Bid/Ask Spread and Volatility in the Corporate Bond Market

Transcription

1 Bd/Ask Spread and Volatlty n the Corporate Bond Market Madhu Kalmpall Faculty of Management McGll Unversty Arthur Warga Department of Fnance, College of Busness Unversty of Houston Correspondence to: Arthur Warga Judge James A. Elkns Professor of Bankng and Fnance College of Busness Admnstraton Unversty of Houston Houston, TX e-mal: warga@uh.edu offce (713) fax (713)

2 Abstract Bd/Ask Spread and Volatlty n the Corporate Bond Market Ths paper examnes the relatonshp between prce volatlty and bd-ask spreads on ndvdual bonds tradng on the NYSE s Automated Bond System. Retal-szed trades and thn volume mandate a data analytc approach that accommodates rregularly spaced transactons and quotes. Latent volatlty for each bond s extracted usng an Autoregressve Condtonal Duraton (ACD) model that provdes nput nto an ordered probt model for observed spreads. For the most part we fnd a sgnfcant negatve relatonshp between latent volatlty and observed spread among the ten most actvely traded bonds on the ABS. The results contrast wth earler fndngs n the foregn exchange market, and suggest that n some thnly traded markets volatlty may proxy for lqudty. 2

3 Bd/Ask Spread and Volatlty n the Corporate Bond Market In ths paper we provde the frst mcrostructure analyss of the relatonshp between bd-ask spreads and volatlty n the market for corporate bonds. The market we examne s the New York Stock Exchange, whch mantans the largest corporate bond exchange 1. NYSE bonds are traded on the Automated Bond System (ABS), whch can be descrbed as a fully automated electronc tradng and nformaton system whose schedules of bd and ask prces are fully transparent. Trades on the ABS are typcally small n sze and average about twenty bonds per trade. Also, lke most ssues avalable for trade n the dealer market, the ABS s llqud. The average tme nterval between two trades for the most actvely traded bond n our sample s about seven mnutes whle for the tenth most actvely traded bond t s about thrty eght mnutes. Tradng actvty declnes rapdly for bonds not among the top ten n volume. The aforementoned features of the ABS market compel us to draw on the statstcal lterature for technques dealng wth rregularly spaced data. Transformng data to regularly spaced ntervals, an approach often employed n mcrostructure studes of more lqud markets, cannot feasbly be mplemented wth ABS data. We employ an ordered probt analyss smlar to that found n Hausman, Lo, and MacKnlay (1992) and Bollerslev and Melvn (1994) to uncover lnks between volatlty and the magntude of the bd-ask spread. The analyss s complcated by the fact that volatlty cannot be measured n the tradtonal manner of employng GARCH or other tme seres methods because the data s too rregular and thn to admt that sort of analyss. To solve ths problem we draw on technques 1 NYSE traded bonds account for about 10% of the market n these bonds n terms of number of trades, but closer to 1% n terms of the dollar value of those trades. There have been several recent ntatves to start up alternatve electronc bond exchanges. Among these are Intervest ( and Bond Connect ( 3

4 developed n Engle and Russell (1998) to estmate proxes for volatlty usng the tme duraton between trades. The dealer market n corporate bonds, whch to ths date has no central trade or reportng system, accounts for most of the dollar volume of corporate bond transactons. Nevertheless, as documented n Dueweke, Hyland, and Sesel (1992) the ABS system accounts for a sgnfcant percentage of the number of transactons n bonds traded there, especally f attenton s restrcted to the most actve ssues. If we restrct ourselves to the most actvely traded bonds on the ABS, t s unlkely that more frequent transactons or quotes wll be avalable from any dealer. Furthermore, as shown n Hong and Warga (1999), prcng on the ABS s n accord wth prcng n the dealer market. ABS s the only corporate bond market capable of carryng out transactons and provdng tme-stamps for quotes and trades. Transacton-based databases from the dealer market, such as the Natonal Assocaton of Insurance Commssoners (NAIC) schedule D database, lack tme stamps and only record transactons by the day they occur 2. In ths paper we wll focus on the top ten most actve ssues on the ABS, thereby assurng that we examne a stream of quotes representng a sgnfcant porton of the approprate quote unverse for those nstruments. In a prevous study, Bollerslev and Melvn (1994) examne the nature of the relatonshp between bd-ask spreads for exchange-rate quotes and the volatlty of the underlyng exchange-rate process. They develop a model for the foregn exchange market characterzed by tradng between market makers and two types of traders vz., nformed traders and lqudty traders. Expected proft of the market makers s obtaned as a sum of ther expected profts from tradng wth the two groups of traders, and s set equal to zero n 4

