Liquidity, Default, Taxes and Yields on Municipal Bonds

Transcription

1 Finance and Economics Discussion Series Divisions of Research & Saisics and Moneary Affairs Federal Reserve Board, Washingon, D.C. Liquidiy, Defaul, axes and Yields on Municipal Bonds Junbo Wang, Chunchi Wu, and Frank Zhang NOE: Saff working papers in he Finance and Economics Discussion Series (FEDS) are preliminary maerials circulaed o simulae discussion and criical commen. he analysis and conclusions se forh are hose of he auhors and do no indicae concurrence by oher members of he research saff or he Board of Governors. References in publicaions o he Finance and Economics Discussion Series (oher han acknowledgemen) should be cleared wih he auhor(s) o proec he enaive characer of hese papers.

2 Liquidiy, Defaul, axes and Yields on Municipal Bonds Junbo Wang, Chunchi Wu and Frank Zhang * July 8, 2005 Absrac We examine he relaive yields of reasuries and municipals using a generalized model ha includes liquidiy as a sae facor. Using a unique ransacion daase, we are able o esimae he liquidiy risk of municipals and is effec on bond yields. We find ha a subsanial porion of he mauriy spread beween long- and shor-mauriy municipal bonds is aribuable o he liquidiy premium. Conrolling for he effecs of defaul and liquidiy risk, we obain implici ax raes very close o he sauory ax raes of high-income individuals and corporaions, and hese ax rae esimaes are remarkably sable over mauriies. * Junbo Wang and Chunchi Wu are a Syracuse Universiy, and Frank Zhang is a he Federal Reserve Board in Washingon DC. Address correspondence o Chunchi Wu, Whiman School of Managemen, Syracuse Universiy, Syracuse, NY el: , fax: and [email protected]. An earlier version of his paper iled Inferring Marginal ax Raes from Green s Model wih Defaul was presened a he 2003 WFA Meeing in Cabo, Mexico. We hank Clifford Ball, John Chalmers, Pierre Collin-Dufresne, Cheng F. Lee, Suresh Sundaresan, Waler orous, Rossen Valkanov, and Yuewu Xu for helpful commens. his paper represens he views of he auhors and does no necessarily represen he views of he Federal Reserve Board or members of is saff.

3 he fixed-income securiies marke is an imporan segmen in he U.S. financial markes. his marke has been paricularly innovaive and experienced considerable growh recenly. No surprisingly, here has been exensive lieraure aemping o explain he yield spreads beween differen fixed income securiies. A subjec ha has long inrigued financial researchers is how he yield spreads beween ax-exemp and axable securiies are deermined. Are defaul and liquidiy risk priced in municipal bonds? Wha porion of hese spreads is aribued o axes, defaul, and liquidiy risk? hese issues are fundamenally imporan from an invesmen perspecive due o he sheer size of he municipal marke, which now approaches.9 rillion dollars. Bond reurns are subjec o differen ax reamens. Ineres on municipal bonds is exemp from federal income axes hough no necessarily exemp from sae axes. By conras, ineres on reasury and governmen agency bonds is subjec o federal income axes bu exemp from sae income axes. In equilibrium, one expecs he afer-ax reurns of axable and ax-exemp bonds o be equal if boh have same mauriy and comparable risk characerisics. he bond marke hus provides an excellen financial laboraory o evaluae he impac of axaion on he relaive values of ax-exemp and axable bonds. he relaive yields of axable and municipal bonds should reflec he ax rae of he marginal invesor who is indifferen beween hese wo bonds. herefore, one ough o be able o infer from he relaive bond yields he implici ax rae of he marginal invesor reasonably expeced o hold hese bonds. Unforunaely, empirical evidence has no conformed very well o his expecaion bu insead indicaes ha municipal bond yields are ofen higher han expeced relaive o yields on U.S. reasury bonds. his anomaly is more pronounced for long-mauriy

4 bonds. he relaively high yields of municipal bonds imply a ax rae lower han expeced for he marginal ax raes of high-income individuals and corporaions. Moreover, he implied marginal ax rae is much lower for long-mauriy municipal bonds han for shor-mauriy bonds of similar qualiy and characerisics. Several hypoheses have been advanced o explain he muni puzzle. he insiuional demand hypohesis suggess ha he marginal ax rae is deermined by insiuional rading aciviy (see Forune, 973; Galper and Peerson, 97; Kimbal, 977; Fama, 997). Commercial banks can purchase municipals o shield heir income from axes. An increase in heir demand causes municipal yields o fall and he implici ax rae o rise. Since commercial banks prefer shor-erm bonds, he implici ax rae would end o be high for hese bonds relaive o long-erm bonds. 2 Oher explanaions for he yield curve anomaly include ax-iming opions (Consaninides and Ingersoll, 984), clienele effecs (Mussa and Kormendi, 979; Kidwell and Koch, 983), and changes in ax regimes (Poerba, 989). While he argumens above have some meri, i remains unclear wheher hey can fully explain he anomalous behavior of municipal yield curves. In an imporan paper, Green (993) proposes an alernaive model o explain he behavior of axable versus axexemp yields. A basic argumen in his model is ha high-ax invesors generally prefer porfolios of axable bonds ha are ax-advanaged (or ax-efficien) o individual axable bonds wih similar preax cash flows. In paricular, hey can avoid axes on coupon Unlike reasuries and municipals, corporae bond ineres is subjec o boh federal and sae axes. 2 Along a similar line on insiuional demand bu wih a differen focus, Green and Odegaard (997) indicae ha many insiuions such as pension funds are eiher no axed a all or have much lower axes han individuals. If any of hese insiuions invess heavily in long-erm axable bonds, he yield on longmauriy axables will be lower. his will lower he yield spread beween axables and ax-exemps as well as he implici ax rae. 2

5 income by consrucing porfolios of axable bonds ha generae offseing losses or invesmen ineres expenses. If hese invesors are marginal across hese porfolios and municipals bonds, hey will apply he same discoun facors o he afer-ax cash flows from boh posiions. Using his relaionship, Green obains invesors implici valuaion of he preax cash flows from par axable bonds. By appealing o he arbirage aciviies of dealers and ax-exemp insiuions, he derives an equilibrium model o explain he relaive yields of axable versus ax-exemp bonds. he inuiion behind his model is ha invesors holding boh axables and municipals may no regard coupon income as fully axable a he margin because of he offseing invesmen ineres elsewhere in heir porfolios. hese implici ax benefis end o increase wih mauriy, hus pulling down he yield curve of axable bonds a he long end. Empirical evidence shows ha Green s model explains a considerable porion of he relaive yield differences beween axable and ax-exemp bonds (see Green, 993). Chalmers (995) finds ha Green s model canno be rejeced. However, alhough his model replicaes he differences in curvaure beween he axable and ax-exemp yield curves reasonably well, i coninues o underesimae he long-erm ax-exemp yields. 3 Also, he predicive abiliy of he model does no hold up very well especially when here are significan changes in sauory ax raes. While changes in ax regimes may be blamed, hese problems can also be caused by missing facors. Of paricular concern is ha defaul and liquidiy risk of municipal bonds are ignored in his model. Municipal bonds are no risk-free and o some exen may even be riskier han corporae bonds in he same raing class due o he unique feaures of municipal asses and less predicable poliical processes (see Hempel, 972; Zimmerman, 977; and 3

6 rzcinka, 982). 4 Alhough municipal bonds were radiionally considered o be only second o U.S. reasuries in safey, defauls on municipal bonds since he lae 970s, along wih oher problems, have raised concern abou he credi risk of municipal bonds. For example, of he municipal bonds issued beween 977 and 998,,765 ou of a oal of 253,850 issues were defauled, wih a face value of $24.9 billion ou of a oal of $375.5 billion (see Livack and Rizzo, 999). hus, he probabiliy of defaul may no be rivial and is of poenially greaer concern for low-raed uninsured municipals. Empirical evidence on he role of defaul risk is inconclusive. Several sudies (e.g., rzcinka, 982; Yawiz, Maloney and Ederingon, 985; Scholes and Wolfson, 992; Kim, Ramaswamy and Sundaresan, 993; Sock, 994; and Liu, Wang and Wu, 2003) show ha credi risk differences explain he relaive yields of axable and axexemp bonds. 5 However, oher sudies (Gordon and Malkiel, 98; Skelon, 983; Ang, Peerson and Peerson, 985; Green, 993; and Chalmers, 998) find ha differenial defaul risk canno explain he municipal bond puzzle. A perplexing finding is ha he erm srucure of municipal bonds remains seeper han ha of he U.S. reasuries even afer he effec of defaul risk is conrolled. An imporan facor compleely lef ou by previous municipal bond pricing models is liquidiy risk. he municipal marke is very illiquid compared o he U.S. reasury bond marke or he equiy, fuures and foreign exchange markes. Several 3 See Green (993), p Municipal asses canno be seized as easily as corporae asses in bankrupcy proceedings because hey may be physically difficul o seize or legally proeced. In addiion, he incenive problem or moral hazard is perceived o be more severe for municipaliies. 5 Kim, Ramaswamy and Sundaresan (993) provide a heoreical explanaion for why defaul risk may cause he erm srucure o have a seeper slope. hey argue ha credi spreads for high-qualiy coupon bonds increase wih mauriy because longer bonds have more coupons subjec o defaul risk. his relaionship beween he credi spread and erm o mauriy can also explain he higher relaive yields of municipal bonds. 4

