127,217,081 transaction data with prevailing quotes used in our study.
7 Following Lin, Sanger, and Booth (1995) and Van Ness et al. (2001), the logarithms of the transaction price and the quote midpoint are used to yield a continuously compounded rate of return for the dependent variable and a relative spread for the independent variable. This transformation can generate estimates of the information asymmetry components as a percent of the effective spread and reduce the problem of price discreteness.
data with prevailing quotes. For each security in our sample, we first compute the dollar effective spread and relative effective spread for each transaction during the normal transaction time of a day, and then calculate their daily averages for each trading day during our studying period. Finally, the annual averages of them are calculated by using their daily averages.
4. The Determinants of Equity Liquidity and Disclosure Practice
In order to construct a system of simultaneous equations of our liquidity measure and the S&P T&D ranking for 3SLS and GMM estimation, we need to specify the models of the liquidity measure and the T&D final ranking. In each model, the dependent variable of the other equation will be used as one of the explanatory variables; that is, both the liquidity measure and the T&D ranking appear as endogenous variables in the simultaneous equations.
Besides, other determinants of the liquidity measure and disclosure practice must be used as exogenous instrumental variables and be controlled for the estimation and tests in this simultaneous system. Because there is more doubt about the extent of the quality of S&P T&D ranking measuring the disclosure practice, the determinants of T&D ranking have to satisfy several conditions for instrumental variables estimation. We discuss these conditions and filter out some inadequate instrumental variables later in Chapter 6.
4.1 The Determinants of the Liquidity Measure
Previous cross-sectional studies of spreads suggest a number of spread determinants other than disclosure policy that should be controlled in the empirical analysis (Welker, 1995).
The closing price, daily dollar volume, return volatility, number of trades per day, and market value, are most common determinants of the spread adopted in these studies such as Agrawal et al. (2004), Brockman and Chung (2003), LSB (1995), Stoll (2000), Van Ness et al. (2001), Welker (1995), and others. In particular, Stoll (2000) models the source of the spread, and find that the closing price, daily dollar volume, return volatility, number of trades per day, and market value, have significant relations to the proportional quoted half-spread. He finds that these variables can explain over 65 percent of the cross-sectional variance in proportional quoted half-spread. Therefore, in addition to the T&D ranking, we follow Stoll (2000) and use stock’s closing price (CLP), daily dollar volume (DOLVOL), return standard deviation
(RETSTD), number of trades (N), and market value (MKV) as our preliminary candidates of control variables of our liquidity measures (, i.e. the proportional quoted half-spread, the quoted half-spread, the effective spread, the relative effective spread, and the information asymmetry component). The definitions of these control variables of liquidity measures are described as follows:
CLPi= the average of closing prices of all trading days during our studying period for firm i. (9)
DOLVOL = the average of daily dollar volume of all trading days during our studying i
period for firm i. (10)
RETSTD
i = the standard deviation of stock’s daily returns in the prior year for firm i.(11)
N
i = the average of daily number of trades during our studying period for firm i. (12)MKV
i = the average of monthly market value during our studying period for firm i.(13)
According to the empirical evidence of Stoll (2000) and other studies mentioned above, we predict that the increases in the dollar volume, number of trades, and market value increase the liquidity of equity and lower the spread. The stock’s return volatility reflects the risk of price change of a stock, and thus we predict that higher return volatility is associated with higher spread. Price controls for the effect of discreteness and is an additional proxy for risk in that low price stocks tend to be riskier (Stoll, 2000).Therefore, we predict that price is positively related with the quoted half-spread, the effective spread and the information asymmetry component, but is negatively related with the proportional quoted half-spread, and
the relative effective spread because the quote midpoint, the denominator used to calculate these two measures, is highly related to the closing price.
4.2 The Determinants of Disclosure Practice
The determinants of disclosure practice used in our study are mainly referred to Lang and Lundholm (1993), Welker (1995), and Ho and Wong (2001). Lang and Lundholm (1993) find that both the market adjusted return and firm size are positively related to disclosure policy, and that the disclosure policy is negatively related to return standard deviation and return-earnings correlation. Welker (1995) follows the findings of Lang and Lundholm (1993) and uses share price, security offering, market adjusted return, and return standard deviation as the determinants of disclosure practice. Ho and Wong test a theoretical framework relating four major corporate governance attributes to the extent of voluntary disclosure provided by listed firms in Hong Kong. They follow several previous works investigating the decision of voluntary disclosure and use firm size (Chow and Won-Boren, 1987), asset-in-place (Hossain et al., 1994), financial leverage (Bradbury, 1992), profitability (Meek et al. 1995) and industry type (Meek et al., 1995) as control variables in their empirical model. Thus, following these studies, we preliminarily choose firm size (Size), return standard deviation (RETSTD), closing price (CLP), asset-in-place (AIP), financial leverage (LEV), profitability (PROFIT), and dummy variable of industry type as the initial candidates of control variables of firm’s disclosure practice. The empirical findings of previous studies mentioned above suggest that the firm size, price, asset-in-place, and profitability are positively related to firm’s disclosure practice, and that return volatility, and financial leverage are negatively related with firm’s disclosure quality.