5 equlbrum. The authors show that, n equlbrum, spreads are proportonal to the condtonal volatlty of the fundamental value of the exchange rate. In a two step process, Bollerslev and Melvn obtan the GARCH estmates of the underlyng volatlty of the exchange rate process and then use them as nputs nto an ordered probt model. The ordered probt model measures the temporal relatonshp between observed spreads (havng a dscrete support) and other predetermned varables (havng contnuous support) lke lagged spreads and volatlty estmates of the exchange rates. Bollerslev and Melvn fnd a postve relatonshp between latent volatlty and observed spreads on the Deutschemark/dollar exchange market. In ths paper, we examne the lnk between volatlty and bd-ask spreads n the ABS market. We estmate latent volatlty of a bond prce process usng the tme duraton between trades (Engle and Russell (1997)). We then examne the relatonshp between bd and ask quotes and the underlyng volatlty of the bond prce process. Examnng the ten most frequently traded bonds on the ABS system, we fnd results that suggest latent volatlty and observed spreads are ether sgnfcantly negatvely related or nsgnfcantly related. Whle our results say nothng about lqud markets (lke foregn exchange and equtes), they do rase doubts about the value of volatlty as a proxy for asymmetrc nformaton or adverse selecton cost n markets lke the ABS that are characterzed by thn tradng. We dscuss how the lack of lqudty and the presence of a relatvely large percentage of unnformed traders mght generate these results. The rest of the paper s developed as follows. Secton I dscusses the organzaton and mcrostructure of the ABS market. Secton II presents the analytcal framework to understand 2 A small sample of hgh yeld bond transactons (data on 67 bonds) begnnng n 1994 s avalable on NASDAQ s Fxed Income Prcng System (FIPS). See Alexander, Edwards, and Ferr (1999) and Hotchkss and Ronen (1999) for 5

6 the determnants of observed spread n the ABS market. Secton III presents the emprcal models used n our study. Secton IV dscusses the data used n the paper. Secton V presents the emprcal mplementaton and results from the study. Secton VI concludes the paper. I. The Automated Bond System The NYSE mantans a fully automated electronc tradng and nformaton system 3 for bonds known as the Automated Bond System (ABS). Unlke ts counterpart stock market, there s no specalst n the NYSE bond market. Instead, there are brokers who are subscrbng members of the ABS. There are 58 ABS member brokers operatng on about 210 termnals. The member brokers usually trade on behalf of ther customers, though at tmes they could trade for ther own account. Member brokers receve lmt orders from the publc and enter the correspondng bd-ask quotes and the respectve quanttes nto the automated system. They also enter ther own quotes nto the system. Lqudty to the ABS market s therefore jontly suppled by publc lmt orders and dealers own quotes. The ABS matches the orders automatcally and nforms the member brokers once an order s executed. The ABS s thus a lmt order market wth a strct prce-tme prorty. The ABS market s also very transparent. All subscrbers to the ABS market have full access to the complete order schedule, whch they can dvulge to nvestors upon request. The ABS market s an outlet for retal trades and odd lot tradng wth an average trade sze close to 20 bonds 4, and a medan trade sze of ten bonds. Most nsttutonal tradng n corporate bonds occurs n the dealer market. Ths means that trades ntated by unnformed a descrpton and analyss of ths data. Only hourly reports are currently avalable for analyss. 3 Further detals of the ABS market are descrbed n Hong and Warga (1999). 4 The nne-bond rule oblgates member brokers to drect trades havng a sze of 9 or less bonds to the ABS market. Wth few exceptons, corporate bonds traded on the ABS have par values of $

