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PAGE 1 1 TWO ESSAYS ON EFFECTS OF INFORMATION AND LIQUIDITY IN ASSET PRICING By THOMAS W. BARKLEY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGR EE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007 PAGE 2 2 2007 Thomas W. Barkley PAGE 3 3 To my parents. PAGE 4 4 ACKNOWLEDGMENTS I would like to sincerely thank Andy Naranjo (my supervisory committee chair), and Mahen Nimalendran (my supervisory committ ee cochair), for all their guidance, encouragement, and advice. I would also like to thank Jason Karceski, Alex Trindade and Milena Petrova for their invaluable comments. I would like to gratefully acknowledge the suggestions from seminar participants at t he University of Florida, Syracuse University, the University of Delaware, Tulsa University, and the University of Massachusetts (Boston). Finally, I am deeply appreciative of the support I received throughout this process from my sister, Sharon Barkley, a nd my current and former colleagues, Aaron Gubin and Xiaohui Gao. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 9 ABSTRACT ................................ ................................ ................................ ................................ ... 10 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 11 2 DETERMINANTS AND TIME VARIATION OF PRICE DISCOVERY: EVIDENCE FROM THE S&P 500 INDEX ACROSS STOCKS, FUTURES, AND OPTIONS MARKETS ................................ ................................ ................................ ............................. 15 Introduction ................................ ................................ ................................ ............................. 15 Price Discovery in Cash and Derivatives Markets ................................ ................................ 17 Research Methodology ................................ ................................ ................................ ........... 19 Lead L ag Relations ................................ ................................ ................................ ......... 20 Information Shares of the Markets ................................ ................................ .................. 21 Generalized Information Shares of the Markets ................................ .............................. 24 Data and Summary Statistics ................................ ................................ ................................ .. 25 Data ................................ ................................ ................................ ................................ .. 25 Prices for the SPDRs ................................ ................................ ................................ 25 Futures prices for the S&P 500 index ................................ ................................ ...... 25 Options prices for the S&P 500 index ................................ ................................ ...... 26 Summary Sta tistics ................................ ................................ ................................ .......... 26 Price Discovery ................................ ................................ ................................ ....................... 28 Lead Lag Relations and Related Results ................................ ................................ ......... 28 Results ................................ ................................ ................................ .......................... 29 Generalized Information Shares of the Markets and Related Results ............................. 30 Determinants of Information Shares through Time ................................ ................................ 32 Transaction Cost Proxies ................................ ................................ ................................ 33 Trading Activity Proxies ................................ ................................ ................................ 34 Macroeconomic News and Calendar Events ................................ ................................ ... 36 Determinants of Information Shares ................................ ................................ ............... 37 Conclusion ................................ ................................ ................................ .............................. 40 PAGE 6 6 3 WHERE IS THE LIQUIDITY? INFORMATION AND TRADING COSTS IN ASSET PRICING ................................ ................................ ................................ ................................ 63 Introduct ion ................................ ................................ ................................ ............................. 63 Research Methodology ................................ ................................ ................................ ........... 66 General Formulation of Latent Variable Models with Measurement Errors .................. 67 Simple Three Indicator/One Latent Variable Model ................................ ....................... 67 Data and Summary Statistics ................................ ................................ ................................ .. 70 Data ................................ ................................ ................................ ................................ .. 70 Preliminary notation, definitions and explanations ................................ .................. 71 Description of liquidity measures ................................ ................................ ............ 72 Data filters ................................ ................................ ................................ ................ 74 Summary Statistics and Estimation of Latent Liquidity Variables ................................ 74 Analysis of Por tfolio Regression Results ................................ ................................ ............... 78 Robustness Checks ................................ ................................ ................................ ................. 83 Conclusion ................................ ................................ ................................ .............................. 84 4 CONCLUSION ................................ ................................ ................................ ..................... 117 APPENDIX A LIQUIDITY PROXIES USED IN RECENT STUDIES ................................ ...................... 119 B DATES OF LIQUIDITY AFFECTING EVENTS ................................ .............................. 128 LIST OF REFERENCES ................................ ................................ ................................ ............. 130 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 134 PAGE 7 7 LIST OF TABLES Table page 2 1 Market returns: summary statistics ................................ ................................ .................... 41 2 2 Lead lag parameter estimates ................................ ................................ ............................ 45 2 3 Gener alized information shares: summary statistics ................................ .......................... 46 2 4 Regression variables used to explain the generalized information shares ......................... 47 2 5 Selected explanatory variables: summary statistics ................................ ........................... 49 2 6 Components of traded volume with no announcement variables included: regression results ................................ ................................ ................................ ................................ 50 2 7 Components of traded volume with announcement variables included: regression results ................................ ................................ ................................ ................................ 51 2 8 Effective spreads with no announcement variables included: regression r esults .............. 53 2 9 Effective spreads with announcement variables included: regression results ................... 54 2 10 Components of traded volume and effective spreads with no announcement variables included: regression results ................................ ................................ ................................ 56 2 11 Components of traded volume and effective spreads with announcement variables included: regression result s ................................ ................................ ................................ 57 3 1 Liquidity measures for the NYSE/AMEX and Nasdaq markets: summary statistics ........ 86 3 2 Liquidity measures and latent liquid ity variables for the NYSE/AMEX markets: summary statistics ................................ ................................ ................................ .............. 88 3 3 Liquidity measures and latent liquidity variables for the Nasdaq market: summary statistics ................................ ................................ ................................ .............................. 89 3 4 Risk factors for the NYSE/AMEX markets: summary statistics ................................ ....... 90 3 5 Risk factors for the Nasdaq market: summary statistics ................................ .................... 91 3 6 Four factor model for the NYSE/AMEX markets: regression results ............................... 92 3 7 Four factor model for the Nasdaq market: regression results ................................ ............ 93 3 8 Six factor model for the NYSE/AMEX markets: regression results ................................ 94 3 9 Six factor model for the Nasdaq market: regression results ................................ .............. 95 PAGE 8 8 3 10 Six factor model with adjustment for tick size periods for the NYSE/AMEX markets: regression results ................................ ................................ ................................ 96 3 11 Six factor model with adju stment for tick size periods for the Nasdaq market: regression results ................................ ................................ ................................ ................ 98 3 12 Annualized mean daily returns on factor mimicking portfolios by tick size period for the NYSE/AMEX markets ................................ ................................ ............................... 100 3 13 Annualized mean daily returns on factor mimicking portfolios by tick size period for the Nasdaq market ................................ ................................ ................................ ............ 101 A 1 Description of liquidity proxies used in recent studies ................................ .................... 120 B 1 Chronology of important events affecting market liquidity ................................ ............ 129 PAGE 9 9 LIST OF FIGURES Figure page 2 1 Monthly averages of daily information shares for the stock, futures, and options markets based on orthogonalized impulse response functions ................................ .......... 59 2 2 Daily information shares for the stock, futures, and options markets based on orthogonalized impulse response functions ................................ ................................ ....... 60 2 3 Monthly averages of daily information shares for the stock, futures, and options markets based on generalized impulse response functions ................................ ................ 61 2 4 Daily information shares for the stock, futures, and options markets based on generalized impuls e response functions ................................ ................................ ............. 62 3 1 Cross sectional liquidity measures and their time variation ................................ ............ 102 3 2 Cross sectional latent liquidity variables and their time variation ................................ ... 113 3 3 Factor mimicking portfolio returns and their time variation ................................ ........... 114 PAGE 10 10 Abstract of Dissertation Presented to the Gradua te School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy TWO ESSAYS ON EFFECTS OF INFORMATION AND LIQUIDITY IN ASSET PRICING By Thomas W. Barkley August 2007 Chair: Andy Naran jo Cochair: Mahen Nimalendran Major: Business Administration Information and liquidity interact when asset prices are to be determined. I study these effects in the price discovery process of the S&P 500 index traded in the cash, futures and options mark ets, and document that transaction costs and market trading activity proxies are important determinants. I also study the liquidity risk premiums associated with stocks traded on different exchanges, and document that there are multiple aspects to liquidit y showing considerable variation over time. Empirical results suggest that some common liquidity measures can be consolidated into two latent liquidity variables: one arising from asymmetric information among traders and another from order processing or di rect transaction costs associated with trading the asset. Taken together, my research suggests that traders pay close attention to information asymmetries and fixed costs of trading when evaluating asset prices; this subsequently influences an informed inv should transact. PAGE 11 11 CHAPTER 1 INTRODUCTION Information asymmetry among market participants and transaction costs are important determinants of asset prices in addition to fundamental factors. In this stud y, I examine the effects of information asymmetry and transaction costs on price discovery and expected returns on assets. First, I consider how these effects relate to an asset that is traded in cash, futures and options markets, particularly looking at w hich market dominates in terms of price discovery. Second, I consider whether information asymmetry and transaction costs are priced factors. When pricing an asset it is important to consider whether there are characteristics associated with it, affecting its value, that are not observable to everyone. This may lead to some traders having an advantage over others because they know specific details about these characteristics. A second factor that should be considered when pricing an asset, no less important than the first, is its liquidity, that is, the relative ease that one will have in buying or low transaction cost. This simple definition reflects the complexity of the concept. Liquidity has These two factors, information asymmetry and liquidity, are closely related to each other. It is often the case that an asset that is hard to value, because it has idiosyncratic fea tures associated with it, will also be difficult to trade. For instance, an investor in the stock market is more likely to acquire stock in a Fortune 500 company that is closely followed by financial analysts and news reporters than in a small firm very fe w people have heard of. What might induce a rational investor to buy stock in the latter business, knowing that it may be difficult to sell the stock at a later date? If the investor has private information about the company and its growth opportunities, t hen the expected return on investment may be relatively easier to PAGE 12 12 to purchase shares in the company if it is believed that, even after all the associated transact ion costs, this is a worthwhile investment. It should be noted that information a trader has about an asset may be public or private. A publicly traded corporation that is subject to the scrutiny of many investors, whose shares are actively traded on a dai deal of public information available for those trying to estimate its stock price. Does this mean that the equity markets always correctly value these securities? Not at all mana gers of the in determining accurate stock prices, but this information may remain undisclosed to the public for considerable periods of time. Complex business transactions and complicated financial reporting may even allow information to become public in a manner that misrepresents the true health of the firm, obfuscating proper assessment of its value. A primary example in this regard is Enron, an innovative c experiencing a cataclysmic decline in value. Once its true worth eventually became known, following probing questions by investigative analysts and reporters, there was nothing the managem ent could do but declare bankruptcy. Private (inside) information had finally become public! In this study, both public and private information are considered albeit in slightly different contexts. An added complication arises when trying to value assets t hat trade in more than one location. Can the price of gold in New Jersey be that much different from its implied price from derivative instruments (futures and options contracts) that are traded at the New York Mercantile Exchange (NYMEX)? If there are pri ce discrepancies, arbitrageurs will match buyers in one PAGE 13 13 market with sellers in the other, until the price differences disappear. In general, price discovery will be concentrated in the market where trading activity is characterized by low transaction costs and greater liquidity. 1 In some cases, however, informed traders may choose to pay slightly greater transaction costs if it allows them to disguise their trades, reduce price impacts, or increase their leverage. This study seeks to disentangle these effec ts in asset pricing. My goal is to answer four primary research questions. First, where does price discovery take place when traders may act upon information they possess but have a choice of markets in which to do so? Second, what are the determinants aff ecting the proportion of price discovery that takes place in each of these and how much to order processing costs? Fourth, can this liquidity decomposition be u sed to improve upon current asset pricing models? In order to answer these questions, my study investigates how the S&P 500 index is traded in the cash, futures and options markets, and how the liquidity of stocks traded in several equity markets affects t heir returns. First, I investigate the price discovery process for the S&P 500 index across stock, futures, and options markets simultaneously. I use transaction level data at the one minute interval and find that there is considerable variation in the inf ormation shares through time and across markets, with a significant shift in the information shares from the futures market to the options market coinciding with the introduction of an automated quotes system for options prices on March 20, 1995. I also fi nd that transaction costs and market trading activity measures are important determinants in explaining information shares across markets and through time. 1 Price discovery is the general process used to determine the price of a specific a sset. The price is dependent on market conditions that affect supply and demand for the asset. PAGE 14 14 Second, I investigate the effects of different sources of liquidity on asset pricing. I show that li quidity measures can be consolidated into two latent liquidity variables: one arising from asymmetric information among traders regarding an asset and another from order processing or direct transaction costs associated with trading the asset. Using transa ction level data on stocks from the New York (NYSE), American (AMEX) and Nasdaq exchanges over an 11 year period from January 1993 to December 2003, I show that some previously considered metrics of liquidity are more closely correlated with the informatio n liquidity factor, whereas others are more closely correlated with the order processing liquidity factor. When both of these factors are used in multibeta asset pricing models that include Fama French and momentum factors, I find that there are significan t premiums associated with both liquidity factors. Controlling for the Fama French and momentum factors, a trading strategy that involves purchasing illiquid stocks and shorting liquid stocks produces statistically and economically significant annualized e xpected returns of approximately 2.7 to 3.1%. Additionally, I find that as tick size changed in the NYSE/AMEX and Nasdaq markets from eighths to sixteenths to decimals, there were shifts in the proportion of asset liquidity that can be attributed to each o f these two components. PAGE 15 15 CHAPTER 2 DETERMINANTS AND TIM E VARIATION OF PRICE D ISCOVERY: EVIDENCE F ROM THE S&P 500 INDEX AC ROSS STOCKS, FUTURES AND OPTIONS MARKET S Introduction The price discovery process across financial markets continues to generate sub stantial interest among academic researchers, regulators, and other financial market participants [e.g., Hasbrouck (1995, 2003), Easley et al. (1998), Huang (2002), and Chakravarty et al. (2004)]. In financial markets, price relevant information is often q uickly disseminated to market participants through news releases, press conferences, analyst reports, and security and financial statement price, for instance, thr ough deductive reasoning based on piecing together information they acquired about that firm (mosaic theory). The enduring interest in understanding the transmission of information into prices reflects its importance for market participants. A better under standing of the price discovery process and its associated effects has implications for market efficiency and for mitigating potentially harmful contagion effects transmitted across financial markets. The price discovery process also has implications for w here an investor trades as well as their asset allocation and hedging decisions. I examine the determinants and time variation of the price discovery process across stock, futures, and options markets for the S&P 500 index. To analyze the permanent compone nts of price innovations simultaneously across these markets, transaction level data and generalized impulse response functions from a vector error correction model are used to calculate the information share associated with a particular market on a daily basis over the sample period from January 29, 1993 to December 31, 1996. The begin date of the sample corresponds to the corresponds to the last available date for t he options on the S&P 500 index traded on the Chicago PAGE 16 16 Board Options Exchange (CBOE). 