Copyright Seunghan Lee

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1 Copyrigh 207 Seunghan Lee

2 Essays on Sock Prices and Equiy Premium Seunghan Lee A disseraion submied in parial fulfillmen of he requiremens for he degree of Docor of Philosophy Universiy of Washingon 207 Reading Commiee: Chang-Jin Kim, Chair Eric Zivo Yu-chin Chen Program Auhorized o Offer Degree: Deparmen of Economics

3 Universiy of Washingon Absrac Essays on Sock Prices and Equiy Premium Seunghan Lee Chair of he Supervisory Commiee: Professor Chang-Jin Kim Deparmen of Economics This disseraion sudies he role of cash flow in explaining sock price variaions and he deerminaion of equiy premium afer correcing for he measuremen error of cash flow growh. In Chaper, we incorporae price-oal payou (dividends plus repurchases) raio ino he models of Binsbergen and Koijen (200) and Campbell and Ammer (993) o reassess he role of cash flow in sock price movemen. We find ha he exising resuls of a high persisence in expeced reurns and a srong dependence of sock price variaion on discoun raes are parly aribuable o he use of price-dividend raio wih measuremen error as a predicor of sock reurns. The incorporaion of price-oal payou raio enables he models i) o improve an in-sample goodness of fi for reurn and cash flow growh, ii) o produce a lower persisence of expeced reurns, which leads o a smaller shock o sock prices from he discoun rae channel, iii) o show a

4 higher conribuion of cash flow channel o sock price movemen in erms of variaions in pricecash flow raio and unexpeced reurn. These resuls apply o medium and large cap porfolios as well as o aggregae marke index. In Chaper 2, we explore he effecs on sock marke variaion of oher facors han sock repurchases ha could accoun for he non-saionariy of price-dividend raio by incorporaing regime shifs in he mean of price-oal payou raio ino he models of Binsbergen and Koijen (200) and Campbell and Ammer (993). Compared o he resuls of Chaper, we achieve i) an improvemen in in-sample goodness of fi for reurn and cash flow growh, ii) a lower persisence and higher volailiy of expeced reurns, iii) sronger role of cash flow channel in sock marke variaion, all of which show ha no only sock repurchases bu also oher srucural facors such as persisen decline in consumpion volailiy affecing he relaionship beween sock prices and cash flows should be aken ino accoun when we aemp o invesigae he sources of sock price variaions. In Chaper 3, we incorporae price-oal payou raio and endogenously generaed consumpion volailiy wih regime shifs ino he dynamic asse pricing model of Bansal, Kiku, Shaliasovich, and Yaron (204) (hereafer, BKSY model ), which sresses he role of a sizable posiive risk premium from he macroeconomic volailiy channel in explaining he equiy premium by inroducing he volailiy risk ino radiional consumpion-based asse pricing model. Our exension of he BKSY model provides a differen idenificaion of he consumpion volailiy risk by including he effecs of he economic agen s revision of expecaion on he volailiy saes on each of hree channels o deermine he equiy premium. From annual samples of 930 o 205, we find ha our model shows a much smaller conribuion of he consumpion volailiy risk o he oal equiy premium, mos of which is now explained by he cash flow risk.

5 This finding applies o cross-secional porfolio reurns as well as o aggregae marke index reurn. Our model also indicaes ha he consumpion volailiy risk is no large enough o reverse a negaive correlaion beween equiy reurn and human capial reurn.

6 TABLE OF CONTENTS Lis of Figures... iv Lis of Tables... v Chaper. Wha Moves he Sock Marke in he Presence of Sock Repurchases?.... Inroducion....2 A Review of he Models Model of Binsbergen and Koijen (200) Model of Campbell and Ammer (993) Descripion of Daa Empirical Resuls Preliminary Resuls In-Sample Goodness of Fi Persisence of Expeced Reurns Role of Cash Flow and Discoun Rae in Marke Variaion Conclusion Tables and Figures... 5 Chaper 2. Wha Moves he Sock Marke in he Presence of Regime Shifs? Inroducion Specificaion of Models A Review of Choi, Kim, and Park s (207) Model An Exension of Campbell and Ammer s (993) Model i