7 (lqudty) traders are lkely to be concentrated on the ABS. These unnformed trades are less lkely than other trades to cause any revson of expectatons among dealers. The average tme nterval between two transactons for the most actvely traded bond n our sample s seven mnutes, whle for the tenth most actvely traded bond t s thrty-eght mnutes. The dstrbuton of the tme ntervals between trades (also referred to as duratons 5 ) s skewed to ts rght,.e. long duratons are more lkely than short duratons. Transacton and quote data on the ABS market are also rregularly spaced. We are also lkely to observe long (short) tradng ntervals followed by long (short) tradng ntervals, a phenomenon referred to as duraton clusterng. II. Transactons, Volume and Volatlty Emprcal evdence, such as Bollerslev and Melvn (1994) ndcates a postve relatonshp between volume and volatlty. A possble explanaton could be that tradng s generated due to asymmetrc nformaton that results from ether dfferental nformaton or dfferences n opnon. The sze of trades or volume reflects the extent of dsagreement among traders about a securty s value. The larger the dsagreement the larger wll be the prce changes and hgher wll be the prce volatlty and tradng volume. Ths forms the bass for adage that t takes volume to move prces. Another explanaton for a postve relatonshp between volume and volatlty s that they are both jontly determned by the number of nformaton events, as postulated by the Mxture of Dstrbutons Hypothess (MDH). Accordng to the MDH, volume and volatlty are postvely correlated only because they are postvely related to the number of nformaton events that serves as a mxng varable. The MDH mples that volume does not have any 5 The term duraton n ths context should not to be confused wth Macaulay s duraton, whch s the negatve of the prce elastcty of a bond wth respect to a change n nterest rates. 7

8 explanatory power n volatlty beyond what s contaned n the mxng varable, a result that s verfed by Jones, Kaul and Lpson (1994). In ths paper, we study the relatonshp between volatlty and spreads for ndvdual bonds. Hence, we would lke to ensure that our volatlty measure captures prce movements only and does not capture volume. Volatlty, n our paper, s measured as an nverse functon of the tme nterval between two successve trades (detals n secton III.A.). When the tme nterval between two successve trades s short, t mples that there s new nformaton that s flowng nto the market rapdly. Ths mples a hgh volatlty. Conversely, when the tme nterval between two successve trades s long, there s no new nformaton that s beng released nto the market. Ths, n turn, mples a low volatlty. Our volatlty measure, therefore, s related to the occurrence of trade as descrbed by the MDH. Volatlty goes up n response to new market nformaton and not n response to a hgher tradng volume. As dscussed n the results secton below, our tests for volume reveal that t has no explanatory value n the ABS market, and s uncorrelated wth our volatlty measure. Ths makes sense n the ABS market because only relatvely low volume trades occur n the frst place, wth most of the volume (although not necessarly frequency) takng place n the dealer market. III. Models for Irregularly Spaced Data A. The Autoregressve Condtonal Duraton Model Quotes n the ABS market do not arrve n equal ntervals. Ths rases the queston of how we estmate latent volatlty for unevenly spaced data. We can aggregate the data over a fxed tme nterval and use a GARCH model as n Bollerslev and Melvn (1994). If we choose too short an nterval there may be many ntervals wth no new nformaton and we may ntroduce some form of heteroscedastcty n the data. If we, however, choose too long an nterval then 8

