Do Momentum, Value, and Size Premia Predict Economic Growth?

Transcription

1 Global Economy and Finance Journal Vol. 8. No.. Sepember 05. Pp. 4 6 Do Momenum, Value, and Size Premia Predic Economic Growh? Mohammed M. Elgammal * and Mohamed Abdelaziz Eissa ** This paper explore wheher marke anomalies can predic economic growh and oher macroeconomic facors using he ime-varying volailiy mehodology. The findings indicae ha risk premia have differen and significan relaionship wih differen macroeconomic facors in he U.S marke. The findings of using differen univariae and mulivariae specificaion of Ordinary Leas Squares and TARCH models sugges ha momenum can predic economic growh while here is no evidence ha value premium, size premium or momenum can do. However here is srong evidence ha he liquidiy crisis can predic he economic growh. Key words: Value Premium; Size Premium; Momenum; Defaul Risk; Term Premium; Financial Crises; Economic Growh. JEL Codes: G0, G, G4. Inroducion Fama and French (99, 993, 995, 996, and 998) argue ha value and size premia are sae variables ha describe changes in he invesmen opporuniy se. Consequenly, i could be expeced ha value and size premium should be relaed o he fundamenal risks in he economy. Vassalou (003) examines he links beween risk premia and economic growh. Oher auhors such as Levis and Liodakis (999) link he value premium o variables such as inflaion. They also link he size premium wih changes in he ineres rae, equiy risk premium, em premium, and inflaion rae. Moreover, Leau and Ludvigson (00) argue ha reurns on value socks are relaed o consumpion growh when he risk aversion is high. The curren paper explore furher he naure of he relaionship beween variables ha are consruced from financial marke raes of reurn and fundamenal measures of oupu associaed wih he real economy using ime- varying mehodology and U.S daa over he period This piece of work is moivaed by he findings in he lieraure which indicae for a mix of relaionships beween sock marke variables and macroeconomic facors. This provides he moivaion o expand our knowledge by examining he relaionship beween he value premium, size premium as well as momenum and macroeconomic condiions. The macroeconomic facors include he change in indusrial producion as a proxy for economic growh, defaul premium as a proxy for aggregae leverage, Federal Ineres * Dr. Mohammed M. Elgammal, Deparmen of Finance and Economics, College of Business and Economics, Qaar Universiy and Faculy of Commerce, Menoufia Universiy, Egyp. m.elgammal@qu.edu.qa ** Dr. Mohamed Abdelaziz Eissa, Deparmen of Finance and Economics, College of Business and Economics, Qaar Universiy and Faculy of Commerce and Faculy of Commerce, Assui Universiy, Egyp. m.eissa@qu.edu.qa

2 Rae as a proxy for liquidiy crisis, and inflaion as a proxy for economic sae. Marke and erm premia are used as sock marke risk facors. Furhermore, his paper aims o examine wheher he value premium, he size premium, and momenum can predic he economic growh. The imporance of his sudy is inspired from he argumen ha linking marke anomalies o economic condiions may add o our knowledge by explain he source of hese anomalies. Furhermore, if he value premium, size premium and momenum conain a risk facor, which predics or precedes economic condiion, hese facors could work as economic signals for recession and inflaion. The findings indicae ha he risk premium facors are forward looking facors and could incorporae expecaions abou fuure macroeconomic condiions. There is evidence ha he marke premium, momenum, and erm premium can predic fuure economic growh as proxied by he change in indusrial producion. These resuls are consisen wih he findings of Fama (98) and Aylward and Glen (000) who repor a posiive relaionship beween marke facor and fuure economic growh in he U.S and inernaional daa respecively. The remainder of his paper is organized as follows. Secion discusses he lieraure review. Secion 3 inroduces a brief descripion for he daa se used in he paper. Secion 4 explains differen mehodologies used in he curren paper, while Secion 6 discusses he empirical analysis while Secion 7 summaries he main conclusions of he paper.. Lieraure Review A growing par of lieraure examines he relaionship beween marke premia (anomalies) and macroeconomic risk facors (see for example, Chan and Chui (996), Cochran (999), Liew and Vassalou (000), Vassalou (003) Vassalou and Xing, (004), Chordia and Shavikumar (00), Black and McMillan(006), Avramov and Chordia (006), Li e al. (009), Lui and Zhang (008), and Bali and Engle (00)). The moivaion for heir work is ofen o invesigae wheher risk premia can work as a proxy for macroeconomic risk and wheher hese anomalies can predic or be prediced by macroeconomic risk facors. The answers o hese quesions are helpful for a number of reasons. Firs, i can enhance our undersanding for he source of he reurn premia. Second, his may be useful for advising policy makers since i may help in forecasing economic growh or differen economic condiions. Third, if risk premia can be prediced by he economic growh hen his may imply ha profiable porfolio sraegies can be prediced using macroeconomic facors. The premise ha macroeconomic facors associaed wih he business cycle can predic sock marke reurns has made a profound impac on he developmen of he asse pricing lieraure [see for example Campbell (99), Ghysels e al. (005), Bali e al. (005), Guo and Whielaw (006) and Bali and Engle (00)]. Fama and French (99, 993, and 998) argue ha value and size premia should be relaed o he fundamenal risks in he economy. Oher auhors such as Levis and Liodakis (999) and Leau and Ludvigson (00) argue ha reurns on value socks are relaed o macroeconomic facors. 4

