Unsystematic Risk. Xiafei Li Cass Business School, City University. Joëlle Miffre Cass Business School, City University

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1 The Universiy of Reading Momenum Profis and Time-Varying Unsysemaic Risk Xiafei Li Cass Business School, Ciy Universiy Joëlle Miffre Cass Business School, Ciy Universiy Chris Brooks ICMA Cenre, Universiy of Reading 6 h Sepember 006 ICMA Cenre Discussion Papers in Finance DP Copyrigh 006 Li, Miffre and Brooks. All righs reserved. ICMA Cenre The Universiy of Reading Whieknighs PO Box 4 Reading RG6 6BA UK Tel: +44 (0) Fax: +44 (0) Web: Direcor: Professor John Board, Chair in Finance The ICMA Cenre is suppored by he Inernaional Capial Marke Associaion

2 ABSTRACT This sudy assesses wheher he widely documened momenum profis can be ascribed o imevarying risk as described by a GJR-GARCH(1,1)-M model. Consisen wih raional pricing in efficien markes, we reveal ha momenum profis are a compensaion for ime-varying unsysemaic risks, common o he winner and loser socks. We also find ha, because losers have a higher propensiy han winners of disclose bad news, negaive reurn shocks increase heir volailiy more han i increases ha of he winners. The volailiy of he losers is also found o respond o news more slowly, bu evenually o a greaer exen, han ha of he winners. Following Hong e al. (000), we inerpre his as a sign ha managers of loser firms are relucan o disclosing bad news, while managers of winner firms are eager o releasing good news. Keywords: Momenum profis, Common unsysemaic risk, GJR-GARCH(1,1)-M JEL classificaions: G1, G14 This version: 31 Augus 006 AUTHOR FOR CORRESPONDENCE: Professor Chris Brooks ICMA Cenre, Business School, The Universiy of Reading PO Box 4, Reading RG6 6BA, Unied Kingdom c.brooks@icmacenre.rdg.ac.uk Tel: +44 (0) Fax: +44 (0)

3 ICMA Cenre Discussion Papers in Finance: DP Inroducion Momenum sraegies ha buy recen winners and sell recen losers are profiable over shor horizons of 3 o 1 monhs (Jegadeesh and Timan, 1993). Price coninuaion has prevailed over ime (Jegadeesh and Timan, 001), across counries (Griffin e al., 003; Liu e al., 1999; Ellis and Thomas, 003), across indusries (Moskowiz and Grinbla, 1999), equiy syles (Chen and De Bond, 004) and asse classes (Okunev and Whie, 003). While he profiabiliy of he relaivesrengh porfolios is no dispued, here is sill a lo of conroversy as o why hese abnormal reurns occur. Two explanaions have been pu forward. The firs is based on psychology and marke inefficiency. Behavioral proponens relae price underand over-reacion o cogniive errors ha invesors make when incorporaing informaion ino prices. For example, invesors may be oo quick o draw he conclusion ha a given sock follows a paricular ideal ype (he represenaiveness heurisic), and hey may be oo slow o updae heir beliefs when confroned wih new, especially conradicory, evidence (he conservaism bias). These behavioral aribues lead firs o momenum as sock prices reac wih delay o firm-specific informaion and, once deviaions from equilibrium are acknowledged, o subsequen mean reversion (Barberis e al., 1998; Daniel e al., 1998; Hong and Sein, 1999). 1 This suggess ha he irraionaliy from which agens suffer may push prices away from fundamenals and allow profiable mispricings o survive. The second explanaion relies on he noion of marke efficiency and argues ha he reurns of he relaive-srengh porfolios are a fair compensaion for he risk and/or rading coss of implemening he sraegies. On balance, however, he evidence suggess ha he profiabiliy of he relaive-srengh porfolios is no solely a compensaion for exposure o higher risks (Jegadeesh and Timan, 1993; Chan e al., 1996; Fama and French, 1996; Griffin e al., 003; Karolyi and Kho, 004; Sadka, 006). Sudies ha allow for ime-variaion in sysemaic risks reach conflicing conclusions. While Chordia and Shivakumar (00), Wu (00) and Wang (003) explain he profiabiliy of he momenum sraegies hroughou ime-variaion in expeced reurns, Grundy and Marin (001), Griffin e al. (003) and Nagel and Lewellen (003) argue ha he momenum 1 Oher behavioral deficiencies ha invesors may suffer from include biased self-aribuion and overconfidence (Daniel e al., 1998) and bounded raionaliy (Hong and Sein, 1999). Jegadeesh and Timan (1993) esimae a marke model, o which Chan e al. (1996) and Fama and French (1996) add he reurn of porfolios sored on size and book-o-marke value. Griffin e al. (003) look a macroeconomic and financial facors ha are in he spiri of he model of Chen e al. (1986). Sadka (006) looks a he role of liquidiy risk. Karolyi and Kho (004) use boosrap experimens and a wide range of reurn-generaing processes. Copyrigh 006 Li, Miffre and Brooks 1

4 ICMA Cenre Discussion Papers in Finance: DP reurns are oo large o be accouned for in erms of ime-varying risks. I is imporan o noe also ha a raionale relaed o ransacion coss has been pu forward as an explanaion for he momenum profis. Lesmond e al. (004) indeed argue ha he momenum profis have lile o do wih risk as hey are simply an illusion induced by rading coss. 3 The conribuion of his aricle o he momenum lieraure is wih regards o he ime-varying unsysemaic risk of he winners and he losers and o he role i may have in explaining he abnormal reurns of momenum sraegies. While several sudies look a variaions in sysemaic risk (Grundy and Marin, 001; Chordia and Shivakumar, 00; Wu, 00; Griffin e al., 003; Wang, 003; Nagel and Lewellen, 006), his sudy is he firs o look a variaions in he unsysemaic risks of he winner and loser porfolios. We do his wihin a GJR-GARCH(1,1)-M framework. 4 The raionale for choosing a GJR formulaion of he GARCH(1,1)-M model sems from he suggesion ha follows. Le us assume ha losers have a propensiy o disclose bad firm-specific news and ha his explains heir underperformance in he holding period. Vice versa, le us assume ha winners have a endency o disclose good firm-specific news and, as a resul, hey ouperform in he holding period. Since he probabiliy of he losers disclosing bad firm-specific news far exceeds ha of he winners, we canno assume ha he winners and he losers will have he same response o negaive reurn shocks. Mos likely, bad news will increase he volailiy of he losers more han i increases ha of he winners. A failure o explicily model he asymmeric response of he losers and winners o bad news migh herefore lead us o under-esimae he volailiy of he losers, and consequenly heir performance, following a price drop or o over-esimae he volailiy of he winners, and consequenly heir performance, following a price rise. This moivaes our hypohesis ha he momenum profis migh, a leas in par, be a compensaion for an asymmeric response of winners and losers o negaive reurn shocks. We draw he following wo conclusions from our analysis. Firs, we idenify some clear paerns in he volailiy of he winner and loser porfolios. The volailiy of he winners is found o be more sensiive o recen news han ha of he losers, whereas by conras, he volailiy of he losers is found o be more sensiive o disan news han ha of he winners. Besides, he volailiy of he losers (wih an average volailiy half-life of 4 3 Lesmond e al. (004) show ha momenum sraegies are highly rading inensive and pick up socks ha are expensive and risky (small, high bea, illiquid, off-nyse exreme performers). Besides, he momenum profis are mainly driven by he losers (Hong e al., 000) and hus shorsale coss also need o be aken ino accoun. 4 GJR-GARCH(1,1)-M sands for Glosen e al. (1993) Generalized Auoregressive Condiional Heeroscedasiciy of order 1,1 wih a Mean erm ha models he condiional risk premium. A number of sudies (Nelson, 1991; Glosen e al., 1993; Rabemananjara and Zakoian, 1993) show ha good news (measured by posiive reurn shocks) and bad news (measured by negaive reurn shocks) have an asymmeric impac on he condiional variance of sock reurns. Copyrigh 006 Li, Miffre and Brooks