The control variables of disclosure practice that we didn’t define yet in section 4.1 are defined as follows:
Size = the total assets of firm i at the end of 2002. (14) i
AIP = the ratio of net book value of fixed assets to total assets of firm i at the end of i
2002. (15)
LEV = the ratio of total debt to total equity of firm i at the end of 2002. (16) i
PROFIT
i= the return on capital employed at the end of 2002. (17)D1 =1, when the firm’s S&P Industry Index Code belongs to the Financials group i
with the codes 700-719, and zero otherwise. (18)
D2 =1, when the firm’s S&P Industry Index Code belongs to the Information i
Technology group with the codes 900-921, and zero otherwise. (19)
5. Data
The report of S&P Transparency and Disclosure study (Patel and Dallas, 2002) only provides the T&D rankings for the constituent firms of S&P 500 index, so the companies studied in this paper are these constituent firms. We use annual basis T&D final ranking (AFR) and composite basis T&D final ranking (CFR) respectively as the proxy for firm’s corporate governance. Because the S&P T&D study report is published on October 16, 2002, we choose whole trading days of 2002 as our studying period.
There are many empirical studies comparing dealer and auction markets, such as NASDAQ and NYSE (Barclay et al, 1999; Huang and Stoll, 1996), and Stoll (2000) indicates that the empirical evidence of these studies shows that market design appears to have an effect on spread. In particular, the spreads in dealer markets are wider than those in auction markets because dealers may have more market power in dealer markets. The reason is that dealers or market makers with stronger market power are expected to increase their revenues by widening spreads. In order to eliminate this difference among the constituent stocks of S&P 500 index, we only choose the stocks listed in NYSE. Under this condition, our sample size becomes 424 stocks. For the same reason, the intraday data used to estimate and calculate our liquidity measures are only the transactions and quotes taken place in NYSE.
The daily intraday transaction and quote data for these 424 stocks are obtained from the Trade and Quote (TAQ) database, which has already been introduced in section 3.2. We use this database to obtain intraday transaction and quote data such as transaction times, transaction prices, and quoted bid and ask prices8. The daily number of trades, daily dollar volume, and closing price of each stock are also obtained from this database. In addition, we
8 There are 301,845,521 intraday quotes and 146,630,782 transaction data of our sample equities obtained from the TAQ database, and we use the data to calculate and estimate our two measures of equity liquidity and the information asymmetry component.
download stock’s daily returns without dividends from the CRSP database to calculate the return standard deviation in prior year. Finally, the accounting data used to calculate other selected variables in our study are all obtained from the Compustat database. After calculating the values of all selected variables, we delete the firm with at least one variable that has missing value. This step reduces our sample size to 341.
6. Research Design
The research design and methodology of this study are described in this chapter. We first calculate the variation inflation factors (VIFs) of the control variables of the liquidity measures and those of firm’s disclosure practice. The variation inflation factor measures the extent of the multicolinearity existing in the selected explanatory variables. The explanatory variables with higher variation inflation factors have more serious multicolinearity problem and are more likely affect the estimation result of the regression. After calculate the variation inflation factors (VIFs) of the control variables of our liquidity measures we find that VIFs of daily dollar volume (DOLVOL), market value (MKV), and daily number of trades (N) are larger than other control variables. When we omit any two variables of them, VIFs of the all independent variables of the liquidity measures will be lower than 2 which means that the multicolinearity problem is solved. Because the OLS coefficient estimates of market value and daily number of trades are less significant than daily dollar volume, and daily dollar volume is more often used in microstructure literature than these two variables, we omit them and keep daily dollar volume in the equation of the equity liquidity. Therefore, the control variables of our liquidity measure are now the closing price (CLP), daily dollar volume (DOLVOL), and return standard deviation in prior year (RETSTD). The VIFs of the predetermined control variables of firm’s disclosure practice are all less than 2, and indicate that there is no serious multicolinearity problem existing in these selected control variables.