9 features of the data wll be smoothed and potentally hdden and mcrostructure aspects of the data wll be lost. These problems are certan to be severe n the ABS market, at least relatve to the markets where aggregatng data over a fxed nterval of tme has been successfully appled (e.g. foregn exchange or equtes). We mtgate the problem by usng an alternatve method to obtan latent volatlty of the bond prce process. Recently, Engle and Russell (1997,1998) ntroduced the Autoregressve Condtonal Duraton (ACD) model to analyze rregularly spaced data. The ACD model focuses on the ntertemporal correlatons of the duratons, where duratons refer to the tme nterval between arrvals. Instead of aggregatng the data to some fxed nterval, the ACD model treats the arrval tmes of the data as a pont process wth an ntensty defned condtonal on past actvty. The ACD model corrects for duraton clusterng n the data 6. Duraton clusterng refers to the phenomenon where long (short) duratons are followed by long (short) duratons. Let the sequence of tme arrval of successve quotes be represented as {t for = 1,2 n.}, where t refers to the arrval tme of the th quote. The stochastc process for {t for = 1,2 n.} s called a pont process. Correspondng to the pont process s the countng process {N(t), t>0}, whch s the number of events that have occurred by tme t. The condtonal ntensty of the pont process (or the hazard rate), refers to the nstantaneous probablty of an event condtonal on past nformaton and s defned as follows. λ( t; N ( t), t,..., t ) = lm 1 N ( t ) t 0 P( N ( t + t) > N ( t) N ( t), t,..., t ) 1 N ( t ) t (1) 6 The GARCH model corrects for volatlty clusterng n the data. Consderng that duratons are nversely related to prce volatlty, the ACD model also ndrectly corrects for volatlty clusterng. 9

10 The condtonal ntensty (hazard rate) unquely defnes a pont process. Engle and Russell n ther ACD model ntroduce a new famly of pont processes and correspondng condtonal ntenstes. Let x refer to the duraton between th and -1 th quote..e x = t - t -1. Accordng the ACD(m,q) model, we have ψ = ω + m j= 1 α j x t j + q j= 1 β ψ j j x for = ψ j 0, for all, = 1,...N (2) where ψ s the condtonal expected duraton gven past nformaton and parameter set θ.e. ψ ε α, β j 0, ω > = 1, 1 E[ x x..., x ; θ] (3) and where m and q refer to the orders of the lags used and { ε } s the error term that s..d and follows a specfed dstrbuton. Under an exponental dstrbuton for the error term, long duratons are as lkely to occur as short duratons. However, n our bond data we fnd that long duratons occur more often than short duratons, a phenomenon that can be captured usng a Webull dstrbuton. Under a Webull dstrbuton, the lkelhood functon of the ACD(1,1) 7 model s defned as 7 The condtonal ntensty of the ACD model.e. λ(t, N(t), t 1,.. t N(t) ) depends upon the dstrbuton of the error term and specfcaton of ψ. 10

11 L( θ) = where ψ ψ = ω N ( T ) = 1 + γ ln + x αx ω = for = 1 (1 β) + βψ Γ(1 + γ ln ψ 1, for > 1 θ = ( γ, ω, α, β,), α, β 0, ω Γ s a Gamma dstrbuton 1 ) γ > 0, α + x Γ(1 + ψ β < 1 (4) The log lkelhood functon n (4) s maxmzed teratvely wth respect to parameters n θ and 1 ) γ subject to the non-negatvty and statonarty condtons above 8. The ACD model gves us the latent condtonal duraton of the quotes. Followng Engle and Russell the condtonal duraton can be n turn used to construct latent volatlty as follows: Defne a new prce process as an average of bd-ask prces. The new prce process does not have the bd-ask bounce n t. Next, thn the prce process by keepng a quote only f ts average prce dffers from the average prce of the prevous quote by at least a constant c. For each bond, the constant c s set equal to the spread wth the hghest frequency for that bond. Ths turns out to be 1/8 for all the bonds. The purpose of excludng quotes whose average prces have moved wthn ± 1/8 s to exclude possble nosy quotes and to nclude only those quotes that have sgnfcant nformaton embedded n them. We refer to the new prce process as the thnned prce process. x γ 8 Maxmum lkelhood estmaton s done usng the BFGS algorthm n GAUSS. 11