2 Depositary Receipts (SPDRs). SPDRs track the S&P 500 index and are traded on the American Stock Exchange. T he second set of prices I use is for futures on the S&P 500 traded on the Chicago Mercantile Exchange (CME), while the third set of prices is for options on the S&P 500 index traded on the CBOE. Three open questions are addressed using the estimated daily information shares for the S&P 500 stock, futures, and options markets over the 1993 to 1996 sample period. First, where does price discovery take place across the three markets? Second, does the price discovery revealed in each market vary over time? Thir d, what are the determinants of where price discovery occurs? In answering these three questions, I contribute to the extant literature in several ways. I show where price discovery takes place by examining the three markets simultaneously. Additionally, I use a longer sample period than has been investigated to date. Finally, I provide new evidence on the time variation of price discovery and the determinants of where price discovery takes place. My results suggest that there is considerable time variation in the price discovery process across stock, futures, and options markets. Consistent with previous findings in the literature, the futures market is often the greatest source of price discovery. Prior to March 20, 1995, the smallest amount of information was impounded in the options market. After March 20, 1995, much higher levels of information shares can be attributed to the options market at the expense share. T he shift in information shares between the options and the futures markets occurred when the CBOE began an automated quote system for options prices. This change greatly increased 2 The CBOE suspended the distribution of its data to the Berkeley Options Database on December 31, 1996 PAGE 17 17 the number of options series that were listed on the exchange. I also find t hat transaction costs and market trading activity play an important role in explaining the information shares for each of the markets. In particular, I find that effective spreads, anticipated and unanticipated volume levels, macroeconomic announcement sur prises, information share momentum, option expiration days, and certain months of the year are significant determinants of the information shares across each of the markets. Price Discovery in Cash and Derivatives Markets There is an extensive literature t hat examines the relations among cash and derivative markets. This research can be separated along two strands: an earlier literature that examines lead lag relations associated with temporary price discrepancies that arise between different markets and a second more recent literature that considers the permanent components of price innovations in markets. Chan (1992), for instance, considers intraday lead lag relations for stock index futures and cash markets and finds that the stock index futures market l eads the cash market. He argues that the futures market is the main source of marketwide information because of differential transaction costs and expected profits, whereas the cash market is the main source of firm specific information. Stephan and Whaley (1990) also examine lead lag relations, but they instead consider options versus cash markets. They find that the stock market leads the options market by fifteen minutes or more during daily trading. Chan et al. (1993) investigate the lead lag relations between stock prices and option prices and conclude that stocks lead options, but that this lead disappears when the tests are run using the average of the bid and ask instead of the transaction price. Finally, Fleming et al. (1996) consider the lead lag r elations among stock, option and futures markets, and provide a trading cost explanation for the relative rates of price discovery in these markets. Their results suggest that for individual stocks the lower direct trading costs and greater liquidity in th e stock market cause it to lead the options market, with PAGE 18 18 leverage effects not having a strong influence. However, for index products, the derivative markets offer substantially lower transaction costs to investors, and typically the futures market tends to lead both the options market and the underlying index market. Looking at the second strand of the literature that examines the permanent components of price innovations in markets, Hasbrouck (1995, 2003) uses orthogonalized impulse response functions from a vector error correction model to measure the information share associated with a particular market. The information share is defined as the proportion of the common implicit efficient price innovation variance that can be attributed to that market. For the 30 stocks comprising the Dow Jones Industrial Average from August to October 1993, Hasbrouck (1995) applied his methodology to the New York Stock Exchange (NYSE) and various regional exchanges on a pairwise basis and found that price discovery is conce ntrated at the NYSE where the median information share is 92.7%. More recently, Hasbrouck (2003) also examined the permanent component of price innovations between various exchange traded funds (such as the S&P 500, S&P 400 Mid Cap index, and Nasdaq 100 in dex), floor traded index futures contracts, electronically traded, small denomination futures contracts (E minis), and sector funds representing component industry portfolios of the S&P 500 index. Over his three month sample period from March 1, 2000 to Ma y 31, 2000, Hasbrouck found that price discovery is still prevalent in the futures market for the S&P 500 and Nasdaq 100 indexes. However, the results are less clear for the S&P 400 Mid Cap index, with the results suggesting that price discovery prevails i n the cash market (the exchange traded fund). discovery in different financial markets. Huang (2002), for instance, examined price discovery on the Nasdaq exchange taking pla ce between electronic communication networks (ECNs) and PAGE 19 19 more traditional market makers, while Chakravarty et al. (2004) investigated information shares for the stock and options markets for sixty different stocks listed on the NYSE for the five year period from 1988 to 1992. Chakravarty et al. (2004) found that the information share of options markets is about 17%. Pursuing a different line of research that examines where informed traders trade, Easley et al. (1998) developed an information based model rela ting the transaction volume in the options market to stock prices. Their model predicted an informational role for the volume n volumes contained information about future stock prices. In my study, I further extend the literature by examining the price discovery process simultaneously across three markets. This is done by considering lead lag relations following the approach of t he first strand of literature, and also by considering information shares for each of the three markets. Rather than look at where price discovery takes place with results for an entire period, I estimate information shares on a daily basis in order to stu dy the time variation of that price discovery and its determinants. Research Methodology I first describe the vector error correction model (VECM) I use to examine the lead lag ere orthogonalized impulse response functions are employed to calculate information shares for the three markets. I then describe a modified approach using generalized impulse response functions. An attractive feature of the generalized impulse response fu nction approach is that I can obtain point estimates of the information shares in contrast to the typical ranges obtained using orthogonalized impulse response functions. I calculate the information share relevant to each market on a daily basis using one minute intraday data and then analyze how these information PAGE 20 20 shares change over time. Finally, I examine the determinants of the information shares across the three markets. Lead Lag Relations Similar to earlier studies, I use a vector error correction mode l to examine the lead lag relations among the three different markets. There are three price variables, representing the midpoint of bid and ask prices of the SPDRs ( S t ), the futures price on the S&P 500 index ( F t ), and the underlying price implied by opti ons prices on the S&P 500 index ( O t ). These variables are collected in the (3 1) column vector p t (Equation 2 1). (2 1) A vector moving average process of the three price series may be formulated in terms of p t the change in the price vector from one period to the next, and e t a (3 1) vector of serially uncorrelated disturbances with mean zero and covariance matrix This formulation is shown in Equation 2 2, where is a polynomial in the lag operator. The covariance matrix of the error terms is shown in Equation 2 3. (2 2) (2 3) If it is assumed that a vector autoregressive (VAR) representation of order m exists for the price levels, then Equation 2 2 can be rewritten as Equati on 2 4. (2 4) where PAGE 21 21 This allows the VECM to be specified as shown in Equation 2 5. (2 5) where 0 is a (3 1) vector of intercept terms with elements j 0 i are (3 3) coefficient m atrices with elements jk ( i ), and is a (3 3) matrix with elements jk such that one or more jk 0. If prices in one market lead those in another, but not conversely, then the coefficient estimates will be significantly different from zero for the fir st variable, but not for the second. Information Shares of the Markets There is some debate in the literature about how price discovery across markets should be measured and what procedures should be implemented. Gonzalo and Granger (1995), for example, us e a common factor component weight in defining the contribution to price discovery in their market microstructure model, and this approach has been applied in several cases in the market microstructure literature. However, the results from using the Gonzal o and Granger approach differ at times from those of Hasbrouck (1995). 3 Baillie et al. (2002) and de Jong (2002) argue that both the Hasbrouck and Gonzalo Granger definitions of contribution to price definition is more concerned with the innovations, they conclude that it provides a more appropriate measure of the amount of information that is generated by each market. that the Pesaran and Shin approach has certain features that ma ke it attractive. In particular, 3 Lehmann (2002), Harris et al. (2002a), Baillie et al. (2002), de Jong (2002), and Harris et al. (2002b) provide a discussion of price discovery approaches. PAGE 22 22 (1998) approach can produce point estimates for information shares when the variance matrix for price innovations is nondiagonal. This does away with the necessity of calculating maxima and minima for the information shares for each of the markets. Looking first at the methodology developed by Hasbrouck (1995), the information share of market j ( S j ) is defined as given in Equation 2 6. (2 6) where denotes the common row vector in ( 1 ) which is the sum of the moving average coefficients, and F denotes the Cholesky factorization of (i.e., the lower triangular matrix such that = FF ). As discussed by Hasbrouck, the long run impact of a disturban ce on each of the prices is intuitively given by ( 1 ) e t If the rows of this matrix are identical, this implies that the long run impact will be the same for all the prices. Finally, the term [ F ] j in Equation 2 6 represents the j th element of the row matr ix F This allows the vector and the matrix F to be expressed more fully, as shown respectively in Equations 2 7 and 2 8. (2 7) (2 8) The information share of each market is calculated. The respective expr essions for the stock, futures, and options markets are given in Equations 2 9, 2 10 and 2 11. (2 9) PAGE 23 23 (2 10) (2 11) arket prices are correlated, the approach does not lead to a unique value for the information share. As can be seen from Equations 2 9, 2 10 and 2 11, the information shares for each of the markets are not symmetrical in the variables. Rather, upper and lo wer bounds may be obtained, and these depend on the order of the variables in the price vector p t and the corresponding covariance matrix In my analysis, I estimate the upper and lower bounds for each of the markets using all (six) possible permutations of the order of the variables. It should be noted that for each permutation of the variables, the information shares for the markets sum to one, but the maximum and minimum information shares for a particular market might be obtained from different permut ations. Then, for each market, the average information share for the period is calculated as the mean of its upper and lower bounds. This is denoted as j { S F O }, and will be referred to as the mean information share for market j While this statistic varies over time for each of the different series, the sum of the mean information shares, does not equal one explicitly. However, the mean information shares can be normalized (by dividing the mean informa tion share of each market by the sum of all three) so that they sum to unity, which allows the relative information shares across markets to be more readily observed. PAGE 24 24 Generalized Information Shares of the Markets Several researchers have shown both theoret ically and empirically that traditional orthogonalized forecast error variance decomposition results based on the widely used Cholesky factorization of VAR innovations are sensitive to ordering of the variables [e.g., Pesaran and Shin ( 1996 1998) and Koop et al. ( 1996 )] To avoid these problems, I employ Pesaran and ( 1998 ) generalized impulse response technique in which an orthogonal set of innovations is constructed that does not depend on the VAR ordering. Pesaran and Shin (1998) demonstrate that if generalized impulse response functions are used instead of orthogonalized impulse response functions, the problem involving upper and lower bounds for the information shares Pesaran and Shin ort hogonalized forecast error variance decompositions. The generalized forecast error variance decomposition can be calculated. From this, I j information share for mark et j but gives a single point estimate for each period rather than upper and lower bounds. Adapting the equation from Pesaran and Shin (1998) to the notation used here, the corresponding generalized information shares are defined shown in Equation 2 12. A nalogously to the information shares for each market given in Equations 2 9, 2 10 and 2 11, the generalized information shares for each market are given in Equations 2 13, 2 14 and 2 15. (2 12) (2 13) (2 14) PAGE 25 25 (2 15) Using the above approach, I calculate generalized information shares for each of the three markets on a daily basis. Note that the generalized information shares are symmetrical in the variables. It sh ould also be observed that the sum of the generalized information shares is not unity, but the fraction of information impounded in each market can be obtained through normalization. Data and Summary Statistics Data The sample period I use ranges from Janu ary 29, 1993 to December 31, 1996. This sample corresponds to the period for which I could obtain complete price data across the stock, futures, and options markets for the S&P 500 index. Prices for the SPDRs I designate the time series of prices for the S PDRs as S t I use quoted prices for SPDRs to track the S&P 500 index 4 One limitation of the earlier literature is the use of nontraded indices that are autocorrelated. I obtain transaction level data for SPDRs from the Transactions and Quotes (TAQ) databa se. The SPDRs were introduced by the American Stock Exchange on January 29, 1993, and so this constrains the start of the three price time series to this date. For each one for that minute. At time t the midpoint of the quoted bid and ask prices for the SPDR is used for S t Futures prices for the S&P 500 index I designate the time series of prices for futures on the S&P 500 index as F t I obtain the futures data from the C ME I use the nearest futures contract on the S&P 500 index (from March, 4 Elton et al. (2002) give an excellent description of SPDRs. PAGE 26 26 June, September, or December) when picking up the latest index future level for each one minute interval. For example, for 1993, between January 1 and March 15, the March contracts are used; between March 16 and June 15, the June contracts are used; and so on. In this way, I obtain the estimated price from the futures contract at time t and this is used for F t Options prices for the S&P 500 index I designate the time series of prices f or options on the S&P 500 index as O t I obtain the options data from the Berkeley Options Database, which only has options data available through December 31, 1996. The CBOE suspended the distribution of its data to the Berkeley Options Database on Decemb er 31, 1996 Using call and put options with the same quote date, the same strike price and the same maturity (i.e., various option series), I estimate the implied underlying stock price using put call parity as expressed in Equation 2 16. (2 16) where S is the implied stock price, C is the call option price, P is the put option price, X is the strike price of the (call and put) options, r is the Treasury bill rate applicable to the maturity of the options, q is the dividend yield on the S&P 500 index, and T is the time to maturity of the (call and put) options. For each one minute interval, the latest quotations for the call option and for the put option within that one minute interval are found, and these two are used to form the pu t call parity. Whenever multiple options are traded, after pairing the call and put option series by maturity and strike price, implied stock prices are calculated for each pair. If there are no new call quotes or no new put quotes (or both), the previous necessary. The value calculated for S at time t is used for O t By using this method, I avoid the need for a volatility estimate and a choice of model for each of the options series. Summary Statistics Tabl e 2 1 provides summary statistics on the S&P 500 returns from the three markets: SPDRs, futures, and options. I calculate the intraday returns using the log of price relatives. The PAGE 27 27 mean, standard deviation and correlation matrix are given for each series, with different subsamples being considered. The summary statistics for the entire sample show that the average return and standard deviation for the options market is higher than either of the other two markets. The higher standard deviation for the option s market returns persists in all of the breakdowns given for the other subsamples shown in Table 2 1. This is due to the fact that options are levered equity. 5 The correlations among the three market returns are highest between the SPDRs and futures market s, followed by the futures and options markets, and lowest between the SPDRs and options markets. This return correlation pattern also persists for the subsamples of the data. The summary statistics of the three market returns for the subsamples shown in T able 2 1 are conditional on various calendar and other event dates. For these subsamples the returns from the three markets and their respective correlations differ based on factors that might be influential in the determination of price discovery market announcement effects, option expirations, calendar month effects and day of the week effects. When the sample is sorted by days of the week, returns are higher on Mondays and Wednesdays compared to the other days. The correlations between the markets are lower on Mondays, but higher on Wednesdays when compared to the other days. Descriptive statistics given by option expiration days reveal that the returns are considerably higher on the option expiration days than on other days. The correlations between th e returns in the options and stock markets (and between the options and futures markets) increase on the expiration days, whereas they decrease between the stock and futures markets on the expiration days. 5 Another potential explanation for the higher realized volatility of the index returns impl ied in the option prices is that some noise may be introduced by using different option series, with possibly nonsynchronous prices for puts and calls in each series. PAGE 28 28 The descriptive statistics conditional on macroeco nomic announcement days suggest that t he returns are greater on days when macroeconomic announcements occur and the correlations between all markets increase. Finally, descriptive statistics are given by calendar month. In this case, returns are highest in January across all markets, and they are lowest, even negative, in December. The highest and lowest correlations between the stock and futures markets occur in November and February, respectively; between the stock and options markets occur in December an d January, respectively; and between the futures and options markets occur in December and January, respectively. Overall, the descriptive statistics show that the returns across the three markets are correlated. The correlation and returns vary conditiona l on both calendar and other news events. This suggests that information shares across markets may be determined by effects related to: the day of the week, whether a macroeconomic announcement has been made that day, whether futures and options contracts are expiring, and even to the month of the year Price Discovery Attention can now be devoted to the analysis of how the returns from these three markets relate to each other. Lead Lag Relations and Related Results Table 2 2 provides the lead lag parameter estimates corresponding to the vector error correction model depicted in Equation 2 5 using ten lags and one minute interval data. The sample period is from January 29, 1993 to December 31, 1996. Up to the sixth lag, all of the coefficients are significan tly different from zero at the 1% level. This demonstrates a strong relation among all three markets. 6 Overall, the results suggest that the causal relations between 6 The interdependence among the three markets is robust to different lag structures and l onger time intervals. PAGE 29 29 the markets are multidirectional. This finding is in contrast to the results reported by C han (1992), Stephan and Whaley (1990), and Chan et al. (1993), where it was found that the futures market led the stock market, which in turn led the options market. However, these studies examined earlier sample periods. A potential explanation for the di fference between my results and those reported earlier is that the lead lag relations between the markets may have adjusted more quickly through time. Consistent with this hypothesis, Chan (1992) also finds evidence that the cash index lagged the futures l ess in the period from January to September 1987 than it did in a similar period from August 1984 to June 1985. daily basis for the three markets. As discussed in the methodology section earlier, I use the midpoint of the maximum and minimum values for each market and normalize it across the three markets so that the daily information shares sum to one. To examine the time varying characteristics of the information shares, I plot the monthly averages of the daily midrange information shares in Figure 2 1 over the 1993 to 1996 sample period. From Figure 2 1, it can be seen that the futures market has the largest info rmation shares, but its magnitude declines through time. Interestingly, on March 20, 1995, the information shares for the options market increase substantially at the expense of the information shares for the futures market. This shift in information share s between the options and the futures markets corresponds to the beginning of the CBOE automated quote system for options prices, which greatly increased the number of options quotes. In Figure 2 2, the daily midrange information shares are plotted for a s ix month window from January 3, 1995 to June 30, 1995 around the CBOE automated quote system event. The sudden change in the levels of information shares between the futures and options market on March 20, 1995 can be seen more PAGE 30 30 dramatically in Figure 2 2. The time varying nature of the information shares is also shown more clearly. Generalized Information Shares of the Markets and Related Results point estimates of the information shares. Figures 2 3 and 2 4 show the normalized generalized information shares for the three markets over the full sample and the same six month subsample as shown in Figures 2 1 and 2 3 and 2 4, it can be seen that the graphs of the generalized information shares are very similar to the Hasbrouck and generalized information shares exceed 0.84 in each case. This suggests that the normalized generalized information share estimates are close in value to the midpoint of the 7 While the normalized information shares are useful in understanding th e percent contribution of each market, a problem arises if simultaneous equation procedures are used to examine the determinants of the normalized information shares across the three markets. With the normalized information shares, there is a singularity p roblem that arises from the imposed constraint that the three dependent variables sum to one. 8 In Table 2 3, I provide summary 7 As a robustness check, I also examined the sensitivity of the information shares to the estimation time frame and various alternative specifications of it. In particular, in addition to calculating information shares on a daily basi s, I also calculated them on a monthly basis. Although the results are not qualitatively different, the monthly estimated generalized information shares were generally smaller in magnitude than the corresponding monthly averages of the daily information sh ares. The monthly generalized information shares also had higher standard deviations and coefficients of variation than the corresponding monthly averages of the daily information shares. I also examined various alternative specifications for the generaliz ed information shares, including using ratios of the shares and changes in the levels of information shares. Using the ratios of the shares, S S,gen / S F,gen and S O,gen / S F,gen or changes in levels of the information shares (i.e., differenced information shar es), resulted in lower adjusted R squares in my subsequent regression analysis. 