7 reasons have conribued o low liquidiy in he municipal bond marke. Firs, he municipal bond marke is a very hin marke; many municipal bonds are raded only a few imes afer issuance (see Downing and Zhang, 2004). Average weekly muni rading volume is generally less han 2 percen of reasury rading volume. On he oher hand, he number of muni bonds far exceeds reasuries; well above one million differen municipal securiies are issued by over 50,000 sae and local governmens (see Fabozzi, 997). hus, mos individual muni bonds are raded infrequenly. Second, he municipal marke is much less ransparen in erms of he availabiliy of basic informaion for rading aciviy. Informaion for individual bond ransacions has no been publicly disclosed unil very recenly and comprehensive rade volume and price daa were only publicly available afer a wo-week lag. 6 hird, he municipal bond marke is also less ransparen in erms of informaion abou he bond issuers because hey are no subjec o he same financial disclosure requiremens as are publicly raded corporaions. 7 Lack of ransparency considerably increases he informaion cos of rading and reduces liquidiy. 8 Alhough i has been long recognized ha he municipal marke is illiquid and liquidiy risk is a poenially imporan deerminan of municipal yields, few sudies have provided a quaniaive assessmen of he size of he liquidiy risk premium. A primary reason for he lack of empirical research is ha reliable ransacion daa for municipal bonds were virually non-exisen unil very recenly. hus, how much municipal bond 6 Beginning in January 2005, he problem of lagged release in rading informaion has diminished. 7 Mos municipal bond issuers only release deailed financial informaion when hey floa a bond, while publicly raded corporaions are required o mainain a quarerly daa feed on heir aciviies (e.g., 0-Q and 0-K repors). 8 Harris and Piwowar (2004) repor ha he effecive spreads in muni bonds average almos 2 percen of price for represenaive reail-sized rades (20,000 dollars) while he average yield o mauriy is close o 6 percen. 5

8 yield is aribuable o liquidiy risk remains unclear. In his paper, we are able o esimae he liquidiy premium of municipal bonds by using he ransacion daabase recenly made available by he Municipal Securiies Rulemaking Board. As such, his paper represens he firs empirical sudy of he effec of liquidiy risk on he relaive municipal bond yield curve using ransacion daa. he model ha we propose accouns for he effecs of boh liquidiy and defaul risk on he relaive yields of axable and ax-exemp bonds. Mos sudies on he liquidiy effec have focused on equiy markes where ransacion daa are easily accessible. An excepion is Harris and Piwowar (2004), which examines ransacion coss and rading volume in he U.S. municipal bond marke. Unlike heir sudies, we focus on he sensiiviy of municipal yields (or expeced reurns) o liquidiy risk and examine is effec on he equilibrium pricing of municipal bonds. Specifically, we invesigae he effec of sysemaic liquidiy risk on bond yields insead of he level of liquidiy cos per se. We consruc a broad liquidiy measure for he municipal marke along he line of Pasor and Sambaugh (2003), which capures emporary price flucuaions induced by order flow. By incorporaing liquidiy as an addiional sae facor in municipal bond yields, we find ha he explanaory power of he model is grealy improved. Our empirical resuls show ha he liquidiy risk premium accouns for a significan porion of municipal bond yields. Resuls sugges ha invesors require a higher yield on hose municipal bonds whose reurns are more sensiive o aggregae marke liquidiy. Wihin a raing class, he sensiiviy of municipal yields o marke-wide liquidiy increases monoonically wih mauriy. A he same ime, conrolling for mauriy, he sensiiviy of municipal yields o marke-wide liquidiy increases 6

9 monoonically as he bond raing drops from AAA o BBB. Liquidiy premium explains abou 7 o 3 percen of he observed municipal yields for AAA bonds, 7 o 6 percen for AA/A bonds and 8 o 20 percen for BBB bonds wih differen mauriies. Ignoring he liquidiy risk effec hus resuls in an underesimaion of municipal bond yields. Including liquidiy risk in he pricing model also helps explain he municipal yield curve anomaly. Long-mauriy municipal yields are high relaive o he equivalen aferax yields of reasury bonds, parly due o liquidiy risk. Our resuls show ha he liquidiy risk premium alone accouns for 65 basis poins (bps) for AAA bonds, 79 bps for AA/A bonds and bps for BBB bonds wih 20-year mauriy. In conras, liquidiy risk premiums are only 4 bps, 6 bps and 23 bps for -year AAA, AA/A and BBB bonds, respecively. hus, he liquidiy premium accouns for a subsanial porion of he mauriy spread beween 20-year and -year bonds. Conrolling for he effecs of defaul and liquidiy risk, we obain implici income ax raes very close o he sauory ax raes of high-income individuals and corporaions. More imporanly, hese implici ax raes are very sable when esimaed from observed yields of bonds wih differen mauriies. Furhermore, our liquidiy premium esimaes are highly correlaed wih radiional liquidiy variables. We find ha municipal bonds wih high volume and rading frequency and larger issue size have a low liquidiy risk premium. hus, he Pasor-Sambaugh mehod, which we employ o consruc he aggregae liquidiy of he municipal bond marke, is quie effecive in absracing he liquidiy feaure of he bonds. Overall, our resuls show ha he generalized model wih liquidiy risk explains he behavior of reasury and municipal yield curves very well. 7

10 he remainder of his paper is organized as follows. Secion I reviews he relaed lieraure on municipal bonds. Secion II proposes a generalized municipal bond model o incorporae he effecs of defaul and liquidiy, and discusses he empirical mehodology. Secion III describes he daa sample and Secion IV presens empirical resuls for municipal bonds of differen raings, mauriies and rading characerisics. Finally, Secion V summarizes major findings and concludes he paper. I. Relaed Lieraure radiional models of he yield relaionship beween axable and ax-exemp bonds assume ha invesors are a he margin on all bonds. hey can rade freely wihou any fricion, and he axaion of long and shor posiions is compleely symmeric. Invesors apply he same discoun facors o he afer-ax cash flows from boh axable and ax-exemp bonds. In addiion, i is assumed ha municipal bonds are defaul-free and priced a par, and invesors hold hem o mauriy. Given hese condiions, i follows ha he yield on he ax-exemp bond (M ) is simply equal o he yield on he axable bond (C ) imes one minus he marginal invesor s ax raeτ : M C ( τ ) () = Miller (977) hypohesizes ha in equilibrium, corporae capial srucure decisions will force he ax rae in () o be he op marginal corporae ax rae. Fama (977) predics ha he equilibrium ax rae equals he highes marginal corporae income ax rae because banks were able o deduc ineres expenses incurred o inves in municipal bonds from heir axable income. Empirical evidence has shown ha he implied ax raes esimaed from () are considerably lower han he sauory ax raes for high-income individuals and 8

11 corporaions, paricularly for long-mauriy municipals. here have been aemps o explain his anomaly. he clienele hypohesis argues ha long- and shor-erm bond markes may be dominaed by differen groups of invesors. Changing ax regimes can also incur invesmen risk and affec bond values, paricularly for long-mauriy municipals (see Poerba, 989). Furhermore, inferior ax-iming opions on municipal bonds may raise he relaive yields especially for long mauriy municipals (see Consaninides and Ingersoll, 984). 9 rzcinka (982) argues ha ignoring he ime-varying risk premium resuls in an underesimaion of he implici marginal ax rae. 0 He suggess including a random inercep erm in he yield relaionship of () o capure he ime-varying risk premium: M = Λ + βc (2) where Λ is he ime-varying risk premium and β = τ. In his model, Λ is included o allow for he differences in defaul risk beween ax-exemp and axable bonds. Yawiz, Maloney and Ederingon (985) demonsrae ha if wo bonds have differen probabiliies of defaul, β will depend on he relaive magniudes of hese probabiliies and hus canno be inerpreed as an esimae of -τ. Specifically, hey show ha in equilibrium he following yield relaionship holds: M = α + β C (3) λ τ where α = ( τ g ), and β =, λ is he defaul probabiliy a ime, τ is he λ λ ordinary income ax rae and τ g is he capial gain (or loss) ax rae. 9 An invesor purchasing a axable bond a a premium can amorize he premium agains ineres income over he remaining life of he bond. By conras, he premium on a ax-exemp bond canno be so amorized. In addiion, capial gains from selling municipal bonds are subjec o federal axes. 9