5 ICMA Cenre Discussion Papers in Finance: DP monhs and 13 days) shows a higher level of persisence han ha of he winners (whose volailiy half-life only equals 3 monhs and 5 days on average). These resuls are consisen wih he findings of Hong e al. (000). Borrowing heir analysis, he sluggish response of losers o (presumably bad) firm-specific news may arise from he relucance of managers of low analys coverage firms o disclose bad news. Vice versa, he rapid response of winners o (in all probabiliy good) firmspecific news could be inerpreed as a srong markeing push of managers of low analys coverage firms o disclose good news. This in urn explains he rapid response of winners, and he sluggish response of losers, o firm-specific announcemens. In oher words, o Hong e al. (000) saemen: bad news ravels slowly, we could add our own: good news ravels fas. We idenify anoher ineresing paern in he volailiy of he winner and losers. Relaive o he volailiy of he winners, he volailiy of he losers clearly shows an asymmeric response o good and bad news: bad news subsanially increases he volailiy of he losers, while i does no impac ha of he winners. This is in line wih wha we expeced. Since, relaive o winners, losers have a higher probabiliy of disclosing bad news, negaive reurn shocks increase heir volailiy more han i increases ha of he winners. The second conclusion of his aricle is wih regards o he hypohesis ha he momenum reurns are a compensaion for ime-varying unsysemaic risk as modeled by he GJR-GARCH(1,1)-M model. We show ha he GJR-GARCH(1,1)-M erms, when added o he radiional marke and Fama and French models, explain he abnormal performance of he momenum sraegies wihou he need o resor o he ransacions cos and illiquidiy issues ha were he focus of Lesmond e al. (004) or Sadka (006). Ineresingly, neiher he GJR-GARCH(1,1) nor he GARCH(1,1)-M specificaions alone could accoun for he abnormal reurn of he relaive-srengh porfolios. I is herefore boh he asymmeric response of he losers o good and bad news and he condiional risk premium embedded in he GARCH(1,1)-M model ha explain he profiabiliy of he momenum sraegies. Alogeher, he resuls indicae ha momenum profis are a compensaion for imevarying unsysemaic risks common o he winners and losers and are herefore consisen wih raional pricing in efficien markes. The remainder of he paper is organized as follows. Secion inroduces he daase, he mehodology employed o consruc he momenum porfolios and he models used o adjus for risk. Secion 3 analyzes how recen news, disan news and negaive reurn shocks impac he volailiy of he winners and losers. I also ess wheher he momenum profis are a compensaion for ime-varying unsysemaic risk common o he winners and losers. Finally, secion 4 concludes he paper wih a summary of our findings. Copyrigh 006 Li, Miffre and Brooks 3

6 ICMA Cenre Discussion Papers in Finance: DP Daa and Mehodology Monhly UK sock prices adjused for dividends are obained from he London Share Price Daabase over he period 8 February 1975 o 31 December To address problems of survivorship bias, we also include socks ha were delised due o merger, acquisiion or bankrupcy. The sample includes all companies wih a leas 3 monhs of available reurns. A oal of 6,155 companies are considered. All socks are ranked in 10 equally-weighed porfolios based on heir pas J-monh cumulaive reurns (J = 3, 6, 1 monhs). The decile porfolio wih he highes cumulaive reurn is ermed he winner porfolio, while he decile porfolio wih he lowes cumulaive reurn is called he loser porfolio. The reurn on he momenum porfolio is hen measured as he reurn difference beween he winner and loser porfolios over he nex K monhs (K = 3, 6, 1 monhs). 6 The resuling porfolio is referred o as he J-K momenum porfolio. The procedure is rolled forward a he end of each holding period o produce new winner, loser and momenum porfolios. The formaion of he relaive-srengh porfolios is herefore non-overlapping, hus reducing he rading frequency and he ransacion coss incurred in porfolio consrucion and ensuring ha saisical ess are valid wihou requiring modificaion of he sandard errors. Our framework is also more realisic in erms of he behavior of invesors han one based on overlapping porfolios where hey would presumably have o vary he amoun of wealh devoed o he sraegies over ime. Tradiionally, performance has been measured by regressing a porfolio s reurns on a se of sysemaic risk facors emanaing from he CAPM of Sharpe (1964) or he hree-facor model of Fama and French (1993), which can be expressed respecively as R R ( RM Rf) ε ( RM Rf) + ssmb + hhml ε = α + β + (1) = α + β + () where R is eiher he reurn on he momenum porfolio or he reurn of he winner and loser porfolios in excess of he risk-free rae, R f is he hree-monh Treasury bill rae, R M is he valueweighed marke reurn on all socks quoed on he London Sock Exchange, SMB and HML are UK-based reurns of Fama and French (1993) size and book-o-marke value porfolios as provided by Nagel 7 and ε is a whie noise error erm. The performance of he porfolios is hen evaluaed by esing he saisical significance of he α coefficien in (1) and (). 5 The reurns o he Fama-French facor porfolios ha we employ subsequenly are only available o December 001, which necessiaes his runcaion of our sample period. 6 We also employed holding periods of 15 monhs duraion, bu he resuls were qualiaively idenical o hose employing a 1-monh horizon and are herefore no repored. Copyrigh 006 Li, Miffre and Brooks 4