8 In my analysis, the patterns and relative market levels of the normalized and nonnormalized information shares are similar. However, a potential problem with normalizing the information shares can arise if one (or more) of the time series of information shares are more volatile compared to the others. It can induce a higher volatility in the PAGE 31 31 statistics over the entire 1993 to 1996 sample period for the generalized information shares, both with and without normalization Given the structural change in the information shares that can be observed in Figures 2 3 and 2 4, summary statistics are computed corresponding to the two periods where the changes take place: before March 20, 1995 (inclusive) and after this date. Table 2 3 shows that there is a substantial increase in the mean of the normalized information shares for the options market, from 0.26 to 0.39, and a corresponding decrease in the mean for the futures market, from 0.54 to 0.45. There is only a small decrease i n the mean for the stock market. On the other hand, the nonnormalized information shares indicate that there is a significant increase only for the options market. Tests for differences in means indicate that the three means of the normalized generalized i nformation shares change significantly after March 20, 1995, but the nonnormalized generalized information shares change significantly only for the options market. This lends support to the idea that the increase in information to the markets came through a fundamental change in the options market on March 20, 1995, in such a way that, on a relative basis, the information impounded in the cash and futures markets decreased. The correlation matrices for the two subperiods, however, are not substantially diff erent. This suggests that there has been a significant change in the level of information to be found in the options and futures markets without there being a change in the pattern of correlations in the information shares among the markets. I also calcula ted the generalized information shares using 5 minute intervals, as opposed to 1 minute intervals. Though not reported, before March 20, 1995, the mean percentages of information attributable to the stock, futures, and options markets from using the 5 minu te relatively stable series when normalizing them. The nonnormalized information shares a re symmetric in the variables used in their calculation as seen in Equations 2 13, 2 14 and 2 15, provide a single value for each market as opposed to a range, and give a measure of the absolute level of information brought to the markets on a particular d ay. PAGE 32 32 intervals are 33%, 40%, and 27%, respectively. The corresponding figures after March 20, 1995 are 30%, 37%, and 33%, respectively. All t statistics are significant at the 1% level for difference in means tests. This suggests that the introduction of the automated quotes system in the options market was associated with an increase in options market information processing, though part of the increase was due to an increase in the frequency of updates. Using the coarser 5 minute intervals tends to smooth th e measured information processing across the markets, though the relative rankings of where the information is processed across the markets are the same as those using the 1 minute interval. Determinants of Information Shares through Time There are several factors that are likely to influence where information is processed. I put forward two principal hypotheses: one related to transaction costs and another related to market trading activity. Transaction costs and leverage opportunities may make it relative ly cheaper to trade in one of the markets, making that market a more likely source of where information is processed. However, given that index level transaction costs are relatively small, it would not be surprising to observe that there is no empirical r elation between transaction costs and information shares. The hypothesized relation between information processing and trading activity is also complicated. Volume is a traditional measure of trading activity and often serves as a liquidity and information proxy. 9 To the extent that differences of opinion or noise trading (liquidity) are driving the trading activity, a negative (or no) relation between volume measures and information shares would be expected However, to the extent that the trading activity is driven by information, a positive relation between volume measures and information shares would be expected Since my study examines cash and derivative markets at the index level, it is 9 Hasbrouck (200 3 ) notes that trading may be endogenous to the price discovery process. However, in my analysis, I decompose trading volumes into expected and unexpected components, making the expected volume exogenous. PAGE 33 33 likely that the trading activity is a result of liquidity or nois e trading. Subrahmanyam (1991) demonstrates that indexes provide a preferred trading medium for uninformed liquidity traders because adverse selection costs are typically lower in these markets than for individual securities. In my analysis, I use vector r egression procedures with information shares as the dependent variables and various transaction cost and trading activity proxies, as well as other control variables, as explanatory variables. In particular, I use the nonnormalized generalized information shares as the dependent variable. The explanatory variables that are considered include effective spreads in each market as a measure of transaction costs, expected and unexpected trading volume in each market as trading activity measures, macroeconomic an nouncements to capture trading activity associated with potential information/differences of opinion, option expiration day indicators, triple witching day indicators, an indicator representing the structural shift after March 20, 1995, and various calenda r indicators including day of the week, month of the year, and end of quarter indicators. Table 2 4 provides a description of each of the variables. Table 2 5 provides summary statistics for the effective spreads and trading volumes that are employed in su bsequent vector autoregressions. Consistent with the transaction cost hypotheses put forward by Fleming et al. (1996), I find that transaction costs, as measured by effective spreads, are least in the stock market and greatest in the options market. Additi onally, the volume of trading is highest in the stock market and lowest in the options market. Difference in means tests also show that the effective spreads and trading volumes are statically different at the 5% level before and after March 20, 1995. Tran saction Cost Proxies As a proxy for transaction costs, I calculate effective spreads for each market each day ask spread for a time series of PAGE 34 34 prices is estimated from the first order serial covariance of price changes or returns, 10 as shown in Equation 2 17. (2 17) If transaction costs play a role in influencing where information is processed, then the coefficient estimates corresponding to the effective spreads in each market (i.e., EFFSPRS, EFFSPRF, and EFFSPRO) should be negative with respect to each of their own markets. As trading costs in one market increase (as measured by effective spreads), traders will choose to go to the other markets, resulting in lower infor mation processing in the more costly market, all else equal. However, the observed empirical relation could plausibly be positive to the extent that the effective spreads are also measuring information effects (the adverse selection component of the spread ), though this effect is likely to be small at the index level. Trading Activity Proxies My second hypothesis is that trading activity is likely to have an influence on information processing. From a theoretical perspective, there are two lines of research on trading volume. One line of research views trading volume as induced by differences of opinion. That is, while investors often share the same public information, they interpret it differently, resulting in trading volume [e.g., Varian (1985) and Harris and Raviv (1993)]. In the second line of theoretical work, trading volume is induced by asymmetric information. These models involve trading among informed traders, uninformed traders, and noise traders (liquidity traders). Investors then try to infer inf ormation from the trading activity of others [Grossman and Stiglitz (1980), Hellwig (1980), Kyle (1985), Admati and Pfleiderer (1988), Foster and Viswanathan (1990), and Kim and Verrecchia (1991a, 1991b)]. In equity markets, the adverse selection 10 For SPDRs, the correlation of bid ask quotes with the corresponding effective spreads over the sample is 0.5. PAGE 35 35 problem f aced by market makers arises from some traders being better informed about firm specific information. In contrast, at the market index level, one might expect a reduced potential for market maker losses to better informed traders, because the information i s primarily macroeconomic (public) information. Several recent studies show that information may be present in transaction volumes. Easley et al. (1998) conclude that option trades associated with positive news (buying a call or selling a put) or negative news (selling a call or buying a put) carry information about future stock price changes. Two important implications are that option pricing models are deficient if markets are imperfect, and that there is information content in volume in equity markets. P an and Poteshman (2006) show that there is statistical and economic significance in predicting the next day four factor adjusted stock return from open buy put call ratios. Their results indicate that option volumes contain information relating to future s tock price movements, and that the predictability associated with this increases with the concentration of informed traders and the leverage of option contracts. Chan et al. (2002) consider the interdependence of net trade volume (buyer initiated trading v olume minus seller initiated trading volume) and quote revisions for actively traded NYSE stocks and their CBOE traded options. They conclude that while stock and option quote revisions both contain information, only stock net trade volume and not option n et trade volume has information content. An implication of these studies is that transaction volumes can potentially have liquidity and information components, and their influence on information shares should therefore be examined separately. Following Bes sembinder and Seguin (1992), I decompose the volumes for each market into a 100 day moving average (VOLSMA, VOLFMA, and VOLOMA for SPDRs, futures, and options moving average volumes, respectively), and expected (VOLSANT, PAGE 36 36 VOLFANT, and VOLOANT) and unexpecte d (VOLSUN, VOLFUN, and VOLOUN) components obtained using an ARIMA(0, 1, 10) specification on the detrended series. The expected components proxy for market liquidity (noise traders), whereas the unexpected trading volume component represents trading due to informed trading or heterogeneous opinions about prices (or noise). I conjecture that higher expected volume should result in either a negative (or no) effect on the information share for its own market. That is, an increase in expected volume all else eq ual suggests that new information is not being revealed in that market. In contrast, I would expect that higher unexpected volume would be either negative or positively related to the information share in that market. Higher unexpected volume could reflect differences of opinion shares would be negative (i.e., less information being processed) or insignificant. The relation would be positive to the extent that the une xpected volume reflected information. Macroeconomic News and Calendar Events I also use macroeconomic announcement s urprises to study the impact of public information releases on information shares Announcement surprises are standardized over the sample p eriod to make their coefficients comparable, and absolute values of these standardized surprises are used to avoid effects being obscured by the changing signs of the surprises. Flannery and Protopapadakis (2002) show that macroeconomic announcements do in fluence equity market returns. U.S. macroeconomic announcement data is obtained from Money market Services (MMS). MMS provides release dates and times as well as the actual release value and median market survey expectation of numerous government macroecon omic variables. Another factor that may affect price discovery is option expiration dates. Ni et al. (2005) show that stock prices are significantly affected by trading in the options market leading up to and on option expiration dates. The authors examine two possible explanations for stock prices PAGE 37 37 clustering around option strike prices: hedge rebalancing by market makers with net purchased positions in expiring options, and stock price manipulation by firm proprietary traders who write new options in the w eek leading up to expiration. Although the authors postulate that it would be much harder to manipulate an index than a particular stock, I nevertheless choose to control for this possibility by including an option expiration day indicator (OPTEXTHD). In a ddition to option expiration day indicators, I also include indicator variables for triple witching (TRWITCHD) and end of quarter (EOQD) days. 11 The end of quarter dummy corresponds to the last week of each quarter of the year, as large funds may be rebalan cing or tilting their portfolios at these times. It is also possible that the information processed in each of the markets may vary by the day of the week since there may be increased trading at the beginning or end of the week, or by the month of the year as there may be seasonality exhibited throughout the year. I therefore include indicator variables to examine these potential effects. Finally, I create a dummy variable s automated quotation system on March 20, 1995 (BREAKD). Determinants of Information Shares Tables 2 6 through 2 8 provide the results of the vector regressions for the generalized information shares using various specifications. In all three of these tabl es, I show regression results both with and without the macroeconomic announcement surprises. In Table 2 6, the components of traded volume are included as regressors, but effective spreads are not; in 11 Triple witching is an event that occurs when the contracts for stock options, stock index options, and stock index futures all expire on the same day. Triple witching days h appen four times a year: the third Friday of March, June, September and December. During the final hour of the day the markets are quite volatile, as traders are quickly offsetting their options/futures positions before the closing bell. PAGE 38 38 Table 2 7, effective spreads are included as regressor s, but volumes are not; and, finally, in Table 2 8, both sets of variables are included. Several general comments can be made about the results in these three tables. First, the coefficient on the indicator variable of whether a particular day is before or after the options automated quotation introduction event, BREAKD, is positive and significant at the 1% level for the options market in all the specifications considered. This gives support to the argument that the automated quotes system for options pric es increased the information processed in that market. Second, the coefficient for the end of quarter variable, EOQD, and either the option expiration day indicator, OPTEXTHD, or triple witching day indicator, TRWITCHD, coefficients are statistically signi ficant for the futures market in all model specifications, suggesting that additional price discovery takes place in this market at times when hedgers and/or mutual fund managers may be rebalancing their portfolios. Third, after accounting for the componen ts of traded volume, the coefficient for the Monday indicator variable (MOND) is negative for all three markets, and statistically significant for the futures market. This suggests a day of the week effect, with information processing decreasing following the weekend. Fourth, the inclusion of macroeconomic surprises does not have much effect on the significance levels of the other variables, although there are a few announcement surprises that are statistically significant in each of the various specificati ons. The results in Table 2 6 generally agree with the hypotheses put forward regarding the components of traded volume. 12 In particular, I find that the trend components of volume for each market (VOLSMA, VOLFMA and VOLOMA) are highly significant for the o ptions 12 As a robustness check, I also decomposed the volume into its expected and unexpected components using various other time series specifications, including specifications that contained other exogenous variables such as day of the week dummies, month of the year dummies, th e option expiration dummy, the triple witching dummy, the break dummy, and macroeconomic announcement dummies for each of the different announcements. The results were similar to those reported. PAGE 39 39 information share, with the first of these also being significant for the stock information share. The anticipated volume components negatively affect the information shares in their own markets, with one of the other two markets having an increase in information share and the other a decrease. The unanticipated volumes negatively affect the information shares in most markets, consistent with the differences of opinion prediction (an exception to this result is the positive coefficient on the unantic ipated SPDR volume, VOLSUN, in the regressions for GIS_S t with no announcement variables in the model specification). In particular, the unanticipated futures and options volumes are statistically significant at the 1% level in the futures information shar e specification, and similarly the unanticipated futures volume is strongly significant in the options information share specification. 13 In Table 2 7, the signs on the parameter estimates for the effective spread measures corresponding to each market (EFFS PRS, EFFSPRF and EFFSPRO) are largely all negative, as hypothesized, with those for the stock market effective spread, EFFSPRS, being statistically significant. An exception to the negative sign occurs for the effect of the options market effective spread, EFFSPRO, on the options market information share. A possible reason for this effect is that market makers in the options market increase their spreads more to compensate for informed trading that takes place. However, if the options market effective sprea ds are interacted with the introduction of the options market automated quotation system indicator (BREAKD), the sign on the options market effective spreads becomes significantly negative in the post auto quote period. 13 As an additional measure of option series liquidity, I also included in the regressions the average number of options series quotes used each day in calculating the implied options prices. The coefficient on this variable was negative and statistically significant at the 5% level for the options market. This sugge sts that a greater number of option series was also associated with more noise trading. PAGE 40 40 The results for the trading volume c omponents in Table 2 8 are very similar to those reported in Table 2 6. However, there are some changes in signs and significance levels for the effective spread variables. This suggests that transaction costs play a relatively less significant role in det ermining where information is processed compared with market trading activity. Finally, from Table 2 8 it can be seen that lagged information shares are statistically significant in affecting the options market information share, suggesting the existence o f some information share momentum effects. Conclusion In this study, I consider the price discovery process across three different markets simultaneously. I use generalized impulse response functions to calculate the information shares across prices for th e S&P 500 index in the stock market (SPDRs), futures market, and options market. I find that there is considerable variation in the information shares through time and across markets. Up until March 20, 1995, I find that the futures market impounds more in formation than the stock or options markets, and, in general, there is slightly more information in the options market than in the stock market. However, after March 20, 1995, there was a significant change in the markets, with a large increase in the shar e of information impounded in the options market at the expense of the futures market. This shift coincides with the introduction of an automated quotes system in the options market. In examining what explains where price discovery occurs, I find that tran saction costs and market trading activity proxies are important determinants. Taken together, my results suggest that the price discovery process is not static and that the factors that influence it include both fundamental and behavioral characteristics. PAGE 41 41 Table 2 1. Market returns: summary statistics Returns series Subsample Parameter S ret F ret O ret Complete sample Obs 381,847 381,847 381,847 Mean ( 10 7 ) 5.446 5.692 1 0.472 Standard deviation ( 10 4 ) 3.124 3.070 7.243 Correlation ( S r et ) 1.000 0.393 0.137 Correlation ( F ret ) 0.393 1.000 0.239 Correlation ( O ret ) 0.137 0.239 1.000 Mondays Obs 71,917 71,917 71,917 Mean ( 10 7 ) 17.473 17.845 25.759 Standard deviation ( 10 4 ) 2.902 2.810 8.697 Correlation ( S ret ) 1.000 0.365 0.096 Correlation ( F ret ) 0.365 1.000 0.182 Correlation ( O ret ) 0.096 0.182 1.000 Tuesdays Obs 78,348 78,348 78,348 Mean ( 10 7 ) 2.343 3.531 0.949 Standard deviation ( 10 4 ) 3.181 3.152 6.861 Cor relation ( S ret ) 1.000 0.391 0.148 Correlation ( F ret ) 0.391 1.000 0.276 Correlation ( O ret ) 0.148 0.276 1.000 Wednesdays Obs 78,043 78,043 78,043 Mean ( 10 7 ) 16.750 19.860 21.920 Standard deviation ( 10 4 ) 3.171 3.065 6.19 4 Correlation ( S ret ) 1.000 0.407 0.169 Correlation ( F ret ) 0.407 1.000 0.278 Correlation ( O ret ) 0.169 0.278 1.000 Thursdays Obs 76,513 76,513 76,513 Mean ( 10 7 ) 3.241 2.546 0.742 Standard deviation ( 10 4 ) 3.108 3.0 80 7.138 Correlation ( S ret ) 1.000 0.399 0.149 Correlation ( F ret ) 0.399 1.000 0.240 Correlation ( O ret ) 0.149 0.240 1.000 Fridays Obs 77,026 77,026 77,026 Mean ( 10 7 ) 0.687 2.443 5.426 Standard deviation ( 10 4 ) 3.23 1 3.212 7.216 Correlation ( S ret ) 1.000 0.398 0.136 Correlation ( F ret ) 0.398 1.000 0.240 Correlation ( O ret ) 0.136 0.240 1.000 PAGE 42 42 Table 2 1. Continued Returns series Subsample Parameter S ret F ret O ret Option expiration days O bs 18,178 18,178 18,178 Mean ( 10 7 ) 29.895 35.678 32.169 Standard deviation ( 10 4 ) 3.066 3.010 5.575 Correlation ( S ret ) 1.000 0.380 0.176 Correlation ( F ret ) 0.380 1.000 0.285 Correlation ( O ret ) 0.176 0.285 1.000 Not o ption expiration days Obs 363,669 363,669 363,669 Mean ( 10 7 ) 4.224 4.194 9.388 Standard deviation ( 10 4 ) 3.127 3.073 7.316 Correlation ( S ret ) 1.000 0.394 0.136 Correlation ( F ret ) 0.394 1.000 0.238 Correlation ( O ret ) 0.136 0.238 1.000 Macroeconomic announcement days Obs 67,087 67,087 67,087 Mean ( 10 7 ) 12.679 11.162 13.601 Standard deviation ( 10 4 ) 3.151 3.197 7.237 Correlation ( S ret ) 1.000 0.398 0.142 Correlation ( F ret ) 0.398 1.000 0.244 Correlation ( O ret ) 0.142 0.244 1.000 Not macroeconomic announcement days Obs 314,760 314,760 314,760 Mean ( 10 7 ) 3.904 4.527 9.805 Standard deviation ( 10 4 ) 3.118 3.043 7.244 Correlation ( S ret ) 1.000 0.392 0.136 Correlation ( F ret ) 0.392 1.000 0.238 Correlation ( O ret ) 0.136 0.238 1.000 January months Obs 25,054 25,054 25,054 Mean ( 10 7 ) 30.925 28.088 50.552 Standard deviation ( 10 4 ) 2.775 2.819 10.700 Correlation ( S ret ) 1.000 0.417 