12 Green (993) proposes a differen model ha considers invesors abiliy o shield coupon income from axaion. axable invesors may form a ax-advanaged porfolio o avoid axes on he cash flows received before mauriy by he following rading sraegy. Suppose here is a par bond wih coupon rae C and mauriy dae and anoher par bond wih coupon rae C/2 and he same mauriy dae bu raded a a discoun. A long posiion wih wo C/2 coupon bonds and a shor wih one C coupon bond will resul in no coupon income and hence, no ne ax liabiliy prior o mauriy. his sraegy can be applied o any bonds wih differen coupons o form a ax-advanaged porfolio. While individual invesors may be precluded from holding his ype of ax-advanaged porfolio due o limiaions on ineres deducions from borrowings and shor posiions, bond dealers are no. herefore, from a dealer s poin of view, cash flows from par bonds and a sequence of pure principal paymens are equivalen. Any difference in price beween a pair of bonds or bond porfolios wih idenical income sreams creaes an arbirage opporuniy for dealers. Specifically, o he invesor who pursues he above sraegy o generae ne zero coupon paymens, he afer-ax cash flow of he posiion is τ ( P ) where P is he cos of he posiion a ime, which is equal o he oal price of wo C/2 coupon bonds minus he price (=) of one C coupon bond assumed equal o par. he price P of his posiion mus hen be equal o he discouned afer-ax value of is cash flow: P = [ τ ( P )] d (4) where d is he afer-ax discoun facor. Solving for P yields 0 A similar argumen is made by Wu and Yu (996) in a differen conex. Wu (99) exends Yawiz e al. (985) o consider invesors risk-averse behavior and finds ha he slope coefficien furher depends on risk premium. 0

13 P ( τ ) d = τd (5) From he dealer s viewpoin, cash flows from par bonds wih mauriy and a sequence of pure principal paymens are equivalen and so hey should have he same price; ha is, Subsiuing P in (5) ino (6) gives = C P + P (6) = = ( τ ) d C + = τd ( τ ) d τd (7) A he same ime, he value of a par municipal bond wih equal mauriy will be equal o = M d + d (8) = Combining (7) and (8), one can obain he following equilibrium relaionship beween he yield curves of municipals and reasuries: 2 M = C ( ) d = τd τ (9) d = τd where d = P τ ( P )) ( is he afer-ax discoun facor for he cash flow a ime, and P is he preax discoun facor of a zero-coupon defaul-free axable bond. he model implies ha he raio of he ax-exemp yield o he axable yield, M /C, increases wih mauriy. When mauriy =, he raio muliplying he afer-ax coupon on he righ side of (9) is equal o one, and M /C gives he ax rae of he marginal invesor. For

14 longer mauriies, he raio muliplying he afer-ax coupon is greaer han one if forward raes are posiive (d < d for < ). he longer he mauriy, he larger his raio, making M increasingly large relaive o C. hus, if one uses he formula - M /C o obain he implici ax rae from he yields of axable and ax-exemp bonds, he resuling esimae will be biased downward. While Green s (993) model is quie appealing, i does no consider he effecs of liquidiy and credi risk. Unlike reasury securiies, municipal bonds are subjec o defaul. In addiion, compared o he reasury marke, he municipal marke is very illiquid. hese wo facors can complicae he equilibrium yield relaionship. Liu, Wang and Wu (2003) consider he effec of defaul risk on municipal yields. hey argue ha ignoring defaul risk may resul in a biased esimaion of he implici marginal income ax rae for long-mauriy bonds. However, several sudies have shown ha for defaul risk o explain he muni yield puzzle, he implied defaul probabiliies for municipals would have o be unreasonably large (see, for example, Poerba, 986; Jordon and Jordan, 990; and Green, 993). Chalmers (998) uses a large sample of municipals over an exended sample period o examine he issue and finds ha defaul risk canno explain he muni yield puzzle. hus, defaul risk alone does no appear o be able o provide he answer o he empirical puzzle. In his paper, we explore he role of liquidiy risk in municipal bond pricing. We ake advanage of a unique ransacion daase recenly made available by he Municipal Securiies Rulemaking Board o esimae he liquidiy risk of municipals and examine is effec on bond yields. o he exen ha illiquidiy can significanly affecs he municipal bond yields, analyzing he effec of liquidiy risk should shed ligh on he muni puzzle. 2 See Green (993) for he deails of derivaion. 2

15 In he following secion, we propose a generalized municipal bond model wih defaul and liquidiy risk and discuss he empirical esimaion procedure. A. he Model II. A Generalized Municipal Bond Pricing Model Following Green (993), we assume ha municipal and reasury bonds are priced a par and boh are noncallable. In addiion, invesors pursue a buy-and-hold sraegy. However, unlike his model, municipal bonds are subjec o defaul. he probabiliy of defaul a ime is λ and he recovery rae is δ when defaul occurs. 3 When here is no defaul, he presen value of he payoff for he municipal bond is M d + d ( λ ) (0) = = Conversely, when defaul occurs, he bond invesor receives a residual (recovery) amoun δ. he presen value of he expeced cash flow of he municipal bond if defaul occurs a ime i, is given by i M = d i + δ λi ( λk ) () k = where δ is expressed in erms of presen value. he value of he municipal bond a ime is equal o he sum of (0) and (). Because we assume ha he municipal bond is priced a par, he pricing formula can be wrien as i i = ( ) + ( ) M d + d λ M d + δ λi λk = = = (2) = i k = Combining he pricing formula for reasuries in (7) wih (2), we obain he following equilibrium relaionship beween municipal and reasury yields: 3 he recovery rae is formulaed as a fracion of he face value. 3

16 M = C = τd ( τ ) d τd d + d = = = i ( λ ) δ λ ( λ ) i i ( ) ( ) λ + d λ λ i= = i= τd i k = i k = k k (3) he pricing formula above is no complee because i does no include he effec of liquidiy risk, which is considered o be a criical facor for municipal bond pricing. Liquidiy is perceived as an imporan feaure of he invesmen environmen. Previous sudies have shown ha he level of liquidiy affecs expeced asse reurns (see, for example, Amihud and Mendelson, 986, 99; Brennan and Subrahmanyam, 996; Brennan, Chordia and Subrahmanyam, 998; and Amihud, 2002). ha he level of liquidiy can affec ransacion cos and asse price is no surprising. Wha is more imporan is wheher liquidiy risk is a sysemaic risk ha affecs equilibrium asse reurns. In an influenial paper, Pasor and Sambaugh (2003) show ha expeced sock reurns are significanly affeced by sysemaic liquidiy risk. hey sugges ha i should be fruiful o examine he liquidiy in he bond marke and is impac on pricing, since he effec of liquidiy risk on bond reurns can poenially be quie differen from ha on sock reurns. 4 o accoun for he effec of liquidiy risk, we add a liquidiy risk variable o (3) and rewrie i in a more compac form: M = Λ + β C + β L (4) L 4 Recen sudies in fixed-income markes have found ha radiional erm srucure models of defaulable bonds explain only a small porion of yield spreads (see, for example, Huang and Huang, 2003). A poenial cause is ha liquidiy risk is no accouned for by hese models. Longsaff, Mihal and Neis (2005) find ha he liquidiy premium accouns for a significan porion of corporae bond spreads. Since 4

17 5 where ( ) ( ) ( ) ( ) + = = = = = = = = = i i k k i i i i k k i d d d d d λ λ λ τ τ λ λ δ λ Λ and ( ) ( ) ( ) + = = = = = = = i i k k i i d d d d d λ λ λ τ τ τ β L β is he sensiiviy of he yield of an individual municipal bond or porfolio o he aggregae liquidiy L of he municipal marke. Equaion (4) saes ha in equilibrium he municipal bond yield equals he adjused reasury bond yield (he firs wo erms on he righ hand side adjused for ax and defaul effecs) plus a sysemaic liquidiy risk premium, which compensaes for he low liquidiy of municipal bonds relaive o reasuries of equal mauriy. his yield model can be applied o municipal bonds of any raing and mauriy by allowing defaul and liquidiy risk o vary. Sandard asse pricing heory suggess ha expeced securiy reurns are relaed o reurns sensiiviies o sae facors. If liquidiy is one of hese sae facors, invesors will require higher expeced reurns on securiies ha are more sensiive o aggregae marke liquidiy. his heoreical argumen holds no only for equiies bu also for fixedincome securiies in general. hus, municipal securiies should be no excepion. If municipals are less liquid han reasury securiies, invesors should demand higher yields he municipal marke is very illiquid by convenional sandards, liquidiy risk could also be very imporan for pricing municipal bonds.