7 2.3 Daa and Esimaion Daa Esimaion Algorihm Empirical Resuls Preliminary Resuls In-Sample Goodness of Fi Persisence of Expeced Reurns Role of Cash Flow and Discoun Rae in Marke Variaion Conclusion Tables and Figures Chaper 3. Is Consumpion Volailiy Risk Large Enough o Explain he Equiy Premium? Inroducion A Review of he BKSY Model An Exension of he BKSY Model Daa and Esimaion Daa Esimaion Algorihm Empirical Resuls Preliminary Resuls News Componens Risk Premium and Roles of Risk Facors Equiy and Human Capial Reurns Conclusion ii

8 3.7 Tables and Figures Bibliography Appendix A. Appendix o Chaper A. Consrucion of Dividends and Repurchases Series Appendix B. Appendix o Chaper B. Priors for he Bayesian Esimaion Appendix C. Appendix o Chaper C. An Exension of he BKSY Model in a Three-Sae Regime Shif C.2 Idenificaion of he Values of a and b iii

9 LIST OF FIGURES Figure.. Price-Dividend Raio and Price-Toal Payou Raio Figure.2. Filered Series of Sock Reurn: Binsbergen-Koijen Model... 2 Figure.3. Filered Series of Cash Flow Growh: Binsbergen-Koijen Model Figure.4. Variance Decomposiions of Unexpeced Excess Reurn Figure 2.. Filered Probabiliies of Sae and Price-Toal Payou Raio Figure 2.2. Filered Series of Sock Reurn and Cash Flow: Binsbergen-Koijen Model. 47 Figure 3.. Model-Implied Equiy Premium for Aggregae Index and Risk Aversion... 8 Figure 3.2. Esimaed Regime Probabilies (Gibbs-Sampling) Figure 3.3. Realized Variance vs. Condiional Consumpion Volailiy Figure 3.4. Cash Flow, Discoun Rae, and Volailiy News iv

10 LIST OF TABLES Table.. Persisence of Price-Dividend Raio and Price-Toal Payou Raio... 5 Table.2. Parameer Esimaes: Binsbergen-Koijen Model ( : Aggregae Marke Index)... 5 Table.3. In-Sample Goodness of Fi: Binsbergen-Koijen Model (R 2 : )... 6 Table.4. Expeced Reurn Persisence and Price Effec: Binsbergen-Koijen Model ( ) Table.5. Variance Decomposiion of Price and Reurn: Binsbergen-Koijen Model ( )... 7 Table.6. Variance Decomposiion of Unexpececd Reurn: Campbell-Ammer Model. 8 Table 2.. Parameer Esimaes: Binsbergen-Koijen Model wih 2-Sae Shifs Table 2.2. Poserior Disribuion of Parameers: Campbell-Ammer Model wih 2-Sae Shifs Table 2.3. In-Sample Goodness of Fi: Binsbergen-Koijen Model wih 2-Sae Shifs ( ) Table 2.4. In-Sample Goodness of Fi: Campbell-Ammer Model wih 2-Sae Shifs Table 2.5. Expeced Reurn Persisence and Price Effec: Binsbergen-Koijen Model wih 2-Sae Shifs ( ) Table 2.6. Variance Decomposiion of Price and Reurn: Binsbergen-Koijen Model wih 2-Sae Shifs ( ) Table 2.7. Variance Decomposiion of Unexpeced Reurn: Campbell-Ammer Model Table 3.. Model-Implied Equiy Premium for Aggregae Index and Porfolios (BKSY Model) Table 3.2. Model-Implied Risk Premium for Equiy, Wealh and Labor Reurns (BKSY Model) Table 3.3. Equiy, Wealh, and Labor Reurn Correlaions (BKSY Model) Table 3.4. Poserior Disribuion of Parameers (Proposed Model) Table 3.5. Model-Implied Equiy Premium for Aggregae Index and Porfolios v

11 Table 3.6. Model-Implied Risk Premium for Equiy, Wealh and Labor Reurns Table 3.7. Equiy, Wealh, and Labor Reurn Correlaions vi