12 Deseasonalze the thnned prce duratons for any possble seasonal (tme-of-the day and dayof-the week) patterns. Choose an ACD(1,1) model wth Webull dstrbuton (WACD(1,1)) as the benchmark model for the data 9. Ft a WACD(1,1) model for the thnned prce process and obtan the condtonal expected prce duratons (ψ ). The ψ { = 1,2,.,N} are a measure of tme per unt prce change. The nverse of ψ represents the prce change per unt of tme, and ths s a measure of volatlty. Engle and Russell (1998) show that volatlty can be estmated as σ = 2 c ψ 2 (5) B. Ordered Probt Model Spreads n the ABS market are n ncrements of eghths, and therefore do not have contnuous support. We, therefore, employ an ordered probt model (Hausman et. al. (1992) and Bollerslev and Melvn (1994)) to study the relatonshp between spreads and volatlty n the ABS market. As we shall explan later n secton IV, spreads observed n the bond market seem to belong to a few dstnct groups. The observed spreads take on a fxed number of dscrete values and can be explaned by a set of predetermned values that have a contnuous support. The observed spread s a functon of a latent spread that s contnuous and s tself a functon of lagged volatlty and lagged spread. Specfcally, our ordered probt model can be wrtten as 9 WACD(1,1,) s a farly general specfcaton and a good startng pont for any specfcaton search (Engle and Russell (1997)). 12

13 ε t k * t = 0 + δ 1ht 1 + δ 2k t 1 ~ N(0,1) δ + (6) (all the varables are expressed n log form) where the condtonal volatlty of the bond prce (h t-1 ) and lagged value of observed spread (k t-1 ) jontly explan the condtonal mean and varance of k * t, the unobserved spread. Furthermore, the ordered probt model requres that there s a one to one mappng between the dscrete observed spread (k t ) and contnuous unobserved spread (k * t) * kt = a j ff kt Aj, j = 1,2,..., m.e. (7) where the a j s are a set of dscrete values that k t can take on and where A j s are a set of m ordered dsjont ntervals that k * t can be parttoned nto. We wll see below n the data secton that an adequate and parsmonous number of parttons m wll be equal to 4 for all bonds wth the excepton of one, for whch we wll choose m=3. IV. Data The bd-ask quote data on corporate bonds covers a perod of approxmately fve months extendng from 10/01/96 to 02/21/97. The data contans bonds that are traded on the NYSE from 9.30 a.m. to 4:00 p.m. every tradng day. We present a sample of quotes for one bond (ssued by Penn Traffc Co.) n Table I. Insert Table I here Next, we determne the bonds wth the hghest number of trades and quotes. We sort all bonds by the total number of transactons and separately by the number of quotes. The top ten bonds n the ntersecton of these two sortngs are presented n Table II and a descrpton of each bond n Table III. As dscussed above, transacton frequency drops off markedly as we move beyond the top ten traded bonds, and so we restrct our attenton to these ε t 13

14 nstruments. All of the bonds examned fall n the non-nvestment grade category (below Baa n ratng). 10 Insert Tables II, III here For the ordered probt analyss, the observed spread has to be grouped nto a fnte number of ordered categores. The frst two columns n Table IV present the frequency dstrbuton of spreads for the top ten bonds. The next two columns present the groups and the respectve spread ntervals we adopt for each bond. V. Results We adopt the followng scheme n mplementng our study. For each of the ten bonds, 1. Obtan prce duratons from the quotes. 2. Obtan thnned prce duratons. 3. Deseasonalze prce duratons for daly and weekly effects. We employ 3 dummy varables 11 to account for tme-of- the day effects and 5 dummy varables to account for day of the week effects. In all we have 15 dummy varables (3 tme- of- the day dummes tmes 5 day-of-the week dummes). We deseasonalze by a) regressng the thnned prce duratons on 15 dummy varables and b) dvdng the thnned prce duratons by the regresson estmate from step a. 4. Ft a WACD(1,1) model to the deseasonalzed thnned prce duratons. 5. Extract latent condtonal expected duratons and duraton based annual prce volatltes usng the WACD(1,1) estmates. 6. Ft an ordered probt model usng the groups specfed n last two columns of Table IV. 10 The bond labeled unrated was orgnally ssued wth a hgh yeld ratng as well. 11 The frst dummy varable ndcates the mornng nterval from 9.30 a.m.-12 a.m., the second dummy varable ndcates the nterval from 12 a.m. - 2 p.m. and the thrd dummy varable ndcates the nterval from 2.pm to 4 p.m. on 14