The second step is to filter out inadequate instrumental variables for instrumental variables estimation methods, 3SLS and GMM. Wooldridge (2002) indicate that the key condition on instrumental variables estimation is that the selected additional instruments for an endogenous variable must be partially correlated with it once all the other exogenous
variables in all equations have been netted out9. In order to check this condition, we require the linear projection of the endogenous variable onto all exogenous variables and then test if the selected instruments are partially correlated with the endogenous variable under OLS procedure. This is called the first-stage regression10. For the all liquidity measures, the results of the first-stage regression reveal that the three control variables, the closing price (CLP), daily dollar volume (DOLVOL), and return standard deviation in prior year (RETSTD), are strongly partially correlated with our liquidity measures. For S&P T&D final rankings, the results of the first-stage regression reveal that only firm size (SIZE), and asset-in-place (AIP) are partially correlated with composite basis final rankings, and that firm size (SIZE), asset-in-place (AIP), and return standard deviation (RETSTD) are partially correlated with annual basis final rankings. Therefore, after we exclude inadequate instrumental variables from the equations, our simultaneous systems of equations can be constructed as follows:
,i Liquidity represents the liquidity measure, and can be replaced by any of our liquidity i
measures: QSP, PSP, ESP, RESP, and the information asymmetry component (INF)11.
In addition to ordinary least squares (OLS), two other advanced estimation methods,
9 See Wooldridge (2002), chapter 5 and chapter 6.
10 We use the “first” command in the “proc syslin” program of SAS software to obtain estimation and test results of the first-stage regression
11 The values ofQSPi,ESPi, and INFi are so small that our estimated coefficients of the control variables of these liquidity measures are also very small, thus we multiply these measures by 100. Consequently, the unit of these measures becomes cents.
three-stage least squares (3SLS) and generalized method of moments (GMM), are applied to estimating these systems of simultaneous equations at last.
7. Empirical Results and Analysis
7.1 Summary Statistics and Correlations
Panel A of Table 1 shows the descriptive statistics of our five liquidity measures and their control variables. Our sample period is from January 1 2002– December 31 2002, 252 trading days. The mean of quoted half-spread (QSP) is about 2.2046 cents per share, and its range is about 3.522 cents. The mean of proportional quoted half-spread (PSP) is around 0.0716 percent with the range from 0.0281 percent to 0.3220 percent. The average effective spread (ESP) is 1.6166 cents with the range about 2.9434 cents, and is about 73 percent of the quoted half-spread. The finding that the average effective spread is less than the average proportional quoted half-spread is consistent with the argument suggested by Lin, Sanger, and Booth (1995)12. The relative effective spread (RESP) has the mean about 0.0519 percent which is about 72 percent of the proportional quoted half-spread, and its range is between 0.0218 percent and 0.2170 percent. The information asymmetry cost of the effective spread (INF) has the average value about 0.6577 cents, and its range is from 0.2172 cents to 1.3402 cents. The average closing price (CLP) for our sample is approximately $38.01, and the range is between $4.56 and $121.73. The mean of daily dollar volume (DOLVOL) is around $66.64 millions and the sample range is from $ 4.41 millions to $610.33 millions. The return volatility (RETSTD) has the average value about 0.0264, and the sample range is from 0.0138 to 0.0768. The Pearson correlation coefficients of our five liquidity measures and their control variables are shown in Panel B of Table 2. There is one thing catching our attention: the information asymmetry component, quoted half-spread, and effective spread are strongly
Panel A of Table 1 shows the descriptive statistics of our five liquidity measures and their control variables. Our sample period is from January 1 2002– December 31 2002, 252 trading days. The mean of quoted half-spread (QSP) is about 2.2046 cents per share, and its range is about 3.522 cents. The mean of proportional quoted half-spread (PSP) is around 0.0716 percent with the range from 0.0281 percent to 0.3220 percent. The average effective spread (ESP) is 1.6166 cents with the range about 2.9434 cents, and is about 73 percent of the quoted half-spread. The finding that the average effective spread is less than the average proportional quoted half-spread is consistent with the argument suggested by Lin, Sanger, and Booth (1995)12. The relative effective spread (RESP) has the mean about 0.0519 percent which is about 72 percent of the proportional quoted half-spread, and its range is between 0.0218 percent and 0.2170 percent. The information asymmetry cost of the effective spread (INF) has the average value about 0.6577 cents, and its range is from 0.2172 cents to 1.3402 cents. The average closing price (CLP) for our sample is approximately $38.01, and the range is between $4.56 and $121.73. The mean of daily dollar volume (DOLVOL) is around $66.64 millions and the sample range is from $ 4.41 millions to $610.33 millions. The return volatility (RETSTD) has the average value about 0.0264, and the sample range is from 0.0138 to 0.0768. The Pearson correlation coefficients of our five liquidity measures and their control variables are shown in Panel B of Table 2. There is one thing catching our attention: the information asymmetry component, quoted half-spread, and effective spread are strongly