0.093 Correlation ( F ret ) 0.417 1.000 0.157 Correlation ( O ret ) 0.093 0.157 1.000 February months Obs 29,303 29,303 29,303 Mean ( 10 7 ) 6.314 6.160 8.064 Standard deviation ( 10 4 ) 3.195 3.386 6.151 Correlation ( S ret ) 1.000 0.360 0.166 Correlation ( F ret ) 0.360 1.000 0.287 Correlation ( O ret ) 0.166 0.287 1.000 March months Obs 34,714 34,714 34,714 Mean ( 10 7 ) 2.969 1.831 4.169 Standard deviation ( 10 4 ) 3.492 3.732 7.211 Correla tion ( S ret ) 1.000 0.400 0.159 Correlation ( F ret ) 0.400 1.000 0.222 Correlation ( O ret ) 0.159 0.222 1.000 PAGE 43 43 Table 2 1. Continued Returns series Subsample Parameter S ret F ret O ret April months Obs 30,851 30,851 30,851 Mean ( 10 7 ) 1.525 1.408 3.562 Standard deviation ( 10 4 ) 3.165 3.257 6.331 Correlation ( S ret ) 1.000 0.384 0.154 Correlation ( F ret ) 0.384 1.000 0.279 Correlation ( O ret ) 0.154 0.279 1.000 May months Obs 32,817 32,817 32,817 M ean ( 10 7 ) 17.356 20.187 26.513 Standard deviation ( 10 4 ) 3.038 3.073 7.496 Correlation ( S ret ) 1.000 0.387 0.130 Correlation ( F ret ) 0.387 1.000 0.249 Correlation ( O ret ) 0.130 0.249 1.000 June months Obs 32,850 32,850 32,850 Mean ( 10 7 ) 3.731 5.998 2.343 Standard deviation ( 10 4 ) 2.931 2.937 6.989 Correlation ( S ret ) 1.000 0.416 0.145 Correlation ( F ret ) 0.416 1.000 0.240 Correlation ( O ret ) 0.145 0.240 1.000 July months Obs 32, 034 32,034 32,034 Mean ( 10 7 ) 1.912 1.373 3.912 Standard deviation ( 10 4 ) 3.550 3.483 6.244 Correlation ( S ret ) 1.000 0.375 0.177 Correlation ( F ret ) 0.375 1.000 0.368 Correlation ( O ret ) 0.177 0.368 1.000 August m onths Obs 34,742 34,742 34,742 Mean ( 10 7 ) 15.828 14.109 26.174 Standard deviation ( 10 4 ) 2.477 2.455 6.366 Correlation ( S ret ) 1.000 0.370 0.128 Correlation ( F ret ) 0.370 1.000 0.245 Correlation ( O ret ) 0.128 0.245 1.000 September months Obs 31,607 31,607 31,607 Mean ( 10 7 ) 18.012 19.071 10.684 Standard deviation ( 10 4 ) 2.695 2.699 4.878 Correlation ( S ret ) 1.000 0.398 0.162 Correlation ( F ret ) 0.398 1.000 0.278 Correlation ( O ret ) 0.162 0.278 1.000 October months Obs 33,537 33,537 33,537 Mean ( 10 7 ) 1.881 4.344 6.669 Standard deviation ( 10 4 ) 2.742 2.717 9.907 Correlation ( S ret ) 1.000 0.415 0.098 Correlation ( F ret ) 0.415 1.000 0.162 Correlation ( O r et ) 0.098 0.162 1.000 PAGE 44 44 Table 2 1. Continued Returns series Subsample Parameter S ret F ret O ret November months Obs 32,010 32,010 32,010 Mean ( 10 7 ) 4.014 4.778 11.441 Standard deviation ( 10 4 ) 3.543 2.940 7.970 Correlation ( S ret ) 1.000 0.426 0.128 Correlation ( F ret ) 0.426 1.000 0.218 Correlation ( O ret ) 0.128 0.218 1.000 December months Obs 32,328 32,328 32,328 Mean ( 10 7 ) 11.042 8.338 6.110 Standard deviation ( 10 4 ) 3.587 3.088 5.070 Correlation ( S ret ) 1.000 0.394 0.210 Correlation ( F ret ) 0.394 1.000 0.369 Correlation ( O ret ) 0.210 0.369 1.000 S ummary statistics in this table are for data from January 29th, 1993 to December 31st, 1996. The time series analyzed are for the daily returns on transactions of the SPDRs, { S ret }, daily returns on spot prices implied from futures on the S&P 500 index, { F ret }, and daily returns on spot prices implied from options on the S&P 500 index, { O ret }. Daily returns are calculated as the logs of price relatives. The mean, standard deviation and correlation matrix are given for the series. There are several subsamples considered following the entire data sample. These subsamples are broken down by: days of the week; days when the op tions on the futures expire compared to other days; days when macroeconomic announcements are made compared to other days; and months of the year. PAGE 45 45 Table 2 2. Lead lag parameter estimates Estimates in equation for S ret ( t ) Estimates in equation for F ret ( t ) Estimates in equation for O ret ( t ) Lag ( k ) S ret ( t k ) F ret ( t k ) O ret ( t k ) S ret ( t k ) F ret ( t k ) O ret ( t k ) S ret ( t k ) F ret ( t k ) O ret ( t k ) 1 0.422 0.557 0.010 0.065 0.066 0.010 0.058 0.441 0.588 (0.002) (0.002) (0.001) (0.002) (0.002) (0. 001) (0.004) (0.004) (0.002) 2 0.325 0.406 0.008 0.047 0.040 0.008 0.049 0.349 0.439 (0.002) (0.002) (0.001) (0.002) (0.002) (0.001) (0.005) (0.005) (0.002) 3 0.266 0.321 0.006 0.038 0.038 0.007 0.033 0.282 0.348 (0.002) (0.002) (0.001) (0.002) (0.002) (0.001) (0.005) (0.005) (0.002) 4 0.220 0.264 0.003 0.033 0.031 0.004 0.040 0.234 0.286 (0.002) (0.002) (0.001) (0.002) (0.003) (0.001) (0.005) (0.005) (0.002) 5 0.182 0.218 0.003 0.026 0.028 0. 004 0.037 0.188 0.226 (0.002) (0.002) (0.001) (0.002) (0.003) (0.001) (0.005) (0.005) (0.002) 6 0.147 0.178 0.003 0.024 0.028 0.003 0.039 0.153 0.194 (0.002) (0.002) (0.001) (0.002) (0.003) (0.001) (0.005) (0.005) (0.002) 7 0. 124 0.145 0.000 0.014 0.025 0.001 0.033 0.117 0.148 (0.002) (0.002) (0.001) (0.002) (0.003) (0.001) (0.005) (0.005) (0.002) 8 0.093 0.110 0.000 0.005 0.020 0.001 0.039 0.074 0.104 (0.002) (0.002) (0.001) (0.002) (0.003) (0.00 1) (0.005) (0.005) (0.002) 9 0.068 0.083 0.000 0.003 0.017 0.001 0.027 0.050 0.076 (0.002) (0.002) (0.001) (0.002) (0.002) (0.001) (0.004) (0.005) (0.002) 10 0.032 0.053 0.000 0.003 0.012 0.000 0.023 0.030 0.039 (0.002) (0. 002) (0.001) (0.002) (0.002) (0.001) (0.004) (0.005) (0.002) Parameter estimates in this table are for the three market lead lag vector autoregressions using ten lags and one minute level transaction data from January 29, 1993 to December 31, 1996. Stan dard errors are given in parentheses. (Obs = 381,847) PAGE 46 46 Table 2 3. Generalized information shares: summary statistics Information share s series Nonnormalized Normalized S ample period Parameter S S,gen S F,gen S O,gen S S,gen,N S F,gen,N S O,gen,N Januar y 29, 1993 to March 20, 1995 (options market pre auto quote period) Obs 540 540 540 540 540 540 Mean 0.054 0.143 0.077 0.198 0.543 0.259 Standard deviation ( 10 2 ) 4.105 6.209 7.572 12.200 16.943 18.338 Correlation ( S S,gen ) 1.000 0.238 0.099 0.819 0.275 0.290 Correlation ( S F,gen ) 0.238 1.000 0.032 0.125 0.470 0.351 Correlation ( S O,gen ) 0.099 0.032 1.000 0.369 0.672 0.866 Correlation ( S S,gen,N ) 0.819 0.125 0.369 1.000 0.241 0.443 Correlation ( S F,gen,N ) 0.275 0.470 0.672 0.241 1.000 0.764 Correlation ( S O,gen,N ) 0.290 0.351 0.866 0.443 0.764 1.000 March 21, 1995 to December 31, 1996 (options market auto quote period) Obs 450 450 450 450 450 450 Mean 0.056 0.147 0.128 0.168 0.447 0.385 Standard deviation ( 10 2 ) 3.854 6.254 6.158 8.569 10.014 9.619 Correlation ( S S,gen ) 1.000 0.381 0.380 0.732 0.377 0.260 Correlation ( S F,gen ) 0.381 1.000 0.631 0.186 0.358 0.208 Correlation ( S O,gen ) 0.380 0.631 1.000 0.161 0.324 0.481 Correlation ( S S,gen,N ) 0.732 0.186 0.161 1.000 0.473 0.398 Co rrelation ( S F,gen,N ) 0.377 0.358 0.324 0.473 1.000 0.620 Correlation ( S O,gen,N ) 0.260 0.208 0.481 0.398 0.620 1.000 Difference in means tests t statistic 0.912 0.990 11.807 4.541 11.071 13. 871 D ata used in this table is from January 29th, 1993 to December 31st, 1996, split into two subsamples: before and after March 20th, 1995. It gives the mean, standard deviation and correlation matrix for the given series of information shares based on a generalized impulse response function ( S gen ). The table also includes the corresponding statistics for the information shares after being normalized to sum to one for each day. PAGE 47 47 Table 2 4. Regression variables used to explain the generalized information shares Variable Description GIS_S t Information share level in the stock market on day t GIS_F t Information share level in the futures market on day t GIS_O t Information share level in the options market on day t MOND FRID Dummy variables representin g the days of the week, with the variable MOND set to 1 when the day is a Monday, and zero otherwise. Similar values are used for TUED through FRID. Due to multicollinearity issues, WEDD was omitted from the regressions. JAND DECD Dummy variables repres enting the months of the year, with the variable JAND set to 1 when the day is in January, and zero otherwise. Similar values are used for FEBD through DECD. Due to multicollinearity issues, MAYD was omitted from the regressions. EOQD Dummy variable set t o 1 when a day falls in the last week of the calendar quarter: March, June, September, or December, and zero otherwise. OPTEXTHD Dummy variable set to 1 when a day is an option expiration day, and zero otherwise. TRWITCHD Dummy variable set to 1 when a d ay is a triple witching day, and zero otherwise. BREAKD Dummy variable set to 1 for days before March 20 th 1995 (inclusive) and zero otherwise. CNSTRC Absolute value of standardized surprise in construction spending announcement HSALC Absolute value of standardized surprise in new home sales announcement PERCC Absolute value of standardized surprise in personal consumption expenditures announcement PERIC Absolute value of standardized surprise in personal income announcement DGORC Absolute value of s tandardized surprise in durable goods orders announcement NAPMC Absolute value of standardized surprise in U.S. N.A.P.M. announcement CPIC Absolute value of standardized surprise in consumer price index announcement CCRDTC Absolute value of standardized surprise in consumer credit announcement HSTRC Absolute value of standardized surprise in housing starts announcement INPRDC Absolute value of standardized surprise in industrial production announcement LINDC Absolute value of standardized surprise in index of leading indicators announcement M2C Absolute value of standardized surprise in monthly M2 announcement PPIC Absolute value of standardized surprise in producer price index announcement RETSLC Absolute value of standardized surprise in retail sa les announcement UNEMPC Absolute value of standardized surprise in civilian unemployment rate announcement VOLSMA 100 day moving average component of trading volume in the stock market on a particular day VOLSANT Anticipated component of trading volume in the stock market on a particular day, using an ARIMA(0,1,10) model VOLSUN Unanticipated component of trading volume in the stock market on a particular day, using an ARIMA(0,1,10) model VOLFMA 100 day moving average component of trading volume in the futures market on a particular day VOLFANT Anticipated component of trading volume in the futures market on a particular day, using an ARIMA(0,1,10) model VOLFUN Unanticipated component of trading volume in the futures market on a particular day, using a n ARIMA(0,1,10) model PAGE 48 48 Table 2 4. Continued Variable Description VOLOMA 100 day moving average component of trading volume in the options market on a particular day VOLOANT Anticipated component of trading volume in the options market on a particular day, using an ARIMA(0,1,10) model VOLOUN Unanticipated component of trading volume in the options market on a particular day, using an ARIMA(0,1,10) model EFFSPRS Effective bid ask spread calculated for the stock market EFFSPRF Effective bid ask spread calculated for the futures market EFFSPRO Effective bid ask spread calculated for the options market This table provides d escription s of the variables used in the vector regressions with generalized information shares as the dependent variables. PAGE 49 49 Table 2 5. Selected explanatory variables: summary statistics Volumes ( 10 3 ) Effective spreads ( 10 4 ) Sample period Parameter Stock Futures Options EFFSPRS EFFSPRF EFFSPRO Complete sample Mean 307.678 66.991 41.003 0.783 1.397 6.912 Standard deviation 291.168 24.775 21.144 0.955 0.686 6.660 Minimum 5.200 11.162 7.099 0.000 0.062 0.020 Median 242.300 64.034 36.627 0.687 1.332 5.872 Maximum 2,742.100 158.195 184.773 16.400 10.376 60.765 Before March 20, 1995, inclusive Mean 294.714 64.617 39.114 0.744 1.428 8.580 Standard deviation 311.478 25.172 20.364 1.029 0.685 6.809 Minimum 5.200 11.162 7.099 0.000 0.062 0 .554 Median 210.750 60.592 35.086 0.617 1.375 7.208 Maximum 2,742.100 158.195 184.773 16.400 10.376 60.765 After March 20, 1995 Mean 342.951 73.451 46.143 0.888 1.313 2.375 Standard deviation 223.810 22.485 22.390 0.705 0.685 3.286 Minimum 9.500 13.543 8.405 0.000 0.121 0.020 Median 293.100 70.641 41.755 0.777 1.254 1.753 Maximum 1,349.800 147.930 128.811 4.550 6.124 31.409 Differ ence in means tests t statistic 2.312 4.563 3.859 2.147 2.009 16.509 T he mean, standard deviation, minimum, median and maximum are shown for the trading volumes and effective spreads that are employed in the vector autoregressions with generalized information shares as dependent variables. Variable definitions are given in Table 2 4 The summary statistics are for the sample period from Janua ry 29, 1993 to December 31, 1995 and for two subsample period s before and after March 20 1995 PAGE 50 50 Table 2 6. Components of traded volume with no announcement variables included: regression results Regressor GIS_S t GIS_F t GIS_O t Intercept 0.039 (0.020) 0.209 (0.029) *** 0.128 (0.037) *** MOND 0.008 (0.005) 0.018 (0.007) *** 0.006 (0.009) TUED 0.001 (0.005) 0.004 (0.007) 0.002 (0.008) THUD 0.001 (0.005) 0.002 (0.007) 0.008 (0.009) FRI D 0.005 (0.005) 0.001 (0.007) 0.002 (0.009) JAND 0.001 (0.008) 0.002 (0.012) 0.027 (0.015) FEBD 0.019 (0.007) ** 0.005 (0.011) 0.011 (0.013) MARD 0.013 (0.008) 0.030 (0.012) ** 0.026 (0.015) APRD 0.011 (0.008) 0.006 (0.011) 0.002 (0.014) JUND 0.017 (0.008) ** 0.013 (0.011) 0.035 (0.014) ** JULD 0.009 (0.007) 0.010 (0.011) 0.009 (0.014) AUGD 0.000 (0.007) 0.001 (0.010) 0.001 (0.013) SEPD 0.014 (0.008) 0.016 (0.012) 0.017 (0.015) OCTD 0.003 (0.007) 0.004 (0.010) 0.004 (0.013) NOVD 0.014 (0.007) ** 0.001 (0.010) 0.007 (0.013) DECD 0.015 (0.008) 0.008 (0.012) 0.02 2 (0.015) OPTEXTHD 0.010 (0.008) 0.023 (0.012) 0.008 (0.015) TRWITCHD 0.002 (0.013) 0.010 (0.019) 0.022 (0.024) EOQD 0.004 (0.007) 0.029 (0.010) *** 0.027 (0.012) ** BREAKD 0.001 (0.005) 0.015 (0.007) ** 0.059 (0.009) *** VOLSMA ( 10 7 ) 0.606 (0.199) *** 0.499 (0.285) 1.340 (0.362) *** VOLSANT ( 10 7 ) 0.111 (0.162) 0.046 (0.232) 0.029 (0.295) VOLSUN ( 10 7 ) 0.001 (0.056) 0.079 (0.080) 0.118 (0.102) VOLFMA ( 10 6 ) 0.298 (0.728) 0.866 (1.044) 3.597 (1.32 5) *** VOLFANT ( 10 6 ) 0.269 (0.163) 0.976 (0.234) *** 0.171 (0.297) VOLFUN ( 10 6 ) 0.191 (0.109) 1.254 (0.157) *** 0.824 (0.199) *** VOLOMA ( 10 6 ) 0.142 (0.715) 0.246 (1.026) 3.600 (1.302) *** VOLOANT ( 10 6 ) 0.141 (0.198) 0.12 0 (0.284) 0.120 (0.361) VOLOUN ( 10 6 ) 0.206 (0.104) ** 0.447 (0.149) *** 0.200 (0.189) GIS_S t 1 0.010 (0.039) 0.021 (0.056) 0.076 (0.071) GIS_F t 1 0.039 (0.027) 0.035 (0.038) 0.048 (0.049) GIS_O t 1 0.003 (0.021) 0.038 (0.029) 0.079 (0.037) ** GIS_S t 2 0.004 (0.039) 0.030 (0.056) 0.129 (0.071) GIS_F t 2 0.040 (0.026) 0.014 (0.037) 0.087 (0.047) GIS_O t 2 0.019 (0.020) 0.012 (0.029) 0.012 (0.037) R esults of regressing the generalized information shares on various explanatory variables, including the compo nents of traded volume, using vector regression procedures are shown Macroeconomic announcement variables are not included. Variable definitions are given in Table 2 4 The frequency of the data is daily, and the sample period runs from January 29, 199 3 to December 31, 1995 Standard err ors are given in parentheses. ( *, **, *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.) PAGE 51 51 Table 2 7. Components of traded volume with announ cement variables included: regression results Regressor GIS_S t GIS_F t GIS_O t Intercept 0.035 (0.021) 0.209 (0.029) *** 0.131 (0.038) *** MOND 0.007 (0.005) 0.015 (0.007) ** 0.004 (0.009) TUED 0.002 (0.005) 0.005 (0.007) 0.002 (0.008) TH UD 0.000 (0.005) 0.001 (0.007) 0.007 (0.009) FRI D 0.005 (0.005) 0.000 (0.007) 0.000 (0.009) JAND 0.003 (0.008) 0.000 (0.012) 0.029 (0.015) FEBD 0.019 (0.008) ** 0.005 (0.011) 0.014 (0.014) MARD 0.010 (0.009) 0.029 (0.012) ** 0.024 (0.016) APRD 0.010 (0.008) 0.005 (0.011) 0.003 (0.014) JUND 0.016 (0.008) ** 0.015 (0.011) 0.034 (0.014) ** JULD 0.008 (0.008) 0.009 (0.011) 0.009 (0.014) AUGD 0.000 (0.007) 0.001 (0.010) 0.001 (0.013) SEPD 0.012 (0.008) 0.016 (0.012) 0.016 (0.015) OCTD 0.003 (0.007) 0.008 (0.010) 0.007 (0.013) NOVD 0.015 (0.007) ** 0.001 (0.010) 0.010 (0.013) DECD 0.013 (0.008) 0.006 (0.012) 0.021 (0.015) OPTEXTHD 0.010 (0.008) 0.021 (0.012) 0.008 (0.015) TRWITCHD 0.000 (0.013) 0.003 (0.019) 0.017 (0.024) EOQD 0.003 (0.007) 0.027 (0.010) *** 0.025 (0.012) ** CNSTRC 0.009 (0.008) 0.027 (0.011) ** 0.022 (0.014) HSALC 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) PERCC 0.064 (0.046) 0 .030 (0.066) 0.065 (0.084) PERIC 0.000 (0.032) 0.017 (0.045) 0.016 (0.058) DGORC 0.002 (0.003) 0.002 (0.005) 0.004 (0.006) NAPMC 0.007 (0.003) 0.007 (0.005) 0.005 (0.006) CPIC 0.008 (0.055) 0.050 (0.078) 0.063 (0.100) CCRDT C 0.001 (0.003) 0.002 (0.004) 0.002 (0.005) HSTRC 0.197 (0.102) 0.086 (0.145) 0.505 (0.185) *** INPRDC 0.005 (0.034) 0.102 (0.049) ** 0.000 (0.063) LINDC 0.002 (0.056) 0.102 (0.080) 0.025 (0.103) M2C 0.001 (0.001) 0.000 (0.002 ) 0.000 (0.002) PPIC 0.026 (0.025) 0.063 (0.035) 0.014 (0.045) RETSLC 0.006 (0.013) 0.004 (0.018) 0.010 (0.024) UNEMPC 0.020 (0.041) 0.006 (0.059) 0.021 (0.075) BREAKD 0.001 (0.005) 0.014 (0.007) ** 0.058 (0.009) *** VOLSMA ( 10 7 ) 0.639 (0.202) *** 0.429 (0.288) 1.415 (0.368) *** VOLSANT ( 10 7 ) 0.105 (0.163) 0.024 (0.232) 0.077 (0.297) VOLSUN ( 10 7 ) 0.010 (0.056) 0.080 (0.081) 0.113 (0.103) VOLFMA ( 10 6 ) 0.502 (0.741) 1.038 (1.056) 3.810 (1.351) *** VOLFANT ( 10 6 ) 0.290 (0.164) 0.988 (0.235) *** 0.148 (0.300) VOLFUN ( 10 6 ) 0.170 (0.112) 1.299 (0.159) *** 0.833 (0.204) *** VOLOMA ( 10 6 ) 0.056 (0.728) 0.400 (1.039) 3.776 (1.328) *** VOLOANT ( 10 6 ) 0.120 (0.200) 0.158 ( 0.285) 0.125 (0.364) VOLOUN ( 10 6 ) 0.195 (0.106) 0.423 (0.151) *** 0.229 (0.193) PAGE 52 52 Table 2 7. Continued Regressor GIS_S t GIS_F t GIS_O t GIS_S t 1 0.009 (0.039) 0.021 (0.056) 0.071 (0.072) GIS_F t 1 0.036 (0.027) 0.017 (0.039) 0.042 (0.050) GIS_O t 1 0.005 (0.021) 0.052 (0.030) 0.085 (0.038) ** GIS_S t 2 0.010 (0.040) 0.028 (0.057) 0.129 (0.072) GIS_F t 2 0.037 (0.026) 0.016 (0.037) 0.093 (0.048) GIS_O t 2 0.020 (0.021) 0.004 (0.029) 0.013 (0.038) R esults of regressing the generalized information shares on various explanatory variables, including the compo nents of traded volume and macroeconomic announcement variables, using vector regression procedures are shown Variable definitions are given in Table 2 4 The frequency of the data is daily, and the sample period runs from January 29, 199 3 to December 31, 1995 Standard err ors are given in parentheses. ( *, **, *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.) PAGE 53 53 Table 2 8. E ffective spreads with no announcement variables included: regression results Regressor GIS_S t GIS_F t GIS_O t Intercept 0.045 (0.007) *** 0.138 (0.011) *** 0.072 (0.012) *** MOND 0.006 (0.004) 0.003 (0.006) 0.004 (0.007) T UED 0.003 (0.004) 0.006 (0.006) 0.001 (0.007) THUD 0.002 (0.004) 0.002 (0.007) 0.008 (0.008) FRI D 0.003 (0.004) 0.004 (0.006) 0.001 (0.007) JAND 0.011 (0.007) 0.008 (0.010) 0.020 (0. 012) FEBD 0.016 (0.006) ** 0.004 (0.010) 0.003 (0.011) MARD 0.016 (0.006) ** 0.002 (0.010) 0.013 (0.011) APRD 0.010 (0.006) 0.008 (0.010) 0.001 (0.011) JUND 0.021 (0.006) *** 0.001 (0.010) 0.023 (0.011) ** JULD 0.010 (0.006) 0.012 (0.010) 0.012 (0.011) AUGD 0.005 (0.006) 0.015 (0.009) 0.013 (0.011) SEPD 0.014 (0.006) ** 0.009 (0.010) 0.008 (0.011) OCTD 0.008 (0.006) 0. 009 (0.009) 0.010 (0.011) NOVD 0.021 (0.006) *** 0.004 (0.010) 0.005 (0.011) DECD 0.021 (0.006) *** 0.006 (0.010) 0.016 (0.011) OPTEXTHD 0.000 (0.007) 0.004 (0.010) 0.002 (0.012) TRWITCHD 0.005 (0.011) 0.047 (0.017) *** 0.008 (0.019) EOQD 0.004 (0.005) 0.013 (0.007) 0.011 (0.008) BREAKD 0.005 (0.003) 0.012 (0.005) ** 0.062 (0.006) *** EFFSPRS 13.689 (5.174) *** 27.977 (8.089) *** 16 .244 (9.115) EFFSPRF 3.710 (10.490) 22.384 (16.399) 15.442 (18.478) EFFSPRO 2.083 (2.270) 0.016 (3.548) 9.589 (3.998) ** GIS_S t 1 0.074 (0.034) ** 0.021 (0.053) 0.046 (0.060) GIS_F t 1 0.049 (0.022) ** 0.018 (0.035) 0.066 (0.039) GIS_O t 1 0.009 (0.019) 0.052 (0.029) 0.030 (0.033) GIS_S t 2 0.000 (0.034) 0.009 (0.053) 0.113 (0.060) GIS_F t 2 0.033 (0.022) 0.052 (0.035) 0.058 (0.039) GI S_O t 2 0.005 (0.019) 0.023 (0.029) 0.007 (0.033) R esults of regressing the generalized information shares on various explanatory variables, including effective spreads, using vector regression procedures are shown Macroeconomic announc ement variables are not included. Variable definitions are given in Table 2 4 The frequency of the data is daily, and the sample period runs from January 29, 199 3 to December 31, 1996 Standard err ors are given in parentheses. ( *, **, *** indicate statist ical significance at the 10%, 5% and 1% levels, respectively.) PAGE 54 54 Table 2 9. Effective spreads with announcement variables included: regression results Regressor GIS_S t GIS_F t GIS_O t Intercept 0.046 (0.007) *** 0.137 (0.011) *** 0.072 (0.013 ) *** MOND 0.006 (0.004) 0.002 (0.006) 0.004 (0.007) TUED 0.003 (0.004) 0.008 (0.006) 0.002 (0.007) THUD 0.002 (0.004) 0.001 (0.007) 0.009 (0.008) FRI D 0.003 (0.004) 0.007 (0.006) 0.0 00 (0.007) JAND 0.010 (0.007) 0.007 (0.010) 0.021 (0.012) FEBD 0.015 (0.007) ** 0.003 (0.010) 0.005 (0.011) MARD 0.017 (0.006) *** 0.002 (0.010) 0.012 (0.011) APRD 0.010 (0.006) 0.008 ( 0.010) 0.000 (0.011) JUND 0.021 (0.006) *** 0.001 (0.010) 0.023 (0.011) ** JULD 0.011 (0.006) 0.013 (0.010) 0.012 (0.011) AUGD 0.005 (0.006) 0.015 (0.009) 0.012 (0.011) SEPD 0.015 (0.007) ** 0.008 (0.010) 0.009 (0.011) OCTD 0.007 (0.006) 0.011 (0.010) 0.010 (0.011) NOVD 0.020 (0.006) *** 0.005 (0.010) 0.003 (0.011) DECD 0.020 (0.007) *** 0.007 (0.010) 0.017 (0.011) OPTEXTH D 0.001 (0.007) 0.005 (0.010) 0.000 (0.012) TRWITCHD 0.005 (0.011) 0.039 (0.017) ** 0.010 (0.019) EOQD 0.005 (0.005) 0.013 (0.007) 0.011 (0.008) CNSTRC 0.005 (0.006) 0.015 (0.009) 0.0 17 (0.010) HSALC 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) PERCC 0.016 (0.034) 0.004 (0.053) 0.020 (0.060) PERIC 0.002 (0.031) 0.018 (0.048) 0.000 (0.055) DGORC 0.004 (0.003) 0.002 (0 .005) 0.003 (0.005) NAPMC 0.003 (0.003) 0.007 (0.004) 0.004 (0.005) CPIC 0.015 (0.052) 0.038 (0.081) 0.063 (0.092) CCRDTC 0.001 (0.002) 0.001 (0.003) 0.001 (0.004) HSTRC 0.108 (0.089) 0.038 (0.138) 0.302 (0.157) INPRDC 0.027 (0.027) 0.073 (0.042) 0.000 (0.048) LINDC 0.017 (0.047) 0.015 (0.072) 0.101 (0.082) M2C 0.001 (0.001) 0.001 (0.002) 0.002 (0.002) PPIC 0.035 (0.023) 0.097 (0.035) *** 0.029 (0.040) RETSLC 0.001 (0.012) 0.005 (0.019) 0.014 (0.021) UNEMPC 0.026 (0.037) 0.060 (0.057) 0.043 (0.065) BREAKD 0.004 (0.003) 0.012 (0.005) ** 0.061 (0.0 06) *** EFFSPRS 14.602 (5.228) *** 28.676 (8.141) *** 16.398 (9.208) EFFSPRF 3.255 (10.577) 20.863 (16.468) 15.744 (18.627) EFFSPRO 1.949 (2.291) 0.119 (3.567) 9.795 (4.035) ** GIS_S t 1 0.077 (0.034) ** 0.023 (0.053) 0.035 (0.060) GIS_F t 1 0.049 (0.023) ** 0.035 (0.035) 0.061 (0.040) GIS_O t 1 0.008 (0.019) 0.065 (0.030) ** 0.035 (0.034) GIS_S t 2 0.004 (0.034) 0.016 (0.054) 0.115 (0.061) GIS_F t 2 0.027 (0.023) 0.050 (0.035) 0.062 (0.040) GIS_O t 2 0.004 (0.019) 0.024 (0.029) 0.011 (0.033) PAGE 55 55 Table 2 9. Continued Results of regressing the generalized information shares on various explanatory variables, including effective spreads and macroeconomic announcement variables, using vector regression procedures are shown Variable definitions are given in Table 2 4 The frequency of the data is daily, and the sample period runs from January 29, 199 3 to December 31, 199 6 Standard err ors are given in parentheses. ( *, **, *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.) PAGE 56 56 Table 2 10. Components of traded volume and effective spreads with no announcement variables included: regression resu lts Regressor GIS_S t GIS_F t GIS_O t Intercept 0.039 (0.021) 0.208 (0.029) *** 0.112 (0.037) *** MOND 0.007 (0.005) 0.017 (0.007) ** 0.007 (0.009) TUED 0.002 (0.005) 0.005 (0.007) 0.002 (0.008) THUD 0.000 (0.005) 0.002 (0.007) 0.009 (0.009) FRID 0.004 (0.005) 0.001 (0.007) 0.003 (0.008) JAND 0.001 (0.008) 0.004 (0.012) 0.023 (0.015) FEBD 0.018 (0.007) ** 0.004 (0.011) 0.009 (0.013) MARD 0.011 (0.008) 0.027 (0.012) ** 0.026 (0.015) APRD 0.010 (0.008) 0.007 (0.011) 0.003 (0.014) JUND 0.015 (0.008) 0.010 (0.011) 0.034 (0.014) ** JULD 0.008 (0.007) 0.012 (0.011) 0. 