SYSTEMATIC LIQUIDITY, CHARACTERISTIC LIQUIDITY AND ASSET PRICING. Duong Nguyen* Tribhuvan N. Puri*

SYSTEMATIC LIQUIDITY, CHARACTERISTIC LIQUIDITY AND ASSET PRICING Duong Nguyen* Trbhuvan N. Pur* Address for correspondence: Trbhuvan N. Pur, Professor of Fnance Char, Department of Accountng and Fnance Charlton College of Busness Unversty of Massachusetts Dartmouth 285 Old Westport Road North Dartmouth, MA 02747 Voce: 508-999-8759 tpur@umassd.edu *Unversty of Massachusetts, Dartmouth

SYSTEMATIC LIQUIDITY, CHARACTERISTIC LIQUIDITY AND ASSET PRICING Abstract Ths paper examnes whether the tradtonal characterstc lqudty premum can be explaned by market lqudty rsk. We fnd that after adjustng for Pastor and Stambaugh market lqudty factor, the level of tradtonal lqudty reman prced. Also, consstent wth prevous studes on market lqudty and asset prcng, we do not fnd stock characterstcs or Fama-French factors determne the mpact of lqudty level on stock return. More nterestngly, we document that the well-known sze-return relatonshp mght smply a proxy for the lqudty-return relatonshp. Our results are consstent n both tme seres and cross sectonal frameworks as well as robust n both NYSE-AMEX and Nasdaq exchanges. 1

I. Introducton Numerous studes, startng from Amhud and Mendelson (1986) have shown that lqudty s an mportant varable that affects the stock prces. Usng varous measures of lqudty, these studes generally support the lqudty premum theory, whch provdes a ratonale for a trade off between return on assets and ther lqudty. In general, hgher rate of returns are assocated wth less lqud assets.. For example, usng bd-ask spread as a measure of lqudty, Amhud and Mendelson (1986) show that the quoted bd-ask spread has a sgnfcant postve effect on stock returns. Smlarly, Eleswarapu and Renganum (1993) usng the same quoted bd-ask spread as a proxy for lqudty fnd that the postve relaton documented n Amhud and Mendelson s restrcted only n January. Brennan and Subrahmanyam (1996) take an nnovatve approach by estmatng the prce mpact of a trade based on Kyle s (1985) model and fnd that t s sgnfcantly postvely related to average returns. Easley, Hvdkjaer, and O Hara (2002) document a smlar result usng ther measure of llqudty called the probablty of nformaton tradng, whch reflects the adverse selecton cost arsng from nformaton asymmetry among traders. Addtonal evdence on postve llqudty-return relaton s provded by Chalmers and Kadlec (1998) usng the amortzed bd-ask spread, by Datar, Nak, and Radclff (1998) usng share turnover, by Brennan, Chorda, and Subrahmanyam (1998) usng dollar tradng volume, and most recently by Hasbrouck (2003) usng a lqudty proxy based on a newly created effectve spread n the daly data. Whle the above cted studes support the lqudty premum noton, t s mportant to note that n these papers, lqudty s consdered as a stock characterstc rather than an aggregate rsk factor of concern to nvestors. The recent dscovery of commonalty n lqudty by Chorda, Roll, and Subrahmanyam (2000), Hasbrouck and Sepp (2001), and Huberman and Halka (2001) 2

has rased a new queston about the role of lqudty n asset prcng. Ther fndngs spurred further research that nvestgates whether market-wde lqudty s an mportant factor n explanng stock returns. A notable work by Pastor and Stambaugh (2003) develops a measure of aggregate lqudty, based on daly prce reversal, and shows that stocks whose returns are more senstve to market lqudty factor command hgher requred rate of return than stocks whose returns are less senstve to market lqudty factor. Jacoby, Fowler, and Gottesman (2000) (JFG) develop a statc one-perod CAPM-based model to demonstrate that the true measure of systematc rsk, when consderng lqudty costs, s based on net (after bd-ask spread) returns. A dynamc verson of the JFG lqudty-adjusted CAPM s presented by Acharya and Pedersen (2005) (assumng overlappng-generatons), where the JFG lqudty-adjusted beta s decomposed nto four components: the standard CAPM beta, and the three betas related to lqudty, one of whch s the Pastor and Stambaugh (2003) lqudty beta and the other two are commonalty n lqudty wth market lqudty and lqudty senstvty to market return. Usng the lqudty measure of Amhud (2002), Acharya and Pedersen test the lqudty-adjusted CAPM and show that ther model sgnfcantly mproves the performance of a standard CAPM for most portfolos. Chan and Faff (2005) examne the role of lqudty n asset prcng for the Australan stock market and suggest augmentng the Fama-French (1993) three-factor model to a four-factor model by ncorporatng the lqudty as the forth factor. The fndngs that have emerged from the recent lterature on lqudty and asset prcng dscussed above obvously lead to a pertnent queston from an asset-prcng perspectve. Does lqudty beta (.e., senstvty of stock return to market lqudty) capture the effect of characterstc lqudty specfc to ndvdual stocks? Alternatvely, f nvestors demand a rsk premum for systematc lqudty, do they stll demand another rsk premum for the lqudty 3

level per se? Ths queston has not been answered conclusvely n the lterature thus far. Pastor and Stambaugh (2003) suggest that stocks wth hgher lqudty betas tend to have hgher average return about 7.5 percent annual. However, they do not control for the level of llqudty, whch has been shown to command a sgnfcant premum n a number of studes (see the above ctatons). Acharya and Pedersen (2005) wthn the framework of the lqudty-adjusted CAPM, show that the expected return of a securty s ncreasng n ts expected llqudty and ts lqudty rsk. They show that llqud securtes also have hgh lqudty rsk. However, ther evdence that the total effect of the lqudty rsk matters over and above market rsk and the level of lqudty. s rather weak. Acharya and Pedersen do not control for the effect of Fama-French factors and ther analyses are lmted to NYSE and AMEX stocks only. Nguyen, Mshra, Prakash and Ghosh (2006) usng turnover rato as a measure of lqudty fnd that a lqudty premum exsts n stock market even after adjustng for market factors, nonmarket factors as well as other stock characterstcs. However, snce ther focus s whether the three-moment CAPM and the four-factor model whch ncludes Fama-French and Pastor- Stambaugh factors can explan lqudty premum, t s not clear whether the market lqudty factor alone can explan the mpact of lqudty level per se. Ths paper bulds on Nguyen et al. (2006). We examne whether the market lqudty factor alone can capture the lqudty level premum. We also examne whether ther fndngs are robust to dfferent measures of lqudty. Ths s mportant because as Brennan and Subrahmanyam (1996) suggest that one of the reasons for the mxed results on lqudty s that dfferent proxes for lqudty are used n the asset prcng lterature.. There are varous measures of lqudty have been used n the lterature. However, they can be categorzed nto two basc types: trade-based measures such as volume, frequency of 4