3 Anderson (997) repors a posiive relaionship beween he size premium and he inflaion, while Levies and Liodakis (999), conversely, argue ha he size and value premiums respond negaively o inflaion raes and he size premium responds posiively o changes in ineres rae and he equiy risk premium and erm spread. Jensen e al. (997, 998), and Kim and Burnie (00) documen a posiive size and value premium in expansion periods (expansive moneary policy) and a negaive or insignifican size and value premiums in he conracion periods (resricive moneary policy). Addiionally, Brennan e al. (00) imply ha value and size premia are priced because hey can predic changes in he invesmen opporuniy se. Building on his, Vassalou (003) argues ha changes in he invesmen opporuniy se can be described by informaion relaed o fuure economic growh. Vassalou (003), among ohers, links he cross-secional variaion of value and size premia o he news relaed o cross-secional variaion of fuure economic growh. Furhermore, Black and McMillan (00) sugges ha examining he relaionship beween he value premium and macroeconomic condiions may be helpful in explaining he source of he value premium. They illusrae ha economic condiions may affec he value premium hrough expeced fuure cash flows. If he economy expands and he expeced cash flows increase, he presen value of projecs will be posiive and he prices of growh socks will increase more rapidly han hose of value socks. Thus, he value premium index will fall in good imes and increase in bad imes. Moreover, Levis and Liodakis (999) and Black and McMillan (00), among ohers, sugges ha he relaionship beween inflaion and he value premium price index could be a posiive relaionship. The sory is ha, he increase in inflaion resuls in a corresponding increase in he nominal risk-free rae as well as discoun rae, which may slow he economy, and, consequenly corporae earnings and sock prices. The decrease in growh socks prices will be greaer han he decrease in value socks prices as growh socks are more sensiive han value socks o fuure earnings. Gregory e al. (003) and Kelly (003) repor posiive correlaion beween he size and value premiums and fuure GDP growh. However, Gregory e al. (003) canno confirm correlaion beween value premium and fuure GDP growh when he size and marke facors are included. Alhough hey find correlaion beween he size premium and he invesmen and consumpion componens of GDP growh, hey canno find such correlaion beween value premium and GDP componens. Addiionally, Bagella e al. (000) sugges ha he value and size porfolios are less exposed o risk relaed o he economic growh (as measured wih he covariance wih GDP) han growh and large porfolios in UK daa. These resuls are consisen wih hose of Avramov and Chordia (006) who argue ha he size premium has conra-cycle behaviour. A significan par of he lieraure suppors he view ha here is a significan relaionship beween reurn premiums and economic fuure growh. For example, Fama (98) repors a significan posiive relaionship beween he marke facor and he fuure economic growh in he U.S marke. This associaion is also confirmed in inernaional daa analysed by Aylward and Glen (000). Also, here are considerable aemps o link Fama-French facors wih macroeconomic facors as well as economic growh (for example see, Liew and Vassalou (000), Leau and Ludvigson (00), Kelly (003), Pekova (006), and Hahn and Lee (006)). However, he relaionships beween hese hree premia and he business cycle facors would benefi from more invesigaion. This paper invesigaes hese poenial relaionships beween he reurn premia and 43

4 macroeconomic risk facors furher o examine if hese premia reflec risk facors can predic he economic growh in he U.S marke over he period of July 954 o July 007. Elgammal and Al-Najjar (05) and Elgammal and McMillan (04) focus on he exen o which leverage and defaul risk play a role in characerising he value premium. The moivaion for considering leverage and defaul risk arose from he economic explanaion of Fama and French (996) and ohers; ha sugges financial disress may be an imporan driver in he exisence of marke anomalies. Elgammal and McMillan (04) argue ha he defaul premium has posiive explanaory power for he value premium. This gives srengh o he view ha he defaul premium capures sysemaic risk in he macro-economy and ha he value premium is associaed wih raional decision making on he par of invesors. This posiive associaion beween defaul and value premia accompanied by evidence for he leverage effec on he value premium, as discussed in Elgammal and Al-Najjar (05), is relevan for he risk-based explanaion for he source of value premium. Alogeher, his provides he moivaion o expand our knowledge by examining he relaionship beween he value premium, size premium as well as momenum and macroeconomic condiions. This paper exends he previous work by considering oher risk facors including size premium, momenum, defaul premium, and erm premium. There are also deeper quesion a is hear, is a desire o explore furher he naure of he relaionship beween variables ha are consruced from financial marke raes of reurn and fundamenal measures of oupu associaed wih he real economy and o examine wheher his financial marke reurns can predic he economic growh. This paper can be differeniaed from he lieraure in many aspecs. Firs of all, monhly daa are used insead of quarerly daa and he daa covers a longer ime period from July 954 o July 007. The defaul premium is added o he Liew and Vassalous (000) model o proxy for financial disress risk. The Fed ineres rae as a proxy for he liquidiy crisis is also added. Moreover, he change in indusrial producion is used as a proxy for economic growh, since he GDP informaion is no available in monhly daa forma. Also, we provide more comprehensive analysis using GARCH, Boosrap and OLS echniques. 3. Daa Descripion The empirical analysis examines monhly daa variables include; value premium; marke premium; size premium; defaul premium, erm premium, inflaion, he change in indusrial producion, and a Federal ineres rae (Fed) for he period of July 954 o July Monhly U.S. oal reurns indices in local currency are colleced from he Morgan Sanley (MSCI) daabase. The value premium (HML) is he difference beween reurns in he op 30 per cen of porfolios sored on book-o-marke and he boom 30 per cen. The defaul premium index is he difference beween reurns on long-erm corporae bonds and long-erm governmen bonds. Toal reurns on he S&P 500 Index and he 30-day US Treasury Bill are used o derive he marke risk premium index. The erm premium index is defined as he difference beween he oal reurn on long-erm (30-years) governmen yield minus shor-erm Treasury bills (TB 30 days). 4 The monhly Federal fund effecive rae and monhly Indusrial Manufacuring producion rae are obained from he Federal Reserve Board daabase- Saisics release- 44