18 (or expeced reurns) from holding municipals o compensae for his risk. Likewise, in he domain of municipal securiies, hose municipals whose reurns have higher sensiiviies ( β ) o aggregae marke liquidiy should offer higher yields han oher L municipals wih lower sensiiviies. Inuiively, he role of liquidiy in securiies pricing would depend on he imporance of liquidiy for a specific invesmen and he liquidiy condiion of a marke relaive o ohers. Since he municipal marke is relaively illiquid compared o oher markes, liquidiy risk would likely be an imporan pricing facor for municipal bonds. When here is a widespread deerioraion in liquidiy, i will be more difficul o liquidae municipal bonds han reasuries securiies. In anicipaion of cosly liquidaion in a low liquidiy environmen, invesors will require higher yields o compensae for his risk regardless of he ax-exemp advanage of municipals. Furhermore, he rade size of municipals is ypically larger han ha of equiy ransacions. Liquidiy is expeced o be more valuable for invesors rading large orders han small orders even in rouine ransacions. In an unusual siuaion when he aggregae marke liquidiy dries up, i will be much more difficul o rade large quaniies. aken ogeher, liquidiy risk should be more serious concern for municipal invesors and if so, his would have a significan implicaion for municipal bond pricing. 5 he relevance of liquidiy risk o municipal bond pricing is measured by he sensiiviy coefficien β L o he aggregae liquidiy of he municipal bond marke. Similar o he risk measure in radiional asse pricing models, β L capures he sysemaic 5 he imporance of liquidiy is well spelled ou by he recen even associaed wih he reducion in personal axes on regular income and dividends by he Bush Adminisraion. he even riggered a sell-off 6

19 risk (liquidiy bea) of individual municipal bonds o he marke-wide liquidiy. We use he aggregae liquidiy measure of he municipal marke iself o esimae liquidiy bea for he following reasons. Firs, since an individual financial marke ypically exhibis commonaliy in liquidiy, i jusifies he esimaion of sysemaic liquidiy risk of a municipal bond by is co-variaion wih he liquidiy innovaions of he overall municipal marke. he raionale is ha hose municipal securiies whose reurns are more exposed o marke-wide liquidiy flucuaions should have higher yields (expeced reurns). Second, he reasury yield (C ) on he righ hand side of he model in (4) has impounded he effec of he reasury liquidiy risk and so here is no need o add he liquidiy innovaions of he reasury marke as an addiional explanaory variable in he municipal yield model. o esimae liquidiy risk β L, we need o consruc a marke-wide liquidiy measure (L) for municipal bonds. In he following, we ouline he procedure for consrucing a measure of aggregae liquidiy for he municipal bond marke in he spiri of Pasor and Sambaugh (2003). he proposed aggregae liquidiy measure capures emporary price changes associaed wih order flow. he fundamenal argumen is ha lower liquidiy ends o correspond o sronger price reversals on he nex rading day, resuling from he order flow in a given direcion on a paricular day. For example, in he absence of privae informaion, a large number of sell orders (or a high sell volume) on a paricular day will cause a greaer price rebound on he nex rading day. his dimension of liquidiy can be gauged by he response of municipal reurns in he nex rading day o he signed volume in he municipal marke as he ax-advanage of municipals was eroded. Because liquidiy was low, he sell-off had a remendous impac on municipal bond prices across he board. 7

20 in he preceding rading day. Specifically, he liquidiy measure for a bond in a monh is he leas squares esimae of he parameer π i, associaed wih he signed volume in he following regression: 6 e e r i, j+, = 0 + ρri, j, + π i, sign( ri, j, ) Voli, j, + ui, j+, ρ (5) where e r i, j, ri, j, rb, j, = is he reurn of municipal bond i on day j, i, j, in excess of he r, equally weighed municipal marke reurn,, ; sign( r e i, j, ) is he signed indicaor which r b j, is equal o if, is posiive, and - if i is negaive; and Vol i, j, is he dollar volume (in e r i j, en-housand dollars) for bond i. 7 In his model, he order flow is measured by volume signed by he conemporaneous excess reurn on a paricular municipal securiy. he order flow is expeced o be followed by a reurn reversal if he municipal securiy is no perfecly liquid. Presumably, he greaer he expeced reversal for a given dollar volume, he lower he liquidiy of he municipal securiy; ha is, π i, is negaive. he model in (5) is esimaed for individual bonds each monh using daily reurn and volume daa. In empirical invesigaion, in order o obain a reliable esimae of π, we selec in each monh only hose bonds which have more han 0 observaions. he liquidiy measure of each individual bond is hen aggregaed over all municipal bonds (N) in he sample monh by monh: N ˆ π = π i, (6) N i= Sysemaic liquidiy risk, β, is measured as he sensiiviy of bond reurns o unexpeced L innovaions in marke-wide liquidiy. o obain he unexpeced liquidiy innovaions 6 For he deail of he derivaion, see Pasor and Sambaugh (2003). 8

21 ( ê ), we esimae he following auoregressive model for he differenced liquidiy measure: ˆ π πˆ ˆ π + e (7) = a0 + a + a2 he above regression is essenially a second-order auoregression in he level series of marke-wide liquidiy. 8 Since he residual erm for municipal bond liquidiy is ypically quie small, we muliply he esimaed ê by 00: L = 00 ˆ (8) e Afer consrucing he marke-wide liquidiy measure, we include i as a sae facor for he municipal bond yield model o esimae he liquidiy risk premium of municipal bonds. B. Esimaion Procedure he municipal yield model in (4) can be esimaed by he nonlinear regression mehod. Since municipal bond yields are serially correlaed, we correc he effec of auocorrelaion. he firs sep in empirical invesigaion is o absrac he liquidiy measure from (5) and (7). he model in (5) is paricularly suiable for our invesigaion of municipal marke liquidiy because i requires only he excess reurn and dollar volume daa. hese daa are readily available from he ransacion records provided by Municipal Securiies Rulemaking Board (MSRB). As noed, o consruc a meaningful liquidiy index, we impose he resricion of a minimal number of 0 ransacions each monh for an individual municipal securiy. Alhough municipals are raded less frequenly, his presens lile difficuly because he MSRB daabase conains 7 Pasor and Sambaugh (2003) find ha his specificaion works beer han oher specificaions wih excess lagged reurns. 8 Pasor and Sambaugh (2003) show ha his ime-series model capures liquidiy innovaions raher well. 9

22 records for more han one million municipal securiies. his large daabase grans us a considerable leeway o choose a suiable sample o esimae marke-wide liquidiy. Afer imposing he consrain of he minimal number of ransacions per monh, we sill have 49,666 bonds ha mee his crierion. his sample size is large enough o represen he overall municipal marke. Noe ha his paricular sample is seleced mainly for esimaion of he marke-wide liquidiy facor. For he esimaion of he municipal yield model in (4), we impose differen crieria o beer conrol he daa sample as explained laer in he daa secion. In he second sep, we form he porfolios of muni bonds by raing and mauriy. here are advanages of esimaing he yield model wih porfolios. Firs, forming porfolios allows us o consruc more regular ime series of municipal yields for regression esimaion, o overcome he problem of infrequen rading. Second, porfolio formaion reduces daa noise associaed wih individual bonds due o recording errors and sale prices. Because he porfolios are grouped by raing and mauriy, we reain conrol on hese wo imporan bond characerisics. We calculae he yield for each porfolio from our daa sample monh by monh. We hen esimae he nonlinear model in (4) using monhly yield daa of each porfolio using he Gauss-Newon mehod. III. Daa Descripion We use he municipal bond daabase provided by he Municipal Securiies Rulemaking Board in our empirical esimaion. he MSRB is he self-regulaory agency esablished by Congress, which develops rules subjec o SEC approval o govern he conduc of brokers and dealers involved in underwriing and rading municipal securiies. Approximaely 2,700 municipal securiies brokers and dealers are regisered wih he 20

23 MSRB. Since 997, he municipal bond indusry has operaed under a mandaory ransacion reporing sysem overseen by he MSRB. All dealer-o-dealer and dealer-ocusomer muni bond ransacions are repored o he MSRB afer he close of business each day. he MSRB hen consolidaes he daily repors. Beginning in July 2000, he MSRB sared releasing elecronic files conaining all municipal bond ransacion daa wo weeks afer acual ransacions ook place. 9 he MSRB ransacion repors conain daa fields including CUSIP, securiy descripion, issue dae, coupon, mauriy dae, rade dae, ime of rade, par amoun of rade, ransacion price, and yield. Useful feaures of he daa include wheher a ransacion is sale o cusomer, purchase from cusomer or iner-dealer rade, and an indicaor showing wheher he rade occurs before he syndicae selemen dae. Addiional informaion on he characerisics of each bond are colleced from Bloomberg, which includes he raing of a bond when i was issued, he issue size and ype (e.g., general obligaion or revenue bonds), wheher he bond is callable or conains a sinking fund provision, and wheher he bond is insured. Zero-coupon reasury yields are obained from he Federal Reserve Board (FRB), where spo raes are esimaed from reasury prices using he Svensson mehod (see Bolder and Sreliski, 999, for deails). he sample period is from July 2000 o June he iniial sample conains a oal of,056,774 bonds, 27,330,633 ransacions and dollar volume of.7 rillion. A noable feaure of he municipal marke is ha mos bonds are no frequenly raded. Compared o he reasury marke, he rading volume on he municipal bond marke is 9 he iniial lag was one monh, bu he MSRB has since sequenially reduced he lag ime o wo weeks, one week and one day. Beginning January, 2005, he lag was subsanially reduced as he MSRB and he Bond Marke Associaion (BMA) parnered o make ransacion daa available wihin fifeen minues of a rade. 2