7 ICMA Cenre Discussion Papers in Finance: DP Embedded in equaions (1) and () is he assumpion ha ε ~ N( 0, σ ) and, hus, ha here is no condiional volailiy in he marke. Since Engle (198), numerous sudies have been wrien on he family of GARCH models (Poon and Granger, 003; Andersen e al., 006; Bauwens e al., 006). The araciveness of he GARCH models sems from he fac ha hey model he condiional variance of asse reurns by aking ino accoun persisence in volailiy (where volailiy shocks oday influence expeced volailiy many monhs from now) and leverage effecs (where negaive reurn shocks impac volailiy more han posiive reurn shocks of he same magniude). These wo feaures are cenral o our hypoheses ha he loser s volailiy shows more persisence and asymmery han ha of he winners. We invesigae wheher momenum profis in he UK are a compensaion for ime-varying risk wihin GJR-GARCH(1,1)-M versions of he marke and Fama and French models: R σ R σ = α + β = ω+ γε = α + β = ω+ γε ( R R ) M f + δσ + ε 1+ ηi 1ε 1 + ( R R ) M f 1+ ηi 1ε 1 + θσ + ssmb 1 θσ + hhml 1 + δσ + ε where σ is he condiional variance of he winner, loser and momenum porfolios, δσ measures he ime-varying risk premium, γ and η relaes o he lagged squared error erm and measures he impac of recen news on volailiy, η also measures any asymmeric response of volailiy o bad and good news (commonly aribued o as leverage effec), I 1 = 1 if ε 1 < 0 (bad news, also called negaive reurn shock) and I 1 = 0 oherwise, θ relaes o he lagged condiional volailiy and measures he impac of old news on volailiy. (3) (4) Wihin he framework of sysems (3) and (4), he following wo hypoheses can be esed. Firs, he coefficiens on condiional volailiy indicae how news impacs he volailiy of he winners and of he losers. In paricular, we analyze he speed of he response of he winners and losers o news and es for he presence of any asymmery in he response of he winners and losers volailiy o good and bad news. Second, he sign and significance of α in he mean equaions of sysems (3) and (4) indicae wheher he momenum reurns are a compensaion for marke risk, he risks associaed wih size and book-o-marke value and ime-varying, unsysemaic risk. 7 These daa are available a hp://faculy-gsb.sanford.edu/nagel/daa/uk_fffac.csv Copyrigh 006 Li, Miffre and Brooks 5

8 ICMA Cenre Discussion Papers in Finance: DP We also es wheher he momenum profis can be explained by a simplified version of he above models in he sandard GARCH(1,1)-M framework. This specificaion models he ime-varying risk premium as in (3) and (4) bu does no allow for asymmeric response of volailiy o good and bad news. Pracically, his breaks down o esimaing he following sysems of equaions ( R R ) R = α + β M f + δσ + ε σ = ω + γε θσ ( R R ) R = α + β M f + ssmb + hhml + δσ + ε σ = ω + γε θσ (5) (6) 3. Empirical Resuls Table 1 presens summary saisics for he winner, loser and momenum porfolios. The rows represen he ranking periods (J = 3, 6 and 1 monhs) and he columns he holding periods (K = 3, 6 and 1 monhs). I is clear from his able ha he winners sysemaically ouperform he losers a he 1% level. Across sraegies, he momenum porfolios earn an average reurn of a monh, wih a range from for he 3-3 sraegy o for he 6-6 sraegy. 8 These resuls corroborae hose of Liu e al. (1999) and Ellis and Thomas (003) for he UK. << Inser Table 1 around here >> Table 1 also repors he monhly sandard deviaions and reward-o-risk raios of each porfolio reurns. Consisen wih raional expecaions, he momenum porfolios wih higher reurns have also more risk. For insance, he 6-6 sraegy earns he highes average reurn (0.0193) and, wih a sandard deviaion of , i is also he second mos volaile sraegy. Wih a reward-o-risk raio of , he 1-6 sraegy generaes he highes average reurn in risk-adjused erms, while he 3-3 sraegy offers he lowes risk-adjused reurn (0.195). The conribuion of he aricle is wih regards o he ime-varying unsysemaic risk of he winner and loser porfolios and he impac ha i may have on momenum profis. Wih his in mind, we firs analyze he performance of he winner, loser and momenum porfolios wihin he sandard marke and Fama and French models and hen allow for ime-varying unsysemaic risk hrough differen specificaions of he GARCH(1,1) model. While doing his, we will also analyze he impac of recen news, old news and bad news on he volailiy of he winners and losers. 8 Noe ha all figures in his sudy refer o monhly proporion reurns raher han percenage reurns, unless oherwise saed. Copyrigh 006 Li, Miffre and Brooks 6

9 ICMA Cenre Discussion Papers in Finance: DP Saic marke and Fama and French models Table repors he OLS esimaes of he marke and Fama and French models (1) and () for he winner, loser and momenum porfolios. 9 In line wih previous research (Jegadeesh and Timan, 1993; Fama and French, 1996; Karolyi and Kho, 004), he resuls indicae ha radiional versions of he marke and Fama and French models fail o explain momenum profis. Regardless of he model, of he ranking period, and of he holding period, he α coefficiens of he momenum sraegies in equaions (1) and () are posiive and significan a he 1% level. The momenum profis esimaed from he marke model range from (3-3 sraegy) o (6-6 sraegy), wih an average reurn a a monh. According o he Fama and French model, he winners ouperform he losers by on average, wih a range of (3-3 sraegy) o 0.0 (1-6 sraegy). << Inser Table around here >> While sysemaic risk explains mos of he over-performance of he winners, i fails o accoun for he under-performance of he losers. Irrespecively of he ranking period, of he holding period and of he risk model considered, he losers indeed have negaive alphas ha are significan a he 1% level. As in Hong e al. (000), he momenum profis are herefore driven by he losers. The facor loadings on R M, SMB and HML in (1) and () sugges ha he winner and loser porfolios end o pick small capializaion socks (s>0) wih high marke risk (β>0). The winners have growh characerisics (h<0) and he losers have value characerisics (h>0). The momenum sraegies are predominanly marke-neural (β=0) and size-neural (s=0) and have negaive loadings on HML. These resuls are consisen wih hose previously repored, including he sudies by Chan e al. (1996) and Liu e al. (1999). 3.. GARCH(1,1) versions of marke and Fama and French models Table 3 repors esimaes of he marke and Fama and French models (3) and (4) ha include a GJR-GARCH(1,1)-M erm. To faciliae reading, he averages across ranking and holding periods of he coefficien esimaes are repored on he lef-hand side of Table 4 for he winners, losers and momenum porfolios. The esimaion mehod is Maximum Likelihood wih Bollerslev-Wooldridge robus sandard errors. We firs analyze how news, wheher i is recen, disan or negaive, impacs he volailiy of he winners and he losers. We subsequenly es for wheher he ime-varying unsysemaic risk common o he winners and losers explains he profiabiliy of he momenum sraegies. 9 Engle (198) s ARCH-LM es provides srong evidence of heeroscedasiciy in he OLS residuals of he marke and Fama-French models. Hence, we use Whie s heeroscedasiciy-robus sandard errors. Copyrigh 006 Li, Miffre and Brooks 7