5 download program. The value, size and momenum prmia indices are obained from Kenneh Frenchs websie. 5 The momenum facor consruced from six value-weigh porfolios formed using independen sors on size and prior reurn of NYSE, AMEX, and NASDAQ socks. Momenum is he average of he reurns on wo (big and small) high prior reurn porfolios minus he average of he reurns on wo low prior reurn porfolios. Big means a firm is above he median marke capializaion on he NYSE a he end of he previous monh; small firms are below he median NYSE marke capializaion. Prior reurn is measured from monh - o -. Firms in he low prior reurn porfolio are below he 30h NYSE percenile. Those in he high porfolio are above he 70h NYSE percenile. All daa are ransformed o he firs difference logged daa o avoid nonsaionary in he raw daa Mehodology Ordinary Leas Squares models (OLS), hreshold Auoregressive Condiionally Heeroscedasic models (TARCH), and Boosrap mehods are used o examine he predicabiliy power of he risk premia for he fuure economic growh. All mehods are used in he conex of ime series analysis. The sandard GARCH (, ) model is defined as follows: V X : N(0, h ) h w h VolX () Where V is a vecor for dependen variables of ineres, X is a vecor of explanaory variables and VolX is a vecor of he condiional volailiy of seleced explanaory variables. Moreover,, and w are non-negaive parameers. I is a necessary and sufficien condiion ha < in order for a finie uncondiional variance o exis (Black and McMillan, 006). Where measures he effec of volailiy shock in period (- ) on volailiy on period () and ( ) measures he speed a which his effec dies away. The hreshold ARCH, or TARCH, model is used o measure he leverage effec on value premium and o allow for asymmeric shocks o volaile moivaed by he reasoning ha good news and bad news have differen predicabiliy for fuure volailiy (see Bollerslev e al., 99; and Glosen e al., 993). The specificaion for his model is: h V X : N(0, h w d h ) VolX () Where d = if d < 0 oherwise = 0. Therefore, here are differenial effecs on he condiional variance where < 0 (an unexpeced decrease in price) denoes bad news and > 0 (an unexpeced increase in price) denoes good news. The impac of good news is given by, he impac of bad news by, and he leverage effec by. The leverage effec reflecs how he decrease in sock prices leads o an increase in financial leverage (since he value of equiy falls relaive o corporae deb); herefore boh he required reurn of equiy and he risk increase (see Chrisie, 98; and Black, 986). 45

6 The (ARCH) effec in he daa is invesigaed before and afer he model esimaed using ARCH LM es. The ARCH es is a Lagrange muliplier (LM) es for auoregressive condiional heeroskedasiciy (ARCH) in he residuals (Engle 98). ARCH in iself does no invalidae sandard leas squares (LS) inference. However, ignoring ARCH effecs may resul in loss of efficiency. If residuals are no condiionally normally disribued, he quasi-maximum likelihood (QML) co-variances and sandard errors are calculaed by he mehod described by Bollerslev and Wooldridge (99) for heeroscedasiciy consisen covariance. Their mehod only affecs he covariance marix, bu does no affec he parameer esimaes. Brooks (008) illusrae ha he usual - and F-ess are valid in he conex of non-linear models, however, here are no flexible enough 7. Thus, in addiion o - and F- ess he Maximised Log Likelihood Funcion (MLLF) is used o es wheher he coefficiens are equal o zero and wheher here any coefficiens need o omied from he regression models. If he null hypohesis of no-serial correlaion is rejeced for he residual of he Leas Squares models, hen he approach of Liew and Vassalou (000) is followed using he Newey-Wes (987) saisic. While in he case of GARCH models he mehodology of Bollerslev and Wooldridge (99) is used o correc for he serial correlaion. In he case of finding any serial correlaion in he squared residuals afer applying Bollerslev and Wooldridges (99) mehodology, we use wo differen mehods o overcome he auocorrelaion problem. The firs mehod is o include he firs lag of he dependen variable in he analysis as an addiional explanaory variable. The second mehod is o apply Boosrap mehods o generae saisical inferences. 5. Empirical Resuls 5. Macro Economic Facors and Differen Premia Invesigae he relaionship beween hese risk premia and he macroeconomic facors may help in explaining he source of hese premia from one side and for esing wheher hese premia could predic he economic crises from he oher side. The TARCH model is used o invesigae wheher he reurn on differen rading sraegies (value premium, size premium, and momenum) and he marke facors (marke premium and erm premium as conrol facors) can explain four macroeconomic facors. These macroeconomic facors include: defaul premium as a proxy for financial disress risk; he change of indusrial producion as a proxy for he economic growh; inflaion rae as a proxy for he economic sae; and, finally, he Fed ineres rae as proxy for he liquidiy crisis. This could be explained in he following model: V V vp Marke Term 3 Size 4 Momenum 5 Season h : N(0, h ) D (3) h w VolSize VolMomnum 4 d h 5 Volv p VolMarke VolTerm 3 46