15 These steps were descrbed n secton III above. Table V presents the WACD(1,1) estmates. Table VI presents ordered probt estmates correspondng to the Table V nputs. Insert Tables V, VI here We have the followng results from Table V: The WACD(1,1) estmates for all bonds are hghly sgnfcant at 5% level 12. Ths ndcates that there s a sgnfcant presence of duraton clusterng n the data. The estmate for γfor all the bonds s sgnfcantly lower than one. Ths ndcates that long duratons are more lkely than short duratons. We have the followng results from Table VI: Examnng the p-values for mean coeffcents n the unobserved spread equaton, we have three groups of bonds. Our man nterest s n the sgn and statstcal sgnfcance of the parameter δ 1, whch determnes the relatonshp between bd-ask spreads and latent volatlty 13 : Group A: Ths group ncludes bonds where we fnd a negatve and statstcally sgnfcant relatonshp between the bd-ask spread and latent volatlty of the bond prce process. The sx bonds n ths group are PNF 05, CLAR 02, BBY 00, PCS 03, AGY 04, and SME 01. Group B: Ths group ncludes bonds where we fnd a negatve but not statstcally sgnfcant relatonshp between the bd-ask spread and latent volatlty of the bond prce process. The two bonds n ths group are SME 04 and STO 01. a week day. NYSE bonds have a U shaped tradng pattern over the day. Our three dummy varables correspond to the three tme ntervals of the U shape. 12 For some bonds, the constant term n the condtonal duraton equaton s sgnfcant at 10% level. 13 The partton coeffcents for the ordered probt model (not reported) are all hghly sgnfcant. 15

16 Group C: Ths group ncludes bonds where we fnd a postve but not statstcally sgnfcant relatonshp between the bd-ask spread and latent volatlty of the bond prce process. Bonds n ths group are HDS 03 and WHX 03. As mentoned n a prevous secton, we also want to examne the relatonshp between volume, volatlty and spreads usng the ordered probt model for ndvdual bonds. One of our arguments for employng the ACD model for volatlty rests on the fact that t sn t proxyng for volume. A major qualfcaton s that tests for volume can only be conducted on a subset of the quote data correspondng to actual transactons. The dentfcaton procedure allowng us to assocate a partcular transacton wth a partcular quote s nexact, and ths leads to a further loss of data. Sample szes per bond declne by between ffty and seventy percent. In results not reported here, we fnd that volume has no sgnfcant explanatory power for spreads. More mportantly, we fnd no sgnfcant correlaton between tradng volume and volatlty 14. Mcrostructure theory decomposes the bd-ask spread nto adverse selecton costs, nventory, and order processng costs. In the present context, brokerage fees that typcally accompany retal-szed orders from brokerage customers can hde order processng costs and nventory costs. It s also qute possble that adverse selecton costs are mnmal because the thnness of the market does not attract market makers wshng to trade on the bass of nformaton flow. The bd-ask spread narrowng n reacton to ncreased volatlty observed here may be a result of the fact that the market we are observng exsts under the shadow of the larger dealer market. Snce t s lkely that lqudty-based tradng s domnatng the ABS 16

17 market, lqudty-based effects not captured n the classcal bd-ask spread decomposton may lead to the result that hgher volatlty smply reflects ncreased lqudty for a bond. Our results suggest that there are crcumstances when employng volatlty as a proxy for adverse selecton costs can be a mstake. For example, Krshnaswamy and Subramanam (1999) and Krshnaswamy et al (1999) both use resdual volatlty n daly stock returns as a proxy for nformaton asymmetry for each frm. The resdual volatlty s defned as the standard devaton of resduals obtaned from market adjusted daly stock returns for a gven frm. If the frm's managers and nvestors are equally well nformed about the economy wde factors nfluencng the frm's value, then the resdual volatlty n a frm's stock returns captures the nformaton asymmetry between managers and nvestors about the specfc frm. In other words, resdual volatlty captures frm specfc uncertanty that remans after removng the uncertanty that s common to the frm's managers and the nvestors from total uncertanty. Frms wth hgher nformaton asymmetry about ther cash flows and value would have hgher resdual volatlty n ther stock returns. However, as the authors note, resdual volatlty, n fact, has two components: the nformaton asymmetry component and a market nnovaton component. To the extent we gnore the market nnovaton component, the resdual volatlty overestmates the nformaton asymmetry component. In the present context, we are examnng a market where lqudty effects may very well domnate both nformaton asymmetry and market nnovatons. VI. Conclusons In ths paper, we examne the relatonshp between quoted bd-ask spreads and volatlty for the ten most actvely traded corporate bonds on the NYSE s Automated Bond System 14 These results are avalable from the authors upon request. The power to detect a relatonshp between volatlty and spread also declnes, but the basc pattern observed n the results presented here on the full sample are mantaned. 17