tradng, dollar value of shares traded, turnover rato, etc., and order-based measures such as quoted spread, effectve spread, quoted depth, etc. Amhud and Mendelson (1986) use bd-ask spread as a measure of lqudty. Brennan and Subrahmanyam (1996) use fxed and varable components of tradng cost as measures of lqudty. Ther measures requre ntraday transacton data, whch s avalable only for short perod of tme. Also, Peterson and Falkowsk (1994) suggest that spread s a poor proxy for lqudty and call for an alternatve measure that may be a better proxy for lqudty of an asset. As a complment to Nguyen et al (2006) usng turnover rato as a measure for lqudty, we use dollar volume as a proxy for lqudty as n Brennan, Chorda, and Subrahmanyam (1998). 1 Dollar volume s related to how quckly a dealer expects to turn around her poston and s related to lqudty n Stoll (1978). Brennan and Subrahmanyam (1995) fnd that tradng volume s an mportant determnant of the measure of lqudty. Chorda et al. (2000) document a strong cross sectonal relatonshp between dollar tradng volume and varous measures of bdask spread and market depth. Furthermore, t s possble to obtan these data over long perods of tme, a requrement approprate for emprcal studes nvolvng asset prcng models. We nvestgate the ssue usng the stocks n NYSE-AMEX from 1963 to 2004 under both tme seres and cross sectonal contexts and fnd smlar results as documened n Nguyen et al (2006). In the tme seres context, we use both the Fama-French three factor model and the fourfactor model that ncludes Fama-French and Pastor-Stambaugh market lqudty factors as models for rsk adjustment. In both cases, we document a generally consstent decrease n the ntercepts from low lqudty portfolos to hgh lqudty portfolos. The result s consstent wth lqudty premum noton n Amhud and Mendelson (1986). The Gbbon-Ross-Shanken statstcs 1 We do not focus on whether turnover rato s a better proxy for lqudty than dollar volume or vce versa snce they are two popular proxes used n the lterature. Our goal s to fnd out whether the results n Nguyen et al (2006) are robust to dfferent measures of lqudty. 5

reject the null hypothess that the tme seres ntercepts are jontly equal to zero, suggestng that the three-factor and four-factor models do not account for lqudty level. Ths also mples that the market lqudty factor alone does not capture the mpact of lqudty level ether. In the cross sectonal test, we work wth ndvdual securtes rather than portfolos. Usng ndvdual securtes n asset prcng tests has several advantages as follows: 1. Guards aganst the data-snoopng bases nherent n portfolo based asset prcng tests (Lo and MacKnlay (1990)). 2. Ths avods the loss of nformaton that results when stocks are sorted nto groups (Ltzenberger and Ramaswamy (1979)), and 3. Ths crcumvents the problem rased by Berk (2000) that sortng data nto portfolos ntroduces a bas n favor of rejectng the model consdered. We fnd that after controllng for Pastor and Stambaugh factor, lqudty level remans prced, suggestng the market lqudty factor does not capture the mpact of lqudty level on expected return. We also focus on a controversy ssue: what explan expected stock returns: rsk factors or equty characterstcs? Danel and Ttman (1997) queston the rsk-based Fama-French model, argung that t s the stock characterstcs, sze and book to market, that explan stock return, not the factor loadng on Fama-French factors. We fnd that the effect of characterstc lqudty s not nfluenced by Fama-French factors or stock characterstcs. In fact, lqudty outweghs sze n explanng average stock return, suggestng that sze may be smply a proxy for lqudty. Fnally, we nvestgate whether dfferences n the measurement of tradng volume on the NYSE-AMEX versus the Nasdaq exchange can affect our results. The volume fgures n Nasdaq have dfferent meanng than those n NYSE-AMEX because of the ncluson of nter-dealer 6

tradng on Nasdaq. We perform separate analyses for NYSE-AMEX and Nasdaq under both tme seres and cross sectonal framework. The results are qualtatvely smlar for both exchanges. Our paper proceeds as follows. Sectonal II presents our methodology and emprcal analyss. Secton III concludes the paper. II. Emprcal Analyss A. Tme seres testng The purpose of tme seres testng s twofold. Frst, we control characterstc lqudty by sortng stocks nto lqudty groups based on ther dollar tradng volume. We then perform tme seres regressons for these lqudty portfolos usng both Fama-French model and a four factor model that ncludes Fama-French and Pastor-Stambaugh market lqudty factors. The tmeseres regresson provdes valdty of the asset prcng model. Also, f the ntercept of regresson s sgnfcant, t ndcates the presence of a premum assocated wth the characterstc lqudty. If market lqudty and Fama-French factors subsume the effect of characterstc lqudty, a systematc ncrease n the ntercepts (or the lqudty premum on portfolos arranged n order of decreasng lqudty), wll not be observed.. In addton, f the ntercepts are jontly equal to zero after controllng for characterstc lqudty, then the asset prcng model as specfed s able to explan stock returns after controllng for lqudty. The asset prcng model, therefore, captures the lqudty effect. On the contrary, f the tme seres ntercepts are not jontly equal to zero, the model does not capture lqudty. To test whether the ntercepts are jontly equal to zero, we use the test developed by Gbbon, Ross, and Shanken (1989). Portfolo formaton procedure Usng NYSE and AMEX stock data, we construct 25 portfolos based on sze and dollar volume, book-to-market rato and dollar volume, and dollar volume only. Specfcally, at the end 7

of each calendar year n the perod 1963-2004, we rank all common stocks lsted on the NYSE and AMEX by market captalzaton and dvde the sample nto fve portfolos of equal sze. We employ annual dollar volume for each stock as a measure of characterstc lqudty. We defne the annual dollar volume for each stock n the sample as the product of average monthly prce and the tradng volume durng the year. Each sze quntle comprses fve groups of portfolos n ncreasng order of dollar volume or lqudty. Each of these fve groups contan equal number of stocks, Followng the portfolo constructon procedure, as descrbed above, we sort portfolos based on book-to-market value and dollar volume. All common stocks n NYSE and AMEX from 1963 to 2004 are ranked by the book-to-market rato n the begnnng of perod, and then dvded nto fve portfolos of equal sze. Wthn each book-to-market quntle, each stock s assgned to one of fve portfolos of an equal number of securtes based on annual dollar volume values. Fnally, all the NYSE and AMEX stocks are sorted nto 25 portfolos based on ther annual dollar volume alone, because the pre-sortng on both sze and book-to-market rato may obvously be nterpreted as lqudty portfolos controlled by sze and book-to-market value. Therefore, as a check for robustness, the analyss s further conducted wth 25 portfolos sorted by dollar volume only. Usng the portfolos constructed above, we compute the equally-weghted-monthly returns for each of the 25 portfolos. The dfference of the portfolo return and the 30-day Treasury bll yeld gves the excess portfolo return. The portfolos are rebalanced every year from 1963 to 2004. 8