7 V are he variables of ineres, including defaul premium, he change in indusrial producion, he Fed ineres rae, and inflaion rae. V is he firs lag of hese variables. VP is he benchmark value premium. Marke is he marke risk premium. Term is he risk erm premium, while Season is a vecor for he seasonal effec for eleven monhs. D is a dummy variable = if he observaion in he period from November 00 o July 007 and =0 oherwise. Table : Macro Economic Facors and Differen Premia (Wih Leverage Effec) V Season h : N(0, h h V w vp Marke Term Size Momenum D VolSize VolMomenum 4 ) 5 d h ( Volvp) VolMarke VolTerm The able presen he regressions resuls from regressing four macroeconomic variables (defaul spread (Defaul), he change in indusrial producion ( IP), he inflaion rae (INF), and he effecive federal ineres rae (FED)) on differen reurn premia over he period of 954:07 o 007:07. The explanaory variables include he firs lag he dependen variable V ), he value premium (vp), he marke premium (Marke), ( erm spread (Term), he size premium (Size), and he momenum. A i ~ X i ; period is A i denoes an ih order ARCH LM es, Qi denoes an ih order Ljung-Box es for residual serial dependency; Q i ~ X i. The sample V denoes variables of ineres. (*, **, ***) denoe a coefficien ha is significan a %, 5% and i 0% levels respecively. VOLDEF, VOLInf, and VOLTerm denoe he volailiy of defaul, he inflaion, and he erm premium as esimaed from GARCH model mean equaion. D is a dummy variable = if he observaion in he period from November 00 o July 007 and =0 oherwise. Dependen variables Defaul ** 0.04* -0.* * 0.8*** 9 0.9*** IP 0.40* ** *** INF 0.36* ** ** *.388* -0.03** 0.* FED 0.47* Dependen variable α Q4 A4 Defaul 0.67* 0.844* -0.00* *** 0.00*** 0.00* IP 0.46* 0.658* *** * INF -0.33* FED * *** * * The VP esimaes in Table () indicae o a posiive associaion beween value premium and defaul premium a 5% level of significance. Conversely, he resuls also indicae ha he condiional volailiy of value premium is negaively associaed wih he condiional variance of defaul premium a % level of significance. Alhough he defaul 47

8 premium increase as value premium do, he decrease in he risk relaed wih value premium resul in an increase in he risk relaed wih defaul premium. Moving o he marke premium, he resuls confirmed a posiive associaion wih he defaul premium, which is consisen wih he inuiion ha he increase in he marke risks my increase he probabiliy of defaul (for more deail, review Liu e al, 007). Addiionally, he condiional volailiy of marke premium has a negaive associaion wih he condiional variance of he change in he Federal ineres rae. Furhermore, he erm premium has a significan negaive relaionship wih boh he defaul risk premium and he change in he inflaion. The predicabiliy power for erm premium for boh he defaul and economic growh are suppored by invesigaing he relaionship beween he condiional volailiy of hese variables. The 3 esimaes in Table () sugges ha he condiional volailiy of erm premium has explanaory power for he condiional variance for boh he defaul premium and he economic growh a 0% level. Conversely, he size premium only shows a predicive power (negaively) for he inflaion rae. The condiional volailiy of he size premium is associaed negaively wih condiional variance of he Fed ineres rae and posiively wih defaul risk premium a % and 0% respecively. Finally, he momenum premium and is condiional volailiy are posiively associaed wih he defaul risk premium and is condiional variance respecively. However, he condiional variance of momenum has a negaive explanaory power for he Federal ineres rae. Overall, he resuls indicae ha risk premia have differen and significan relaionship wih differen macroeconomic risk facors. These resuls may lead us o suppor he risk explanaions for reurn premia and invie us o wonder abou he abiliy for his premia o predic macroeconomic growh. 5. Economic Growh and Risk Premia Liew and Vassalou (000) invesigae wheher book-o-marke raio, size, and momenum could be risk facors ha forecas economic growh. Liew and Vassalou (000) firs run a univariae regression as follows: GDPgrowh (4) (, 4) a b* FacorRe( 4, ) e(, 4) Where GDP growh is growh rae for a counrys GDP and FacorRe is marke, value, size, and momenum premia. Liew and Vassalou (000) findings confirm a posiive relaionship beween fuure economic growh and boh value and size premia. However, he reurns on he momenum sraegy appear o conain lile, if any, informaion abou fuure economic growh. Furhermore, Liew and Vassalou (000) run anoher regression model ha includes business cycle variables and he marke facor in addiion o differen premia: GDPgrowh f * DY e (, 4) (, 4) a b * MKT g * TERM ( 4, ) c * Facor Re h * IDPgrowh ( 4, ) q ( 4, ) (, 4) d * TB (5) TB Where is he Treasury Bill yield or Call Money Rae; DY is dividend yield on counry marke capializaion index; TERM is en-year governmen yield minus one monh IDPgrowh 4, ) reasury bill yield; ( is pas one-year growh in counry indusrial producion; 48