10 ICMA Cenre Discussion Papers in Finance: DP << Inser Tables 3 and 4 around here >> The paern of condiional volailiy The coefficiens γ and η in sysems (3) and (4) relae o he lagged squared error erm and, herefore, o he impac of recen news on volailiy. The average γ+η/ of he condiional marke model in Table 4 equals for he winners and 0.16 for he losers. The average γ+η/ of he condiional Fama and French model is for he winners and for he losers. Clearly, recen news impacs he volailiy of he winners more han i impacs ha of he losers. Wih only one excepion (for he 3-3 winner in he Fama and French model), he conclusion holds hroughou in Table 3, irrespecive of he ranking period, of he holding period and of he model considered. The coefficien θ in sysems (3) and (4) reflecs he effec of lagged condiional variance and capures he impac of old news on volailiy. The resuls of he condiional marke model in Table 4 indicae ha he average θ coefficien of he winners (0.5785) is lower han ha of he losers (0.7911). The same conclusion applies o he condiional Fama and French model, for which he winners have an average θ coefficien of and he losers an average θ coefficien of I is clear herefore ha old news has more impac on he volailiy of he losers han on he volailiy of he winners. Looking a he esimaes of θ in Table 3, i appears ha he conclusion holds for he vas majoriy of he porfolios, he 1-1 winner in he marke model being he only excepion. The asymmeric coefficiens (η) in Tables 3 and 4 sugges ha bad news has differen impacs on he volailiy of he winners and on he volailiy of he losers. For he losers, he mean of he η coefficiens is for he condiional marke model and 0.03 for he condiional Fama and French model. Wih only a few excepions, hese coefficiens are significan a he 5% level in Table 3. Clearly, herefore, bad news increases he volailiy of he losers. For he winner porfolios, however, he average η coefficien in Table 4 equals for he condiional marke model and for he condiional Fama and French model, wih 14 ou of 18 coefficiens ha are insignifican a he 5% level in Table 3. I follows ha he announcemen of bad news does no have any noiceable impac on he volailiy of he winners. I may be he case ha socks whose recen performance has already been poor are hi much harder by furher bad news han socks recenly performing well, which are able o absorb bad news more easily. The evidence of Tables 3 and 4 hus far indicaes ha, wih relaively few excepions, he losers have higher η and θ, and lower γ, han he winners. Tables 3 and 4 also repor he persisence in volailiy of he winners and losers, measured as γ+η/+θ. The volailiy of he losers appears o be Copyrigh 006 Li, Miffre and Brooks 8

11 ICMA Cenre Discussion Papers in Finance: DP more persisen han ha of he winners. Indeed, he average γ+η/+θ of he losers (winners) equals (0.8339) for he condiional marke model and (0.7885) for he condiional Fama and French model. For he condiional marke model, his convers ino volailiy half-lives of 3 monhs and 18 days for he winners and 8 monhs for he losers. The volailiy half-lives esimaed from he condiional Fama and French model equal monhs and 0 days for he winners and 18 monhs for he losers. Clearly and wih only one excepion ou of 18 regressions 10, he volailiy persisence of he losers exceeds ha of he winners. The srong impac of old news idenified for he losers and he persisence in heir volailiy are in suppor of he saemen of Hong e al. (000) ha bad news ravels slowly. When a firm wih no or low analys coverage receives bad news, is managers are likely o wihhold ha news as disclosing i would pu downward pressure on price. Since losers are more likely han winners o si on bad news, hey are also more likely o wihhold informaion. For he losers, his convers ino higher volailiy persisence (or higher volailiy half-lives) and higher sensiiviy of volailiy o disan news. The resuls in Tables 3 and 4 also give credence o our own proposiion ha, for winners, good news ravels fas. Managers of no or low coverage firms have srong incenives o disclose good news he minue i arrives as his simulaes he share price. Since winners are, by definiion, more likely han losers o receive good news, hey are more eager o disclose informaion. This convers in our seing ino a higher sensiiviy of winners volailiy o recen news and less volailiy persisence (or lower volailiy half-lives). Finally, we explain he asymmeric response of losers o negaive reurns shocks as follows. Relaive o winners, he probabiliy ha losers disclose bad news is far greaer. Thus he announcemen of a bad piece of news does no aler he volailiy of winners (as bad news is expeced o be ransiory only) while i pushes up ha of losers. When losers do disclose bad news, invesors inerpre his as a sign ha heir beliefs were correc, leading hem o sell he losers. As a resul, heir volailiy increases and becomes more persisen. The impac of ime-varying firm specific risk on momenum profis Tables 3 and 4 also repor, hrough δ, he impac of condiional volailiy on he reurns of he winners, losers and momenum porfolios. An increase in condiional volailiy decreases he reurn of boh he winners and he losers, bu increases he momenum reurns. The δ coefficiens of he momenum porfolios from he condiional marke model range from (1-6 sraegy) o (6-3 sraegy) (Table 3) wih an average a in Table 4. 6 (9) coefficiens ou of 9 are significan a he 5% (10%) level. Similar resuls are repored for he condiional Fama and French 10 The excepion is for he 1-1 winner in he condiional marke model (Table 3). Copyrigh 006 Li, Miffre and Brooks 9