Gbbon, Ross, Shanken (1989) test (GRS) We estmate the tme-seres regresson of the excess returns on the 25 portfolos (sorted by sze and dollar volume, by book-to-market rato and dollar volume, and by dollar volume alone) on the four-factor model usng ordnary least squares as follows: r (, t) = α + β ( R R ) + δ SMB + γ HML + ψ LIQ + e (1) mt ft t t t t where (, ) s the excess return on portfolo n month t, ( rt mt ft R R ), SMB, HML are the Fama and French (1993) three factors related to market premum, frm sze, and the book-tomarket rato, and LIQ t s the Pastor and Stambaugh (2003) lqudty factor n month t. In order to make a comparatve analyss wth the four-factor model stated above, we also examne the bench-mark Fama-French 3-factor model alone can explan the lqudty premum. The tme seres regresson model s as follows: r (, t) = α + β ( R R ) + δ SMB + γ HML + e (2) mt ft t t t t t where (, ) s the excess return on portfolo n month t and ( rt mt ft R R ), SMB, and HML are the Fama and French (1993) three factors related to market premum, frm sze, and the book-tomarket rato n month t. Our argument s that f nether the three-factor nor the four-factor model s capable of capturng lqudty level then the Pastor-Stambaugh market lqudty factor alone cannot capture characterstc lqudty ether. We test the null hypothess that the characterstc lqudty, f proxed by the dollar volume, has no effect on expected stock returns and that the ntercepts n these tme seres regressons are jontly equal to zero usng the Gbbon, Ross, Shanken (1989) F-test. Brefly, the Gbbon, Ross, and Shanken test procedure can be summarzed as follows: t t 9

Let N be the number of tme seres observatons, L be number of portfolos, K be the number of regresson parameters ncludng the constant term, and X be the observaton matrx. Then, the GRS test statstc s gven by 1 ( A' A) N K L + 1 L * ( N K) * ω where A s the column vector of the regresson parameters, s the varance-covarance matrx of the resduals from the regresson, and 1, 1 1,1 ω s the dagonal element of ( X ' X ) 1. Under the null hypothess that the regresson constants are zero, ths statstc has an F-dstrbuton wth L and (N K L + 1) degrees of freedom. The tme seres results are reported n Table 1, 2, and 3. We observe a consstent pattern n the ntercepts as reported n Tables 1 and 2. The ntercepts are generally decreasng from the lowest lqudty group (group 1) to the hghest lqudty group (group 5). 2 These results mply that more lqud stocks demand hgher expected return than less lqud stocks after controllng for rsk usng the Fama-French and Pastor-Stambaugh market lqudty factors. The evdence that the ntercepts generally decrease from low lqudty to hgh lqudty portfolos wthn each sze or book-to-market group also suggests that the sze and book-to-market rato do not relate to lqudty. In order to check the robustness of results,, we perform the same analyss for the 25 portfolos sorted by dollar volume only. The results are strkngly smlar, as evdent from Table 3. 2 The results for the sze group 5 (largest sze group) and book-to-market group 1 (lowest book-to-market group) are less sgnfcant. The ntercepts generally decrease from the low lqudty group to hgh lqudty group but not consstently. The dfference n the ntercepts between the hghest lqudty and lowest lqudty groups n these two sze and book-to-market groups are not negatvely sgnfcant as n other cases. These evdences mply that lqudty may be less mportant for large or low book-to-market stocks than t s for smaller sze or hgher book-to-market stocks. 10

Our results also ndcate that the systematc lqudty measure of Pastor and Stambaugh does not account for the characterstc lqudty level. If the lqudty beta subsumes the lqudty level per se, we should not observe systematc dfferences n the ntercepts from the tme seres regressons for lqudty portfolos n both three-factor and four-factor models. However, the evdence n Tables 1, 2, and 3 generally shows a monotonc decrease n the ntercepts from low lqudty to hgh lqudty portfolos. The dfferences n the ntercepts between the hghest lqudty and lowest lqudty group of portfolos are statstcally sgnfcant and negatve. The GRS statstcs are also reported n Tables 1, 2, and 3. In all cases, the F-tests strongly reject the null hypothess that ntercepts are jontly equal to zero for both the four-factor and the Fama- French three-factor models at the 1 percent level. Overall, our results suggest that nether of the two models consdered here capture the effect of lqudty preference à la Amhud and Mendelson (1986). B. Cross-sectonal tests We use cross-sectonal regressons to drectly nvestgate the relatonshp between lqudty and stock returns after controllng for other varables. In partcular, for each month t n the sample perod, we perform cross-sectonal regressons as follows: Lqudty and stock characterstcs R t = γ 0 t + γ 1t Beta + γ 2t Sze + γ 3t BM + γ 4t DV + ε t (3) Lqudty and factor loadngs R t = γ 0 t + γ 1t FRm Rf + γ 2t FSMB + γ 3t FHML + γ 4t FLIQ + γ 5t DV + ε t (4) where Beta, Sze, BM, and DV are, respectvely, the market beta, market value of equty, bookto-market rato, and dollar volume value (as a proxy for the characterstc lqudty) of frm. FRm Rf SMB, F, and F are the factor loadngs of frm on the Fama-French common factors, HML 11

FLIQ s the factor loadng of frm on the Pastor-Stambaugh market lqudty factor. The factor loadngs for each month are estmated usng return and factor observaton from the prevous 60 months. We requre a stock to have a mnmum of 24 monthly observatons avalable for the estmaton. The coeffcents from the cross-sectonal regressons are averaged over tme usng the Ltzenberger and Ramaswamy (1979) methodology. Ths methodology weghts the coeffcents by ther precson when summng across the cross-sectonal regressons and thus corrects for the neffcency under tme-varyng volatlty wth the standard Fama-MacBeth (1973) procedure. 3 Our dataset conssts of all the NYSE and AMEX stocks from January 1963 to December 2004. 4 Monthly data on returns are collected from the Center for Research n Securty Prces (CRSP) and the book values are extracted from the Compustat tapes. We measure the dollar volume value of every stock n each month t as the natural logarthm of the average dollar volume of the prevous three months,.e., durng months t-3, t-2, t-1. 5 We construct the book-to-market varable (natural logarthm of book value to market value for ndvdual frms) as suggested by Fama and French (1992). We defne the log of frm sze as the natural logarthm of total market captalzaton of frm, at the end of the pror month (month t-1). In our sample, the book-to-market varable has a mnmum value of 7.81 and a maxmum value of 4.40 wth a mean of 0.31. The sze varable ranges from 5.46 to 20.18 and has a mean of 12.37 (Table 4). 3 See Ltzenberger and Ramaswamy (1979) for more detal on the procedure. 4 Our complete sample runs from 1963 to 2004. However, the estmaton perod runs from 1968 to 2004 snce we lose the frst fve year of data when estmatng the factor loadngs. 5 We also compute dollar volume on the bass of sx month and twelve months of tradng volume. The results are qualtatvely smlar. 12