9 q (, 4) and are he residuals of he regression. Again, he previous resuls are confirmed; boh he value premium and size premium have posiive relaionships wih fuure economic growh. We expand Liew and Vassalous (000) work by using monhly daa insead of quarerly daa and covering a longer ime period from July 954 o July 007. The defaul premium is added o he Liew and Vassalous (000) model o proxy for financial disress risk. The Fed ineres rae as a proxy for he liquidiy crisis is also added. Moreover, he change in indusrial producion is used as a proxy for economic growh, since he GDP informaion is no available in monhly daa forma. Also, boh GARCH mehods and OLS are used in running he regression. The regressions ake he following form: IP (, ) f * DY a b * MKT g * TERM (, ) h* FED c * Facor Re (, ) (, ) j * Defaul q d * TB (, ) (6) Where IP is he economic growh as proxied by he change in indusrial producion; MKT is he monhly marke premium as he difference beween marke porfolio rae of reurn and he risk-free rae; FacorRe sands for he rae of reurn on value, size, and momenum sraegies; TB is he Treasury bill yield; DY is dividend yield on marke capializaion index; Term is he difference beween he rae of reurn of 30 yearsgovernmen bonds and TB; Fed is he Federal ineres rae; Defaul is he defaul premium as he difference beween he yield on long erm corporae bonds and he rae of reurn of long erm governmenal bond; and q are he residuals of he regression. The variables are rebalanced annually. Since, variables are observed a monhly frequencies, hus consecuive annual raes have eleven overlapping monhs. This induces serial correlaion in he residuals of our regressions. To correc for his, we follow Liew and Vassalou (000) approach using he Newly - Wes (987) esimaors and se he parameer equal o hree. 5.. Univariae Analysis The Ordinary Leas Squares (OLS) mehodology is applied o esimae he model illusraed in equaion (6) in differen univariae regressions. The resuls repored in Table () indicae ha he value premia, erm premium or size premium canno explain he fuure economic growh as proxied by he annual growh of indusrial producion. However, he marke premium esimaes in Table () confirms he resuls of Fama (98), Aylward and Glen (000), and Liew and Vassalou (000) who repor a posiive and saisically significan relaionship beween he marke facor and fuure economic growh in boh he U.S and inernaional conex. Moreover, he Momenum premium esimaes in Table () are negaively associaed wih he economic growh. 3 This may indicaes ha he winners conver o be losers when he economy slowdowns. Similarly, business cycle variables including Fed ineres rae, Treasury- bills yield, and dividend yield have negaive relaionships wih he economic growh. This suggess ha he decrease in hese variables enhance he economic growh. These could explain he race beween differen cenral banks in decreasing he ineres raes o face he recessions and financial crises. In he same conex, he 49

10 repored posiive relaionship beween economic growh and defaul premium implies ha he increase in defaul risk may predic fuure economic growh. In he rebalancing periods, he decrease in he governmen bonds ineres rae, especially shor erm ineres raes, wih relaively high corporae bonds ineres rae may enhance he prosperiy of his corporae secor and help he economics o recover. Table : Economic Growh and Differen Anomalies, Univariae Regressions Using he OLS IP(, ) a b* MKT(, ) c * Facor Re(, ) d * TB f * DY g * TERM k * FED j * Defaul q (, ) (, ) (, ) Where IP is he economic growh as proxied by he change in indusrial producion; MKT is monhly marke premium as he difference beween marke porfolio rae of reurn and he risk-free rae; FacorRe sands for he rae of reurn on value, size and momenum sraegies; TB is he Treasury bill yield; DY is dividend yield on marke capializaion index; Term is he difference beween he rae of reurn of 30 yearsgovernmen bonds and TB; Fed is he federal ineres rae; Defaul is he defaul premium as he difference beween he yield on long erm corporae bonds and he rae of reurn of long erm corporae bond; and q are he residuals of he regression Adjused Marke VP LVP SVP Size Momenum TB DY 4 Term Fed Defaul 0.38* Mulivariae analysis Esimaes of ordinary leas squares mehod (%) ** * ** 3.4 To run mulivariae versions of he equaion (6), he dividend yield is excluding from he model because he dividend yield daa is no available before 965 and he resuls of he mulivariae model for he period of March 965 o July 007 shows ha he dividend yield canno explain he change in indusrial producion. This invies us o believe ha omiing he dividend yield from he model will no affec he goodness fi of our model. 5 The new model is as follows: IP (, ) g * TERM a b* MKT k * FED (, ) (, ) c * Facor Re j * Defaul (, ) (, ) q d * TB (, ) (7) 50

11 Table (3) shows a negaive coefficien for he momen premium. This momenum premium effec is absorbed by including he business cycle variables in he model. As expeced, he business cycle facors show a predicabiliy power for economic growh. In deail, boh he reasury-bills ineres rae and Federal Reserve ineres rae are negaively associaed wih he economic growh. This indicaes ha he economic growh posiively responds o he reducion in he ineres raes during he liquidiy crisis periods. This evidence increases our rus in he effeciveness of using he reducions in he federal ineres rae o overcome he liquidiy crisis and o enhance he economic growh. Finally, he marke premium, he erm premium and defaul spread have posiive associaions wih he economic growh. However, including he momenum in he model absorb he explanaory power of defaul spread. This finding invies us o wonder abou he relaionship beween he momenum sraegy and defaul spread. Invesigaion his relaionship is ou of his paper ineres, however, i could be a possible furher research opporuniy. 6 Table 3: Economic Growh and Differen Anomalies (Mulivariae OLS Regressions) IP(, ) a b* MKT(, ) c * Facor Re(, ) d * TB g * TERM k * FED j * Defaul q (, ) (, ) (, ) Where IP is he economic growh as proxied by he change in indusrial producion; MKT is monhly marke premium as he difference beween marke porfolio rae of reurn and he risk-free rae; FacorRe sands for he rae of reurn on value, size and momenum sraegies; TB is he Treasury bill yield; Term is he difference beween he rae of reurn of 30 years- governmen bonds and TB; Fed id he Federal ineres rae; Defaul is he defaul premium as he difference beween he yield on long erm corporae bonds and he rae of reurn of long erm corporae bond; and q are he residuals of he regression. Marke VP Size Momenum TB Term Fed Defaul Adjused 0.46* * * ** * ** * *** -0.03* 0.49** * * 0.35** -0.03* 0.6** * * 0.33** * * * 0.3*** * (%) 5... Esimaes from using a TARCH model Using he TARCH models give many advanages. The firs advanage is ha he TARCH models can deal wih non-normal disribued variables and can capure nonlineariy. Second, he TARCH model measures he leverage effec. Finally, he TARCH models 5