12 ICMA Cenre Discussion Papers in Finance: DP model, for which δ equals on average, wih 6 (8) coefficiens ou of 9 ha are significan and posiive a he 5% (10%) level. This suggess ha here is a posiive relaionship beween imevarying risk and momenum reurn: A 1% increase in condiional volailiy leads, on average, o a 0.43% increase in monhly momenum reurns. The facor loadings on R M, SMB and HML for he condiional volailiy model in Table 3 indicae ha he winners and he losers have value characerisics (h>0) and are iled owards smallcapializaion socks (s>0) wih high marke risk (β>0). The laer wo characerisics appear o corroborae he evidence from he uncondiional Fama and French model (Table ). As he loadings of he losers on R M, SMB and HML are ypically higher han hose of he winners, he momenum porfolios have coefficiens on he hree Fama and French facors ha are predominanly negaive. The main conribuion of his paper is o es wheher he momenum profis are a compensaion for ime-varying unsysemaic risk as described by he GJR-GARCH(1,1)-M model. If his is indeed he case, hen he α coefficiens of he momenum sraegies should be saisically indisinguishable from zero when hese erms are incorporaed ino he risk aribuion model. This conjecure is suppored uniformly a he 5% level for boh he condiional marke and Fama and French models. The GJR-GARCH(1,1)-M marke model is able o explain he momenum reurns, since he alpha esimaes are reduced boh in magniude and in saisical significance. The alphas indeed range from (1-3 sraegy) o (1-6 sraegy), wih a mean a The GJR- GARCH(1,1)-M Fama and French model does a good job of explaining he momenum profis oo, wih an average alpha of and a range of (1-3 sraegy) o (6-6 sraegy). Clearly, he resuls of Tables, 3 and 4 sugges ha adding a GJR-GARCH(1,1)-M srucure o he models radiionally used o measure performance is crucial o explaining he abnormal reurn of momenum sraegies. Ineresingly, he considerable reducion in relaive price srengh reurns afer allowing for ime-varying risk seems o sem from an increase in he performance of he loser porfolios. This suggess ha he underperformance of he losers idenified in Table is in par due o heir sluggish and asymmeric reacion o bad news. Robusness of he resuls o he specificaion of he GARCH(1,1) model In his secion, we es wheher he momenum profis can be explained by a simplified version of he condiional models. Table 5 repors he parameer esimaes of sysems (5) and (6) for he winner, loser and momenum porfolios. Table 5 herefore assumes ha he reurn and condiional Copyrigh 006 Li, Miffre and Brooks 10

13 ICMA Cenre Discussion Papers in Finance: DP volailiy of he momenum porfolios are beer described by a GARCH(1,1)-M model. 11 To faciliae reading, he averages of he coefficien esimaes are also repored on he righ-hand side of Table 4. << Inser Table 5 around here >> The omission of he leverage effec in Table 5 does no aler he main conclusions of Table 3 wih regards o he paern of volailiy for he winners and he losers. For example, Tables 3, 4 and 5 all documen ha he volailiy of he winners (W) is more sensiive o recen news han he volailiy of he losers (L); namely, γ W > γl. Similarly, he impac of old news on volailiy in Tables 3, 4 and 5 is sronger for he losers; namely, θ L > θw. Finally, volailiy in all hree ables is found o be more persisen for he losers; namely, γl + ηl + θl > γ W + ηw + θw in Table 3 and γ L + θ L > γ W + θw in Table 5. 1 As a resul, he average volailiy half-lives are much smaller for he winners han for he losers. Across GARCH specificaions, ranking periods, and holding periods, he volailiy half-life of he winners is 3 monhs and 5 days on average, while ha of he losers is 4 monhs and 13 days. The omission of he leverage effec however has a direc impac on he significance of he imevarying risk parameer δ in Table 5. Ou of he 18 δ coefficiens esimaed for he momenum sraegies in Table 3, 17 were significan a he 10% level. When, as in Table 5, he impac of news on volailiy is assumed o be symmeric, he number of significan δ coefficiens drops o 3. As a resul, he marke and Fama and French models wih GARCH(1,1)-M erms are less able o explain he momenum profis. Though largely insignifican in Table 5, he average abnormal reurns of he momenum sraegies in Table 4 equal a monh for he GARCH(1,1)-M marke model and for he GARCH(1,1)-M Fama and French model. These average α coefficiens are in excess of he and average abnormal reurn repored on he lef-hand side of Table 4 for he GJR-GARCH(1,1)-M marke model and he GJR-GARCH(1,1)-M Fama and French model, respecively. 11 We also examined a pure GJR-GARCH(1,1) ha is, a model wihou a condiional volailiy erm in he mean equaion. However, unsurprisingly, i did no explain he observed momenum profis since in such a model, here is no linkage beween he ime-varying volailiy and he reurns. Therefore, he esimaes from his model are no included in he paper, bu are available from he auhors on reques. 1 Again here are a few excepions ( γ L > γw for he 3-3 and 3-1 winners of he condiional Fama and French model) bu hese are exremely rare. Copyrigh 006 Li, Miffre and Brooks 11

14 ICMA Cenre Discussion Papers in Finance: DP To summarize, he evidence in Tables 3, 4 and 5 suggess ha i is boh he asymmeric response of he losers o good and bad news and he condiional risk premium ha explain he profiabiliy of he momenum sraegies. Neiher he leverage effec, nor he condiional risk premium in isolaion can explain he abnormal performance of he momenum sraegies. I is he ineracion beween wo ha drives he momenum reurns. To judge he relaive meris of models (1) o (6), he Akaike informaion crierion (AIC) is calculaed for he winners, losers and momenum porfolios. AIC rades off beer model fi for greaer numbers of parameers, and hus a preferred model is one wih he lowes value of he crierion. The resuls are repored in Table 6 for differen specificaions of he marke and Fama and French models. These specificaions include he saic models (1) and (), he GJR- GARCH(1,1)-M models (3) and (4), and he GARCH(1,1)-M models (5) and (6). << Inser Table 6 around here >> For a given specificaion of he risk-reurn relaionship, he daa always favor he Fama and French model over he marke model. This indicaes ha he size and book-o-marke value risk facors add explanaory power o he models over and above ha provided by he marke reurn. More perinen o our sudy, he daa evidenly prefer he GJR-GARCH(1,1)-M models o he saic approaches. The GJR-GARCH(1,1)-M marke and Fama and French models have he lowes AIC in he vas majoriy of he cases, and never rank las in erms of AIC. These resuls for he GJR- GARCH (1,1)-M models compare favorably o he AIC of he GARCH(1,1)-M. Irrespecive of he ranking and holding periods, he saic versions of he marke and Fama and French model sand ou as having he highes values of he AIC. This suggess ha ou of he hree specificaions of he marke and Fama and French models, he saic versions provide he wors accoun of he reurns of he winner, loser and momenum porfolios, while he ime-varying condiional volailiy models allowing for asymmeries provide he bes. 4. Conclusions This aricle considers wheher he widely documened momenum profis are a compensaion for ime-varying unsysemaic risk as described by he family of auoregressive condiionally heeroscedasic models. The moivaion for esimaing a GJR-GARCH(1,1)-M model sems from he fac ha, since losers have a higher probabiliy han winners o disclose bad news, one canno assume a symmeric response of volailiy o good and bad news. Neiher can we presuppose ha he speed of adjusmen of volailiy o news is he same for he winners and he losers. This suggesion sems from he fac ha for firms wih no or low analyss coverage bad news ravels Copyrigh 006 Li, Miffre and Brooks 1