24 much smaller. For example, in June 2004, he average weekly volume (oal par value raded) on he municipal marke is billion, while he average weekly reasury ransacion is billion, according o New York Fed s weekly survey on primary reasury dealers conduced each Wednesday. Infrequen rading is a key facor conribuing o low liquidiy in his marke. o consruc he daa sample for our empirical esimaion of he municipal yield model in (4), we mach he raw MSRB daa wih bond characerisic informaion from Bloomberg and impose he following screening crieria. 20 We firs drop rades ha occur on or before he underwriing syndicae selemen dae, and keep only secondary marke rades. his filer reduces he number of bonds o 805,50 and he number of ransacions o 22,967,938. We hen eliminae bonds wih unknown credi raings, leaving 686,859 bonds and 2,554,555 rades in he sample. Since our municipal model holds for sraigh bonds, we delee bonds wih embedded opion feaures (i.e., bonds wih call and sinking fund provisions). Due o he fac ha he majoriy of municipal bonds are callable, his filer decreases he sample subsanially o 4,626 bonds and 2,49,008 rades. We also eliminae bonds ha carry variable raes or irregular coupons. his resricion removes 85 bonds and 2,500 ransacions. o focus on bonds ha are relaively frequenly raded in order o consruc he porfolios wih enough observaions, we keep only hose ransacions ha are wihin one year from he issuance dae. his sep excludes 6,37 bonds and leaves 53,070 bonds and 883,753 ransacions in he sample. In addiion, we hrow away ransacions wih obvious errors in prices or wih missing prices. his filer drops 207 bonds and 7,54 rades. Finally, for a similar concern abou liquidiy, we 22

25 exclude hose bonds ha are less han six monhs away from mauriy. Our final sample conains 48,278 bonds wih a oal of 753,268 secondary marke ransacions. We group he individual bond daa according o heir raings and mauriies. Because here are very few speculaive bonds in our daa sample, we include only bonds in he following raing classes: AAA, AA/A and BBB. In he original daabase, AA and A bonds are grouped ogeher and so we keep hem in one group. here are very few rade and ransacion price daa for bonds wih long mauriy. We herefore lump (equally weighed) all bonds wih mauriies from 8 o 22 years o form long-erm porfolios. his enables us o assemble a larger number of observaions in porfolios o examine he empirical properies of long-erm municipals. he average mauriy for hese long-erm porfolios is very close o 20 years: 9.9 years for AAA, 9.5 years for AA/A and 9.9 years for BBB bonds. 2 For convenience, hese porfolios are placed under he 20-year caegory for he corresponding raing class. able I provides he summary saisics for he hree raing groups of municipals, and reasuries by mauriy. Panel A shows ha yields of AAA bonds are lower han hose of AA/A bonds which, in urn, are lower han hose of BBB bonds. Yields of reasury bonds wih he same mauriy are generally greaer han hose of AAA and AA/A bonds. However, reasury yields may be lower han BBB yields, indicaing ha he defaul and liquidiy premia may ouweigh he ax-exemp advanage for bonds in his raing class. Figure plos he ime-series of municipal and reasury yields for mauriies from one o en years. 20 As noed earlier, his sample selecion procedure applies o our yield model esimaion. For he consrucion of he liquidiy index, we impose a less sringen resricion ha only requires a minimum of 0 ransacions per monh for each individual bond. 23

26 Panel B of able I shows monhly averages of he number of ransacions, rading volume (in par amoun), and he number of bonds for each raing-mauriy porfolio. For each monh we calculae he number of bonds and ransacions, and oal par volume for each porfolio and hen average hem over all monhs in he enire sample period. As shown, he AA/A bonds have he larges number of ransacions, volume and number of bonds for mos mauriy groups, followed by AAA and BBB bonds. In erms of he number of ransacions, he five-year mauriy bonds are highes whereas bonds in he 20- year mauriy group are lowes. Panel A of able II summarizes he yield spreads beween reasuries and AAA bonds, beween AAA and AA/A bonds and beween AA/A and BBB bonds. Average differences beween reasury and AAA yields are around 70 basis poins. Average yield differences beween AA/A and AAA bonds, and beween BBB and AA/A are abou 0 and 50 basis poins, respecively. he erm srucure of he yield spread beween reasuries and AAA bonds exhibis a hump shape. he spread declines beyond he fiveyear mauriy, which confirms he previous finding ha prime municipal bond yields rise relaive o reasury yields when mauriy ges longer (see Green, 993). Panel B repors erm premiums for reasuries and municipals. he erm premium is obained by subracing from he yield for a given mauriy he corresponding yield of one-year mauriy. Consisen wih previous findings, average yields for reasuries increase less rapidly wih mauriy han do hose of municipals. However, average erm premiums are only higher for he 20-year municipal group relaive o reasury bonds. his is somewha differen from previous findings, suggesing ha he relaive seepness 2 he shape of he yield curve beween 8 and 22 years is close o linear and so an equally weighed average yield is very close o he average yield of 20-year bond. 24

27 of he yield curves may vary by sample periods. By conras, average erm premiums for AAA municipals are higher han hose for BBB municipals a all mauriies. he columns reporing he minimum values of he erm premium show negaive numbers for reasuries a all mauriies whereas hey are all posiive for municipals. Resuls show ha while he yield curves of reasuries may rever, his phenomenon has never occurred for municipal bonds. IV. Empirical Resuls A. Esimaion of he Municipal Yield Model We nex esimae he municipal yield model using he monhly yield series for each mauriy-raing group. Esimaing he municipal bond yield model requires spo raes of pure discoun bonds. he preax discoun facor P embedded in he afer-ax discoun facor d a ime is he inverse of one plus he spo rae of a pure discoun bond o he power of. We can express he afer-ax discoun facor d as a funcion of he preax discoun facor P and he marginal income ax rae. By subsiuing he definiion of he afer-ax discoun facor d = P /( τ ( P )) ino he model and using he spo rae daa obained from he FRB, we can direcly esimae he marginal income ax rae and defaul probabiliy from he observed municipal and reasury bond yields. he nonlinear municipal yield model is esimaed for bond groups wih differen raings and mauriies. In addiion o spo raes, we need o consruc he aggregae municipal bond marke liquidiy index before esimaing he yield model. We esimae liquidiy measures for individual bonds each monh using he regression model in (5) and aggregae hem over all bonds o obain he monhly series of he municipal marke liquidiy index. 25

28 Panel A of Figure 2 plos he esimaes of he aggregae liquidiy index for he muni marke. By consrucion, negaive liquidiy index values imply posiive liquidiy coss. he aggregae liquidiy measure shows occasional downward spikes. he larges downward spike occurs in Sepember 200 when he marke was shu down due o he erroris aack a he New York World rade Cener. he second larges spike occurs in he fall of 2002 when he marke was jiered by he episode of WorldCom. he hird larges spike occurs around July 200 when he Enron scandal began o unravel. Anoher major downward spike occurs afer he announcemen of he ax cu by he Bush Adminisraion on May 23, 2003, which riggers a sell-off in he municipal bond marke as he ax-exemp advanage of municipals is eroded. 22 Overall, he aggregae liquidiy measure consruced from he Pasor-Sambaugh mehod appears o pick up significan evens quie effecively. he median value of he aggregae liquidiy measure is -2.37%. Excluding he exreme value of Sepember 200, he mean liquidiy index is -3.66%. hese numbers sugges ha he average liquidiy cos is around 2.4% o 3.7%, which represens he cos for a $0 housand rade in consan municipal bond marke dollars of year he correlaion beween he liquidiy measure and he aggregae municipal bond marke reurn is 0.05, indicaing ha he liquidiy cos is somewha lower when he marke performance is beer. 22 According o he ax bill passed May 23, 2003, he highes income ax rae for individuals is reduced o 35% reroacive o January, he nex hree raes are 33%, 28% and 25%. his ax ac acceleraes he ax reducion scheduled for 2004 hrough 2006 by he Economic Growh and ax Relief Reconciliaion Ac of 200. he new ax law also increases he axable income level for he 0% bracke. Oher effecs of he 2003 ax ac include child ax credi, marriage ax breaks, alernaive minimum ax, business bonus depreciaion and small-business spending (see he repor of he Wall Sree Journal May 23, 2003). 26