12 help o deermine wheher he dependen variable is ime-varying or no. The TARCH model version of equaion (7) is illusraed as follows: IP (, ) a b * MKT (, ) c * Facor Re (, ) d * TB g * TERM k * FED : N(0, h ) (, ) j * Defaul (, ) q (, ) (8) h w h d Where ( ) measures he effec of volailiy shock in period (-) on volailiy on period (), and ( ) measures he speed a which his effec dies away. Moreover, d = if < 0 oherwise d = 0. The parameer ( ) measures he leverage effec on value premium. The impac of good news is given by and he impac of bad news by ( ). 5

13 Table 4: Economic Growh and Differen Anomalies Using TARCH Model IP(, ) a b * MKT(, ) c * Facor Re (, ) d * TB g * TERM k * FED (, ) j * Defaul q(, ) : N(0, h ) h w h d Where IP is he economic growh as proxied by he change in indusrial producion; MKT is monhly marke premium as he difference beween marke porfolio rae of reurn and he risk-free rae; FacorRe sands for he rae of reurn on value, size and momenum sraegies; TB is he Treasury bill yield; Term is he difference beween he rae of reurn of 30 years- governmen bonds and TB; Fed id he Federal ineres rae; Defaul is he defaul premium as he difference beween he yield on long erm corporae bonds and he rae of reurn of long erm corporae bond; and q are he residuals of he regression. Panel A : Using Bollerslev and Wooldridge (99)Heeroskedasiciy consisen covariance mehodology Marke VP Size Momenum TB Term Fed Defaul (%) * 0.03* * -0.00* * 0.05** Panel B : Including he firs lag of he dependen variable IP(, ) a LIP(, ) b * MKT( g * TERM k * FED (, ) j * Defaul : N(0, h ) h w h d, ) c * Facor Re q (, ) (, ) d * TB Marke VP Size Momenum TB Term Fed Defaul * * 0.03** * 0.08* Panel C : Using Boosrap mehodology Marke VP Size Momenum TB Term Fed Defaul (%) - 0.* * ** In conras wih he ordinary leas squares regressions resuls, he TARCH resuls repored in Table (4, Panel A) indicae ha boh value premium and momenum have a negaive explanaory power for he economic growh. Addiionally, he resuls repored in Table (4, Panel A) suppor he OLS resuls repored in Table (3) wih respec o he explanaory power of marke premium, and reasury bill yields and federal ineres rae for he fuure economic growh. However, he erm premium loses is predicabiliy power. The findings also indicae a negaive relaionship beween defaul spread and fuure economic growh. These resuls are consisen wih he findings of Liew and Vassalou (000) who repor ha boh he value and size premium conain significan informaion abou he fuure economic growh (for he period of July 978 o July 996), and ha informaion is similar in naure o he informaion conained in popular business cycle variables. Alogeher he resuls appear o suppor he hypohesis of Fama and French (99, 993, 006, 007) ha boh value and size premium are working as sae variables in he conex of iner-emporal capial asses pricing model, as hese variables can predic he changes in he invesmen opporuniy se. 53

14 The conradicion beween he OLS resuls and he TARCH findings could be explained by he auo-correlaion srucures of GARCH models (for more deail, see Francq and Zakoian (000)). To es for he serial correlaion we use he Ljung-Box Q-saisics and heir p-values. The Q- saisics capure serial correlaion in he residuals. Even afer applying Bollerslev and Wooldridge (99) mehodology, he squared residuals have some auo-correlaions. One way of furher examining he disribuion of he residuals is o plo he quaniles. Theoreical qunile-quanile plo (QQ-plo) is used o assess wheher he daa in a single series follow a specified heoreical disribuion; e.g. wheher he daa are normally disribued (Cleveland, 994). If he errors have a normal disribuion, he QQ-plo should lie on a sraigh line. If he QQ-plo does no lie on a sraigh line, he wo disribuions (errors disribuion and heoreical/normal disribuion) differ along some dimensions. The paern of deviaion from lineariy provides an indicaion of he naure of he mismach. Plo () indicaes ha i is primarily large negaive and posiive shocks ha are driving he deparure from normaliy. Two differen mehods are applied o deal wih he auo-correlaion problem. The firs mehod is o include he firs lag of he dependen variable in he analysis as an addiional explanaory variable. The second mehod is applying he Boosrap mehods o generae saisical inferences. Using he firs lag of he economic growh as an explanaory variable in he equaion (8) yield he following equaion: IP (, ) a LIP (, ) b * MKT (, ) c * Facor Re (, ) d * TB g * TERM k * FED : N(0, h ) (, ) j * Defaul (, ) q (, ) (9) h w h d Where LIP(, ) is he firs lag of he annual growh in he indusrial producion where L IP IP. The resuls illusraed in Table (4, panel B) show ha including he (, ) (, ) firs lag of he dependen variable absorbs he explanaory power of he marke premium, value premium, and federal ineres rae. In addiion, here is evidence for a leverage effec in he model. All oher resuls are similar o hose of he original model in Panel A. 54