15 ICMA Cenre Discussion Papers in Finance: DP slower han good news (Hong e al., 000) and hus, he volailiy of he losers may respond more slowly o news han ha of he winners. The resuls sugges ha he ime-varying unsysemaic volailiy of he winners indeed differs from ha of he losers. For example, he volailiy of he winners is found o be more sensiive o recen news and less persisen han ha of he losers. The converse, ha he volailiy of he losers is found o be more sensiive o disan news and more persisen han ha of he winners, also holds. This gives suppor o he idea ha he ime-varying risk of companies wih no or low analys coverage depends on he naure of he informaion ha is been disclosed: Good news is disclosed earlier, and impacs volailiy sooner, han bad news. Relaive o he volailiy of he winners, ha of he losers also clearly shows a more asymmeric response o good and bad news. As losers have a higher propensiy o disclose bad news, negaive reurn shocks increase heir volailiy more han i increases ha of winners. We also documen ha he GJR-GARCH(1,1)-M models explain much of he profiabiliy of he momenum sraegies, and cerainly have more descripive power han he commonly used size and value risk facors. Ineresingly, neiher he GJR-GARCH(1,1) nor he GARCH(1,1)-M specificaions alone could accoun for he abnormal reurn of he relaive-srengh porfolios. I is herefore boh he asymmeric response of he losers o good and bad news, he sluggish response of losers o bad news and he condiional risk premium embedded in he GARCH(1,1)-M model ha explain he profiabiliy of he relaive-srengh porfolios. Alogeher, he resuls indicae ha he momenum profis are a compensaion for ime-varying unsysemaic risks ha are common o he winner and loser porfolios. The profiabiliy of momenum sraegies is herefore consisen wih raional pricing in efficien markes. Several sudies (Jegadeesh and Timan, 1993; Fama and French, 1996; Nagel and Lewellen, 006 o name a few) have highlighed he failure of he uncondiional and condiional asse pricing models o explain momenum reurns. We demonsrae ha resoring o behavioral facors microsrucure effecs as he only possible explanaion may be premaure. Copyrigh 006 Li, Miffre and Brooks 13

16 ICMA Cenre Discussion Papers in Finance: DP References Andersen, T. G., Bollerslev, T., Chrisoffersen, P. F., Diebold, F. X Volailiy and correlaion forecasing. In G. Ellio, C. W. J. Granger and A. Timmermann Eds.. Handbook of Economic Forecasing Amserdam: Norh-Holland. Barberis, N, Schleifer, A., Vishny, R., 1998, A model of invesor senimen. Journal of Financial Economics 49, Bauwens, L., Lauren, S., Rombous, J. V. K., 006. Mulivariae GARCH models: A survey. Journal of Applied Economerics 1, Chan L. K. C., Jegadeesh, N., Lakonishok, J., Momenum sraegies. Journal of Finance 51, Chen, H-L., De Bond, W., 004. Syle momenum wihin he S&P-500 index. Journal of Empirical Finance 11, Chen, N-F., Roll, R., Ross, S. A., Economic forces and he sock marke. Journal of Business 59, Chordia T, Shivakumar, L., 00. Momenum, business cycle and ime-varying expeced reurns. Journal of Finance 57, Daniel, K, Hirshleifer, D., Subrahmanyam, A., Invesor psychology and securiy marke under- and overreacions. Journal of Finance 53, Ellis, M., Thomas, D. C., 003. Momenum and he FTSE 350. Journal of Asse Managemen 5, Engle, R. F., 198. Auoregressive condiional heeroscedasiciy wih esimaes of he variance of UK inflaion. Economerica 50, Fama, E. F., French, K., Common risk facors in he reurns on socks and bonds. Journal of Financial Economics 33, Fama, E. F., French, K., Mulifacor explanaions of asse pricing anomalies. Journal of Finance 51, Glosen L. R., Jagannahan, R., Runkle, D. E., On he relaion beween he expeced value and he volailiy of he nominal excess reurn on socks. Journal of Finance 48, Griffin, J. M., Ji, X., Marin, S., 003. Momenum invesing and business cycle risk: Evidence from pole o pole. Journal of Finance 58, Grundy B. D., Marin, J. S., 001. Undersanding he naure of he risks and he source of he rewards o momenum invesing. Review of Financial Sudies 14, 1, Hong, H., Lim, T., Sein, J., 000. Bad news ravels slowly: Size, analys coverage, and he profiabiliy of momenum sraegies. Journal of Finance 55, Hong, H., Sein, J., A unified heory of underreacion, momenum rading and overreacion in asse markes. Journal of Finance 54, Copyrigh 006 Li, Miffre and Brooks 14

17 ICMA Cenre Discussion Papers in Finance: DP Jegadeesh, N., Timan, S., Reurns o buying winners and selling losers: Implicaions for sock marke efficiency. Journal of Finance 48, Jegadeesh, N., Timan, S., 001. Profiabiliy of momenum sraegies: An evaluaion of alernaive explanaions. Journal of Finance 56, Karolyi, A., Kho, B-C., 004. Momenum sraegies: Some boosrap ess. Journal of Empirical Finance 11, Lesmond, D. A., Schill, M. J., Zhou, C., 004. The illusory naure of momenum profis. Journal of Financial Economics 71, Liu W., Srong, N., Xu, X., The profiabiliy of momenum invesing. Journal of Business Finance and Accouning 6, Moskowiz, T. J., Grinbla, M., Do indusries explain momenum?. Journal of Finance 54, Nagel, S., Lewellen, J., 006. The condiional CAPM does no explain asse pricing anomalies. Journal of Financial Economics forhcoming. Nelson D. B., Condiional heeroskedasiciy in asse reurns: A new approach. Economerica 59, Okunev, J., Whie, D., 003. Do momenum-based sraegies sill work in foreign currency markes?. Journal of Financial and Quaniaive Analysis 38, Poon, S. H., Granger, C. W. J., 003. Forecasing volailiy in financial markes: A review. Journal of Economic Lieraure 41, Rabemananjara R., Zakoian, J. M., Threshold ARCH models and asymmeries in volailiy. Journal of Applied Economerics 8, Sadka, R., 006. Momenum and pos-earnings-announcemen drif anomalies: The role of liquidiy risk. Journal of Financial Economics forhcoming. Sharpe, W. F., Capial asse prices: A heory of marke equilibrium under. condiions of risk. Journal of Finance 19, Wang, K. Q., 003. Asse pricing wih condiional informaion: A new es. Journal of Finance 58, Wu, X., 00. A condiional mulifacor model of reurn momenum. Journal of Banking and Finance 6, Copyrigh 006 Li, Miffre and Brooks 15