We estmate betas for each securty followng Amhud and Mendelson (1986). In partcular, at the end of each year, all the NYSE-AMEX stocks are sorted nto 25 portfolos based on ther pre-rankng betas usng the past 5 year returns. Once the portfolos are formed, portfolo betas are computed usng the fve-year wndow. Portfolo betas are then assgned to each ndvdual frm wthn the portfolos. By estmatng betas at the portfolo level, we elmnate potental measurement errors that may occur f we estmate betas at the ndvdual frm level. Our results of cross sectonal regressons are reported n Table 5 and 6. Table 5 presents correlatons between the dollar volume and other stock characterstcs. Panel A shows that sze s negatvely correlated wth the book-to-market rato wth a factor of -0.35, whle beta s postvely correlated wth the dollar volume wth a factor of 0.04, respectvely. We also observe that sze has a very strong correlaton wth dollar volume (0.90). Ths mght cause multcolnearty n the regresson results. To remove the effect of multcolnearty, we orthogonalze sze on dollar volume n the cross-sectonal analyss. For each month, sze s regressed on dollar volume crosssectonally and the resduals from the regresson are used as a measure for sze n the analyses. The correlaton between dollar volume and sze resdual now s 0.18 (see Panel B) Table 6 summarzes the results of our cross-sectonal regressons of stock returns on dollar volume after controllng for varous stock characterstc varables, the Fama-French and Pastor-Stambaugh factor loadngs. We fnd that the dollar volume varable s sgnfcantly negatvely related to stock returns n all the models. Panel A reports the regresson of stock return on the dollar volume and other characterstc varables. The evdence of a lqudty premum s documented here. Dollar volume s negatvely correlated to stock returns (coeffcent = -0.0034, t-stat = -15.34). We then estmate several multvarate regressons to examne whether the lqudty level s stll prced after controllng for explanatory varables other than sze. We 13

fnd that the premum for lqudty stll exsts. For example, when controllng for book-to-market, the dollar volume coeffcent s equal to -0.0021 (t-stat = -9.14). However, when controllng for sze, the sgnfcance of dollar volume decreases as more varables are added. For example, the magntude of t-stat of the dollar volume s equal to 4.72 when only sze s ncluded. It decreases to 3.63 when both sze and book-to-market are ncluded, and goes down to 0.28, whch s nsgnfcant, when sze, beta, and book-to-market are all ncluded. The reason for the decrease of sgnfcance level of the dollar volume, when sze s ncluded, may be due to a very strong correlaton between sze and dollar volume (0.90). To remove the mult-collnearty, we regress sze on dollar volume cross sectonally. The resduals taken from these regressons are used to replace sze n the testng models. The results presented n Table 6, Panel B confrms once agan the presence of a lqudty premum. We fnd that the dollar volume s agan negatvely correlated to return, whether sze alone or sze along wth other characterstc varables s ncluded. Another mportant observaton from the results reported n Table 6 s that the effect of dollar volume domnates that of sze n explanng cross-sectonal stock return. Sze becomes nsgnfcant when only the dollar volume s ncluded or when both dollar volume and book-tomarket are ncluded. Even when sze s replaced by the sze resdual n the regresson to remove the multcollnearty between sze and dollar volume, the coeffcents on sze resdual are stll not sgnfcant when dollar volume alone or dollar volume and book-to-market are ncluded. The mplcaton s that sze, the well-known determnant of stock return, may be just a proxy for lqudty. In other words, lqudty proxed by dollar tradng volume has stronger effect on stock return than sze does. C. Nasdaq stocks 14

Our analyss up to ths pont has consdered NYSE and AMEX stocks only. We separate Nasdaq stocks from NYSE-AMEX stocks snce we are nterested n fndng out whether our results are drven by the desgn of the tradng process. Nasdaq volume can be consdered to be overstated relatve to NYSE-AMEX volume due to the ncluson of nter-dealer tradng on Nasdaq snce tradng on Nasdaq s done almost entrely through the market makers whereas on the NYSE-AMEX, most tradng s done drectly between buyng and sellng nvestors. We perform both tme seres and cross sectonal regressons for Nasdaq stocks and report the results n Tables 7, 8, and 9. The results are very smlar to those obtaned for NYSE-AMEX stocks. In partcular, n all 25 portfolos sorted by sze and dollar volume, by book-to-market and dollar volume, and by dollar volume, the ntercepts consstently decrease from the low lqudty to the hgh lqudty group wth few exceptons n the cases of largest sze and hghest book-to-market groups. The GRS test statstcs reject the null hypothess that the 25 ntercepts are jontly equal to zero for both the four-factor and three-factor models. The cross sectonal analyses reported n Table 9 also ndcate that the dollar volume s negatvely related to stock returns after controllng for stock characterstcs, Fama-French and Pastor-Stambaugh factor loadngs. The evdence that the dollar volume domnates sze n explanng cross sectonal stock return s vald n ths case also. Therefore, our orgnal results, obtaned usng NYSE and AMEX stocks are robust to dfferences n the measurement of tradng volume on the NYSE-AMEX versus the Nasdaq exchange. III. Concluson Ths paper prmarly concerns wth provdng evdence on whether the market lqudty can explan the lqudty premum. Our analyss uses a four-factor asset prcng model that ncludes Fama-French and Pastor-Stambaugh market lqudty factors. In ths model of rsk 15