15 Quaniles of Normal Quaniles of Normal Elgammal & Eissa Figure : Quiniles of he Residuals of (TARCH) Models agains he Normal Disribuion Quaniles of he Residuals of Mulivariae TARCH-in main Model Quaniles of Residuals of Mulvariae TARCH Model Following Davison and Flachaire (008) and Ioannaidis and Peel (005), we apply he wild boosrap mehod wih reference o equaion (8). Firsly, equaion (8) is esimaed by he TARCH mehod. Then, he residuals esimaed of his regression ( q ˆ (, ) ) is used o generae a new series of residuals as follows: u f ˆ ), (9) * ( q(, ) Where f ( qˆ (, ) ), is a ransformaion of he TARCH residual ( q ˆ (, ) ) and he ( ) are muually independen drawings, compleely independen of he original daa, from an auxiliary wo-poin disribuion has he following properies: 55

16 3 E( ) 0, E( ), and E( ) (0) ( 5 ) / wih probabiliy p ( 5 ) /( 5) () ( 5 ) / wih probabiliy p Thus, for each boosrap sample, he exogenous explanaory variables are reused unchangeably, as are he TARCH residuals ( q ˆ (, ) ) from he esimaion using he original observed daa. Consequenly, any non-normaliy and heeroskedasiciy in he * esimaed residuals ( q ˆ (, ) ) is preserved in he creaed residuals ( u ). We creae 0,000 ses of residuals. The resuls displayed a Panel (c) of Table (4) are similar o he findings of he Leas Squares model repored in Table (3). There is no evidence ha value premium, size premium or momenum can predic he economic growh. However here is srong evidence ha he liquidiy crisis can predic he economic growh Esimaes of GARCH in mean model The variance for economic growh is added o he main equaion (8). The new equaion is: IP (, ) a b * MKT (, ) c * Facor Re (, ) d * TB g * TERM k * FED : N(0, h ) (, ) j * Defaul (, ) h q (, ) () h w h d h Where ( ) is he condiional variance for he period (). We replicae our previous analysis for equaion (8) on equaion (). The findings repored in Table (5) Panels A, B, and C suppored our previous findings. There is no evidence ha value premium, size premium or momenum can predic he economic growh. However here is srong evidence ha he liquidiy crisis can predic he economic growh. The single difference ha he findings show a srong leverage effecs on all panels. Furhermore, he variance esimaes Table (5) sugges ha he economic growh is ime-varying variable. 56

17 Table Error! No ex of specified syle in documen.: Economic Growh and Differen Anomalies Using TARCH-In Main Model IP(, ) a b * MKT(, ) c * Facor Re( g * TERM k * FED (, ) j * Defaul h : N(0, h ) h w h d, ) d * TB q (, ) Where IP is he economic growh as proxied by he change in indusrial producion; MKT is monhly marke premium as he difference beween marke porfolio rae of reurn and he risk-free rae; FacorRe sands for he rae of reurn on value, size and momenum sraegies; TB is he Treasury bill yield; Term is he difference beween he rae of reurn of 30 years- governmen bonds and TB; Fed id he Federal ineres rae; Defaul is he defaul premium as he difference beween he yield on long erm corporae bonds and he rae of reurn of long erm corporae bond; and q are he residuals of he regression. Panel A : Using Bollerslev and Wooldridge (99)Heeroskedasiciy consisen covariance mehodology Marke VP Size Momenum TB Term Fed Defaul (%) 0.036* * 0.09* * 0.046** *.03* Panel B : Including he firs lag of he dependen variable IP(, ) a LIP(, ) b * MKT( g * TERM k * FED (, ) j * Defaul : N(0, h ) h w h d, ) c * Facor Re h q (, ) (, ) d * TB Marke VP Size Momenum TB Term Fed Defaul (%) * -0.03* * 0.074*** 0.07*** 93.3 Panel C : using Boosrap mehodology Marke VP Size Momenum TB Term Fed Defaul (%) 0.* * ** *.0433* Conclusion This paper provides an analysis of he relaionship beween marke risk premia and nondiversable macroeconomic risk facors using GARCH models in order o inform us abou variaions in he condiional volailiy of he addiional variables. This allows for an invesigaion of he associaions beween boh he mean value of variables and he volailiy of hese variables. An examinaion of he predicabiliy associaed wih risk premia for fuure economic growh also ook place. The findings sugges ha reurn premia explain macroeconomic risk facors in differen paerns. This may sugges ha hese premia are proxy for fundamenal risk facors and also suppor he raional explanaion for hese premia. In deail, he findings sugges ha he value premium can posiively explain he defaul premium; however he condiional volailiy of value 57