12 ACKNOWLEDGEMENTS Firs of all, I would like o express my graiude o my advisor Professor Chang-Jin Kim for his careful guidance, inellecual simulus, and imely advice provided whenever I had been mired in difficulies while wriing he disseraion. He has lisened o my rough idea in a very paien manner, guided me o develop i ino more feasible opics for disseraion, and provided me wih a lo of helpful analyic and economeric ools o address he opics along wih his unflagging pursui of new research. A lo of feedbacks, suppors, and encouragemen from my commiee members, Eric Zivo and Yu-chin Chen, have also become an indispensable par for his disseraion. Professor Zivo helped me o consruc echnical background for financial economerics and gave many helpful commens for he disseraion. I received from Professor Chen very useful advice abou how o presen my disseraion in he presence of he audience from liseners sandpoin. She also provided me wih heoreical background for a link beween macroquaniies and asse prices. I would have never compleed his disseraion wihou heir guidance and advice. I also wan o grealy appreciae financial suppors from he Minisry of Finance in Korea and from he Deparmen of Economics, Universiy of Washingon. Mos of all, seadfas love and suppor from my wife and moher have encouraged me o overcome many personal adversiies hroughou he whole process of he Ph.D. program. I canno hank boh of hem enough for heir devoional suppor and uncondiional love. vii

13 DEDICATION To my wife, Daerim Kim, and moher, Chunsuk Lee viii

14 Chaper. WHAT MOVES THE STOCK MARKET IN THE PRESENCE OF STOCK REPURCHASES?. INTRODUCTION The radiional approach o modeling he variaions in sock reurns and dividend growh employs price-dividend raio as a predicor of sock reurn and dividend growh in a predicive regression se-up. Campbell and Shiller (988), Fama and French (988), Campbell and Ammer (993), and Cochrane (2008), among ohers, follow his approach. Since he price-dividend raio is inimaely linked o ime variaion in expeced reurns and in expeced dividend growh raes from he perspecive of he presen value ideniy of Campbell and Shiller (988), an enormous amoun of aenion in he finance lieraure has been focused on wheher sock reurns and dividend growh raes are predicable by price-dividend raio. Alhough a lo of empirical evidence has been uncovered showing ha reurns are predicable by financial raios, such as price-dividend raio or price-earnings raio, wheher price-dividend raio is appropriae as a predicor for reurn and dividend growh has been quesioned in a non-negligible manner by oher sudies. Sambaugh (986a, 999), Hodrick (992), and Nelson and Kim (993) poin ou ha he saisical significance of reurn predicabiliy can be weaker when he saisical ess are adjused in consideraion of a high persisence or near-uni roo propery of price-dividend raio. Chen (2009) and Koijen and van Nieuwerburgh (20) documen a srong insabiliy of reurn and dividend growh predicabiliy sensiive o he choice of sample periods. Paye and Timmermann (2006) repors an evidence in favor of breaks in he OLS coefficien in he

15 2 predicive regression of sock reurns on price-dividend raio, while Leau and van Nieuwerburgh (2008) and Choi, Kim, and Park (207) repor some evidence for srucural shifs in he mean of price-dividend raio. There have been a group of sudies aemping o resolve his issue by correcing for he measuremen error of price-dividend raio, exacerbaed by a recen srong populariy of sock repurchases as a way of ransferring firms cash flow o sockholders. Boudoukh, Michaely, Richardson, and Robers (2007) and Roberson and Wrigh (2006) show ha repurchase-adjused price-dividend raio (hereafer, price-oal payou raio) more srongly predics U.S. sock reurns and has a beer saisical propery such as a relaively low persisence. Kim and Park (203) aemp o adjus a declining dividend-price raio, using a change in he fracion of radiional dividend-paying firms so ha he adjused dividend series can have a more sable one-o-one long-run relaionship wih sock price. Ohers ry o disconnec a srong link beween price-dividend raio as a predicor for reurns and expeced reurn by adoping he laen variables approach which incorporaes unobservable variables, such as expeced reurn and expeced dividend growh, and heir dynamics explicily ino he model. Brand and Kang (2004), Binsbergen and Koijen (200), and Rychkov (202) follow his approach and show a srong improvemen of in-sample goodness of fi for dividend growh relaive o he radiional approach. Alhough a lo of effors o resolve he reurn predicabiliy issue from price-dividend raio has been made, he issue of wha moves sock price did no receive much aenion recenly since he exising view ha almos all aggregae sock reurn innovaion is driven by discoun rae news raher han cash flow news has been regarded as unquesionable. The radiional approach such as Campbell and Ammer (993) and Cochrane (2008, 20) documen ha mos of or more