adjustment, the lqudty factor controls for non-dversfable lqudty rsk. Our results support the Amhud and Mendelson (1986) argument that expected stock return s a postve functon of llqudty as a characterstc both n tme seres and cross sectonal frameworks. In partcular, tme seres tests based on the three-factor Fama-French model or the four-factor model that ncludes Fama-French and Pastor-Stambaugh market lqudty factors, demonstrate a consstently decreasng pattern n the ntercepts from low lqudty portfolos to hgh lqudty portfolos suggestng a characterstc lqudty premum that can not be captured by the market-wde lqudty factor. Further, the Gbbon-Ross-Shanken statstcs reject the null hypothess that the tme seres ntercepts are jontly equal to zero, suggestng that nether the three-factor nor the four-factor model s able to capture lqudty preference. Ths mples that the market lqudty factor does not account for the stock-specfc lqudty level. In the cross sectonal tests, the two-step generalzed least squares (GLS) framework of Ltzenberger and Ramaswamy (1979), leads us to conclude that, after controllng for stock characterstcs such as Fama-French and Pastor-Stambaugh factor loadngs, the dollar volume s statstcally sgnfcant and negatvely correlated wth stock returns. Ths result s also consstent wth the lqudty premum noton n Amhud and Mendelson (1986) as documented n our tme seres tests Yet another mportant fndng from the cross sectonal test s that sze becomes nsgnfcant when dollar volume s ncluded, or when both dollar volume and book-to-market are ncluded. In order to remove the strong correlaton between sze and dollar volume n the regresson, sze s replaced by the sze resdual. We fnd that the coeffcents on the sze resdual become nsgnfcant when only dollar volume or dollar volume and book-to-market are ncluded. The mplcaton s that sze, a well-known determnant of stock returns, may be just 16

servng as a proxy for lqudty. Ths means that lqudty proxed by dollar tradng volume s a better determnant of stock returns than sze. We also perform analyss for Nasdaq stocks to see whether the dfferences n volume measures arsng from tradng process on Nasdaq whch substantally dffers from that on NYSE and AMEX may have any mpact on our results. Our fndngs confrm that the noton of characterstc lqudty preference as n Amhud and Mendelson stll holds n both tme seres and cross sectonal contexts. Our fndngs strengthen the results of Nguyen et al (2006). Combned wth ther study, we show that lqudty level s an mportant varable n asset prcng and that the Pastor- Stambaugh market lqudty and Fama-French factors, and stock characterstcs (sze and bookto-market) do not capture the effect of lqudty level. The mplcaton for nvestors s that they need to ncorporate lqudty preference n ther decson makng regardless of the specfcatons of ther asset prcng models used to adjust for rsk. Alternatvely, the search for a ratonal asset prcng model that can capture the mpact of characterstc lqudty s stll open. 17

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Eleswarapu, V. R. and M. R. Renganum, 1993. The seasonal behavour of the lqudty premum n asset prcng, Journal of Fnancal Economcs 34, 373 386. Fama, E. and K. French, 1992. The cross-secton of expected stock returns, Journal of Fnance 47, 427 465. Fama, E. and K. French, 1993. Common rsk factors n the returns on stocks and bonds, Journal of Fnancal Economcs 33, 3 56. Fama, E. and J. D. MacBeth, 1973. Rsk, return and equlbrum: Emprcal tests, Journal of Poltcal Economy 81, 607 636. Gbbons, M., S. Ross, J. Shanken, 1989. A test of the effcency of a gven portfolo, Econometrca 57, 1121 1152. Hasbrouck, J., and D. J. Sepp, 2001, Common factors n prces, order flows, and lqudty, Journal of Fnancal Economcs 59, 383-411. Jacoby, G., D.J. Fowler, and A.A. Gottesman, 2000. The captal asset prcng model and the lqudty effect: a theoretcal approach, Journal of Fnancal Markets 3, 69 81. Ltzenberger, R. and K. Ramaswamy, 1979. The effect of personal taxes and dvdends on captal asset prces: theory and emprcal evdence, Journal of Fnancal Economcs, 163 196. Lo, A., and C. Macknlay, 1990. Data snoopng bases n tests of fnancal asset prcng models, Revew of Fnancal Studes, 431-468. Nguyen, D., S. Mshra, A. Prakash, and D. Ghosh, 2006. Lqudty and asset prcng under the three-moment CAPM paradgm, forthcomng n the Journal of Fnancal Research. Pástor, L., Stambaugh, R.F., 2003. Lqudty rsk and expected stock returns. Journal of Poltcal Economy 111, 642-685. Peterson, M., and D. Falkowsk, 1994. Posted versus effectve spreads: Good prces or bad 19

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Table 1: Intercepts from tme seres regressons of the 25 portfolos sorted by sze and dollar volume for the four-factor and three-factor models Ths table reports the value of the ntercepts obtaned four-factor and three-factor models for 25 portfolos of NYSE-AMEX stocks sorted accordng to sze and dollar volume. Dollar volume for each stock s defned as the average of number of shared tradng multpled by stock prce durng the year. Portfolos are formed yearly for the perod 1963-2004. Wthn each calendar year, all stocks n the sample are allocated nto fve sze portfolos based on ther market equty rankng. Each sze quntle s then subdvded nto fve lqudty portfolos usng the dollar volume value. Panel A presents ntercepts from the tme seres regresson of four-factor model as n the followng equaton r (, t) = α + β ( Rmt R ft ) + δ SMBt + γ HMLt +ψ LIQt + et where rt (, ) s the excess return on portfolo n month t, and ( Rmt R ft ), SMBt, HMLt, are Fama and French (1993) three factors related to market premum, frm sze, and the book-to-market rato n month t. LIQ t s the Pastor and Stambaugh (2003) lqudty factor. Panel B presents ntercepts from the tme seres regresson of three-factor model as n the followng equaton r (, t) = α + β ( Rmt R ft ) + δ SMBt + γ HMLt + et.the last column represents the dfference between lqudty group 5 and lqudty group1. The bottom of each panel presents the Gbbons, Ross, Shanken (1989) test of the hypothess that the ntercepts jontly equal zero for the four-factor model and three-factor model. Intercepts are reported n percentage terms (t-statstcs are n parentheses). Panel A: Four-factor model Lqudty group Sze group 1 2 3 4 5 5-1 1 0.0107 0.0037-0.0012-0.0022-0.0109-0.0216 (3.52) (1.54) (-0.59) (-1.11) (-4.00) (-8.64)*** 2 0.0027 0.0007-0.0012-0.0051-0.0121-0.0149 (2.50) (0.64) (-1.02) (-4.13) (-6.48) (-7.70)*** 3 0.0019-0.0001-0.0012-0.0041-0.0082-0.0101 (2.25) (-0.12) (-1.19) (-3.56) (-5.59) (-6.47)*** 4 0.0015-0.0002-0.0003-0.0015-0.0049-0.0065 (1.87) (-0.27) (-0.31) (-1.41) (-3.52) (-4.64)*** 5 0.0000 0.0001-0.0011-0.0007-0.0010-0.0010 (0.00) (0.08) (-1.39) (-0.95) (-1.30) (0.38) F-value for Gbbons, Ross, Shanken, test that the ntercepts jontly equal to zero s 5.22*** (sgnfcant at 1 percent level) 21