18 (ABS). We fnd a negatve and statstcally sgnfcant relatonshp between volatlty and observed spreads for sx out of the ten bonds n our sample. The other four bonds reveal no statstcally sgnfcant relatonshp, wth two of them negatve and two of them postve. The type of market we observe probably drves our results. The ABS s a retal- and odd lot-drven electronc exchange. Bd-ask spreads appear to be domnated by lqudty effects that are not captured n the classcal decomposton provded by mcrostructure theory. Our results pont to the need to develop a decomposton of bd-ask spreads that encompass lqudty effects. Even very lqud markets have perods where ndvdual securtes requre long tme ntervals for transactons to take place. The thnness of the ABS market allows us to see that lack of lqudty may lead to a relatonshp between volatlty and spread that s counter to the one that exstng decompostons would suggest. There contnues to be no evdence of a postve relatonshp between volatlty and spread. 18

19 References: Alexander, G.J., A.K. Edwards and M.G. Ferr, Tradng Volume and Lqudty n Nasdaq s Hgh Yeld Bond Market, Manuscrpt, Securty and Exchange Commsson, Offce of Economc Analyss. Bollerslev, T. and M. Melvn, 1994 Bd-ask spreads and volatlty on the foregn exchange market, Journal of Internatonal Economcs, 36, Dueweke, D., Hyland, M. and F. Sesel, "Measurng the New York Stock Exchange's Share of Corporate Tradng Volume." Extra Credt, The Journal of Hgh Yeld Research, September/October 1992, Merrll Lynch Global Securtes Research & Economcs Group. Engle, R. and J. Russell, 1997, Forecastng the frequency of changes n quoted foregn exchange prces wth the ACD model, Journal of Emprcal Fnance, 4, Engle, R. and J. Russell, 1998, ACD: a new model for rregularly space transacton data, Econometrca, Vol. 66, 5, Glosten, L, 1987, Components of the bd-ask spread and the statstcal propertes f transacton prces Journal of Fnance, 42, Glosten, L. and L. Harrs, 1988, Estmatng the components of bd-ask spread Journal of Fnancal Economcs, 21, Hausman, J., A. Lo and C. MacKnlay, 1992 An ordered probt analyss of transacton stock prces, Journal of Fnancal Economcs, 31, Hong, G. and A. Warga, 1999, An emprcal study of bond market transactons, Forthcomng, Fnancal Analysts Journal. Hotchkss, E. and T. Ronen, "Informatonal lnks between bond and stock markets: An ntradaly analyss". Manuscrpt, Boston College. Huang, R. and H. Stoll, 1997 The components of bd-ask spread: A general approach Revew of Fnancal Studes, Vol.10, 4, Jones, C., G. Kaul, and M. Lpson, 1994, Transactons, Volume and Volatlty Revew of Fnancal Studes, Vol. 7, 4, Krshnaswamy, S. and Subramanam, V. 1999, "Informaton asymmetry, valuaton, and the corporate spn-off decson", Journal of Fnancal Economcs, 53,

20 Krshnaswamy, S., Spndt, P. and Subramanam, V. 1999, "Informaton asymmetry, montorng, and the placement structure of corporate debt", Journal of Fnancal Economcs, 51, Ln, J., G. Sanger and G. Booth, 1995, Trade sze and components of bd-ask spread Revew of Fnancal Studes, Vol8, 4, Roll. R, 1984, A smple effectve measure of the effectve bd-ask spread n an effcent market Journal of Fnance, 4,