29 Panel B of Figure 2 plos he innovaions of he liquidiy measure. he innovaion series appears o be serially independen. he auocorrelaion of innovaions of he liquidiy measure is -0.4, which is relaively small. We employ his innovaion series in he nonlinear regression model o capure he effecs of unanicipaed liquidiy shocks on yields of municipal bonds. able III repors he esimaes of he generalized municipal bond model wih liquidiy risk. 23 Parameer esimaes for ax rae and defaul probabiliy are expressed in percenage erms, and sandard errors are repored in parenheses. he esimaes of he liquidiy risk parameer are very significan and of a negaive sign. Since he liquidiy measure L also has a negaive sign, he negaive coefficien of he liquidiy facor ranslaes ino a posiive effec on municipal bond yields. he sensiiviy of municipal bond yields o he liquidiy facor increases significanly wih mauriy, suggesing a much higher liquidiy risk for longer-erm bonds. For example, he liquidiy risk coefficien in absolue value for 0-year bonds is more han hree imes ha of one-year bonds for each raing class. his difference is even more sriking for he 20-year bond group. Moreover, he sensiiviy of yields o liquidiy increases as credi risk increases, indicaing ha lower qualiy bonds have higher liquidiy risk. his resul lends suppor o he conenion of a posiive correlaion beween credi and liquidiy risk. he esimaes of marginal income ax rae and defaul parameer are all highly significan. he esimaed marginal ax raes are around 32 o 33 percen. wo ineresing paerns are observed. Firs, he esimaes of implici ax raes are very close o he maximum sauory income ax brackes of high-income individuals and 23 he recovery rae is se equal o 0.4 whose value is very close o ha used by Duffee (999) and Elon e al. (200). 27

30 corporaions. Second, hese implici ax rae esimaes are very sable over mauriies. hese findings conras sharply wih previous findings ha he implici ax raes are subsanially below he sauory ax raes of high-income individuals and corporaions, and ha he esimaes of he implici ax rae declines drasically wih mauriy. In some sudies, he esimaed implici income ax raes for municipal bonds wih mauriy longer han 20 years are merely half of ha for one-year municipal bonds. 24 By conras, our empirical esimaes do no exhibi hese anomalies in he implici income ax raes. Resuls sugges ha he so-called municipal yield puzzle may well be aribuable o missing facors in he radiional models. he esimaes of defaul probabiliies are consisen wih raings. hese esimaes are annualized defaul probabiliies. he implied defaul probabiliies are in line wih previous esimaes. 25 Given mauriy, esimaed defaul probabiliies increase monoonically as he raing decreases. Wihin each raing class, he defaul probabiliy esimaes exhibi an upward rend wih mauriy. he upward-sloping erm srucure of he defaul probabiliy is consisen wih empirical evidence on invesmen-grade bonds. Overall, he model wih liquidiy risk explains he relaive yield curves of municipal bonds very well. he goodness-of-fi in erms of high R 2 is quie good across all raings and mauriies. he resuls sugges ha personal axes, liquidiy and defaul risk are imporan deerminans of municipal bond yields. B. Decomposiion of Municipal Bond Yields he resuls above show significan effecs of liquidiy risk on municipal bonds of differen raings and mauriies. A quesion of paricular ineres is how much municipal 24 See able 3 in Green (993, p. 239). 25 See, for example, Yawiz e al. (985). 28

31 bond yield can be aribued o liquidiy risk. he yield model allows us o separae he effec of liquidiy risk from he combined effec of personal axes, defaul risk and riskfree (reasury) raes, which is nonlinear in naure due o he ineracive effecs among hese variables. We firs employ he parameer esimaes of defaul probabiliy, ax raes and liquidiy risk o calculae he municipal bond yields. We hen separae hese municipal bond yield esimaes ino he liquidiy and non-liquidiy componens. able IV repors he resuls of yield decomposiion, where he esimae of each spread componen is expressed in magniude (%) and in he proporion of he observed yield (% yield) for each yield componen. We repor he yield componens for each raing and mauriy group. In addiion, boh observed yields and oal yield esimae (he sum of liquidiy and non-liquidiy componens) are repored in he leading column of each raing class. he liquidiy componen of municipal yields increases wih mauriy and credi risk in erms of boh he magniude and proporion of observed yields. he liquidiy spread in basis poins increases from 4 o 65 for AAA bonds as mauriy rises from one o 20 years. Correspondingly, he liquidiy spread in he proporion of he observed yield increases from 7 o 3 percen. For AA/A bonds, he liquidiy spread increases from 6 o 79 bps, which accouns for abou 7 o 6 percen of he observed yields of differen mauriies. For BBB bonds, i increases from 23 o bps, or abou 8 o 20 percen of he observed yield. he resuls show ha he amoun of liquidiy premium is sizable for mos bonds and i is paricularly large for lower-qualiy long-erm municipal bonds. he non-liquidiy yield componen (including effecs of axes, defaul and riskfree raes) also increases wih mauriy and credi risk. his increase is associaed more 29

32 wih he change in defaul risk han wih axes since he esimaes of marginal ax raes are no maerially differen over mauriies and across raings. As mauriy increases, he probabiliy of defaul increases for hese invesmen-grade municipal bonds. Similarly, as he raing decreases, defaul probabiliy increases. Since he defaul probabiliy has a posiive effec on municipal yield, his increase in defaul probabiliy conribues o he increase in he non-liquidiy yield componen. However, he non-liquidiy yield componen in percenage erms declines over mauriies. Alhough he non-liquidiy yield componen increases in magniude wih mauriy, observed yields appear o increase faser, due o an increase in liquidiy risk as mauriy ges longer. As a resul, he proporion of he non-liquidiy componen o he observed spread declines wih mauriy. By conras, he proporion of he liquidiy componen o he observed spread increases wih mauriy. his finding suggess ha liquidiy risk is a more imporan facor conribuing o he rising mauriy premium of municipals relaive o reasuries. he liquidiy premium accouns for a subsanial porion of he mauriy premium. For example, as shown in Panel B of able II, he mauriy premium for AAA bonds is 34 bps for wo-year bonds and 298 bps for 20-year bonds, a difference of 264 bps. In conras, he corresponding mauriy premium for reasuries increases from 4 o 277, a 236 bps difference. I appears ha he mauriy premium increases faser for long-mauriy municipal bonds. Bu if we adjus he mauriy premium of 20-year municipals by he incremenal liquidiy premium of 48 bps (65-7 bps), we come up wih an adjused mauriy premium of only 26 bps, which is lower han he corresponding mauriy premium increase of 30

33 reasuries. 26 hus, i seems ha liquidiy risk is he driving force behind he high yields of municipals relaive o reasuries a long mauriy. Chalmers (998) finds ha differenial defaul risk alone canno explain he municipal yield puzzle. Our resuls are consisen wih his view. C. Likelihood Raio ess We nex conduc he likelihood raio es o see if liquidiy risk adds significan explanaory power o he municipal bond model. I is sraighforward o perform he likelihood raio es on he incremenal explanaory power of liquidiy risk. he es saisic is C U ( SSR SSR ) / k LR = (9) U SSR /( n K) where SSR C is he sum of he squared residuals of he consrained model, which imposes he condiion ha β = 0, SSR U is he sum of he squared residuals of he unconsrained L (full) model, K (= 3) is he number of explanaory variables, k (= ) is he number of coefficiens resriced o be zero, and n (= 48) is he number of observaions. he es saisic LR of he nonlinear yield model follows an F disribuion wih (k, n-k) degrees of freedom if he disurbance erm is normal under he null hypohesis ha he resriced coefficiens are zero (see Gallan, 987). 27 able V repors he resuls of likelihood raio ess. he criical F value is 4.0 a he five percen level. Resuls show ha likelihood raio ess rejec he null hypohesis of β = 0 for all mauriy-raing groups. Consisen wih he -ess in able III, resuls L show ha liquidiy risk adds significan explanaory power o he municipal model. 26 his calculaion assumes ha reasury bond s liquidiy risk is negligible and so i may oversae he effec of municipal liquidiy risk. However, he qualiaive effec of municipal liquidiy risk holds rue. 3

34 hus, he effec of liquidiy risk should be incorporaed ino he model in order o beer explain he behavior of he relaive municipal-reasury yield curves. D. Liquidiy and Bond Characerisics Previous sudies have shown ha liquidiy may vary wih securiies wih differen characerisics and rading aciviies such as coupon, issuance size, volume, and frequency of rades. In his secion, we examine wheher bonds wih cerain radiional liquidiy characerisics end o have differen liquidiy spreads. We firs rank individual municipals monh-by-monh based on coupon rae, size of he bond issue, volume, and rading frequency and sor hem ino hree porfolios: high, medium and low. We hen calculae average coupon rae, issue size, frequency of rades and yield each monh over all bonds in each porfolio. For volume, we sum all rades each monh for each individual bond and hen ake an average over all bonds in a porfolio. able VI repors averages of coupon rae, issue size, volume and frequency of rades per bond in he high and low porfolios. hese are mean saisics calculaed over all monhs. Coupon raes range from 2.5 o 6.7 percen. he average number of rades for an individual bond per monh is no more han wo for he low-frequency porfolios across raings. For high-frequency porfolios, he number of rades for an individual bond per monh ranges from 7 o 3 for AAA and AA/A bonds, and 5 o 33 for BBB bonds. he difference in he size of issues beween he high and low groups is greaer for BBB bonds, whereas he difference in volume is greaer for shorer-mauriy higher-grade bonds. 27 his saemen holds rue for he nonlinear model. 32