18 ICMA Cenre Discussion Papers in Finance: DP Table 1 Summary saisics of he reurns of he winner, loser and momenum porfolios Winner (Loser) is an equally-weighed non-overlapping porfolio conaining he 10% of socks ha performed he bes (wors) over a given ranking period. Momenum is a porfolio ha buys he winner porfolio and sells he loser porfolio shor. Reurns are measured as proporions raher han percenages. Reward-o-risk raio is he raio of he monhly mean o he monhly sandard deviaion. The p-values in parenheses are for he significance of he mean. They are based on heeroscedasiciy and auocorrelaion robus (Newey-Wes) sandard errors. Holding period of 3 monhs Holding period of 6 monhs Holding period of 1 monhs Winner Loser Momenum Winner Loser Momenum Winner Loser Momenum Panel A: Ranking period of 3 monhs Mean (0.0) (0.) (0.04) (0.01) (0.08) (0.00) (0.01) (0.09) (0.01) Sandard deviaion Reward-o-risk raio Panel B: Ranking period of 6 monhs Mean (0.00) (0.05) (0.00) (0.00) (0.0) (0.00) (0.00) (0.08) (0.00) Sandard deviaion Reward-o-risk raio Panel C: Ranking period of 1 monhs Mean (0.00) (0.13) (0.00) (0.00) (0.04) (0.00) (0.00) (0.11) (0.00) Sandard deviaion Reward-o-risk raio

19 Table Saic marke and Fama and French models ICMA Cenre Discussion Papers in Finance: DP The able repors coefficien esimaes for equaions (1) and () for he winner, loser and momenum porfolios. Winner (Loser) is an equallyweighed non-overlapping porfolio conaining he 10% of socks ha performed he bes (wors) over a given ranking period. Momenum is a porfolio ha buys he winner porfolio and shor sells he loser porfolio. α measures he porfolio abnormal performance, β measures he marke risk of he porfolio, s and h are he porfolio loadings on he size and book-o-marke value facors as measured by Fama and French (1993). MM refers o he marke model and FFM refers o he Fama and French model. Whie s heeroscedasiciy robus -saisics are in parenheses. Holding period of 3 monhs Holding period of 6 monhs Holding period of 1 monhs Winner Loser Momenum Winner Loser Momenum Winner Loser Momenum MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM Panel A: Ranking period of 3 monhs α (-0.87) (-.33) (-3.81) (-6.4) (3.46) (4.11 ) (0.03) (-0.71) (-4.59) (-7.80) (4.8) (6.05 ) (-0.8) (-1.01) (-4.68) (-8.49) (4.60) (6.47 ) β (11.79) (6.08 ) (1.15) (13.64 ) (-1.6) (-1.73) (11.35) (.83 ) (1.06) (13.77 ) (-1.11) (-1.39) (16.03) (9.46 ) (1.4) (17.58 ) (0.3) (-0.49) s (17.45 ) (11.98 ) (-0.89) (16.45 ) (1.7 ) (-1.05) (17.3 ) (14.98 ) (-0.69) h (-1.43) (1.69 ) (-.05) (-1.58) (.3 ) (-.36) (-.10) (4.3 ) (-4.04) Panel B: Ranking period of 6 monhs α (1.05) (1.34 ) (-4.78) (-7.89) (5.67) (7.03 ) (1.8) (1.75 ) (-5.4) (-9.03) (6.60) (8.13 ) (0.07) (-0.39) (-4.77) (-8.3) (4.89) (6.64 ) β (11.8) (.13 ) (11.78) (13.31 ) (-1.9) (-1.64) (11.87) (.39 ) (11.77) (13.77 ) (-0.80) (-1.1) (15.39) (31.08 ) (1.09) (15.50 ) (-0.39) (-0.94) s (16.84 ) (1.04 ) (-1.49) (17.19 ) (1.87 ) (-1.31) (17.65 ) (13.59 ) (-0.99) h (-.47) (.57 ) (-.89) (-.6) (.79 ) (-3.03) (-.1) (4.7 ) (-3.9) Panel C: Ranking period of 1 monhs α (1.69) (.68 ) (-4.46) (-7.06) (5.63) (7.0 ) (.00) (3.3 ) (-5.01) (-8.66) (6.68) (8.69 ) (0.64) (0.76 ) (-4.59) (-8.53) (5.48) (7.73 ) β (13.71) (4.79 ) (10.89) (11.54 ) (0.7) (-0.19) (13.6) (4.14 ) (10.48) (11.58 ) (0.7) (-0.40) (16.15) (35.74 ) (1.47) (16.48 ) (0.51) (-0.46) s (16.97 ) (10.73 ) (-0.84) (17.08 ) (1.35 ) (-1.73) (18.87 ) (14.96 ) (-1.71) h (-.97) (3.35 ) (-4.07) (-.57) (4.56 ) (-4.71) (-.43) (5.13 ) (-4.91) 17