010 (0.014) AUGD 0.000 (0.007) 0.001 (0.010) 0.001 (0.013) SEPD 0.013 (0.008) 0.015 (0.012) 0.019 (0.015) OCTD 0.004 (0.007) 0.006 (0.010) 0.003 (0.013) NOVD 0.014 (0.007) ** 0.001 (0.0 10) 0.006 (0.013) DECD 0.013 (0.008) 0.005 (0.012) 0.025 (0.015) OPTEXTHD 0.009 (0.008) 0.022 (0.012) 0.008 (0.015) TRWITCHD 0.002 (0.013) 0.011 (0.019) 0.019 (0.024) EOQD 0.004 (0.007 ) 0.029 (0.010) *** 0.027 (0.012) ** BREAKD 0.003 (0.005) 0.013 (0.007) 0.067 (0.009) *** VOLSMA ( 10 7 ) 0.602 (0.199) *** 0.492 (0.285) 1.418 (0.361) *** VOLSANT ( 10 7 ) 0.112 (0.162) 0.034 (0. 232) 0.099 (0.294) VOLSUN ( 10 7 ) 0.007 (0.057) 0.096 (0.081) 0.135 (0.103) VOLFMA ( 10 6 ) 0.412 (0.730) 0.720 (1.046) 3.838 (1.325) *** VOLFANT ( 10 6 ) 0.284 (0.163) 0.957 (0.233) *** 0.194 (0.296) VOLFUN ( 10 6 ) 0.200 (0.111) 1.277 (0.159) *** 0.778 (0.202) *** VOLOMA ( 10 6 ) 0.011 (0.719) 0.032 (1.030) 3.980 (1.305) *** VOLOANT ( 10 6 ) 0.137 (0.202) 0.103 (0.290) 0.111 (0.368) VOLO UN ( 10 6 ) 0.209 (0.104) ** 0.456 (0.149) *** 0.206 (0.189) EFFSPRS 19.233 (16.320) 26.731 (23.373) 30.697 (29.620) EFFSPRF 31.709 (22.624) 63.283 (32.403) 53.372 (41.063) EFFSPRO 4.689 (2.499) 7.348 (3.579) ** 12.850 (4.535) *** GIS_S t 1 0.010 (0.039) 0.021 (0.056) 0.078 (0.071) GIS_F t 1 0.039 (0.027) 0.037 (0.038) 0.054 (0.049) GIS_O t 1 0.005 (0.021) 0.042 (0.029) 0.082 (0.037) ** GIS_S t 2 0.001 ( 0.039) 0.026 (0.056) 0.113 (0.071) GIS_F t 2 0.039 (0.026) 0.010 (0.037) 0.086 (0.047) GIS_O t 2 0.019 (0.020) 0.012 (0.029) 0.021 (0.037) R esults of regressing the generalized information shares on variou s explanatory variables, including the compo nents of traded volume and effective spreads, using vector regression procedures are shown Macroeconomic announcement variables are not included. Variable definitions are given in Table 2 4 The frequency of the data is daily, and the sample period runs from January 29, 199 3 to December 31, 1995 Standard err ors are given in parentheses. ( *, **, *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.) PAGE 57 57 Table 2 11. Components of traded v olume and effective spreads with announcement variables included: regression results Regressor GIS_S t GIS_F t GIS_O t Intercept 0.035 (0.021) 0.210 (0.030) *** 0.114 (0.038) *** MOND 0.007 (0.005) 0.014 (0.007) ** 0.006 (0. 009) TUED 0.003 (0.005) 0.006 (0.007) 0.002 (0.008) THUD 0.000 (0.005) 0.001 (0.007) 0.009 (0.009) FRID 0.005 (0.005) 0.000 (0.007) 0.002 (0.009) JAND 0.001 (0.008) 0.002 (0.012) 0.0 24 (0.015) FEBD 0.019 (0.007) ** 0.004 (0.011) 0.013 (0.014) MARD 0.009 (0.009) 0.027 (0.012) ** 0.024 (0.016) APRD 0.009 (0.008) 0.007 (0.011) 0.003 (0.014) JUND 0.014 (0.008) 0.012 (0 .011) 0.034 (0.014) ** JULD 0.007 (0.008) 0.011 (0.011) 0.010 (0.014) AUGD 0.000 (0.007) 0.001 (0.010) 0.001 (0.013) SEPD 0.011 (0.008) 0.014 (0.012) 0.018 (0.015) OCTD 0.004 (0.007) 0.010 (0.010) 0.005 (0.013) NOVD 0.015 (0.007) ** 0.001 (0.010) 0.008 (0.013) DECD 0.011 (0.008) 0.004 (0.012) 0.024 (0.015) OPTEXTHD 0.010 (0.008) 0.020 (0.012) 0.010 (0.015) TRWITCHD 0 .001 (0.013) 0.004 (0.019) 0.015 (0.024) EOQD 0.003 (0.007) 0.027 (0.010) *** 0.025 (0.012) ** CNSTRC 0.009 (0.008) 0.027 (0.011) ** 0.021 (0.014) HSALC 0.000 (0.000) 0.000 (0.000) 0.000 ( 0.000) PERCC 0.069 (0.046) 0.039 (0.065) 0.064 (0.083) PERIC 0.000 (0.032) 0.017 (0.045) 0.023 (0.058) DGORC 0.002 (0.003) 0.002 (0.005) 0.004 (0.006) NAPMC 0.006 (0.003) 0.007 (0.005) 0.005 (0.006) CPIC 0.018 (0.055) 0.037 (0.078) 0.057 (0.100) CCRDTC 0.002 (0.003) 0.001 (0.004) 0.002 (0.005) HSTRC 0.202 (0.101) ** 0.078 (0.145) 0.481 (0.185) *** INPRDC 0.005 (0.034) 0.101 (0.049) ** 0.005 (0.062) LINDC 0.006 (0.056) 0.115 (0.080) 0.027 (0.102) M2C 0.001 (0.001) 0.000 (0.002) 0.001 (0.002) PPIC 0.026 (0.025) 0.064 (0.035) 0.018 (0.045) RETSLC 0.006 (0.013) 0.004 (0.018) 0.010 (0.024) UNEMPC 0.023 (0.041) 0.002 (0.059) 0.022 (0.075) BREAKD 0.003 (0.005) 0.012 (0.007) 0.066 (0.009) *** VOLSMA ( 10 7 ) 0.632 (0.202) *** 0.424 (0.287) 1. 488 (0.367) *** VOLSANT ( 10 7 ) 0.109 (0.163) 0.015 (0.232) 0.138 (0.297) VOLSUN ( 10 7 ) 0.018 (0.057) 0.098 (0.081) 0.128 (0.104) VOLFMA ( 10 6 ) 0.619 (0.742) 0.886 (1.057) 3.996 (1.351) *** VO LFANT ( 10 6 ) 0.306 (0.164) 0.969 (0.234) *** 0.169 (0.299) VOLFUN ( 10 6 ) 0.175 (0.114) 1.323 (0.162) *** 0.780 (0.207) *** VOLOMA ( 10 6 ) 0.210 (0.731) 0.173 (1.040) 4.097 (1.330) *** VOLOANT ( 10 6 ) 0.111 (0.204) 0.142 (0.291) 0.114 (0.371) VOLOUN ( 10 6 ) 0.201 (0.106) 0.435 (0.151) *** 0.239 (0.193) PAGE 58 58 Table 2 11. Continued Regressor GIS_S t GIS_F t GIS_O t EFFSPRS 23.149 (16.485) 27.030 (23.474) 28.582 ( 30.009) EFFSPRF 35.698 (22.834) 63.729 (32.515) 48.473 (41.566) EFFSPRO 4.737 (2.521) 8.114 (3.590) ** 12.724 (4.589) *** GIS_S t 1 0.007 (0.039) 0.022 (0.056) 0.072 (0.071) GIS_F t 1 0.036 (0.027) 0.020 (0.039) 0.047 (0.050) GIS_O t 1 0.008 (0.021) 0.056 (0.030) 0.088 (0.038) ** GIS_S t 2 0.007 (0.040) 0.024 (0.057) 0.112 (0.072) GIS_F t 2 0.035 (0.026) 0.012 (0.037) 0.093 (0.048) GIS_O t 2 0.019 (0.021) 0.003 (0.029) 0.020 (0.038) R esults of regressing the generalized information shares on various explanatory variables, including the compo nents of traded volume and effective spreads, using vector regression procedures are s hown Macroeconomic announcement variables are also included. Variable definitions are given in Table 2 4 The frequency of the data is daily, and the sample period runs from January 29, 199 3 to December 31, 1995 Standard err ors are given in parentheses. ( *, **, *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.) PAGE 59 59 Figure 2 1. Monthly averages of daily information shares for the stock, futures, and options markets based on orthogonalized impulse response functions. This gr aph depicts the monthly averages of the daily information shares from February, 1993 to December, 1996 for each of the three markets (stock, futures, and options). The information shares were calculated using orthogonalized impulse response functions. Thes e averages are monthly means of the daily midrange values obtained for the information shares. The information shares are normalized to sum to one for each month. PAGE 60 60 Figure 2 2. Daily information shares for the stock, futures, and options markets based on orthogonalized impulse response functions. This graph depicts the daily information shares from January 3, 1995 to June 30, 1995 for each of the three markets (stock, futures, and options). The six month sample period corresponds to a window around the o ptions market auto quote initiation. The information shares are daily averages of the maximum and minimum values obtained using orthogonalized impulse response functions. The information shares are normalized to sum to one for each day. PAGE 61 61 Figure 2 3. Mon thly averages of daily information shares for the stock, futures, and options markets based on generalized impulse response functions This graph depicts the monthly averages of the daily information shares from February, 1993 to December, 1996 for each o f the three markets (stock, futures, and options). The information shares were calculated using gener alized impulse response functions. These averages are monthly means of the daily values obtained for the information shares. The information shares are nor malized to sum to one for each month. PAGE 62 62 Figure 2 4. Daily information shares for the stock, futures, and options markets based on generalized impulse response functions This graph depicts the daily information shares from January 3, 1995 to June 30, 19 95 for each of the three markets (stock, futures, and options). The six month sample period corresponds to a window around the options market auto quote initiation. The information shares are the daily values obtained using generalized impulse response fun ctions. The information shares are normalized to sum to one for each day. PAGE 63 63 CHAPTER 3 WHERE IS THE LIQUIDI TY? INFORMATION AND TRADING COSTS IN ASS ET PRICING Introduction In the past decade, there has been a marked increase in research that examines asset liquidity effects in financial markets. The basic hypothesis is that less liquid assets should be priced to offer higher expected returns relative to more liquid assets, controlling for various risks and other factors. Several studies using many different measures of liquidity have been conducted that demonstrate the tenability of this hypothesis [e.g., Chordia et al. ( 2000 2001), Amihud (2002), Breen et al. (2002), Pstor and Stambaugh (2003), Chordia et al. (2005)]. 14 These studies generally find that the re are liquidity effects in asset pricing, though the sources of these effects and the sizes of the liquidity premiums vary. The variation in results, however, is not surprising given that there are various aspects to liquidity. Amihud (2002) goes so far a s to suggests three characteristics that can be used to describe market liquidity: tightness, depth, and resiliency. Tightness refers to the cost of turni ng around a position over a short period of time. Depth refers to the size of an order needed to change a price by a given amount. Resiliency refers to the speed at which prices tend to revert back to an underlying equilibrium value following a random, uni nformative shock to the market. Quoted bid ask spreads, effective bid ask spreads, and proportional bid ask spreads are the most commonly considered liquidity proxies and can be the number of limit impact or return reversal measures are often used. 14 Table A 1 provides a summary of the principal liquidity measures used in the literature. PAGE 64 64 Along similar lines, Black (1971) describes a market (for a stock) as liquid if four conditions hold. First, bid and ask prices should always be available to satisfy the needs of immediacy that some traders have. Secondly, the bid ask spread should be small. Thirdly, assuming an absence of special information, for large block trades that are executed over a longer period of time, the average price that will be obtained should not be very different from the current market price. Finally, for a trader seeking to buy or sell large block immediately, a premium or discount will be realized, where the magnitude of the premium or discount will in the sense that almost any amount of stock can be bought or sold im mediately; and an efficient market, in the sense that small amounts of stock can always be bought or sold very near the current market price, and in the sense that large amounts can be bought or sold over long periods of time at prices that, on average, ar a liquid market suggests that it is almost infinitely tight, very deep, and resilient enough that prices will ultimately tend towards their underlying value. Persaud (2002) considers diversity t o be a fourth aspect of liquidity. The argument is that with an increased number of market participants there will be a greater diversity of opinion regarding the value of an asset. This means that a market will be more liquid the greater the number of pla yers willing to trade on both sides of the current market price. Liquidity dries up if everyone wants to buy at the same time or sell at the same time, as there is then no one to trade with. Diversity of opinion about the value of an asset may be assessed in terms of order measure, described by Easley et al. (1996) and Easley et al. (2002). PAGE 65 65 Researchers have also been creative in devising new measures, some of w hich incorporate particular stock per dollar volume traded. The probability of informed trading (PIN) measure described by Easley et al. (2002) serves as a p roxy for information based liquidity inasmuch as it quantifies the asymmetric information possessed by certain traders buying and selling a particular asset. Given the measurement problems in defining the various dimensions of liquidity, more recent studie s have used a combination of several variables to encapsulate liquidity. For instance, Bharath et al. (2006) create an information asymmetry index based on four market microstructure liquidity proxies in order to examine the influence on capital structure decisions. Chen (2005) uses principal component analysis to extract the first principal component from seven liquidity measures, and creates a variable that is utilized in an asset pricing framework to show that liquidity is priced. In this study, I propos e that liquidity has more than one dimension that is priced. In particular, I use latent variable techniques to examine two separate liquidity components: a component associated with asymmetric information among traders relating to a particular asset and a nother component associated with order processing costs involved in trading the asset (direct trading costs). Theoretical models of the bid ask spread also show that there are generally two transaction cost components to the bid ask spread an adverse sel ection and order processing component. Controlling for Fama French and momentum factors, I find that there are economically and statistically significant premiums associated with the information and trading cost liquidity components. Additionally, I demons trate that as tick size changed from eighths to sixteenths to decimals in the markets for the New York Stock Exchange (NYSE), American Stock Exchange PAGE 66 66 (AMEX) and Nasdaq, there have been shifts in the proportion of asset liquidity premiums that can be attrib uted to each of these two components. In particular, the overall unconditional liquidity premium has remained relatively constant over the eleven year sample period from 1993 to 2003. However, controlling for size, the liquidity premium for both liquidity components has increased somewhat during the decimal period relative to the earlier eighths and sixteenths periods. Research Methodology Numerous models in financial economics are formulated in terms of theoretical or hypothetical concepts that are not dir ectly observable or measurable (i.e., latent variables). However, several indicators or proxies for these unobservable variables are often available, although these proxy variables generally measure the unobservable variable with error. Liquidity is a conc ept that is difficult to define; however, there are several proxies or indicator variables that have been developed. Therefore, latent variable models provide an ideal framework to examine the effects of liquidity on asset pricing. In this study, I use a s imple three variable model to estimate latent liquidity factors, which are then used to formulate mimicking portfolios used in asset pricing tests. The components of liquidity are examined along two different dimensions that heretofore have not been explic itly considered together: information based and trade based liquidity Using structural latent variable models, I estimate latent liquidity variables in each of these two dimensions by using liquidity measures that exhibit a common liquidity factor. The id ea is that about that asset, thus discouraging uninformed traders from participating in the market for that asset unless they are compensated for doing so. On liquidity is also based on trading costs. Thus, an asset that is highly sought after and trades PAGE 67 67 frequently will have economies of scale for market makers, and so the overall transaction costs will be reduced. Genera l Formulation of Latent Variable Models with Measurement Errors Suppose that y is a p 1 vector of observable indicator variables, and z is a q 1 vector of unobservable latent variables. Furthermore, assume that y is linearly related to z through the parame ter matrix plus an error term e with variance covariance matrix 15 The multiple indicator/multiple latent variable models can then be formulated as shown in Equation 3 1. (3 1) The model depicted in Equation 3 1 can be estimated using several techniques including maximum likelihood and weighted least squares. This model has several advantages for estimating measure s of liquidity. First, the information from severa l proxies is used efficiently. Second, the errors in the structural equation and any measurement errors in the proxy variables are explici tly modeled. Third, the model allows for correlation among the err or terms and latent variables. Finally, under general conditions, the latent variable estimation technique provides cons istent estimates, allowing researchers and practitioners to make correct inferences. Simple Three Indicator/One Latent Variable Model Suppose there are three indicator variables ( y 1 y 2 y 3 ) that measure one latent variable ( z ) with errors ( e 1 e 2 e 3 ) tha t have zero means and variances i = 1, 2, 3. The indicator variables and the latent variable a re assumed to have zero means. Furthermore, assume the indicator variables are correlated through the latent variable z z is uncorrel ated with the errors and the errors are uncorrelated with each other. This leads to the latent variable model that is characterized by Equations 3 2, 3 3 and 3 4. 15 The models are also referred to as linear structural models with measuremen t errors, analysis of covariance structures, path analysis, causal models, and content variable models. PAGE 68 68 (3 2) (3 3) (3 4) Th e parameters (the i s ) and error variances (the s) can be consistently estimated using the information in the sample variance covariance matrix of the observable indicator variables (the y i s). T he sample variance covariance matri x for the y i s is shown in Equation 3 5. (3 5) The variance covariance stru cture implied by the system of Equations 3 2 to 3 4 is given in Equation 3 6. (3 6) If it is assumed that the errors and the latent va riable are uncorrelated and that = 1 the sample moments ( the s ij s) provide six pieces of information to consistently estimate the six parameters ( i and i = 1, 2, 3). For this simple model, the metho d of moments provides a unique solution for the six unknown parameters in terms of the six sample moments, which is depicted in Equation 3 7. (3 7) Note that it is not necessary to observe the latent variable in order to estimat e th e parameters of the model. The moments of the sample data contain sufficient information to ident ify the PAGE 69 69 structural parameters. For the model represented by Equations 3 2 to 3 4 the solution is unique, and hence the estimates are also maximum likelihood e stimates. If the number of indicator variables exceeds three and the number of latent variables is greater than one, the model may not be exactly identified. In this case, one can use maximum likelihood or weighted least squares techniques to obtain consis tent estimates. Furthermore, one can obtain standard errors for the parameter estimates through the Hessian matrix. Given the parameter estimates, the underlying latent variable can be measured conditional on the observed indicator variables. If the y i s an d z are assumed to be jointly distributed multivariate normal, then the underlying latent variable conditional on the y i s is given by E quation 3 8. (3 8) Given the model represented by Equations 3 2 to 3 4, the estimated value for t he latent variable may be obtained as shown in Equation 3 9. (3 9) where It can be seen that the latent variable is an optimally weighted sum of the observed indicator variables, where the weights are related to the error variance associated with the indicator variable and the loadings on the latent variable. In the suggested framework, as I seek to differentiate between information based liquidity and trade based liquidity, two sets of three proxies each are used to estimate the two latent variables. The three liquidity proxies used in the estimation of the information based liquidity variable, LIQ_INFO are the asymmetric information component of the proportional spread ( AI ), PAGE 70 70 Easley et PIN ), and the negative of the Amivest liquidity ratio ( AMIV ), which is described in studies by Amihud et al. (1997), and Berkman and Eleswarapu (1998). Each of these three measures proxy for informed t rading, but they arguably reflect different aspects of liquidity: the asymmetric information component is a cost based measure reflecting the tightness of the market, the Amivest liquidity ratio is a volume based measure associated with depth, and PIN may be considered a proxy for diversity of opinion about a stock. The trade based liquidity variable, LIQ_TRAD is also estimated using three proxies: the order processing component of the proportional spread ( OP (2002) dollar volume measure ( BHKDVOL ), and the negative of the logarithm of the anticipated volume of trading obtained from a 100 day moving average ( LN MA VOL ). This last variable, like the Amivest liquidity ratio, is a volume based measure of market depth, the dollar v olume measure is a price reversal measure reflecting resiliency, and the order processing component of the spread is linked to the tightness of the market. By estimating the two liquidity variables independently through these simple three indicator/one lat ent v ariable m odel s, each of them is exactly identified. Data and Summary Statistics Data The sample period for the data ranges from January 1, 1993 to December 31, 2003, with the beginning date corresponding to the initial formation of my liquidity portfo lios and the availability of the Transactions and Quotes (TAQ) database. Daily liquidity measures for NYSE/AMEX and Nasdaq listed stocks are obtained either directly or by calculation from the TAQ database. For each firm, these variables are merged with da ily data from the Center for Research in Securities Prices (CRSP) database by CUSIP number and ticker symbol. Before PAGE 71 71 providing summary statistics, some preliminary notation, definitions and explanations are given, followed by descriptions of the liquidity variables. Additionally, certain customary filters are imposed on the data sample, and these are also discussed. Preliminary notation, definitions and explanations At any given time t l et Q bid t and Q ask t be, respectively, the quoted bid price and ask pr ice. Let Q m t = ( Q bid t + Q ask t ) be the midpoint of the quoted prices, S t be the bid ask spread (measured in dollar terms), S t / Q m t be the percentage spread for a quote (measured in percentage terms), P t be the transaction price, and V t be the transactio n volume. Let N be the number of quotes in a day, occurring at times t 0 t 1 t 2 t N where t 0 = 0. For a transaction occurring at time t we define the matched quote as the nearest quote that can be obtained that precedes the transaction by at least 5 s econds The i mpact measure at time t c onsiders how much of an impact a trade of size (volume) V t will have on quoted (bid or ask) prices over a 5 minute span. Thus, f or each trade, the impact measure at time t ( I t ) is as given in Equation 3 10. or (3 10) Transaction prices may be thought of as incorporating a true price ( P *) a bid ask bounce component ( B t ) and an error term ( ) ; quoted prices would not include the bid ask bounce. Thus, a system of equations is obtained as shown in Equation 3 11. (3 11) If it is assumed that, on average, the bounce component will be half of the spread, then it follows that B t = S t PAGE 72 72 A r eturn difference between transaction prices an d quotes can be calculated. For a transaction occurring at time t n the next quote that is at least 5 seconds after the transaction is obtained, and the midpoint of this quote are together used to calculate the return between the transaction and the quote. Finally, the return difference is obtained as the return between transaction and quote at time t n and the return between transaction and quote at time t n 1 This is defined as shown in Equation 3 12. (3 12) Description of liquidity measures I use the following variables in the remainder of the study. The first fourteen variables are calculated on a daily basis for each day d and each stock i The equivalent variables are denoted in upper case when they are averaged on a monthly basi s for each month m The last seven variables are calculated on a monthly basis for each month m and each stock i for months where at least 15 days of trading are available. 