18 premium is negaively associaed wih he condiional variance of defaul. This means ha; however, he defaul premium increase as value premium do, he decrease in he risk relaed wih value premium resul in an increase in he risk relaed wih defaul premium. Furhermore, he resuls confirm a posiive associaion beween he marke premium and he defaul premium in consisen wih he inuiion ha he increase in he marke risks my increase he probabiliy of defaul (for more deail, review Liu e al, 007). Addiionally, he condiional volailiy of marke premium has a negaive associaion wih he condiional variance of he change in he Federal ineres rae. Furhermore, he erm premium has significanly negaive relaionship wih boh he defaul risk premium and he change in he inflaion. The predicabiliy power of he erm premium for boh he defaul and economic growh are suppored by invesigaing he relaionship beween he condiional volailiy of hese variables. Conversely, he size premium only shows a predicive power (negaively) for he inflaion rae, while is condiional volailiy is associaed negaively wih condiional variance of he Fed ineres rae and posiively wih defaul risk premium. Finally, he momenum premium and is condiional volailiy are posiively associaed wih he defaul risk premium and is condiional variance respecively. However, he condiional variance of momenum has a negaive explanaory power for he Federal ineres rae. Overall, he resuls indicae ha he risk premia have differen and significan relaionship wih differen macroeconomic risk facors. All he previous findings, which highligh an associaion beween differen premia and macroeconomic facors, moivae us o invesigae he predicabiliy power of he risk premium for he fuure economic growh. We find evidence ha he momenum can predic he economic growh. However, we canno find any similar evidence for boh value and size premium. These resuls are consisen wih Liew and Vassalou (000) who repor a predicabiliy power for value and size premia in inernaional daa bu hey do no find his predicabiliy power in he U.S daa wih excep for he period of July 978 o July 996. This may mean ha he failure of risk premia o predic he economic growh is specified o he U.S marke. This creaes needs o do more invesigaion o our model in inernaional conex and also in differen ime periods which will be one our furher research ineres. The empirical work in his paper conribues o our knowledge by providing addiional evidence for he posiive associaion beween Macroeconomic condiions (as proxied by defaul, inflaion, and he change in indusrial producion) and differen risk premia (momenum, size and value premia). This appears o suppor he raional explanaion for he reurn premia which may ac as a proxy for fundamenal risk. Endnoes The size premium is defined by Fama and French (99, 993) as a rae of reurn on a zero- invesmen porfolio, which is long on small marke equiy socks and shor on big marke equiy socks. The value premium is a rae of reurn on a zero- invesmen porfolio, which is long on wih socks which have large book-o-marke raio( value socks) and shor on low book-o-marke socks ( growh socks). Alhough he GDP is widely used in he lieraure as a proxy for he economic growh, i is also common in he lieraure o use he change in he indusrial producion as a proxy for he economic growh in he monhly daa because of he unavailabiliy of GDP in monhly daa [for example, see Black and McMillan (004) and Mouselli (008)]. Furhermore, Andreou e al. (000) argue ha he Indusrial producion accouns for 6.6% of he UK GDP in 995 and 5.9% for he US in

19 3 The period of July 954 o July 007 is he longes available se of daa for all of variables of ineres before he las financial crisis. 4 According o Fama and French (993), he reasury- bill rae is supposed o proxy for he general level of expeced reurns on bonds so ha erm premium proxies for he deviaion of long-erm bond reurns from expeced reurns due o shifs in ineres raes. While he defaul premium is a proxy for he change in he economic condiions ha modify he defaul likelihood. 5 I hank Kenneh French for making he daa available on his websie: hp://mba.uk.dramouh.edu/pages/ken.french/. 6 The Augmened Dickey-Fuller (ADF) is used o es he uni roo in he daa. The resuls indicae ha all variables conain a single uni roo in he level, hus we differeniae all he variables. The resuls of he Augmened Dickey-Fuller (ADF) indicae ha he firs differences of all variables are saionary. All resuls are available upon reques. 7 The variance equaion in GARCH model has non-linear srucure. 8 Residuals are found o be non-condiionally normally disribued, hus he Quasi-Maximum Likelihood (QML) are calculaed by he mehod described by Bollerslev and Wooldridge (99) for heeroscedasiciy consisen variance. The only change in he defaul regression is ha he erm premium condiional variance loses some explanaory power as is significance level urns from 5% o be 0%. Wherever, he erm premium loses is explanaory power for he DIP. 9 The seasonal effecs for monhs from March and April are significan a 0% level. 0 Following Engel (00) we es for auocorrelaions of squared sandardized residuals indicaes. There is no evidence for serial correlaion in he model. The dividends daa are only available for he period of March 965 o July 007. Thus, for he mulivariae models, we run wo differen versions for every regression. The firs version covers he period of March 965 o July 007including he dividends. The dividends is excluding from he second version, which execued for he period of July 954 o July 007. Reseing he parameer q in he Newly-Wes esimaor a alernaive values of 4, 5 or 6 produce qualiaively he same resuls. 3 Liew and Vassalou (000) repor insignifican negaive associaion beween momenum and economic growh. This may be due o he shor ime period used by hem. 4 The dividend daa are only available from he period of March 965 o July The dividend daa are only available from he period of March 965 o July 007. Thus, we remove he dividend from he mulivariae regression. We run a mulivariae regression for he period of March 965 o July 007 including he dividend, however he log likelihood raio for redundan variables was wih probabiliy indicae ha he dividend canno explain he economic growh and can be omied from he model. All resuls are available up on reques. 6 There is a negaive correlaion beween he annual momenum rae of reurn and he annual defaul spread. The correlaion coefficien is References Anderson, R 997, Marke Timing Models, Irwin, Chicago. Andreou, E, Obsorn, R.D & Sensier, M 000, A Comparison of he Saisical Properies of Financial Variables in he USA, UK and Germany over he Business Cycle, The Mancheser School, vol. 68, pp Aylward, T & Gelen, J 000 Some Inernaional Evidence on Sock Prices as Leading Indicaors of Economic Aciviy, Applied Financial Economics, vol. 0, no., pp Avramov, D & Chordia, T 006, Predicing Sock Reurns, Journal of Financial Economics, vol. 8, no., pp Bagella, M, Becchei, L & Carpenieri, A 000 The Firs Shall Be Las, Size and Value Sraegy Premia a he London Sock Exchange, Journal of Banking and Finance, vol. 4, no. 6, pp Bali, T, Cakici, N, Yan, X & Zhang, Z 005, Does Idiosyncraic Risk Really Maer?, The Journal of Finance, vol. 60, no., pp

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