20 ICMA Cenre Discussion Papers in Finance: DP Table 3 Condiional marke and Fama and French models wih a GJR-GARCH (1, 1)-M erm The able repors coefficien esimaes for sysems (3) and (4) for he winner, loser and momenum porfolios. Winner (Loser) is an equallyweighed non-overlapping porfolio conaining he 10% of socks ha performed he bes (wors) over a given ranking period. Momenum is a porfolio ha buys he winner porfolio and shor sells he loser porfolio. α measures he porfolio abnormal performance, β measures he marke risk of he porfolio, s and h are he porfolio loadings on he size and book-o-marke value facors as measured by Fama and French (1993), δσ is he ime-varying risk premium. The condiional variance of he porfolio reurns follows a GJR-GARCH(1,1) srucure as = ω+ γε 1+ ηi 1ε 1 + θσ 1 σ, where ω, γ, η and θ are esimaed parameers and I -1 akes a value of 1, when ε -1 is negaive and a value of 0, oherwise. MM refers o he marke model and FFM refers o he Fama and French model. Bollerslev-Wooldridge robus -saisics are in parenheses. Holding period of 3 monhs Holding period of 6 monhs Holding period of 1 monhs Winner Loser Momenum Winner Loser Momenum Winner Loser Momenum MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM Panel A: Ranking period of 3 monhs α (-0.17) (.48) (-1.41) (1.67) (-0.44) (-0.10) (1.55) (.15) (.64) (1.74) (-0.19) (0.48 ) (0.7) (3.11) (10.0) (.14) (0.1 ) (0.45 ) β (14.87) (34.9) (15.71) (15.89) (-1.67) (-3.61) (.31) (8.14) (19.30) (1.94) (-0.90) (-4.) (4.08) (7.37) (45.65) (38.61) (.19 ) (0.61 ) s (1.85) (18.48) (-3.56) (1.36) (.51) (-4.91) (5.19) (3.53) (-.38) h (1.07) (4.43) (-3.3) (.4) (6.9) (-4.34) (.10) (8.39) (-3.87) δ (-0.08) (-.66) (-0.07) (-3.31) (1.65 ) (1.49 ) (-1.11) (-.05) (-3.34) (-4.33) (1.63 ) (1.78 ) (-0.0) (-3.17) (-7.91) (-3.39) (.09 ) (1.91 ) ω (.90) (.4) (1.1) (1.45) (1.63 ) (1.4 ) (3.0) (3.48) (1.69) (1.48) (1.64 ) (1.51 ) (.00) (1.58) (-0.1) (.7) (1.48 ) (1.4 ) γ (3.09) (.49) (1.73) (1.4) (.75 ) (.56 ) (.5) (.65) (-.63) (1.3) (3.45 ) (3.97 ) (.7) (.15) (-0.53) (-0.56) (.89 ) (.94 ) η (-.15) (0.0) (1.11) (.06) (-.41) (-.6) (-0.41) (-0.4) (3.4) (.63) (-.46) (-.60) (-0.83) (-1.31) (6.97) (3.1) (-.3) (-1.88) θ (5.71) (10.06) (1.84) (7.88) (6.79 ) (7.84 ) (4.1) (3.18) (16.1) (1.95) (5.7 ) (7.39 ) (8.68) (4.0) (31.56) (11.98) (8.44 ) (10.03 ) γ +η/+θ

21 ICMA Cenre Discussion Papers in Finance: DP Table 3 Coninued Holding period of 3 monhs Holding period of 6 monhs Holding period of 1 monhs Winner Loser Momenum Winner Loser Momenum Winner Loser Momenum MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM MM FFM Panel B: Ranking period of 6 monhs α (.37 ) (.95) (3.5) (.05) (-1.44) (0.19 ) (1.9) (3.54) (4.1) (1.53) (0.98 ) (1.73 ) (0.34) (3.4) (.86) (1.83) (-0.) (-0.7) β (18.76 ) (48.31) (17.51) (3.8) (-0.35) (-3.6) (3.41) (35.16) (15.53) (.16) (-1.11) (-3.55) (4.31) (30.7) (10.99) (19.7) (0.89 ) (-1.03) s (5.08) (18.44) (-6.06) (5.5) (19.6) (-4.04) (.71) (18.81) (-.7) h (0.88) (5.88) (-5.55) (-1.16) (7.07) (-7.9) (-0.14) (5.17) (-6.11) δ (-.11) (-.55) (-3.66) (-4.37) (5.85 ) (.56 ) (-0.51) (-.43) (-4.74) (-4.48) (.8 ) (.0 ) (-0.06) (-.95) (-3.3) (-3.96) (.8 ) (3.0 ) ω (3.0 ) (3.40) (.99) (1.38) (1.74 ) (.06 ) (.39) (3.9) (.81) (1.9) (1.31 ) (1.53 ) (.45) (1.76) (.01) (1.71) (1.53 ) (1.37 ) γ (.66 ) (1.91) (-8.10) (1.1) (6.11 ) (3.13 ) (.16) (.34) (-3.69) (1.49) (.69 ) (.61 ) (3.39) (1.96) (-0.70) (1.6) (.0 ) (.3 ) η (-0.8) (1.6) (4.08) (3.0) (-5.38) (-3.13) (-1.55) (0.78) (3.17) (.08) (-.49) (-.9) (-.00) (1.01) (.96 ) (1.65) (-1.67) (-1.37) θ (.34 ) (.46) (10.88) (19.40) (1.93 ) (5.97 ) (3.47) (.3) (13.39) (18.17) (9.74) (9.6 ) (6.63 ) (.41) (6.73) (11.64) (8.99 ) (11.49 ) γ +η/+θ Panel C: Ranking period of 1 monhs α (1.35) (3.36) (3.1) (.7) (-1.58) (-1.31) (.1) (4.68) (.9) (1.3 ) (1.5 ) (0.5 ) (0.18) (.87) (.5) (1.38) (-0.7) (-0.3) β (6.31) (31.43) (16.53) (18.75) (.38 ) (1.3 ) (16.1) (34.33) (14.93) (9.14 ) (0.68 ) (-0.85) (6.61) (69.71) (14.87) (34.46) (.68 ) (-0.43) s (18.67) (15.9) (-1.19) (.31) (19.40 ) (-3.64) (35.00) (0.56) (-3.1) h (-0.95) (8.5) (-4.68) (-0.55) (9.70 ) (-9.4) (0.31) (11.33) (-8.74) δ (-0.56) (-3.14) (-3.56) (-4.45) (3.7 ) (3.3 ) (-1.43) (-3.58) (-.99) (-3.10) (1.64 ) (.36 ) (0.5) (-.33) (-.79) (-.6) (.64 ) (.35 ) ω (.5) (.4) (.30) (1.58) (1.77 ) (1.15 ) (1.7) (.44) (1.80) (1.43 ) (0.94 ) (1. ) (.1) (3.79) (.78) (.9) (1.6 ) (1.90 ) γ (.57 ) (.39) (-3.75) (0.41) (4.4) (4.00 ) (.48) (1.78) (-1.88) (-0.31) (.45 ) (.60) (3.15 ) (1.51) (-1.53) (1.09) (.33 ) (.17 ) η (-1.89) (-0.04) (3.50) (.9) (-3.06) (-.58) (-0.39) (0.9) (.1) (.65 ) (-.5) (-1.46) (-.36) (.43) (.3) (.4 ) (-.03) (-0.53) θ (8.51 ) (3.74) (8.13) (1.44) (14.61 ) (3.3 ) (.58) (3.66) (18.37) (16.64 ) (1.77 ) (10.95) (6.09 ) (9.69) (7.) (7.30) (1.6 ) (8.86 ) γ +η/+θ