16 D m is the number of trading days in month m Average quoted spread = qspr i,d = Average proportional quoted spread = pqspr i,d = Average effective spread = espr i,d = Average proportional effective spread = pespr i,d = Standard deviation of the quote return, during the day = lndev i,d 16 As a result of September 11, 2001, there are insufficient trading days available for calculating these measures during that month. PAGE 73 73 Mean price impact measure = impactm i,d = George Kaul Nimalendran (GKN) order processing component of the spread = op i,d = where cov i,d is the covariance of the return differences during the day GKN asymmetric information component of the spread = ai i,d = pspr i,d op i,d Total volume for the day = totvol i,d = 100 day moving average of traded volume = mavol i,d Total dollar volume for the day = dtotvol i,d = where is the closing price for stock i on day d Number of shares outstanding = shrout i,d Market capitalization (closing price times number of shares outstanding) = mktcap i,d Natural logarithm of market capitalization = lnmktcap i,d = Reciprocal of average daily turnover for a month, where this is given as the average daily total volume for the current month divided by the average daily number of shares o utstanding from the previous month = RTURNOVER i,m = Amivest liquidity ratio = AMIV i,m = where ret i,d is the daily return on the stock ILLIQ i,m = where ret i,d is the daily return on the stock Natural logarithm of average anticipated daily traded volume for a month = LNMAVOL i,m = Probability of information based trading = PIN i,m PAGE 74 74 Pstor Stambaugh (PS) return reversal measure, using a dollar volume specification = PSDVOL i,m Breen Hodrick Korajczyk (BHK) return reversal measure, using a dollar volume specification = BHKDVOL i,m Data filters Consistent with the literature, I eliminate certain observations that may have been recorded in er ror or are outliers in one form or another. Explicitly, observations are discarded where any of the following conditions apply: QSPR i m is greater than $5 the ratio ESPR i m / QSPR i m is greater than 4 PQSPR i m is greater than 0.5 PESPR i m is greater than 0 .4 LNDEV i m is nonpositive IMPACTM i m is negative OP i m is nonpositive PIN i m is equal to zero or one PSDVOL i m is equal to zero BHKDVOL i m is equal to zero the average over month m of the midprice for stock i is less than $5 or greater than $1,000 Additio nally, if AI i m is negative then AI i m is set to zero. This leaves 185,632 firm month observations for the NYSE/AMEX markets, and 153,058 firm month observations for the Nasdaq market Summary Statistics and Estimation of Latent Liquidity Variables Table 3 1 provides summary statistics for the liquidity variables, after averaging them by month. The table gives the means, standard deviations, minimum and maximum values for the variables for the NYSE/AMEX and Nasdaq markets over the period from January, 1993 to December, 2003. For NYSE/AMEX stocks, the quoted spreads across all stocks over the entire sample period average 16.7 cents, and the corresponding figure for effective spreads is 5.4 cents (for Nasdaq stocks, the corresponding numbers are 24.9 cents and 9.9 cents, respectively). This suggests that tick sizes may have an effect on determining the prices at which very liquid stocks PAGE 75 75 trade. For NYSE/AMEX stocks, the average proportional quoted spread across all stocks is 0.85%, and this can be decomposed usi ng the GKN approach into order processing costs of 0.46% and asymmetric information costs of 0.39% (for Nasdaq stocks, the corresponding numbers are 1.52%, 0.92%, and 0.60%, respectively). The average total traded volume per day in the NYSE/AMEX markets is 454,000 shares, the average daily turnover is about 0.12%, the probability of informed trading for the average stock is 0.13, and the average firm size is $4.5 billion. (The corresponding numbers for the Nasdaq market are 541,000 shares, 0. 2 8 % turnover, P IN of 0.19 for the average stock, and $1.4 billion for the average firm size.) As a first step in determining the number of liquidity factors, I performed some exploratory factor analyses and found that two factors were sufficient to explain the cross sect ional relation among the six liquidity measures in each of the markets. 17 Three proxies were used to estimate the first (information based) latent liquidity variable LIQ_INFO namely 100 AI i m AMIV i,m /100,000,000, and PIN i m These variables are calculate d for each stock i and for each month m Similarly, three other proxies were used to estimate the second (trade based) latent liquidity variable LIQ_TRAD namely 100 OP i m LNMAVOL i m /100, and 10 BHKDVOL i,m I truncated the upper and lower 0.5% of the obs ervations for each of these variables before estimating the latent variable models to eliminate extreme outlier estimation problems. Figure 3 1 shows the time variation of the 21 defined variables over the period from January, 1993 to December, 2003 for th e NYSE/AMEX and Nasdaq markets. Of particular interest in Figures 3 1G and 3 1H for the components of the proportional bid ask spread, some of the sharpest declines occur in July 1997 and February 2001. These dates correspond to the 17 The number of principal components was determined based on whether the corresponding eigenvalues were greater than one or if the total variance explained by the principal components was greater than or equal to 80% for each month of the sample period. PAGE 76 76 beginning of the sixtee nths and decimal tick size periods, respectively. Interestingly, there is an increase in these measures during the sixteenths period, commencing around July 1998. This is the beginning of a series of liquidity draining events that occurred in 1998, namely the unwinding of the US dollar/yen carry trade in July, the Russian debt crisis in August, and the collapse of Long Term Capital Management (LTCM) in September. 18 The financial crises in mid 1998 also seem to have had long term effects on the Amivest liquid ity measure for the firms, as shown in Figure 3 1P, and the BHK dollar volume measure, as shown in Figure 3 1U. In both cases, aggregate liquidity seems to have improved more in the NYSE/AMEX markets than in the Nasdaq market. The logarithm of anticipated trading volume, as shown in Figure 3 1R shows an improving trend in liquidity for the NYSE/AMEX markets, but substantial variability for the Nasdaq market. Finally, Figure 3 1S shows that the average PIN across all firms trends downwards over the sample pe riod for the NYSE/AMEX markets, but has remained relatively level for the Nasdaq market. This may be explained in part by increased analyst coverage and improvements in the dissemination of stock related information to the general public, especially for th ose listed on NYSE/AMEX, so that an increasing proportion of these firms are more transparent to investors. Other time trends in variables that should be noted are for the price impact and reciprocal of turnover measures. In Figure 3 1F, it can be seen tha t there is a marked increase in the average price impact measure in mid 1998 more interestingly, this increase persists to the end of the sample period. In Figure 3 1O, annual peaks are observed in the reciprocal of turnover measure these occur in Janu ary each year, suggesting that there is a marked decrease in stock turnover in January. This is consistent with many funds, institutions, and individuals rebalancing their 18 T able B 1 provides a chronology of important dates affecting market liquidity during the sample period. PAGE 77 77 portfolios at the end of December of the previous year, and then not changing their portfolio again during the first few days of the new year. Taken together, all of these trends confirm the idea that liquidity cannot easily be summarized in one variable. The tightness of the markets seems to have improved over time, with smaller tick siz es leading to narrower bid ask spreads. On the other hand, the increase in the price impact measure over time, suggests that block traders may find it more difficult to buy or sell large volumes of stock without affecting prices. This implies that there ma y be a large tradeoff between improved liquidity and immediacy for smaller (retail) investors, at the expense of institutional traders who may find it more difficult to execute large block trades. Figure 3 2 shows the time variation over the same sample pe riod for the two latent liquidity variables. In Figure 3 2A, the level and variation for the information based liquidity variable, LIQ_INFO appears lower for the NYSE/AMEX markets than for the Nasdaq market. The chart shows that on aggregate there is less illiquidity due to asymmetric information for the NYSE/AMEX markets. Similar patterns can be observed in Figure 3 2B for the trade based liquidity variable, LIQ_TRAD Overall, the aggregate trade based variables seem to be more sensitive to market wide sh ocks, whereas the aggregate information based variable for the NYSE AMEX markets seem to be trending downwards slightly as with the PIN measure shown in Figure 3 1S. Finally, summary statistics for the liquidity measures and the two latent liquidity variab les, LIQ_INFO and LIQ_TRAD are displayed in Tables 3 2 and 3 3. Similarly, Tables 3 4 and 3 5 display summary statistics for the risk factors employed in the asset pricing models specified in the next section. In the correlation matrices given in Tables 3 2 and 3 3, it can be seen that there is positive correlation between all the liquidity measures and the two variables LIQ_INFO and PAGE 78 78 LIQ_TRAD The correlations between LIQ_INFO and the three liquidity proxies used to estimate it are higher than between LIQ_ INFO and the three proxies used to estimate LIQ_TRAD The converse is not true for the Nasdaq market, but the measures of liquidity used to estimate LIQ_TRAD performed better than other combinations, when used across the different markets It is not surpri sing to see that LIQ_INFO and LIQ_TRAD are correlated (even though they represent different aspects of liquidity) because higher transaction costs would result when trading stocks that have a high degree of information asymmetry associated with them, and v ice versa. Analysis of Portfolio Regression Results Now I focus attention on the question of whether or not each of these liquidity components is priced, and if so, what returns might be expected. In this section, I regress the value weighted excess return s for eight portfolios on the three Fama French factors, the momentum factor, and two liquidity factor mimicking portfolios. Having obtained the measures for the liquidity of stock i in month m I form portfolios based on deciles for each of the two latent variables LIQ_INFO and LIQ_TRAD during the month of December of each year, beginning in 1992. Then, following the approach described by Fama and French (1993), I construct two liquidity factor mimicking portfolios, IML_INFO and IML_TRAD This is done by s ubtracting the simple average return of the three lowest decile portfolios (liquid stocks) from the corresponding simple average return of the three highest decile portfolios (illiquid stocks). These factors are computed on a daily basis for the following year. Figure 3 3 displays the time series of monthly returns on these two liquidity factor mimicking portfolios over the sample period and for the different markets. In addition, Figure 3 3 also shows the monthly returns for the Fama French three factors a nd the momentum factor. It is noteworthy that some of the extreme negative returns associated with the liquidity factors PAGE 79 79 occur during documented liquidity crises: in August and October 1998 (following the Russian default and LTCM collapse), and in March/Ap ril 2000 (following the bursting of the technology bubble). In Table 3 4, for the NYSE/AMEX markets, the correlation between the liquidity factors and the size factor is seen to be fairly large (0.689 for IML_INFO and 0.706 for IML_TRAD ), whereas the corre lation between the liquidity factors and the book to market factor is much smaller (0.215 for IML_INFO and 0.196 for IML_TRAD ). In sharp contrast, for the Nasdaq market the correlations of the liquidity factors with size are close to zero (0.027 for IML_IN FO and 0.032 for IML_TRAD ), but the correlations with the book to market factor are large (0.666 for IML_INFO and 0.624 for IML_TRAD ). This suggests that liquidity premiums may be tied to different characteristics in different markets: the size of firms ma tters more to investors in the NYSE/AMEX markets, whereas the value versus growth aspect of a stock matters more to investors in the Nasdaq market. In the approach used by Fama and French (1993), 55 size and book to market portfolios were constructed, and their value weighted excess returns were regressed on three factors: MKT SMB and HML pa rtitioned by size, the information based liquidity variable LIQ_INFO and the trade based liquidity variable LIQ_TRAD The partition is based on the median value for each of the three variables. On average over the eleven year sample period, some of these portfolios contain more firms than others, particularly the portfolios of large liquid stocks and small illiquid stocks. Three sets of regressions are used to test whether information based liquidity and trade based liquidity are priced. First, portfolio r eturns are regressed against the Fama French three PAGE 80 80 factors and the momentum factor, as a benchmark case. Second, I add both of the liquidity factors to these regressors. Finally, I introduce two dummy variables, D_8ths and D_16ths which are set to one for the eighths and sixteenths tick size periods respectively and zero otherwise. I then include as regressors the interaction of these dummy variables with the liquidity factors. Tables 3 6 to 3 11 provide the results of these regressions for the NYSE/AMEX a nd Nasdaq markets. Comparing Tables 3 6 and 3 8 for each of the portfolios, the adjusted R 2 increases when the two liquidity factors are added to the four factor model. Eight of the sixteen estimated parameters associated with the liquidity factors are sta tistically significant at the 1% level. These results provide support for the assertion that liquidity is priced for both liquidity components. 19 Even stronger results are obtained for the Nasdaq market, as seen in the comparison between Tables 3 7 and 3 9. In this case, thirteen of the sixteen estimated parameters are statistically significant at the 1% level; in particular, the information based liquidity factor is not significant only for small liquid firms. A possible inference that can be made is that l iquidity, both information based and trade based, plays a more important role in asset pricing for Nasdaq stocks than for NYSE/AMEX stocks. A reason for this could be the larger size and greater media coverage of NYSE/AMEX firms. In Tables 3 10 and 3 11, I augment my model by including the interaction effects of the liquidity factors with two dummy variables, D_8ths and D_16ths These dummy variables are set to one during the eighths and sixteenths tick size periods, respectively, and zero otherwise. Thus, positive coefficients estimated for these regressors imply higher returns during one of these periods relative to the decimal period. Most of the coefficients for the interacted regressors are 19 I also used model specifications that included either one or the other of the two liquidity factors, but found that the adjusted R 2 was not as high. Th is suggests that the inclusion of both factors leads to a better model specification. PAGE 81 81 not statistically significant, with some exceptions in each mar ket. In the NYSE/AMEX markets, for the portfolios of small firms, the signs on the coefficients indicate an information based liquidity premium during the sixteenths tick size period relative to the decimal period. Offsetting this premium, a trade based li quidity discount relative to the decimal period is observed. For the Nasdaq market, only one portfolio appears to be noticeably more interesting the portfolio of large stocks that are informationally liquid and transactionally illiquid. This time there i s an information based liquidity discount during both the eighths and sixteenths tick size periods relative to the decimal period, and a trade based liquidity premium during these periods relative to the decimal period. In Tables 3 12 and 3 13, the overall liquidity premiums are examined in more detail over the tick size periods. I control for the effects of size, LIQ_INFO and LIQ_TRAD by finding differences between the returns on the portfolios. I multiply the difference between the liquidity betas in eac h of the periods by the average factor return across the entire sample period. More explicitly, the annualized return reported for the eighths tick size period, controlling for size, is obtained as shown in Equation 3 13. (3 13) I n this case, for the NYSE/AMEX markets, = 1.5192 and = 1.8230 are measured in basis points per day and are obtained from Table 3 4; analogous results are obtained PAGE 82 82 for the Nasdaq market from Table 3 5. The other estimates shown in Tables 3 12 and 3 13 are calculated in a similar manner across the price discreteness regimes. In the first column of Table 3 12, taking the difference between the portfolio of small illiquid stocks and the portfolio containing large li quid stocks after controlling for the Fama French and momentum factors, it is found that the premium is fairly stable over time (2.613% per year in the eighths regime to 2.692% per year during the decimal period). In the second column of Table 3 12, it can be seen that, controlling for size as per Equation 3 13, the average combined liquidity premium in the NYSE/AMEX markets decreases from 2.587% to 2.417%, and then increases during the decimal period to 3.148%. The results in the third and fourth columns s how different U shaped patterns for the liquidity premiums. In each of these columns, I control for size and one of the liquidity variables the returns can then be interpreted as the portion of the premium attributable to variation in the other liquidity variable. Thus, in the third column, there is a U shape in the premium for trade based liquidity, decreas ing from 1.736% to 1.508% for the transition from eighths to sixteenths, and then increasing to 2.301% in the decimal period. Finally, in the fourth c olumn, there is an inverted U shape in the premium for information based liquidity, rising from 0.851% to 0.909% and then falling to 0.847% in the decimal period. One possible explanation for this shape is that the sixteenths period coincided with several liquidity shocks as discussed earlier. Thus, the information based costs were higher during this period, even though tick size was lower than during the eighths period. In Table 3 13, t he results in the third and fourth columns again show U shaped patterns for the liquidity premiums but this time in the opposite direction to those for the NYSE/AMEX markets Thus, in the third column, there is a n inverted U shape in the premium for trade based liquidity, risi ng from 1. 328 % to 1. 922 % for the transition from eighths to sixteenths, and then PAGE 83 83 de creasing to 1.545 % in the decimal period. Finally, in the fourth column, there is a U shape in the premium for information based liquidity, dropp ing from 0.432 % to 1.062 % and then in creasing to 0. 215 % in the decimal per iod. Taken together, these numbers suggest that different aspects of liquidity affect market returns, depending on the market. Both for the NYSE/AMEX and Nasdaq markets, it appears that trade based liquidity carries a greater premium than information based liquidity. It is also the case that, after controlling for firm size, the liquidity risk premium during the decimal period is greater than during either the eighths or sixteenths tick size periods. Robustness Checks I performed several robustness checks a nd obtained qualitatively similar results. First, in addition to using daily returns in the analysis, I examined monthly results by averaging daily stock returns during each month, constructing portfolios with monthly returns instead of daily, and regressi ng the value weighted excess returns against monthly risk factors. The results from using the monthly data were qualitatively similar to the results from using daily data Second, I experimented with two other specifications for the creation of the liquidi ty factor mimicking portfolios: in the first specification, the return for the first decile portfolio (liquid stocks) was subtracted from the tenth decile portfolio (illiquid stocks); in the second specification, the return for the second decile portfolio (liquid stocks) was subtracted from the ninth decile portfolio (illiquid stocks), eliminating potential outliers. The variances for the returns on these portfolios are higher than with my original specification, and the correlations with the other risk fac tors are also somewhat different. Nevertheless, the results obtained are similar to the ones I have shown. Third, I included interaction effects between the liquidity factors and a dummy variable indicating when the aggregate market return was positive, D_ MKT_UP This dummy variable PAGE 84 84 was set equal to one on any day when the overall market return was positive and zero otherwise. Many of the liquidity betas for these interaction terms were negative, suggesting that an increase in the return on the market cause s a decrease in the expected liquidity return premium, but none of them were statistically significant. Fourth, instead of utilizing eight size LIQ_INFO LIQ_TRAD portfolios in the regressions, I tried using nine size LIQ_INFO portfolios in one set of regre ssions, and nine size LIQ_TRAD portfolios in a second set. Under these specifications, I again found that liquidity betas were statistically significant, especially for the illiquid portfolios regardless of firm size. In both sets of regressions the liquid ity betas for the portfolios of large liquid stocks were statistically significant and negative, indicating a discount for these portfolios. This concurs with the empirical observation that higher prices are paid for more liquid assets. Conclusion In this study, I show that liquidity measures can be consolidated into two latent liquidity variables: one arising from asymmetric information among traders regarding an asset and another from order processing or direct transaction costs associated with trading th e asset. I also show that when both of these latent liquidity variables are used in multibeta asset pricing models that include Fama French and momentum factors, there are significant premiums associated with both liquidity factors. Model specifications th at include only one or the other of these components of liquidity do not perform as well as specifications that include both. Additionally, I find that as tick size changed in the NYSE/AMEX markets from eighths to sixteenths to decimals, there were shifts in the proportion of asset liquidity that can be attributed to each of the two liquidity components. Overall, the levels of liquidity in the NYAM/AMEX markets improve over time as tick sizes decrease from eighths to sixteenths to decimals, but do not chang e much (or worsen) for the Nasdaq market. Some liquidity measures indicate PAGE 85 85 deterioration in liquidity: price impacts have increased over time, resulting in increased transaction costs to investors. This is offset by decreasing asymmetric information across the markets, as measured by the probability of informed trading in stocks, which may have come about through increased analyst coverage and increased accessibility to information about companies through the internet and other media. Taken together, my res ults suggest that institutional investors may be losing out to retail investors with the implementation of decimal tick sizes: although transaction costs have decreased overall, the decrease in information related liquidity costs has been greater. Finally, my results suggest that, despite changes in the levels of liquidity over time, a profitable trading strategy can be