35 able VII repors yields for high and low porfolios averaged over all monhs. Yields are lower for municipals wih larger issuance size, and higher volume and rading frequency. By conras, here is no clear paern of yields for bonds wih differen coupon raes. he difference in he yields for bonds wih differen issuance size, volume and rade frequency may reflec varying liquidiy risk in hese bond groups. In addiion o rade frequency and volume, we also examine he paern of rade size and is effecs on bond yields. Consisen wih he finding of Downing and Zhang (2004), volume and rade size conain very similar informaion. Since he yield paerns for he porfolios ranked by volume and rade size are quie similar, we skip he resuls for rade size for breviy. 28 We nex esimae he municipal yield model for he high and low porfolios ranked in erms of hese characerisics. Since he esimaes of defaul probabiliy and marginal income ax raes are similar o hose in able III, we only repor esimaes of liquidiy risk parameers for he ineres of breviy. able VIII repors esimaes of he liquidiy risk parameer for differen raing classes and mauriies. All parameer esimaes are significan a leas a he five percen level. he resuls show ha he liquidiy bea ( β ) is lower in absolue value for bonds wih high issuance size and volume. his paern is consisen across raings. A similar paern is found for he groups wih high and low frequency of rades. Alhough liquidiy bea also ends o be lower for high-coupon porfolios, he relaionship is somewha weaker. In general, he size of liquidiy bea increases as raing decreases and mauriy increases. L 28 hese resuls are available upon reques. 33

36 We nex esimae he yields for each porfolio and decompose hem ino liquidiy and non-liquidiy componens. able IX repors he liquidiy spreads for each characerisic porfolio boh in percenage (%) and proporion of he observed spread (% yield). he resuls show ha he liquidiy spread is lower when issue size, rading volume and frequency of rades are higher. he difference in liquidiy spreads beween high and low porfolios ends o increase wih mauriy and credi risk. On average, he differences in he liquidiy risk premiums beween he porfolios of high- and low-issue size are 9 bps (2.3%) for AAA bonds, 7 bps (4.5%) for AA/A bonds and 23 bps (5.%) for BBB bonds. he differences beween high- and low-volume porfolios are 9 bps (2.%), 5 bps (3.8%) and 20 bps (4.4%), for AAA, AA/A and BBB bonds, respecively. he differences beween high and low frequency of rades are 4 bps (0.6%), 6 bps (4.0%) and 4 bps (0.5%) for he hree raing groups, respecively. For he coupon porfolios, we also find ha higher coupon bonds end o have lower liquidiy spreads for AA/A and BBB bonds. he differences in he liquidiy spreads beween high- and lowcoupon porfolios are 5 bps (.3%) and 6 bps (2.6%), for hese wo raing groups. However, here is no clear paern for he spread differences in high- and low-coupon groups over mauriies for AAA bonds and he average liquidiy spreads are quie close for hese wo groups. In summary, liquidiy risk of municipal bonds is highly correlaed wih radiional liquidiy variables. When municipal bonds are sored ino high and low porfolios based on rading aciviy and bond characerisics, we find subsanial differences in liquidiy spreads. In general, hose municipals wih higher volume and rade frequency, and larger issue size have lower liquidiy risk and liquidiy spreads. he resuls sugges ha he 34

37 aggregae liquidiy measure and esimaed sensiiviies o marke-wide liquidiy capure he liquidiy feaures of municipal bonds very well. Invesors require higher yields for bonds wih higher liquidiy risk and he size of his liquidiy spread is of economic significance. V. Conclusions Previous sudies have been unable o explain he municipal puzzle associaed wih long-erm yields. Green (993) suggess ha dealer arbirage aciviies in he marke for reasury bonds subsanially reduce he impac of axes on long-mauriy axable bond prices and herefore reduce yields of axable bonds relaive o yields of ax-exemp bonds. Alhough his sudy shows ha his arbirage facor had explanaory power for he spread beween long-erm municipal bonds and reasuries, a subsanial porion of he long-erm municipal spread was sill lef unexplained. A possible reason is ha he effecs of defaul and liquidiy risk were lef ou. In his paper, we propose a generalized model ha incorporaes he effecs of liquidiy, defaul risk and personal axes on municipal bond yields. he model explains he yields of municipal bonds relaive o hose of reasury bonds very well. We find ha long-erm municipal bond yields are higher han he equivalen afer-ax reasury yields largely because boh liquidiy risk and defaul risk are higher. On he oher hand, he ax effec appears o be quie sable over mauriies. Empirical evidence shows ha liquidiy risk is an imporan deerminan of municipal bond yields. A subsanial porion of municipal bond yields is aribuable o liquidiy risk. he sensiiviy of municipal yields o marke-wide liquidiy increases monoonically wih credi risk and mauriy. Liquidiy premiums are higher for bonds 35

38 wih lower raings. More imporanly, he liquidiy premium in percenage of observed municipal yields increases over mauriies, which conribues significanly o he high yields of long-erm municipal bonds relaive o reasuries. For AAA municipals, he liquidiy premium increases from 7 o 3 percen of he observed yield, or from 4 o 65 basis poins as bond mauriy increases from one o 20 years. he gap is even wider for BBB bonds, which increases from 8 o 20 percen of he observed yield, or from 23 o basis poins. hus, a subsanial porion of he mauriy premium for long-erm municipal bonds is due o he liquidiy premium. In addiion, defaul risk significanly affecs yields of municipal bonds. he effec of defaul risk is sronger for lower-qualiy and longer-mauriy bonds. his defaul effec parially explains why yields of municipal bonds end o be high relaive o yields of reasuries of equal mauriy, especially for long-mauriy bonds. Consisen wih previous findings, personal axes are an imporan deerminan of he relaive municipal yield. Unlike pas sudies, our esimaes of implici ax raes are very close o he maximum sauory income ax raes of high-income individuals and corporaions. Furhermore, hese implici ax rae esimaes are remarkably sable over mauriies. he anomalies of declining implici income ax raes over mauriies documened in previous sudies disappear afer we conrol for he effecs of liquidiy and defaul risk. Finally, when we furher sor municipal bonds ino porfolios based on he radiional variables of liquidiy, we find ha liquidiy spreads esimaed from he yield model are highly correlaed wih hese variables. hus, he model appears o capure he liquidiy risk of municipal bonds quie well. Our findings sugges ha liquidiy risk 36

39 should be accouned for in order o explain more saisfacorily he relaive yields of axexemp and axable bonds. 37

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42 Liu, S. X., J. Wang and C. Wu, 2003, Effecs of credi qualiy on he relaion beween ax-exemp and axable yields, Journal of Fixed Income 3, Longsaff, F. A., S. Mihal and E. Neis, 2005, Corporae yield spreads: Defaul risk or liquidiy? New evidence from he credi-defaul swap marke, Journal of Finance, forhcoming. Miller, M., 977, Deb and axes, Journal of Finance 32, Mussa, M. L. and R. C. Kormendi, 979, he axaion of Municipal Bonds, American Enerprise Insiue, Washingon DC. Pasor, L. and R. F. Sambaugh, 2003, Liquidiy risk and expeced sock reurns, Journal of Poliical Economy, Poerba, J. M., 986, Explaining he yield spread beween axable and ax-exemp bonds, in H. Rosen (ed.), Sudies in Sae and Local Public Finance, Universiy of Chicago Press, Chicago. Poerba, J. M., 989, ax reform and marke for ax-exemp deb, Regional Science and Urban Economics 9, Scholes, M. S. and M. A. Wolfson, 992, axes and Business Sraegy: A Planning Approach, Prenice-Hall, Englewood Cliffs, NJ. Skelon, J. L., 983, Relaive risk in municipal and corporae deb, Journal of Finance 38, Sock, D., 994, erm srucure effecs on defaul risk premia and he relaionship of defaul-risky ax-exemp yields o risk-free axable yields: A noe, Journal of Banking and Finance 8, rzcinka, C., 982, he pricing of ax-exemp bonds and he Miller hypohesis, Journal of Finance 37, Wu, C., 99, A cerainy equivalen approach o municipal bond defaul risk esimaion, Journal of Financial Research 4, Wu, C. and C. H. Yu, 996, Risk aversion and he yield of corporae deb, Journal of Banking and Finance 20, Yawiz, J. B., K. J. Maloney and L. H. Ederingon, 985, axes, defaul risk, and yield spreads, Journal of Finance 40, Zimmerman, J., 977, he municipal accouning maze: An analysis of poliical incenives, Journal of Accouning Research, supplemen,