16 han price-dividend variaion corresponds o discoun rae variaion. Even he laen variables approach produces a similar resul for his issue. Binsbergen and Koijen (200) repor ha 7.9% and 25.3% of variaions in price-dividend raio and unexpeced reurns are explained by discoun raes, while dividend growh accouns for only 4.9% of variaion in price-dividend raio when every monh s dividends are reinvesed in he sock marke. We aemp o reassess he roles of cash flow and discoun rae in sock price variaions since he exising dominaing view seems couner-inuiive in ha boh fundamenal and senimenal facors are likely o ac on he sock price movemens in a more balanced way. We exend he use of price-oal payou raio o he issue of wha moves sock price alhough i has been mainly employed o improve he reurn predicabiliy in a predicive regression. We employ he exising models of Campbell and Ammer (993) and Binsbergen and Koijen (200), one from he radiional approach and he oher from he laen variables approach because we aribue he underesimaed role of cash flow in sock price movemens o he measuremen error of price-dividend raio, no o he misspecificaion of he model. We use annual sample from 946 o 205 and quarerly sample from he firs quarer of 952 o he fourh quarer of 205 and he main findings can be summarized as follows. Firs, he incorporaion of price-oal payou raio insead of price-dividend raio ino he model of Binsbergen and Koijen (200) improves he in-sample goodness of fi for boh reurn and cash flow growh. For he annual aggregae marke index, 3 2 R increases from 9.% o 0.6% for sock reurn and from 7.0% o 22.4% for cash flow growh. The improvemen in he explanaory power also appears in medium and large cap porfolios, alhough no as eviden in small cap porfolio.

17 4 Second, he use of price-oal payou raio reduces boh persisence of expeced reurns and changes in sock prices from discoun rae channel. For he annual aggregae marke index, he persisence of expeced reurns declines from 0.92 o 0.83, which is ranslaed as a 4.8%p smaller sock price change in a response o an % expeced reurn shock. The reducion in sock price variaion from he discoun rae channel due o a lower persisence in expeced reurns is observed from all sizes of firms. Third, cash flow plays a non-negligible role in sock price variaion wih he incorporaion of price-oal payou raio ino he models of Binsbergen and Koijen (200) and Campbell and Ammer (993). Cash flow accouns for 25% and 72% of annual variaions in price-oal payou raio and unexpeced reurns, respecively, much higher han when using price-dividend raio (6% and 35%, respecively). The increase in he role of cash flow is eviden mainly in large cap firms. From he quarerly samples, we can observe a similar increase in he relaive imporance of cash flow in sock price variaions from he model of Campbell and Ammer (993). Cash flow accouns for 73% of oal variaion in unexpeced quarerly excess reurns, 23%p higher han when we use price-dividend raio. The remainder of his chaper is organized as follows. Secion.2 provides a review of he models of Binsbergen and Koijen (200) and Cambpell and Ammer (993). Secion.3 explains how o consruc he daa used o he models. Secion.4 provides he empirical resuls and heir implicaions for persisence of expeced reurns and sock price variaions. Secion.5 concludes..2 A REVIEW OF THE MODELS In his secion, we provide a review of wo models we use o derive he subsequen empirical resuls.

18 .2. Model of Binsbergen and Koijen (200) 5 Binsbergen and Koijen (200) propose a laen variables approach wihin he presen value framework of Campbell and Shiller (988). They explicily specify he dynamics for unobservable variables such as expeced reurn and expeced dividend growh, boh of which are relaed wih price-dividend raio in he measuremen equaion in he sae-space represenaion. Alhough we use he noaions for dividend d + and price-dividend raio pd + in his secion, hey are naurally replaced wih oal payou (dividends plus repurchases) and price-oal payou raio. Their model sars from he presen value ideniy of Campbell and Shiller (988), which connecs price-dividend raio, fuure expeced reurns, and fuure expeced dividend growh: k pd E d E r j j = + + r D + j+ - + r + j+ r j= 0 j= 0 - å å (.), where r + is sock reurn from ime o +, E + is expecaion operaor, condiional upon he informaion available up o ime +, k and r are log-linearizing consans, and D is he firs difference operaor. They specify he dynamics of expeced reurns m and expeced dividend growh g as an AR() process: m = d + d ( m - d ) + e (.2) m g = g + g ( g - g ) + e (.3) g D d = g + e (.4) d + + Plugging equaions (.2)-(.4) ino equaion (.), hey obain a linear relaionship among price-dividend raio, expeced reurn, and expeced dividend growh:

19 pd = A - B ( m - d ) + B ( g - g ) (.5) k g 0 -d0, where A º + - r - r, B º - rd, and B 2 º - rg. They rearrange hese equaions as one ransiion equaion: µ µ g g + = g g + e + (.6) and wo measuremen equaions by subsiuing he ideniy equaion (.5) ino equaion (.2): µ d D d+ = g 0 + g + e+ (.7) ( ) ( ) µ m g pd = - d A + B g - d g + d pd - B e + B e (.8) This se-up allows hem o compue he likelihood of he model using a Kalman Filer and esimae he parameers. Wih his process, hey filer ou expeced dividend growh and expeced reurn from he realized value of dividend growh and price-dividend raio..2.2 Model of Campbell and Ammer (993) Campbell and Ammer (993) also sar from he presen value ideniy of Campbell and Shiller (988) o derive an equaion for unexpeced excess reurn in erms of anoher news erms. Wih he equaion, hey decompose he variance for unexpeced excess reurn ino variance and covariance erms for oher news erms. By aking he operaor for he revision of expecaion ( E + - E ) on boh sides of equaion (.), hey obain: j j j + - r D + j+ = + - r + j+ = + - r + j+ + + j+ j= 0 j= 0 j= 0 å å å (.9) ( E E ) d ( E E ) r ( E E ) ( e i ), where e + is excess sock reurn and i + is ineres rae.

20 Rearranging equaion (.9), hey express unexpeced excess reurn in erms of oher news componens: 7 j j j = + - r D + j r + j r + j+ j= 0 j= j= 0 å å å (.0) ( E E ) e ( E E ) d ( E E ) e ( E E ) i ( NR, + NCF, + NDR, + NIR, + = - - ) To derive he values for each news componen in equaion (.0), hey include excess sock reurn, ineres rae, relaive bill rae, and dividend-price raio ino a se of sae variables Z + and assume ha Z + follows a VAR() process: ( ) ' Z º e i rb dp (.) Z+ = A + BZ + u+, u ~ (0, ) + N S (.2), where rb + is he relaive bill rae, defined as he level of he shor rae relaive o a -year backwards moving average of shor raes. Using he dynamics for Z + componens in equaion (.0) as follows:, hey derive he analyical soluion for each of news ( E - E ) Z = B u (.3) j + + j+ + N º ( E - E ) s Z = s u (.4) ' ' R, ' j j ' DR, + º ( + - ) r + = + j= N E E s å B u s Qu (.5) ' j j ' IR, + º ( + - ) 2 r + = 2( 4 + ) + j= 0 N E E s å B u s I Q u (.6) N = N + N + N (.7) CF, + R, + DR, + IR, +

21 8 -, where Q º rb( I - rb) is he marix of he long-run responses, s n is an n indicaion 5 vecor wih he n h elemen equal o uniy and he remaining elemens equal o zero, and I N is an N N ideniy marix..3 DESCRIPTION OF DATA We use annual daa from 946 o 205 and quarerly daa from he firs quarer of 952 o he fourh quarer of 205. As Chen (2009) documens, he dynamics for sock reurn and dividend show a differeniaed paern beween pre-war and pos-war periods. To avoid a possible noise from he prewar sample, we resric our sample for analysis o poswar period. Before he 95 Treasury-Fed accord, he ineres raes did no move much because, during he world war II, he Fed pledged o keep he ineres rae on Treasury bills fixed a 0.375%. We sar our quarerly sample ha includes ineres raes from he period when he Fed is allowed o effecively change ineres raes. We collec aggregae sock reurn and price-dividend raio from monhly reurns wih dividend and wihou dividend on he value-weighed porfolio of all NYSE, AMEX, NASDAQ, and ARCA socks in he CRSP daa. We consruc monhly sock price afer normalizing he iniial sock price o one and muliply i by monhly reurns wihou dividend. By combining he monhly sock price wih monhly reurn wih dividend, we can obain monhly dividend series. Monhly dividend series are aggregaed over 2 monhs and divided by he end-of-period sock price o derive annual and quarerly dividend-price raio. Toal payou-price raio is also consruced in a similar way. The only difference beween hem is ha he repurchase-adjused dividend-price raio is consruced, using adjused monhly reurns wihou dividend for each firm lised in he U.S. sock marke, following he mehodology of Bansal, Dimar, and