implemented by purchasing illiquid stocks and shorting liquid stocks. Such a strategy produces statistically and economically significant a nnualized expected returns of approximately 2.7% (NYSE/AMEX) to 3.1% (Nasdaq), after controlling for Fama French and momentum factors. Avenues for future research include exploration of where liquidity discovery takes place and the persistence of liquidity both at the firm level and at an aggregate market level. The same analysis can be performed for other markets, such as the commodities or debt markets. Exploration of these issues is of significant interest to researchers and practitioners alike, as the minimization of transaction costs and optimal choice of where to trade securities can have considerable impact on the actual realized returns of large institutional portfolios. PAGE 86 86 Table 3 1. Liquidity measures for the NYSE/AMEX and Nasdaq markets: summary statistics NYAM/AMEX (Obs = 185,632) Nasdaq (Obs = 153,058) Variable Multiple Mean Standard deviation Minimum Maximum Mean Standard deviation Minimum Maximum QSPR i,m ( 10 0 ) 0.167 0.124 0.012 4.919 0.249 0.191 0.010 4.85 2 PQSPR i,m ( 10 1 ) 0.085 0.070 0.002 0.859 0.152 0.112 0.002 1.554 ESPR i,m ( 10 1 ) 0.545 0.453 0.048 22.243 0.994 0.741 0.053 21.549 PESPR i,m ( 10 2 ) 0.283 0.251 0.010 4.253 0.606 0.437 0.013 5.889 LNDEV i,m ( 10 2 ) 0.235 0.232 0.005 10.910 0.346 0.248 0.003 3.403 IMPACTM i,m ( 10 4 ) 0.129 0.141 0.000 11.900 0.342 0.219 0.005 3.977 OP i,m ( 10 2 ) 0.461 0.452 0.015 28.451 0.916 0.658 0.014 10.667 AI i,m ( 10 2 ) 0.387 0.328 0.000 7.385 0.600 0.548 0.000 11.037 TOTVOL i,m ( 10 6 ) 0.454 1.272 0.000 81.077 0.541 2.575 0.001 122.124 MAVOL i,m ( 10 6 ) 0.444 1.193 0.000 35.959 0.525 2.431 0.000 105.623 DTOTVOL i,m ( 10 8 ) 0.168 0.522 0.000 21.412 0.186 1.120 0.000 58.868 SHROUT i,m ( 10 9 ) 0.115 0.337 0.000 11.145 0.044 0.243 0.000 10.816 MKTCAP i,m ( 10 10 ) 0.453 1.644 0.000 57.813 0.138 1.095 0.001 55.272 LNMKTCAP i,m ( 10 2 ) 0.207 0.017 0.144 0.271 0.196 0.013 0.156 0.270 RTURNOVER i,m ( 10 3 ) 0.812 4.425 0.000 475.161 0.352 4.230 0.000 1,037.981 AMIV i,m ( 10 8 ) 0.223 0.542 0.000 18.104 0.162 0.748 0.000 38.866 ILLIQ i,m ( 10 6 ) 0.089 0.281 0.000 16.100 0.106 0.314 0.000 23.600 LNMAVOL i,m ( 10 2 ) 0.116 0.017 0.050 0.174 0.117 0.016 0.057 0.185 PIN i,m ( 10 0 ) 0.130 0.111 0.000 0.919 0.194 0.115 0.000 0.795 PSDVOL i,m ( 10 2 ) 0.091 4.262 256.389 231.184 0.257 4.397 132.93 1 173.469 BHKDVOL i,m ( 10 1 ) 0.270 0.749 0.298 23.985 0.371 0.833 0.316 29.570 PAGE 87 87 Table 3 1. Continued S ummary statistics in this table are for data from January, 1993 to December, 2003 for the NYSE/AMEX and Nasdaq markets. The observations are for firm months, that is, for each variable the mean for each firm is computed for the month. The mean, standard deviation, minimum value, and maximum value are given for the variables. For firm i and month m the variables are define d as: QSPR is the average quoted spread; PQSPR is the average proportional quoted spread; ESPR is the average effective spread; PESPR is the average proportional effective spread; LNDEV is the average of daily standard deviations of quote returns; IMPACTM is the average of daily price impact means; OP is the average of daily order processing components of the proportional quoted spread; AI is the average of daily asymmetric information components of the proportional quoted spread; TOTVOL is the average dail y trading volume; MAVOL is the average of daily 100 day moving average components of trading volume; DTOTVOL is the average daily dollar volume; SHROUT is the average daily number of shares outstanding; MKTCAP is the average daily market capitalization of the firm; LNMKTCAP is the average of the logarithm of daily market capitalization of the firm; RTURNOVER is reciprocal of the current s average daily volum s average number of shares outstanding; AMIV is the monthly Ami vest liquidity ratio; ILLIQ is the average daily Amihud illiquidity measure; LNMAVOL is the natural logarithm of the current month's average anticipated daily volume; PIN is the probability of information based trading; PSDVOL is the Pastor Stambaugh measu re with a dollar volume specification; and BHKDVOL is the Breen Hodrick Korajczyk measure with a doll ar volume specification. PAGE 88 88 Table 3 2. Liquidity measures and latent liquidity variables for the NYSE/AMEX markets: summary statistics Variable AI i,m AMIV i, m PIN i,m OP i,m BHKDVOL i,m LNMAVOL i,m LIQ_INFO i,m LIQ_TRAD i,m Multiple ( 10 2 ) ( 10 3 ) ( 10 3 ) ( 10 2 ) ( 10 1 ) Mean 0.395 0.190 0.132 0.453 0.116 0.227 0.785 0.524 Standard Deviation 0.312 0.384 0.108 0.394 0.016 0.518 0.864 1.006 Minimum 0.000 8.250 0.000 0.021 0.165 0.000 5.558 2.864 Maximum 2.298 0.001 0.616 3.719 0.072 10.007 5.249 8.875 Correlations AI i,m 1.000 0.362 0.526 0.769 0.527 0.552 0.645 0.548 AMIV i,m 0.362 1.000 0.388 0.334 0.641 0.199 0.523 0.301 PIN i,m 0.526 0.388 1.000 0.471 0.653 0.361 0.766 0.411 OP i,m 0.769 0.334 0.471 1.000 0.550 0.651 0.546 0.712 BHKDVOL i,m 0.527 0.641 0 .653 0.550 1.000 0.497 0.698 0.591 LNMAVOL i,m 0.552 0.199 0.361 0.651 0.497 1.000 0.473 0.765 LIQ_INFO i,m 0.645 0.523 0.766 0.546 0.698 0.473 1.000 0.641 LIQ_TRAD i,m 0.548 0.301 0.411 0.712 0.591 0.765 0.641 1.000 Summary statistics in this table are for monthly data from January, 1993 to December, 2003, for the NYSE/AMEX markets. The mean, standard deviation, minimum value, maximum value, and correlation matrix are given for the liquidity measures used to obtain the latent liquidity variables, LIQ_INFO and LIQ_TRAD For firm i and month m the variables are defined as: AI is the average of daily asymmetric information components of the proportional quoted spread; AMIV is the negative of the monthly Amivest liquidity ratio; PIN is the probability of information based trading; OP is the average of daily order processing components of the proportional quoted spread; BHKDVOL is the Breen Hodrick Korajczyk measure with a dollar volume specificati on; and LNMAVOL is the negative of the natural logarithm of the current month's average anticipated daily volume. LIQ_INFO is the information based latent liquidity variable and LIQ_TRAD is the non information based variable. (Obs = 190,529) PAGE 89 89 Table 3 3. L iquidity measures and latent liquidity variables for the Nasdaq market: summary statistics Variable AI i,m AMIV i,m PIN i,m OP i,m BHKDVOL i,m LNMAVOL i,m LIQ_INFO i,m LIQ_TRAD i,m Multiple ( 10 2 ) ( 10 3 ) ( 10 3 ) ( 10 2 ) ( 10 1 ) Mean 0.580 0.118 0 .192 0.904 0.117 0.317 1.106 0.229 Standard Deviation 0.483 0.264 0.110 0.611 0.015 0.591 0.856 1.159 Minimum 0.000 6.553 0.000 0.043 0.171 0.000 5.215 4.167 Maximum 4.835 0.001 0.597 6.686 0.071 8.7 46 5.585 7.173 Correlations AI i,m 1.000 0.333 0.489 0.684 0.581 0.607 0.832 0.565 AMIV i,m 0.333 1.000 0.320 0.318 0.587 0.203 0.543 0.315 PIN i,m 0.489 0.320 1.000 0.401 0.623 0.399 0.765 0.428 OP i,m 0.684 0.318 0.401 1.000 0.437 0.432 0.576 0.564 BHKDVOL i,m 0.581 0.587 0.623 0.437 1.000 0.505 0.766 0.615 LNMAVOL i,m 0.607 0.203 0.399 0.432 0.505 1.000 0.587 0.576 LIQ_INFO i,m 0.8 32 0.543 0.765 0.576 0.766 0.587 1.000 0.660 LIQ_TRAD i,m 0.565 0.315 0.428 0.564 0.615 0.576 0.660 1.000 S ummary stat istics in this table are for monthly data from January, 1993 to December, 2003, for the Nasdaq market Th e mean, standard deviation, minimum value, maximum value, and correlation matrix are given for the liquidity measures used to obtain the latent liquidity variables, LIQ_INFO and LIQ_TRAD For firm i and month m the variables are defined as: AI is the aver age of daily asymmetric information components of the proportional quoted spread; AMIV is the negative of the monthly Amivest liquidity ratio; PIN is the probability of information based trading; OP is the average of daily order processing components of th e proportional quoted spread; BHKDVOL is the Breen Hodrick Korajczyk measure with a dollar volume specification; and LNMAVOL is the negative of the natural logarithm of the current month's average anticipated daily volume. LIQ_INFO is the information based latent liquidity variable and LIQ_TRAD is the non information based variable. (Obs = 1 5 0, 298 ) PAGE 90 90 Table 3 4. Risk factors for the NYSE/AMEX markets: summary statistics Variable MKT SMB HML UMD IML_INFO IML_TRAD Mean 0.034 0.009 0.018 0.048 0 .015 0.018 Standard Deviation 1.060 0.596 0.642 0.822 0.562 0.591 Minimum 6.650 4.560 4.900 7.270 3.676 4.362 Maximum 5.310 2.910 3.850 5.120 2.875 2.707 Correlations MKT 1.000 0.1 79 0.679 0.074 0.541 0.529 SMB 0.179 1.000 0.206 0.121 0.689 0.706 HML 0.679 0.206 1.000 0.026 0.215 0.196 UMD 0.074 0.121 0.026 1.000 0.057 0.055 IML_INFO 0.541 0.689 0 .215 0.057 1.000 0.907 IML_TRAD 0.529 0.706 0.196 0.055 0.907 1.000 Summary statistics in this table are for daily data from January, 1993 to December, 2003, for the NYSE/AMEX markets. The mean, standard deviation, minimum va lue, maximum value, and correlation matrix are given for the risk factors in the regressions, namely the Fama French three factors, the momentum factor, and the two liquidity factors, IML_INFO and IML_TRAD The variables are defined as follows: MKT is the market risk premium; SMB is the Fama French size factor; HML is the Fama French book to market factor; UMD is the momentum factor; IML_INFO is the liquidity risk factor obtained from the information based latent liquidity variable LIQ_INFO ; and IML_TRAD is the liquidity risk factor obtained from the trade based latent liquidity variable LIQ_TRAD (Obs = 2,746) PAGE 91 91 Table 3 5. Risk factors for the Nasdaq market: summary statistics Variable MKT SMB HML UMD IML_INFO IML_TRAD Mean 0.034 0.009 0.018 0. 048 0.004 0.018 Standard Deviation 1.060 0.596 0.642 0.822 1.259 1.256 Minimum 6.650 4.560 4.900 7.270 9.726 10.514 Maximum 5.310 2.910 3.850 5.120 6.325 6.984 Correlations MKT 1.00 0 0.179 0.679 0.074 0.648 0.620 SMB 0.179 1.000 0.206 0.121 0.027 0.032 HML 0.679 0.206 1.000 0.026 0.666 0.624 UMD 0.074 0.121 0.026 1.000 0.077 0.046 IML_INFO 0.648 0. 027 0.666 0.077 1.000 0.910 IML_TRAD 0.620 0.032 0.624 0.046 0.910 1.000 S ummary statistics in this table are for daily data from January, 1993 to December, 2003, for the Nasdaq market The mean, standard deviation, minimu m value, maximum value, and correlation matrix are given for the risk factors in the regressions, namely the Fama French three factors, the momentum factor, and the two liquidity factors, IML_INFO and IML_TRAD The variables are defined as follows: MKT is the market risk premium; SMB is the Fama French size factor; HML is the Fama French book to market factor; UMD is the momentum factor; IML_INFO is the liquidity risk factor obtained from the information based latent liquidity variable LIQ_INFO ; and IML_TRA D is the liquidity risk factor obtained from the trade based latent liquidity variable LIQ_TRAD (Obs = 2,746) PAGE 92 92 Table 3 6. Four factor model for the NYSE/AMEX markets: regression results Dependent variable: Portfolio returns Regressor B_L1_L2 B_L1_I2 B_ I1_L2 B_I1_I2 S_L1_L2 S_L1_I2 S_I1_L2 S_I1_I2 Intercept 0.016 *** 0.030 *** 0.016 0.027 *** 0.020 0.018 0.022 0.037 *** (0.005) (0.010) (0.009) (0.009) (0.013) (0.009) (0.011) (0.006) MKT 0.967 *** 0.922 *** 0.986 *** 0.739 ** 1.080 *** 0.968 *** 1.057 *** 0.923 *** (0.011) (0.019) (0.018) (0.017) (0.023) (0.017) (0.020) (0.012) SMB 0.176 *** 0.366 *** 0.289 *** 0.277 *** 0.650 *** 0.598 *** 0.658 *** 0.660 *** (0.015) (0.025) (0.024) (0.024) (0.0 31) (0.027) (0.029) (0.019) HML 0.345 *** 0.582 *** 0.529 *** 0.441 *** 0.600 *** 0.614 *** 0.579 *** 0.639 *** (0.019) (0.032) (0.033) (0.026) (0.033) (0.029) (0.035) (0.018) UMD 0.024 ** 0.141 *** 0.126 *** 0.042 ** 0.038 0.098 *** 0.101 *** 0.083 *** (0.012) (0.016) (0.018) (0.018) (0.021) (0.019) (0.022) (0.015) Mean no. of firms 507.7 29.8 69.1 40.7 47.0 84.9 45.5 514.2 Adj. R 2 0.927 0.677 0.785 0.619 0.657 0.726 0.699 0.854 Eight portfolios are created by partitioning the sample of firms into two by size and by each of the two liquidity variables. The value weighted excess daily returns on these portfolios are regressed against the Fama Fr ench three facto rs and the momentum factor for the complete sample period from January, 1993 to December, 2003 for the NYSE/AMEX markets The portfolios are labeled as follows: B and S represent big and small firms (above and below the median value of mar ket cap in the sample); L1 and I1 represent liquid and illiquid firms (above and below the median value of the information based liquidity variable, LIQ_INFO ); and L2 and I2 represent liquid and illiquid firms (above and below the median value of the non i nformation based liquidity variable, LIQ_TRAD ). The portfolios are re sorted at the beginning of each year. The parameter estimates are reported in annualized percentage terms. Standard errors are given in parentheses. (*, **, *** indicate statistical sign ificance at the 10%, 5% and 1% levels, respectively.) (Obs = 2,746) PAGE 93 93 Table 3 7. Four factor model for the Nasdaq market: regression results Dependent variable: Portfolio returns Regressor B_L1_L2 B_L1_I2 B_I1_L2 B_I1_I2 S_L1_L2 S_L1_I2 S_I1_L2 S_I1_I2 Intercept 0.053 *** 0.048 ** 0.039 ** 0.033 0.078 *** 0.089 *** 0.085 *** 0.099 *** (0.014) (0.023) (0.018) (0.021) (0.025) (0.027) (0.031) (0.017) MKT 1.309 *** 1.089 *** 1.105 *** 1.030 *** 1.251 *** 1.057 *** 1.088 *** 0.991 *** (0.023) (0.031) (0.026) (0.026) (0.034) (0.037) (0.038) (0.028) SMB 0.639 *** 0.974 *** 0.930 *** 0.900 *** 1.104 *** 0.927 *** 0.937 *** 0.911 *** (0.032) (0.045) (0.036) (0.033) (0.045) (0.047) (0.053) (0.034) HML 0.841 *** 0.011 0.185 *** 0.097 ** 0.016 0.092 0.050 0.085 (0.039) (0.055) (0.048) (0.048) (0.063) (0.062) (0.065) (0.046) UMD 0.046 0.089 *** 0.183 *** 0.031 0.019 0.029 0.045 0.138 *** (0.024) (0.028) (0.023) (0.024) (0.032) (0.028) (0.033) (0.024) Mean no. of firms 377.5 21.5 39.5 52.7 78.6 54.9 37.0 403.9 Adj. R 2 0. 86 7 0. 489 0. 661 0. 504 0. 526 0. 427 0. 359 0. 605 Eight portfolios are created by partitioning the sample of firms into two by size and by each of the two liquidity variables. The value weighted excess daily returns on these portfolios are regressed against the Fama French three facto rs and the momentum factor for the complete sample p eriod from January, 1993 to December, 2003 for the Nasdaq market The portfolios are labeled as follows: B and S represent big and small firms (above and below the median value of market cap in the sample); L1 and I1 represent liquid and illiquid firms (a bove and below the median value of the information based liquidity variable, LIQ_INFO ); and L2 and I2 represent liquid and illiquid firms (above and below the median value of the non information based liquidity variable, LIQ_TRAD ). The portfolios are re so rted at the beginning of each year. The parameter estimates are reported in annualized percentage terms. Standard errors are given in parentheses. (*, **, *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.) (Obs = 2,746) PAGE 94 94 Tab le 3 8. Six factor model for the NYSE/AMEX markets: regression results Dependent variable: Portfolio returns Regressor B_L1_L2 B_L1_I2 B_I1_L2 B_I1_I2 S_L1_L2 S_L1_I2 S_I1_L2 S_I1_I2 Intercept 0.023 *** 0.026 *** 0.018 ** 0.018 ** 0.022 0.016 0.022 0.033 *** (0.005) (0.010) (0.008) (0.009) (0.013) (0.009) (0.011) (0.006) MKT 0.897 *** 0.962 *** 0.976 *** 0.841 *** 1.060 *** 0.988 *** 1.065 *** 0.970 *** (0.010) (0.021) (0.019) (0.016) (0.024) (0.019) (0.022) (0. 013) SMB 0.060 *** 0.231 *** 0.334 *** 0.059 0.721 *** 0.531 *** 0.632 *** 0.504 *** (0.017) (0.034) (0.030) (0.031) (0.042) (0.036) (0.042) (0.023) HML 0.379 *** 0.563 *** 0.530 *** 0.389 *** 0.608 *** 0.604 *** 0.573 *** 0. 616 *** (0.016) (0.032) (0.031) (0.025) (0.033) (0.029) (0.035) (0.018) UMD 0.036 *** 0.134 *** 0.129 *** 0.025 0.041 ** 0.095 *** 0.099 *** 0.075 *** (0.011) (0.016) (0.017) (0.017) (0.021) (0.019) (0.022) (0.014) IML_INFO 0.126 *** 0.065 0.422 *** 0.559 *** 0.073 0.068 0.150 ** 0.196 *** (0.026) (0.054) (0.045) (0.044) (0.064) (0.052) (0.061) (0.033) IML_TRAD 0.239 *** 0.143 *** 0.459 *** 0.013 0.174 *** 0.038 0.100 0.053 (0.025) (0.055 ) (0.046) (0.045) (0.057) (0.050) (0.055) (0.029) Mean no. of firms 507.7 29.8 69.1 40.7 47.0 84.9 45.5 514.2 Adj. R 2 0.9 41 0.6 82 0.7 98 0.6 74 0.65 9 0.72 7 0. 700 0.8 6 4 Eight portfo lios are created by partitioning the sample of firms into two by size and by each of the two liquidity variables. The value weighted excess daily returns on these portfolios are regressed against the Fama French three factors, the momentum factor and the t wo liquidity factors, IML_INFO and IML_TRAD for the complete sample period from January, 1993 to December, 2003, for the NYSE/AMEX markets. The portfolios are labeled as follows: B and S represent big and small firms (above and below the median value of m arket cap in the sample); L1 and I1 represent liquid and illiquid firms (above and below the median value of the information based liquidity variable, LIQ_INFO ); and L2 and I2 represent liquid and illiquid firms (above and below the median value of the non information based liquidity variable, LIQ_TRAD ). The portfolios are re sorted at the beginning of each year. The parameter estimates are reported in annualized percentage terms. Standard errors are given in parentheses. (*, **, *** indicate statist ical si gnificance at the 10%, 5% and 1% levels, respectively.) (Obs = 2,746) PAGE 95 95 Table 3 9. Six factor model for the Nasdaq market: regression results Dependent variable: Portfolio returns Regressor B_L1_L2 B_L1_I2 B_I1_L2 B_I1_I2 S_L1_L2 S_L1_I2 S_I1_L2 S_I1_I2 Intercept 0.054 *** 0.042 0.045 ** 0.036 0.075 *** 0.082 *** 0.087 *** 0.096 *** (0.011) (0.023) (0.018) (0.020) (0.025) (0.026) (0.030) (0.015) MKT 1.114 *** 1.146 *** 1.120 *** 1.148 *** 1.309 *** 1.136 *** 1.217 *** 1.162 *** (0.020) (0.033) (0.028) (0.028) (0.038) (0.040) (0.045) (0.024) SMB 0.700 *** 0.957 *** 0.924 *** 0.863 *** 1.087 *** 0.903 *** 0.899 *** 0.858 *** (0.021) (0.043) (0.035) (0.030) (0.044) (0.044) (0.051) (0.028) HML 0.39 7 *** 0.087 0.252 *** 0.194 *** 0.133 0.235 *** 0.257 *** 0.291 *** (0.036) (0.066) (0.053) (0.053) (0.073) (0.069) (0.073) (0.044) UMD 0.010 0.095 *** 0.164 *** 0.001 0.023 0.032 0.011 0.113 *** (0.015) (0.028) (0.023 ) (0.021) (0.032) (0.026) (0.031) (0.018) IML_INFO 0.317 *** 0.229 *** 0.353 *** 0.405 *** 0.032 0.236 *** 0.426 *** 0.151 *** (0.033) (0.060) (0.048) (0.069) (0.073) (0.077) (0.093) (0.050) IML_TRAD 0.194 *** 0.376 *** 0.310 *** 0.094 0.181 *** 0.438 *** 0.093 0.294 *** (0.037) (0.064) (0.052) (0.071) (0.064) (0.081) (0.075) (0.058) Mean no. of firms 377.5 21.5 39.5 52.7 78.6 54.9 37.0 403.9 Adj. R 2 0.9 17 0. 504 0. 673 0. 540 0. 531 0. 447 0. 383 0. 686 Eight portfolios are created by partitioning the sample of firms into two by size and by each of the two liquidity variables. The value weighted excess daily returns on these portfolios are regresse d against the Fama French three factors, the momentum factor and the two liquidity factors, IML_INFO and IML_TRAD for the complete sample period from January, 1993 to December, 2003, for the Nasdaq market The portfolios are labeled as follows: B and S re present big and small firms (above and below the median value of market cap in the sample); L1 and I1 represent liquid and illiquid firms (above and below the median value of the information based liquidity variable, LIQ_INFO ); and L2 and I2 represent liqu id and illiquid firms (above and below the median value of the non information based liquidity variable, LIQ_TRAD ). The portfolios are re sorted at the beginning of each year. The parameter estimates are reported in annualized percentage terms. Standard er rors are given in parentheses. (*, **, *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.) (Obs = 2,746) PAGE 96 96 Table 3 10. Six factor model with adjustment for tick size periods for the NYSE/AMEX markets: regression results Depe ndent variable: Portfolio returns Regressor B_L1_L2 B_L1_I2 B_I1_L2 B_I1_I2 S_L1_L2 S_L1_I2 S_I1_L2 S_I1_I2 Intercept 0.022 *** 0.026 *** 0.019 ** 0.015 0.022 0.015 0.024 ** 0.032 *** (0.005) (0.010) (0.008) (0.008) (0.013) (0.009) (0.011) (0.006) MKT 0.899 *** 0.960 *** 0.964 *** 0.850 *** 1.053 *** 0.984 *** 1.047 *** 0.971 *** (0.010) (0.021) (0.018) (0.016) (0.024) (0.019) (0.022) (0.012) SMB 0.063 *** 0.230 *** 0.330 *** 0.064 ** 0.711 *** 0.523 *** 0.606 *** 0.496 *** (0.018) (0.035) (0.031) (0.032) (0.043) (0.036) (0.042) (0.024) HML 0.380 *** 0.563 *** 0.526 *** 0.390 *** 0.602 *** 0.599 *** 0.559 *** 0.612 *** (0.016) (0.032) (0.030) (0.025) (0.033) (0.029) (0.035) (0. 017) UMD 0.037 *** 0.130 *** 0.112 *** 0.035 ** 0.032 0.086 *** 0.080 *** 0.075 *** (0.011) (0.017) (0.018) (0.018) (0.022) (0.020) (0.023) (0.015) IML_INFO 0.086 0.046 0.292 *** 0.550 *** 0.123 0.107 0.314 *** 0.072 ( 0.051) (0.106) (0.095) (0.081) (0.092) (0.087) (0.108) (0.062) IML_TRAD 0.260 *** 0.126 0.520 *** 0.151 ** 0.072 0.153 0.134 0.194 *** (0.051) (0.112) (0.090) (0.075) (0.080) (0.084) (0.098) (0.057) IML_INFO D_8ths 0.0 78 0.070 0.112 0.175 0.185 0.036 0.714 *** 0.143 (0.060) (0.132) (0.110) (0.096) (0.137) (0.105) (0.136) (0.074) IML_INFO D_16ths 0.022 0.009 0.177 0.012 0.318 ** 0.385 *** 0.539 *** 0.221 *** (0.069) (0.138) (0.121) (0.109) (0.141) (0.120) (0.142) (0.081) IML_TRAD D_8ths 0.095 0.052 0.196 ** 0.226 *** 0.008 0.119 0.377 *** 0.107 (0.055) (0.126) (0.097) (0.086) (0.116) (0.097) (0.121) (0.065) IML_TRAD D_16ths 0.021 0. 004 0.024 0.251 ** 0.226 0.347 *** 0.263 0.261 *** (0.065) (0.137) (0.115) (0.105) (0.127) (0.118) (0.135) (0.074) Mean no. of firms 507.7 29.8 69.1 40.7 47.0 84.9 45.5 514.2 Adj. R 2 0.9 41 0.6 82 0. 802 0.6 81 0.6 60 0.7 31 0. 704 0.8 65 PAGE 97 97 Table 3 10. Continued Eight portfolios are created by partitioning the sample of firms into two by size and by each of the two liquidity variables. The value weighted excess daily retur ns on these portfolios are regressed against the Fama French three factors, the momentum factor, the two liquidity factors, IML_INFO and IML_TRAD and interactions of these factors with dummy variables for different tick size periods. The complete sample c overs the period from January, 1993 to December, 2003, for the NYSE/AMEX markets. The portfolios are labeled as follows: B and S represent big and small firms (above and below the median value of market cap in the sample); L1 and I1 represent liquid and il liquid firms (above and below the median value of the information based liquidity variable, LIQ_INFO ); and L2 and I2 represent liquid and illiquid firms (above and below the median value of the non information based liquidity variable, LIQ_TRAD ). The portf olios are re sorted at the beginning of each year. The parameter estimates are reported in annualized percentage terms. Standard errors are given in parentheses. (*, **, *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.) (Ob s = 2,746) PAGE 98 98 Table 3 11. Six factor model with adjustment for tick size periods for the Nasdaq market: regression results Dependent variable: Portfolio returns Regressor B_L1_L2 B_L1_I2 B_I1_L2 B_I1_I2 S_L1_L2 S_L1_I2 S_I1_L2 S_I1_I2 Intercept 0.054 ** 0.038 0.045 ** 0.030 0.067 *** 0.072 *** 0.082 *** 0.091 *** (0.011) (0.023) (0.018) (0.020) (0.025) (0.026) (0.030) (0.014) MKT 1.124 *** 1.229 *** 1.186 *** 1.200 *** 1.388 *** 1.245 *** 1.282 *** 1.232 *** (0.022) (0.03 4) (0.029) (0.030) (0.038) (0.039) (0.046) (0.025) SMB 0.709 *** 1.021 *** 0.962 *** 0.916 *** 1.170 *** 1.012 *** 0.964 *** 0.919 *** (0.023) (0.043) (0.036) (0.033) (0.046) (0.045) (0.053) (0.029) HML 0.411 *** 0.132 0.271 *** 0.258 *** 0.233 *** 0.373 *** 0.357 *** 0.361 *** (0.037) (0.068) (0.054) (0.054) (0.074) (0.071) (0.075) (0.045) UMD 0.009 0.053 0.109 *** 0.002 0.020 0.031 0.020 0.094 *** (0.018) (0.030) (0.024) (0.024) (0.037) (0.031) (0.033) (0.020) IML_INFO 0.244 ** 0.392 *** 0.660 *** 0.510 *** 0.200 0.162 0.529 *** 0.271 *** (0.102) (0.140) (0.143) (0.111) (0.177) (0.170) (0.205) (0.105) IML_TRAD 0.258 ** 0.082 0.434 *** 0.121 0.052 0.535 ** 0.118 0.312 *** (0.109) (0.141) (0.148) (0.116) (0.181) (0.177) (0.207) (0.108) IML_INFO D_8ths 0.099 0.785 *** 0.472 *** 0.178 0.338 0.235 0.231 0.250 ** (0.108) (0.159) (0.155) (0.145) (0.200) (0.194) (0.246) ( 0.118) IML_INFO D_16ths 0.056 0.520 *** 0.020 0.207 0.429 ** 0.248 0.145 0.092 (0.115) (0.161) (0.167) (0.131) (0.201) (0.195) (0.241) (0.117) IML_TRAD D_8ths 0.057 0.426 *** 0.150 0.061 0.014 0.280 0.078 0. 