43 able I Descripive Saisics Panel A of his able repors he mean and sandard deviaion of yields for he 2 porfolios formed by raing (AAA, AA/A, BBB) and mauriy (-, 2-, 3-, 5-, 7-, 0-, and 20-year) as well as he reasury yields of corresponding mauriy. We calculae he yield of each porfolio monh by monh and hen repor mean and sandard deviaion of hese monhly yield series. Panel B repors he monhly average of he number of ransacions, par amoun raded, and he number of bonds for municipal bond porfolios grouped by raings and mauriy. he sample period is from July 2000 o June Daa sources: he Federal Reserve Board, Bloomberg and he MSRB. Panel A. Yields of reasuries and Municipals Mauriy reasury Mean Sandard Deviaion Municipals reasury Municipals AAA AA/A BBB AAA AA/A BBB Panel B. rading Characerisics of Municipal Bond Porfolios Number of ransacions (per Par Volume Mauriy monh) (million) Number of Bonds AAA AA/A BBB

44 able II Summary Saisics for he Spreads of Municipal Bonds All yield series are monhly and repored as annual percenages. Panel A presens he mean, minimum and maximum of he spreads of he municipal bond porfolios formed by raing and mauriy. P is he yield spread beween reasury and AAA municipal bonds, PG is he yield spread beween AAA and AA/A municipal bonds; GM is he yield spread beween AA/A and BBB municipal bonds. Panel B repors he mauriy spreads for each raing class. Mauriy spread is calculaed by subracing from he yield for a given mauriy group he corresponding yield for one-year mauriy. *** represens significance a he % level. Panel A. Yield Spreads beween Differen Bonds Mauriy Mean Minimum Maximum P PG GM P PG GM P PG GM 0.58 *** 0.9 *** 0.53 *** *** 0.0 *** 0.52 *** *** 0.08 *** 0.5 *** *** 0.06 *** 0.5 *** *** 0.06 *** 0.58 *** *** 0.06 *** 0.53 *** *** 0.09 *** 0.46 *** Panel B. Mauriy Spreads Mean Minimum Maximum Mauriy reasury Municipal reasury Municipal reasury Municipal AAA AA/A BBB AAA AA/A BBB AAA AA/A BBB *** 0.34 *** 0.24 *** 0.23 *** *** 0.64 *** 0.52 *** 0.50 *** ***.7 ***.03 ***.02 *** ***.6 ***.47 ***.52 *** ***.92 ***.78 ***.78 *** *** 2.98 *** 2.88 *** 2.8 ***

45 able III Esimaes of he Municipal Yield Model his able repors parameer esimaes of defaul probabiliy, ax rae and liquidiy risk for he municipal yield model in (4), M = Λ + βc + β LL, where M is he yield on he municipal and C is he yield on he reasury of mauriy, and L is he innovaion of municipal marke-wide liquidiy. he sample period is from July 2000 o June All yield series are monhly. Municipal bonds are separaed ino hree differen raing caegories: AAA, AA/A and BBB, and seven mauriies. Sandard errors are repored in parenheses. *, ** and *** represen significance a he 0%, 5% and % levels, respecively. Mauriy ax Rae Defaul Probabiliy AAA AA/A BBB Liquidiy R 2 ax Rae Defaul Probabiliy Liquidiy R2 ax Rae Defaul Probabiliy Liquidiy R2 Value 33.7 *** 0.27 *** *** 32.63*** 0.33*** -0.07* 33.06*** 0.605*** -0.02*** Sd. Err (. 53) (0.02) (0.02) (.34) (0.03) (0.04) (3.2) (0.05) (0.03) Value *** 0.76 *** ** 32.59*** 0.273*** *** 32.67*** 0.728*** -0.20*** Sd. Err (.59) (0.04) (0.03) (.66) (0.04) (0.03) (3.6) (0.07) (0.03) Value 3.78 *** 0.8 *** ** 3.89*** 0.39*** *** 32.02*** 0.753*** -0.55*** Sd. Err (.72) (0.03) (0.02) (.88) (0.05) (0.03) (3.47) (0.08) (0.04) Value 32.6 *** *** *** 3.94*** 0.428*** -0.37*** 32.4*** 0.877*** -0.95*** Sd. Err (2.38) (0.07) (0.03) (2.5) (0.06) (0.04) (6.24) (0.6) (0.04) Value *** 0.57 *** ** 32.38*** 0.65*** -0.60*** 3.87*** 0.92*** *** Sd. Err (2.52) (0.07) (0.04) (2.7) (0.08) (0.04) (8.76) (0.24) (0.03) Value *** *** -0.9 *** 32.2*** 0.8*** -0.27*** 32.42*** 0.977** -0.39*** Sd. Err (3.72) (0.) (0.06) (3.43) (0.2) (0.05) (.75) (0.36) (0.05) Value *** ** *** 32.77*** 0.63*** -0.35*** 3.9***.2*** *** Sd. Err (7.35) (0.22) (0.05) (6.2) (0.8) (0.06) (7.58) (0.29) (0.06)

46 Mauriy able IV Componens of Municipal Bond Yields Repored below are observed yields, esimaed yields, he yield componen associaed wih ax, defaul and risk-free raes (nonliquidiy componen), and he componen associaed wih liquidiy risk for porfolios formed by raings and mauriy. he liquidiy and non-liquidiy componens are expressed boh in magniude (in percenage) and in he proporion of he observed spread. Yield AAA AA/A BBB Non-liquidiy Liquidiy Non-liquidiy Liquidiy Non-liquidiy Yield Yield Componen Componen Componen Componen Componen Liquidiy Componen Obs. Es. % % Yield % % Yield Obs. Es. % % Yield % % Yield Obs. Es. % % Yield % %Yield

47 able V Likelihood Raio ess his able repors he likelihood raio es saisics under he resricion ha he effec of liquidiy risk is equal o zero (i.e., β L = 0) in he nonlinear municipal yield model in (4). he es saisics follow an F disribuion wih (, n-3) degrees of freedom. he criical F value is 4.0 a he five percen level. Mauriy AAA Bonds AA/A Bonds BBB Bonds F (,n-3) F (,n-3) F (,n-3)

48 able VI Characerisics of Municipal Bonds his able repors he average coupon rae, issue size, volume and rade frequency of he municipal bond porfolios formed by raing and mauriy. We rank all bonds based on each characerisic and divide hem ino low, medium and high groups. Repored here are he characerisics of low and high groups. AAA AA/A BBB Mauriy Low High Low High Low High Coupon Issue Size (million) oal Volume (million) Frequency of rades

49 able VII Municipal Yields of Porfolios Ranked by Bond Characerisics his able repors average annualized yields of he low and high porfolios ranked by coupon raes, issue size, volume and frequency of rades. AAA AA/A BBB Mauriy Low High Low High Low High Coupon Issue Size (million) oal Volume (million) Frequency of rades

50 able VIII Liquidiy Risk Parameer Esimaes for Porfolios Ranked by Characerisics his able repors he esimaes of he liquidiy risk parameer ( β L ) for porfolios ranked by coupon, issue size, volume, and frequency of rades, respecively, for each raing and mauriy class. All parameer esimaes are significan a leas a he five percen level. Coupon Mauriy AAA AA/A BBB Low High Low High Low High Issue Size rading Volume Frequency of rades

51 Mauriy able IX Esimaes of Liquidiy Spreads for Differen Characerisic Porfolios his able repors he esimaes of liquidiy risk premium in magniude (%) and proporion of he observed spread (% yield) for each high and low porfolio ranked by coupon raes, issue size, volume, and frequency of rades, respecively, for each raing and mauriy class. Coupon AAA AA/A BBB Low High Low High Low High % % Yield % % Yield % % Yield % % Yield % % Yield % % Yield Mean Issue Size Mean rading Volume Mean Frequency of rades Mean

52 Figure. Yields for Differen Municipal Raing/Mauriy Porfolios and reasuries Monhly yield series are ploed from July 2000 o June 2004 for differen raing porfolios and reasuries wih mauriies of, 2, 3, 5, 7 and 0 years Monh 06/200 06/ /2003 year AAAyear AA/Ayear BBByear 0 Monh 06/200 06/ / year AAA2 year AA/A2 year BBB2 year Monh 06/200 06/ / year AAA3 year AA/A3 year BBB3 year 0 Monh 06/200 06/ / year AAA5 year AA/A5 year BBB5 year Monh 06/200 06/ / year AAA7 year AA/A7 year BBB7 year 0 Monh 06/200 06/ / year AAA0 year AA/A0 year BBB0 year 50

53 Figure 2. Aggregae Municipal Marke Liquidiy and Innovaions of Liquidiy Panel A shows he ime series of aggregae municipal marke liquidiy while Panel B shows he innovaions of municipal marke liquidiy. Liquidiy and is innovaions are expressed in percenage erms on he verical axis. We use he innovaion series o esimae sysemaic liquidiy risk. Panel A: Aggregae Municipal Bond Marke Liquidiy 0 Aggregae Marke Liquidiy Monh 2/ /200 2/200 06/2002 2/ /2003 2/2003 Panel B: Innovaions in Liquidiy 0.0 Innovaions of Marke Liquidiy Monh 2/ /200 2/200 06/2002 2/ /2003 2/2003 5