Panel B: Three-factor model Lqudty group Sze group 1 2 3 4 5 5-1 1 0.0112 0.0041 0.0008-0.0009-0.0074-0.0186 (4.24) (1.98) (0.46) (-0.55) (-3.10) (-8.50)*** 2 0.0016 0.0002-0.0014-0.0040-0.0106-0.0122 (1.74) (0.29) (-1.38) (-3.73) (-6.56) (-7.31)*** 3 0.0015-0.0004-0.0013-0.0039-0.0080-0.0095 (2.06) (-0.51) (-1.40) (-3.90) (-6.29) (-7.01)*** 4 0.0010-0.0003-0.0005-0.0019-0.0048-0.0058 (1.32) (-0.40) (-0.63) (-2.00) (-3.97) (-4.75)*** 5-0.0001 0.0000-0.0009-0.0007-0.0012-0.0011 (-0.20) (0.02) (-1.32) (-1.17) (-1.84) (-1.07) F-value for Gbbons, Ross, Shanken, test that the ntercepts jontly equal to zero s 5.17*** (sgnfcant at 1 percent level) 22

Table 2: Intercepts from tme seres regressons of the 25 portfolos sorted by book-tomarket and dollar volume for the four-factor and three-factor models Ths table reports the value of the ntercepts obtaned four-factor and three-factor models for 25 portfolos of NYSE-AMEX stocks sorted accordng to book-to-market and dollar volume. Dollar volume for each stock s defned as the average of number of shared tradng multpled by stock prce durng the year. Portfolos are formed yearly for the perod 1963-2004. Wthn each calendar year, all stocks n the sample are allocated nto fve portfolos based on ther book-to-market ratos rankng. Each book-to-market quntle s then subdvded nto fve lqudty portfolos usng the dollar volume. Panel A presents ntercepts from the tme seres regresson of four-factor model as n the followng equaton r (, t) = α + β ( Rmt R ft ) + δ SMBt + γ HMLt +ψ LIQt + et where rt (, ) s the excess return on portfolo n month t, and ( Rmt Rft ), SMBt, HMLt, are Fama and French (1993) three factors related to market premum, frm sze, and the book-to-market rato n month t. LIQ t s the Pastor and Stambaugh (2003) lqudty factor. Panel B presents ntercepts from the tme seres regresson of three-factor model as n the followng equaton r (, t) = α + β ( Rmt R ft ) + δ SMBt + γ HMLt + et.the last column represents the dfference between lqudty group 5 and lqudty group1. The bottom of each panel presents the Gbbons, Ross, Shanken (1989) test of the hypothess that the ntercepts jontly equal zero for the four-factor model and three-factor model. Intercepts are reported n percentage terms (t-statstcs are n parentheses). Panel A: Four-factor model Book-to-market Lqudty group group 1 2 3 4 5 5-1 1-0.0005-0.0031-0.0030-0.0010 0.0003 0.0008 (-0.34) (-2.43) (-2.28) (-0.87) (0.31) (0.47) 2 0.0031-0.0027-0.0023-0.0018-0.0008-0.0039 (2.23) (-2.15) (-1.94) (-1.70) (-0.73) (-2.37)** 3 0.0028-0.0001-0.0029-0.0018-0.0024-0.0053 (2.08) (-0.07) (-2.73) (-1.82) (-2.38) (-3.16)*** 4 0.0035 0.0013-0.0001-1.1787-0.0006-0.0041 (2.12) (1.10) (-0.13) (-0.00) (-0.54) (-2.15)** 5 0.0098 0.0026-0.0003-0.0017-0.0024-0.0122 (3.90) (1.41) (-0.23) (-1.02) (-1.76) (-4.89)*** F-value for Gbbons, Ross, Shanken, test that the ntercepts jontly equal to zero s 2.41*** (sgnfcant at 1% level) 23

Panel B: Three-factor model Book-to-market Lqudty group group 1 2 3 4 5 5-1 1-0.0000-0.0030-0.0024-0.0007 0.0001 0.0002 (-0.05) (-2.81) (-2.07) (-0.71) (0.13) (0.11) 2 0.0016-0.0024-0.0024-0.0018-0.0017-0.0033 (1.38) (-2.21) (-2.41) (-1.95) (-1.79) (-2.34)** 3 0.0011 0.0001-0.0024-0.0010-0.0025-0.0036 (0.98) (0.17) (-2.59) (-1.14) (-2.71) (-2.45)** 4 0.0034 0.0013-0.0002-0.0006-0.0005-0.0039 (2.39) (1.28) (-0.22) (-0.62) (-0.52) (-2.38)** 5 0.0106 0.0033-0.0002-0.0007-0.0003-0.0109 (4.88) (2.12) (-0.15) (-0.48) (-0.24) (-5.02)*** F-value for Gbbons, Ross, Shanken, test that the ntercepts jontly equal to zero s 2.33*** (sgnfcant at 1 percent level) 24

Table 3: Intercepts from tme seres regressons of the 25 portfolos sorted by dollar volume for the four-factor and the three-factor model. Ths table reports the value of the ntercepts obtaned four-factor and three-factor models for 25 portfolos of NYSE-AMEX stocks sorted accordng to dollar volume. Dollar volume for each stock s defned as the average of number of shared tradng multpled by stock prce durng the year. Portfolos are formed yearly for the perod 1963-2004. Wthn each calendar year, all stocks n the sample are allocated nto 25 portfolos based on ther average dollar volume durng the prevous year. Panel A presents ntercepts from the tme seres regresson of fourfactor model as n the followng equaton on portfolo n month t, and ( the book-to-market rato n month t. R regresson of three-factor model as n the followng equaton mt ft r(, t) = α + β ( R R ) + δ SMB + γ HML + ψ LIQ e where rt (, ) s the excess return mt ft t t t + R ), SMB, HML, are Fama and French (1993) three factors related to market premum, frm sze, and LIQ t t t s the Pastor and Stambaugh (2003) lqudty factor. Panel B presents ntercepts from the tme seres r, t) = α + β ( R R ) + δ SMB + γ HML + e (. The bottom of each panel presents the Gbbons, Ross, Shanken (1989) test of the hypothess that the ntercepts jontly equal zero for the four-factor model and three-factor model. Intercepts are reported n percentage terms (t-statstcs are n parentheses). mt ft t t t t Dollar volume sorted group 1 3 5 7 9 11 13 15 17 19 21 23 25 Panel A: Four-factor model 0.0102 0.0009-0.0002-0.0002-0.0031-0.0025-0.0033-0.0038-0.0039-0.0035-0.0021-0.0021-0.0017 (3.40) (0.49) (-0.16) (-0.16) (-2.85) (-2.41) (-3.10) (-3.50) (-3.81) (-3.44) (-2.22) (-2.19) (-2.04) F-value for Gbbons, Ross, Shanken, test that the ntercepts jontly equal to zero s 2.40*** (sgnfcant at 1 percent level) Panel B: Three-factor model 0.0108 0.0017-0.0005-0.0004-0.0028-0.0018-0.0030-0.0029-0.0036-0.0034-0.0020-0.0020-0.0018 (4.13) (1.08) (-0.40) (-0.40) (-3.10) (-2.03) (-3.27) (-3.22) (-3.98) (-3.81) (-2.43) (-2.40) (-2.37) F-value for Gbbons, Ross, Shanken, test that the ntercepts jontly equal to zero s 2.53*** (sgnfcant at 1 percent level) 25