090 (0.119) (0.158) (0.160) (0.151) (0.195) (0.196) (0.227) (0.124) IML_TRAD D_16ths 0.073 0.463 *** 0.122 0.260 0.530 ** 0.349 0.250 0.091 (0.123) (0.167) (0.175) (0.136) (0.209) (0.205) (0.247) (0.123) Mean no. of firms 377.5 21.5 39.5 52.7 78.6 54.9 37.0 403.9 Adj. R 2 0.9 17 0. 511 0. 680 0. 546 0. 542 0. 468 0. 390 0. 697 PAGE 99 99 Table 3 11. Continued Eight portfolios are created by partitioning the sampl e of firms into two by size and by each of the two liquidity variables. The value weighted excess daily returns on these portfolios are regressed against the Fama French three factors, the momentum factor, the two liquidity factors, IML_INFO and IML_TRAD and interactions of these factors with dummy variables for different tick size periods. The complete sample covers the period from January, 1993 to December, 2003, for the Nasdaq market The portfolios are labeled as follows: B and S represent big and smal l firms (above and below the median value of market cap in the sample); L1 and I1 represent liquid and illiquid firms (above and below the median value of the information based liquidity variable, LIQ_INFO ); and L2 and I2 represent liquid and illiquid firm s (above and below the median value of the non information based liquidity variable, LIQ_TRAD ). The portfolios are re sorted at the beginning of each year. The parameter estimates are reported in annualized percentage terms. Standard errors are given in pa rentheses. (*, **, *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.) (Obs = 2,746) PAGE 100 100 Table 3 12. A nnualized mean daily returns on factor mimicking portfolios by tick size period for the NYSE/AMEX markets Controlling for: Tick size period No control Size Size and LIQ_INFO Size and LIQ_TRAD Eighths 2.613 2.587 1.736 0.851 Sixteenths 2.515 2.417 1.508 0.909 Decimals 2.692 3.148 2.301 0.847 Annualized mean daily returns are calculated for each of the eight portfolios used in the third model specification, for three different tick size periods. For the NYSE/AMEX markets, the dates in the sample employed for the eighths tick size period are January 1, 1993 to June 23, 1997; for the sixteenths tick size period the dates are J une 24, 1997 to January 28, 2001; and for the decimal period they are January 29, 2001 to December 31, 2003. The difference between estimated portfolio liquidity betas is calculated across ti ck size periods. These differences are then multiplied by the ann ualized liquidity premi ums on the liquidity factors (from Table 3 4) to obtain the liquidity cost of capital in each of the periods. By considering differences between returns for combinations of portfoli os, it is possible to control for size and for each of the liquidity variabl is for the return difference between the portfolios containing the smallest most illiquid stocks and the largest most liquid stocks. The values are report ed in annualized percentage terms. PAGE 101 101 Table 3 13. A nnualized mean daily returns on factor mimicking portfolios by tick size period for the Nasdaq market Controlling for: Tick size period No control Size Size and LIQ_INFO Size and LIQ_TRAD Eighths 2.290 0.896 1.328 0.432 Sixteenths 3.1 59 0.860 1.922 1.062 Decimals 3.114 1.330 1.545 0.215 Annualized mean daily returns are calculated for each of the eight portfolios used in the third model specification, for thre e different tick size periods. For the Nasdaq market the dates in the sa mple employed for the eighths tick size period are January 1, 1993 to June 1, 1997; for the sixteenths tick size period the dates are June 2, 1997 to April 8, 2001; and for the decimal period they are April 9, 2001 to December 31, 2003. Th e difference betw een estimated portfolio liquidity betas is calculated across tick size periods. These differences are then multiplied by the annualized liquidity premiums on the liquidity factors (from Table 3 4) to obtain the liquidity cost of capital in each of the peri ods. By considering differences between returns for combinations of portfolios, it is possible to control for size and for each of the liquidity variabl is for the return difference between the portfolios containi ng the smallest most illiquid stocks and the largest most liquid stocks. The values are reported in annualized percentage terms. PAGE 102 102 A Figure 3 1. C ross sectional liquidity measures and their time variation. The graphs shown in this figure are for month ly averages of the daily liquidity measures described in the study. The complete sample covers the period from January, 1993 to December, 2003, for the NYSE/AMEX and Nasdaq markets. The liquidity measures shown in the graphs are described in what follows. A) QSPR is the average quoted spread. B) PQSPR is the ave rage proportional quoted spread. C) ESPR is the ave rage effective spread. D) PESPR is the averag e proportional effective spread. E) LNDEV is the average of daily stand ard deviations of quote ret urns. F) IMPACTM is the aver age of daily price impact means. G) OP is the average of daily order processing components of the proportional quoted spread. H) AI is the average of daily asymmetric information components of the proportional quoted spread. I) TOTVOL is t he average daily trading volume. J) MAVOL is the average of daily 100 day moving avera ge components of trading volume. K) DTOTVOL is the average daily dollar volume. L) SHROUT is the average dai ly number of shares outstanding. M) MKTCAP is the average daily ma rket capitalization of the firm. N) LNMKTCAP is the average of the logarithm of daily market capitalization of the firm. O) RTURNOVER is reciprocal of the current s average daily volum e divided by s avera ge number of shares outstanding. P) AMIV is the monthly Amivest liquidity ratio. Q) ILLIQ is the average daily Amihud illiquidity measure. R) LNMAVOL is the natural logarithm of the s a verage anticipated daily volume. S) PIN is the probabil i ty of information based trading. T) PSDVOL is the Pastor Stambaugh measure wit h a dollar volume specification. U) BHKDVOL is the Breen Hodrick Korajczyk measure with a doll ar volume specification. PAGE 103 103 B C Figure 3 1. Continued PAGE 104 104 D E Figure 3 1. Continued PAGE 105 105 F G Figure 3 1. Continued PAGE 106 106 H I Figure 3 1. Continued PAGE 107 107 J K Figure 3 1. Continued PAGE 108 108 L M Figure 3 1. Continued PAGE 109 109 N O Figure 3 1. Continued PAGE 110 110 P Q Figure 3 1. Continued PAGE 111 111 R S Figure 3 1. Continued PAGE 112 112 T U Figure 3 1. Continued PAGE 113 113 A B Figure 3 2. C ross sectional latent liquidity variables and their time variation. The graphs shown in this figure are for monthly averages of the daily latent liquidity variables. The complete sample covers the perio d from January, 1993 to December, 2003, for the NYSE/AMEX and Nasdaq markets. The latent liquidity variabl es shown in the graphs are described in what follows. A) LIQ_INFO is the information based liquidity variable. B) LIQ_TRAD is the non information ba sed liquidity variable. PAGE 114 114 A B Figure 3 3. F actor mimicking portfolio returns and their time variation. The graphs shown in this figure are for monthly return s given as percentages for the factor mimicking portfolios estimated for the period from Jan uary, 1993 to December, 2003, for the NYSE/AMEX and Nasdaq markets. The risk factors shown in the graphs are described in what follows. A) MKT is the return on the market minus the risk free rate B) SMB is the return on the Fama French size factor. C) HML is the return on the Fama French book to market factor. D) UMD is the return on the momentum factor. E) IML_INFO NYAM is the return on the information based liquidity factor for the NYSE/AMEX markets. F) IML_TRAD NYAM is the return on the non inform ation based liquidity factor for the NYSE/AMEX markets. G) IML_INFO NASD is the return on the information based liquidity factor for the Nasdaq market. H) IML_TRAD NASD is the return on the non information based liquidity factor for the Nasdaq market. PAGE 115 115 C D E Figure 3 3. Continued PAGE 116 116 F G H Figure 3 3. Continued PAGE 117 117 CHAPTER 4 CONCLUSION The results of this study show that information about an asset and liquidity of the asset are very important characteristics in determining its price. Severa l important research questions were considered. First, this study shows that price discovery relating to the value of the S&P 500 index is concentrated in the futures market, followed by the options market, and then the stock market. Second, it was found t hat key determinants affecting the information shares in the markets are transaction costs (such as bid ask spreads) and market trading activity proxies (such as anticipated volumes); the (public) information conveyed by macroeconomic announcements seemed to play little role. Third, in examining the liquidity of many stocks traded in the NYSE, AMEX and Nasdaq markets, it was found that their liquidity measured by proxies for tightness, depth, resiliency, and diversity of opinion, could be decomposed into tw o parts. Fourth, both the information based and trade based liquidity were found to be statistically significant in asset pricing models. It is suggested that a potentially profitable trading strategy that can be implemented is to purchase illiquid stocks and short liquid stocks, even after controlling for size, book to market and momentum effects. The findings of this study should be of interest to market makers, long term investors, and regulators. The latter need to consider the trade offs in liquidity t hat exist between institutional and retail investors. In many situations, what may benefit one type of trader will hurt another. By better able to set rules in pla ce that will balance the needs of the many different types of traders in the market. Long term investors sometimes ignore the transaction costs associated with relatively illiquid securities; this study provides a framework for these investors to assess ho w PAGE 118 118 to order processing costs. Market makers will frequently adjust their spreads or quoted depth based on inventory levels, asset price volatility or the likel ihood that they are negotiating with an informed trader. Using an asset pricing model that explicitly incorporates liquidity may help a market maker in determining the optimal amount of liquidity they wish to offer, both in terms of bid and asked prices as well as order sizes. Finally, principal avenues for further research include: the development of a more formal theory characterizing the trade offs between the precision of privately held information, market liquidity, and leverage associated with particu lar assets; investigation into the determinants of information based and trade based liquidity, particularly relating to assets that may be liquid with respect to one component but not the other; and further study into the correlations of liquidity measure s during market crises. PAGE 119 119 APPENDIX A LIQUIDITY PROXIES US ED IN RECENT STUDIES Recent studies have developed a number of measures of liquidity. Table A 1 seeks to categorize some of the more common measures into five broad areas: Order based measures Tr ade based measures Price reversal measures Price impact measures Order imbalance measures Within each of these categories, there are several subcategories, where measures are grouped partly by intrinsic similarities and partly by the studies that make use of them. Some of the measures are more commonly recognized than others, but references are given for each subcategory. The list is not exhaustive, and certainly may be extended in future work. PAGE 120 120 Table A 1. Description of liquidity proxies used in recent s tudies Measure category Description References 1 (a) Order Based Measures (related to the Bid/Ask Spread) QSPR is the quoted bid ask spread associated with the transaction. PQSPR is the quoted bid ask spread divided by the mid point of the prevailing bid ask quote (in percent). ESPR is the effective spread, that is, the difference between the execution price and the mid point of the prevailing bid ask quote. PESPR is the effective spread divided by the mid point of the prevailing bid ask quote (in percent) Chordia, Roll and Subrahmanyam (2001), Chordia, Sarkar and Subrahmanyam (2005), Chen (2005), Korajczyk and Sadka (200 7 ) 1( b ) Quoted Spread The aggregate liquidity level during month t is: where is the number of firms in month t is the daily average relative quoted spread for stock i on day d in month t this is the average of every best bid and offer (BBO) eligible quote from the open until just prior to the market close divided by the quote midpoint. Chen (2005) 1( c ) Transaction based Spread The aggregate liquidity level during month t is: where is the daily average relative effective spread for stock i on day d in month t this is the average of the absolute value of the difference between each transaction price and the midpoint of the most recent quote, which is at least 5 seconds prior to the trade, divided by the quote midpoint. Amihud and Mendelson (1986), Cho rdia, Roll and Subrahmanyam (2000), Hasbrouck and Seppi (2001), Huberman and Halka (2001), Jones (200 2 ), Baker and Stein (200 4 ) PAGE 121 121 Table A 1. Continued Measure category Description References 1( d ) Adverse Selection and Order Processing Components of the Spread Let be the return to stock i at time t based on transaction prices. Let be the return to stock i at time t *, based on the midpoint of the bid and ask quotes. The time subscripts on the return s differ because it is assumed that the quotes are updated following each transaction. Hence, t > t Let be the difference in returns based on the transaction prices and quote midpoints for stock i at time t Let S i be the quot ed spread, and let i be the fraction of the quoted spread due to order processing costs. Then, and (1 i ) is the fraction of the quoted spread due to adverse selection costs. George, Kaul and Nimalendran (1991) 1( e ) Adverse Selection and Order Processing Components of the Spread Let P t be the transaction price at time t Let Q t be the quote midpoint. Let Z t = P t Q t be one half of the effective spread. Let be the proportion of the effective spread due to adverse selection Let = ( + 1)/2 be the order persistence parameter, which measures the probability that a buy (sell) order will be followed by another buy (sell) order. The adverse selection and order persistence parameters are estimated from the following pair of equ ations: Lin, Sanger and Booth (1995) 1(f) Order Based Measures (related to the Depth of Quotes) DEP is the average of the quoted bid and ask depths. $DEP is the average of the ask depth times ask pri ce and bid depth times bid price. CompositeLiq = PQSPR / $DEP where spread and depth are combined in a single measure intended to measure the average slope of the liquidity function in percent per dollar traded. Chordia, Roll and Subrahmanyam (2001), Chord ia, Sarkar and Subrahmanyam (2005) PAGE 122 122 Table A 1. Continued Measure category Description References 2(a) Trade Based Measures Volume is the total share volume during the day. $Volume is the total dollar volume (number of shares multiplied by the transact ion price) during the day. NumTrades is the total number of transactions during the day. Chordia, Roll and Subrahmanyam (2001) 2 ( b ) Trade Based Measures Turnover is the ratio of monthly volume and shares outstanding: where is the volume for stock i on day j in month t is the shares outstanding for stock i at the end of month t Chen ( 2005), Korajczyk and Sadka (2007 ) 3 (a) Price Reversal Measures (related to Dollar Volume) The regression estimated for each stock for each month is: where is the return on stock i on day d in month t is where is the return on the NYSE/AMEX CRSP value weighted market return on day d in month t is the dollar volume for stock i on day d in month t The ordinary least squares estimate of is a proxy for sto ck i in month t The market wide liquidity measure is constructed from the individual stock measures by averaging all of the individual measures during the month and inflating by the ratio of total market capitalization at the end of month t 1 to total market capitalization at month 0. Pstor and Stambaugh (200 3 ), Chen (2005) PAGE 123 123 Table A 1. Continued Measure category Description References 3 (b) Price Reversal Measures (related to Dollar Volume) Substitute concurrent returns for lagged returns in 4(a). The regression estimated for each stock for each month is: The adjusted market wide measure, is obtained by taking the cross measures. This series is then scaled by where is the total dollar value at the end of month t 1 of the stocks included in the cross sectional average in month t and is the corresponding value for the first month in the sample. [An alternative scaling factor that is used is where is the 24 month moving average of the corresponding liquidity measure over months t 24 to t 1, and is the corresponding value for the first month in the sample.] Breen, Hodrick, and Korajczyk (200 2 ), Chen (2005) 3 (c) Price Reversal Measures (related to Turnover) Substitute turnover scaled by average daily t urnover during the previous month for dollar volume. The regression estimated for each stock for each month is: where is turnover defined as dollar volume for stock i on da y d in month t divided by the market capitalization of firm i at the end of month t 1 is the average daily turnover for stock i in month t 1 [ The estimate of the aggregate liquidity measure is the average of across all stocks i in month t ] Chen (2005) 3 (d) Price Reversal Measures (related to Turnover) Substitute concurrent returns for lagged returns in 3 (c). Chen (2005) PAGE 124 124 Table A 1. Continued Measure category Description References 4 (a) Price Imp act Measures For each stock for each month: where is the number of trading days in month t The market wide measure is the simple average of the individual stock measures. The resulting time series is then inflated by the ratio of total market capitalization at the end of month t 1 to total market capitalization at the end of month 0. Amihud (2002), Acharya and Pedersen (2005), Chen (2005), Korajczyk and Sadka (200 7 ) 4 (b) Price impact measures where is the 24 month moving average of the market wide turnover through months t 24 to t 1, and is the value of the turnover for the first month in the sample. is the number of stocks included in the cross sectional average in month t Chen (2005) PAGE 125 125 Table A 1. Continued Measure category Description References 4 (c) Price impact measures The regression estimated is: where is the transaction price for the j th trade of asset i in month t is the direction of the j th trade of asset i in month t is the unexpecte d direction of trade is the signed volume of the j th trade of asset i in month t is the unexpected signed volume of trade (1) is the permanent variable component of price impact as it measures how much the valuation of the asset changes given a shock to signed trading volume, (2) is the transitory variable component of price impact since the effect of signed volume fo r this trade, has an effect of on the price of trade j an effect of on the price of trade j +1, and no effect on subsequent prices. (3) is the permanent fixed component of price impact. (4) is the transitory fixed component of price impact. Glosten and Harris (1988), Korajczyk and Sadka (200 7 ) PAGE 126 126 Table A 1. Continued Measure category Description References 5 (a) Orde r Imbalances Korajczyk and Sadka (200 7 ) 5 (b) OI is defined as the dollar value of buys less the dollar value of sells each day, divided by the total dollar value of buys and sells Chordia, Sarkar and Subrahmanyam (2005) 5(c) Probability of Informed Trading (PIN) where is the probability that new information arrives at the beginning of a trading day is the arrival rate of orders from informed tr aders (on information event days) is the arrival rate of orders from uninformed buyers is the arrival rate of orders from uninformed sellers Easley, Hvidkjaer and (200 6 ) This tabl e provide s description s of variables used to proxy for liquidity in a number of the recent studies cited in the text. The variables are categorized according to their similarities with each other. As notation used may differ from one study to anot her, and for the sake of consistency, the notation employed here may differ at times from that used in the original studies. In some of th e papers cited, the liquidity measures are calculated for individual stocks on a daily or monthly basis, while in others the sa me measure is used in an aggregated form across all stocks in the sample. PAGE 127 127 PAGE 128 128 APPENDIX B DATES OF LIQUIDITY AFFECTING EVENTS During the sample period covered in this study, from January 1993 to December 2003, several events took place that had profound effe cts on aggregate stock market liquidity. A timeline including some of these important dates is given in Table B 1. The list of dates is not exhaustive, and certainly may be extended to dates outside the sample period. Further information regarding the date s listed can be found in the studies by Chordia et al. (2005), Kabir and Hassan (2005), and Borio and McCauley (1996), as well as on the internet. PAGE 129 129 Table B 1. Chronology of important events affecting market liquidity Date (s) Notes March 1, 1994 to May 31, 1994 Bond market crisis March 20, 1995 CBOE introduces its automated quote system for options on the S&P 500 index June 2, 1997 Nasdaq minimum tick size goes from eighths to sixteenths of a dollar June 24, 1997 NYSE minimum tick size goes from eight hs to sixteenths of a dollar July 2, 1997 to December 31, 1997 Asian financial crisis: crashes in Thailand, Hong Kong, South Korea, and elsewhere October 27, 1997 Mini crash: The Asian financial crisis came to a head in this crash; it was the third lar gest point drop for the Dow Jones Industrial Average (as at February 27, 2007): 512.61 points, 6.37% October 28, 1997 Rebound: The NYSE and Nasdaq markets both trade over 1 billion shares in a day July 6, 1998 to December 31,1998 Russian default cris is August 1998 to September 1998 Long Term Capital Management (LTCM) crisis September 23, 1998 Government and exposed commercial banks announce LTCM bailout January 14, 2000 Dow Jones Industrial Average peaks March 10, 2000 Nasdaq peaks March 2000 D ot com bubble crash April 14, 2000 Mini crash: The second largest point drop for the Dow Jones Industrial Average (as at February 27, 2007): 617.78 points, 5.66% January 29, 2001 NYSE minimum tick size goes from sixteenths of a dollar to decimals Apri l 9, 2001 Nasdaq minimum tick size goes from sixteenths of a dollar to decimals September 17, 2001 Post 9/11 crash: This was the largest point drop for the Dow Jones Industrial Average (as at February 27, 2007): 684.81 points, 7.13% October 9, 2002 Sto ck market downturn: Sharp drop in stock prices during 2002 in stock exchanges across the United States, Canada, Asia, and Europe, reaching five year lows in October Dates of important events affecting liquidity in the U.S. equity markets are shown for the sample period commencing January 1, 1993 and ending December 31, 2003. 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Requirements for the degree of Doctor of Philosophy in finance were completed at the University of Florida during the summer of 2007. Before entering the doctoral program, Tom worked for Enron (Res earch Group) in Houston, TX, and the Risk Analytics Group at Florida Power & Light in Juno Beach, FL. Other experience includes work in the U.K., the Bahamas, and Brazil. Upon graduation from the University of Florida, he will join Syracuse University, NY, market microstructure, derivative securities, risk management, investments, and corporate finance. 