21 Table I Sample quotes on the ABS screen. The sample bond s ssued by Penn Traffc Company. The bd and ask prces wth the respectve quantty of bonds bd are reported. Tcker Date Tme Bd # of bonds Ask # of bonds Symbol Prce Prce PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF PNF

22 Table II The top ten bonds along wth the respectve number of trades 15, quotes and trade matched quotes are lsted below. Tcker CUSIP # Quotes Trades Symbol 1 PNF AD SME AC CLAR AA BBY AB PCS AD STO AK HDS AA WHX AH AGY AE SME AD Table III Bond Descrptors Company Name CUSIP # Coupon Maturty Ratng 1 Penn Traffc Co AD 9 5/8 4/15/2005 Caa2 2 Servce Merchandse Inc AC 9 12/15/2004 B2 3 Clardge Hotel AA 11 ¾ 2/1/2002 Ca 4 Best Buy Co AB 8 5/8 10/1/2000 B2 5 Payless Cashways Inc AD 9 1/8 4/15/2003 B3 6 Stone Contaner Corp AK 9 7/8 2/1/2001 B1 7 Hlls Stores Co AA 10 ¼ 9/30/2003 Unrated 8 Wheelng-Pttsburgh Corp AH 9 3/8 11/15/2003 B1 9 Argosy Gamng Co AE 13 ¼ 6/1/2004 B1 10 Servce Merchandse Inc AD 8 3/8 1/15/2001 Ba 15 We have excluded all quotes wth negatve spreads. There are 2-4 such quotes for every bond. 22

23 Table IV Frequency table for spreads for the top ten bonds. The frst three columns ndcate the frequences and percentage of frequences for the ndcated spread, for each bond. The last two columns ndcate the number of ordered groups along wth the respectve spreads used for ordered probt model. Spreads # of quotes % of quotes Groups Spreads PNF > ( ] ( ] ( ] ( ] > SME > ( ] ( ] ( ] ( ] > CLAR > ( ] ( ] ( ]

24 ( ] > BBY > ( ] ( ] ( ] ( ] > PCS > ( ] ( ] ( ] ( ] > STO > ( ] ( ] ( ] 0 0 ( ] 0 0 >5 0 0 HDS

25 > ( ] ( ] ( ] ( ] > WHX > ( ] ( ] ( ] 0 0 ( ] 0 0 >5 0 0 AGY > ( ] ( ] ( ] ( ] > SME >

26 ( ] ( ] ( ] ( ] >

27 Table V Ths table presents the maxmum lkelhood estmates for the WACD(1,1) model for the top ten bonds Quotes log lkelhood g w a b PNF T stat SME T stat CLAR T stat BBY T stat PCS T stat STO T stat (23.433) HDS T stat WHX T stat AGY T stat SME T stat

28 28 Notes: The lkelhood functon of the WACD(1,1) model s gven by (4) dstrbuton Gamma a s 1 0, 0,,,),,,, = ( = 1 for ) (1 > 1 for, where ) 1 (1 ) 1 (1 ln ln ) ( 1 ) ( 1 Γ < + > = + + = + Γ + Γ + = = β α ω β α β α γ ω θ β ω ψ βψ α ω ψ ψ γ ψ γ γ γ θ γ T N x x x x L The log lkelhood functon n (4) s maxmzed teratvely wth respect to parameters n θ 1. The log lkelhood values are reported usng the optmal parameter estmates.

29 Table VI Maxmum lkelhood estmates for the ordered probt model Quotes d 0 d 1 d 2 PNF Std. Error p value SME std. Error p value CLAR std. Error p value BBY std. Error p value PCS std. Error p value STO std. Error p value HDS std. Error p value WHX std. Error p value AGY std. Error p value SME std. Error p value Notes: The estmated ordered probt model s of the form * k δ + δ h + δ k + ε t t = 0 1 t 1 2 t 1 ε ~ N(0,1) t 29