Table 4: Summary statstcs Ths table reports basc statstcs on varables of concern for NYSE-AMEX stocks over the perod 1963-2004. Book-to-market varable s the natural logarthm of the book to market rato. Sze s the natural logarthm of frm s total market captalzaton n the pror month. Dollar volume s computed as the natural logarthm of average monthly tradng volume multply by prce durng the prevous three months. Beta s computed as follows. Frst, at the end of each year, all stocks n NYSE-AMEX are sorted nto 25 portfolos based on ther pre-rankng betas usng the past 5 year returns. Once the portfolos are formed, portfolos betas are computed usng the fve-year wndow. Portfolos betas are then assgned to each ndvdual frm wthn the portfolos. Varable Mean Standard Devaton Mnmum 25 th Percentle 50 th Percentle 75 th Percentle Maxmum book-tomarket -0.3128 0.7988-7.8186 4.3981-0.7720-0.2571 0.2080 dollar volume 10.8544 2.6374 2.0636 8.9478 10.7686 12.7192 20.0558 sze 12.3659 2.1100 5.4595 10.7995 12.3380 13.8387 20.1804 beta 1.0744 0.3046 0.2488 0.8681 1.0890 1.2768 2.0196 26

Table 5: Smple correlatons Ths table reports tme seres averages of monthly cross-sectonal correlaton of varables n asset prcng tests for all NYSE-AMEX stocks over the perod 1963-2004. Book-to-market varable s the natural logarthm of the book to market rato. Sze s the natural logarthm of frm s total market captalzaton n the pror month. Dollar volume s computed as the natural logarthm of average monthly tradng volume multply by prce durng the prevous three months. Beta s computed as follows. Frst, at the end of each year, all stocks n NYSE-AMEX are sorted nto 25 portfolos based on ther pre-rankng betas usng the past 5 year returns. Once the portfolos are formed, portfolos betas are computed usng the fve-year wndow. Portfolos betas are then assgned to each ndvdual frm wthn the portfolos. Sze resdual s the resdual from the cross-sectonal regresson of sze on dollar volume. Panel A provdes the correlatons between dollar volume and other stock characterstcs. Panel B provdes the correlatons between sze resdual and other varables. Panel A: Correlatons among dollar volume and stock characterstcs beta book-to-market sze dollar volume beta 1.0000-0.1172-0.0981 0.0386 book-to-market -0.1172 1.0000-0.3501-0.3638 sze -0.0981-0.3501 1.0000 0.9001 dollar volume 0.0386-0.3638 0.9001 1.0000 Panel B: Correlaton between gamma resdual and beta, book-to-market, and dollar volume beta book-to-market dollar volume sze resdual 0.0386-0.3639 0.1793 27

Table 6: Average slopes of monthly cross-sectonal regresson Ths table reports average slopes of monthly cross-sectonal regressons of returns on dollar volume usng monthly ndvdual securty data of NYSE-AMEX stocks over the perod 1963-2004 after controllng for stock characterstcs as well as for market factors. In each month, a cross-sectonal regresson s estmated wheren the ndvdual stock return s the dependent varable and the explanatory varable set comprses varous combnatons of the dollar volume wth other varables correspondng to each asset prcng model. The book-to-market varable s the natural logarthm of book to market rato. Sze s the natural logarthm of frm s total market captalzaton at the pror month. Dollar volume s computed as the natural logarthm of average monthly tradng volume multply by prce durng the prevous three months. Beta s computed as follows. Frst, at the end of each year, all stocks n NYSE-AMEX are sorted nto 25 portfolos based on ther pre-rankng betas usng the past 5 year returns. Once the portfolos are formed, portfolos betas are computed usng the fve-year wndow. Portfolos betas are then assgned to each ndvdual frm wthn the portfolos. Sze resdual s the resdual from the cross-sectonal regresson of sze on dollar volume The GLS estmates of average slopes and assocated t-statstcs (n parentheses) are calculated usng the Ltzenberger and Ramaswamy (1979) procedure. Panel A presents the results for dollar volume and sze, book-to-market, beta. Panel B presents the results for dollar volume, beta, book-to-market, and the sze resdual (calculated from cross-sectonal regresson). Panel C presents the results for dollar volume and factor loadngs on three common factors of Fama-French (1993) and Pastor and Stambaugh (2003) market lqudty factor. Panel A: dollar volume and characterstc varables: sze, book-to-market rato, beta Constant Dollar volume Book-to-market sze Beta 0.0201-0.0034 (20.34) (-15.34) 0.0151-0.0021 0.0021 (14.44) (-9.14) (10.26) 0.0216-0.0025-0.0001 (19.23) (-4.72) (-0.70) 0.0260-0.0034-0.0055 (22.00) (-15.58) (-9.54) 0.0158-0.0019 0.0021 0.0001 (13.26) (-3.63) (9.97) (0.42) 0.0254 0.0001 0.0017-0.0009-0.0057 (16.83) (0.28) (8.37) (-4.29) (-9.09) Panel B: dollar volume, sze resdual, and other characterstcs Constant Dollar volume Book-to-market Sze resdual Beta 0.0207-0.0021 0.0017-0.0009-0.0057 (16.47) (-8.71) (8.39) (-4.28) (-9.07) 0.0191-0.0032-0.0001 (19.38) (-14.43) (-0.72) 0.0143-0.0021 0.0021 0.0001 (13.81) (-8.87) (9.97) (0.41) 28

Panel C: dollar volume and factor loadngs on four factors Constant Dollar volume SMB HML Rm-Rf LIQ 0.0081-0.0003-0.0024 0.0020-0.0032-0.0004 (10.75) (-4.97) (-17.00) (13.90) (-13.96) (-1.19) 0.0021-0.0002 0.0014 0.0012 (3.39) (-3.50) (10.30) (4.28) -0.0016 0.0017 0.0014 (-11.76) (11.96) (4.74) 0.0004-0.0011 0.0014 (2.92) (-8.99) (4.70) 0.0018-0.0022 0.0008 (7.00) (-10.01) (2.47) 0.0088-0.0004-0.0020-0.0022 0.0001 (11.86) (-6.49) (-14.54) (-10.37) (0.41) 0.0067-0.0004-0.0017 0.0011 (9.19) (-7.42) (-12.77) (3.83) 0.0064-0.0005-0.0021 0.0016 (8.64) (-7.46) (-15.63) (11.84) 0.0080-0.0003-0.0022 0.0020-0.0030 (10.80) (-5.09) (-16.15) (13.95) (-13.86) 29

Table 7: Intercepts from tme seres regressons of the 25 portfolos sorted by sze and dollar volume for Nasdaq stocks Ths table reports the value of the ntercepts obtaned four-factor and three-factor models for 25 portfolos of Nasdaq stocks sorted accordng to sze and dollar volume. Dollar volume for each stock s defned as the average of number of shared tradng multpled by stock prce durng the year. Portfolos are formed yearly for the perod 1983-2004. Wthn each calendar year, all stocks n the sample are allocated nto fve sze portfolos based on ther market equty rankng. Each sze quntle s then subdvded nto fve lqudty portfolos usng the dollar volume value. Panel A presents ntercepts from the tme seres regresson of four-factor model as n the followng equaton r (, t) = α + β ( Rmt R ft ) + δ SMBt + γ HMLt +ψ LIQt + et where rt (, ) s the excess return on portfolo n month t, and ( Rmt Rft ), SMBt, HMLt, are Fama and French (1993) three factors related to market premum, frm sze, and the book-to-market rato n month t. LIQ t s the Pastor and Stambaugh (2003) lqudty factor. Panel B presents ntercepts from the tme seres regresson of three-factor model as n the followng equaton r (, t) = α + β ( Rmt R ft ) + δ SMBt + γ HMLt + et.the last column represents the dfference between lqudty group 5 and lqudty group1. The bottom of each panel presents the Gbbons, Ross, Shanken (1989) test of the hypothess that the ntercepts jontly equal zero for the four-factor model and three-factor model. Intercepts are reported n percentage terms (t-statstcs are n parentheses). Panel A: Four-factor model Lqudty group Sze group 1 2 3 4 5 5-1 1 0.0246 0.0186 0.0166 0.0099 0.0023-0.0223 (7.19) (5.22) (4.20) (2.05) (0.32) (-3.87)*** 2 0.0052 0.0022 0.0005 0.0000-0.0118-0.0170 (2.98) (1.08) (0.22) (0.00) (-2.41) (-3.73)*** 3 0.0036 0.0006-0.0008-0.0053-0.0131-0.0167 (2.33) (0.37) (-0.39) (-2.05) (-3.42) (-4.24)*** 4 0.0028-0.0005-0.0016-0.0079-0.0103-0.0131 (2.34) (-0.47) (-1.09) (-3.81) (-3.32) (-3.99)*** 5 0.0020-0.0014-0.0033-0.0045-0.0025-0.0045 (1.84) (-1.22) (-2.37) (-2.41) (-1.04) (-1.70)* F-value for Gbbons, Ross, Shanken, test that the ntercepts jontly equal to zero s 9.40*** (sgnfcant at 1 percent level) 30

Panel B: Three-factor model Lqudty group Sze group 1 2 3 4 5 5-1 1 0.0249 0.0192 0.0167 0.0104 0.0055-0.0194 (7.96) (5.87) (4.62) (2.35) (0.86) (-3.66)*** 2 0.0044 0.0024 0.0009 0.0006-0.0095-0.0139 (2.74) (1.26) (0.40) (0.20) (-2.12) (-3.32)*** 3 0.0037 0.0006 0.0002-0.0042-0.0111-0.0148 (2.65) (0.40) (0.14) (-1.76) (-3.15) (-4.09)*** 4 0.0020-0.0004-0.0015-0.0069-0.0100-0.0120 (1.85) (-0.39) (-1.09) (-3.63) (-3.50) (-3.98)*** 5 0.0021-0.0014-0.0032-0.0039-0.0015-0.0036 (2.10) (-1.33) (-2.45) (-2.28) (-0.70) (-1.49) F-value for Gbbons, Ross, Shanken, test that the ntercepts jontly equal to zero s 9.98*** (sgnfcant at 1 percent level) 31

Table 8: Intercepts from tme seres regressons of the 25 portfolos sorted by book-tomarket and dollar volume for Nasdaq stocks Ths table reports the value of the ntercepts obtaned four-factor and three-factor models for 25 portfolos of Nasdaq stocks sorted accordng to book-to-market and dollar volume. Dollar volume for each stock s defned as the average of number of shared tradng multpled by stock prce durng the year. Portfolos are formed yearly for the perod 1983-2004. Wthn each calendar year, all stocks n the sample are allocated nto fve portfolos based on ther book-to-market ratos rankng. Each book-to-market quntle s then subdvded nto fve lqudty portfolos usng the dollar volume. Panel A presents ntercepts from the tme seres regresson of four-factor model as n the followng equaton r (, t) = α + β ( Rmt R ft ) + δ SMBt + γ HMLt +ψ LIQt + et where rt (, ) s the excess return on portfolo n month t, and ( Rmt Rft ), SMBt, HMLt, are Fama and French (1993) three factors related to market premum, frm sze, and the book-to-market rato n month t. LIQ t s the Pastor and Stambaugh (2003) lqudty factor. Panel B presents ntercepts from the tme seres regresson of three-factor model as n the followng equaton r (, t) = α + β ( Rmt R ft ) + δ SMBt + γ HMLt + et.the last column represents the dfference between lqudty group 5 and lqudty group1. The bottom of each panel presents the Gbbons, Ross, Shanken (1989) test of the hypothess that the ntercepts jontly equal zero for the four-factor model and three-factor model. Intercepts are reported n percentage terms (t-statstcs are n parentheses). Panel A: Four-factor model Book-to-market Lqudty group group 1 2 3 4 5 5-1 1 0.0059-0.0036-0.0121-0.0118-0.0023-0.0082 (1.65) (-1.11) (-4.68) (-5.11) (-0.99) (-2.01)** 2 0.0072-0.0034-0.0048-0.0056-0.0046-0.0118 (2.17) (-1.32) (-2.42) (-2.89) (-1.99) (-3.10)** 3 0.0102 0.0037-0.0009-0.0020-0.0046-0.0148 (3.69) (1.53) (-0.43) (-1.01) (-1.69) (-4.15)*** 4 0.0148 0.0074 0.0038-0.0007-0.0010-0.0158 (5.60) (2.86) (1.65) (-0.30) (-0.37) (-4.42)** 5 0.0299 0.0184 0.0101 0.0120 0.0022-0.0277 (8.37) (5.68) (3.34) (3.08) (0.56) (-6.34)*** F-value for Gbbons, Ross, Shanken, test that the ntercepts jontly equal to zero s 7.17*** (sgnfcant at 1% level) 32