22 9 Lundblad (2005). Appendix A. provides echnical deails of he consrucion of sock repurchase daa. For he calculaion of sock reurns in excess of risk-free rae, monhly yields on 30-day U.S. Treasury bill are used. For he consrucion of size-sored porfolios, we updae each firm s marke capializaion every monh and sor all lised firms in he U.S. sock marke by he descending order of heir updaed marke capializaion every monh. Top 30% firms are included in large cap porfolio, he nex 40% firms in medium cap porfolio, and boom 30% firms in small cap porfolio..4 EMPIRICAL RESULTS.4. Preliminary Resuls In Figure., we provide price-dividend raio and price-oal payou raio series consruced by he mehodology given in Secion.3. By adding sock repurchases o he original dividend series, he price-oal payou raio shows more saionary dynamics han price-dividend raio. Price-oal payou raio for large cap porfolio moves in a similar way o price-oal payou raio for he aggregae marke index, while price-oal payou raios for small and medium cap porfolios show somewha differen movemens from he aggregae index series. Unil early 980s, price-dividend raio and price-oal payou raio had no exhibied any significan difference beween each oher, while he gap beween hem began o manifes iself afer he inroducion of SEC rule 0b-8 in 982, which allows firms o more freely repurchase heir own socks raded in he sock marke wihou sock price manipulaion charges. In 2004, he Bush Adminisraion inroduced a ax holiday for corporaions ha repariaed profis hey were holding abroad, which aced as anoher incenive for ock repurchases insead of dividend

23 paymen. Our price-oal payou series in Figure. are consisen wih he evens which srongly affeced a recen increase in sock repurchases. The improvemen in saionariy of price-oal payou raio is provided in Table., by esimaing heir AR() coefficiens. Regardless of wheher we include pre-war period in he sample, price-oal payou raio exhibis much lower persisence han price-dividend raio, ypically regarded as a beer saisical propery. In Table.2, we provide he esimaes for parameers of he model of Binsbergen and Koijen (200) by comparing he esimaes beween using price-dividend raio and using priceoal payou raio as one of he observable variables in he measuremen equaion. The parameer of our ineres is he persisence and volailiy of expeced reurn ( d and s m ) since hey deliver imporan implicaions for sock marke dynamics and he predicabiliy of reurns. By incorporaing sock repurchases ino he cash flow, he persisence of expeced reurn declines from 0.92 o 0.827, while is volailiy increases from 0.06 o More deailed descripion of he persisence of expeced reurn is given in subsecion In-Sample Goodness of Fi The incorporaion of sock repurchases ino cash flow from firms o shareholders improves he in-sample goodness of fi in he model of Binsbergen and Koijen (200) for boh sock reurn and cash flow growh. Table.3 shows ha, for he annual aggregae marke index, he value of 2 R rises from 9.% o 0.6% for sock reurn and from 7.0% o 22.4% for cash flow growh. We can also observe he improvemen in he explanaory power for boh sock reurn and cash flow growh of medium

24 and large cap porfolios, while small cap porfolio exhibis a mixed resul beween sock reurn and cash flow growh in erms of 2 R. The beer in-sample goodness of fi achieved from he incorporaion of sock repurchase is graphically represened in Figure.2 and Figure.3. The boom panels of Figure.2 and Figure.3 provide filered series for expeced reurn and expeced cash flow growh agains he realized reurn and he realized cash flow afer sock repurchases are added o he original dividend series. They capure he variaions of he realized values beer han in he upper panels of Figure.2 and Figure.3, boh of which are drawn wihou he consideraion of sock repurchases..4.3 Persisence of Expeced Reurns As seen from he parameer esimaes of he Binbergen-Koijen model in Table.2, he consideraion of sock repurchases reduces persisence of expeced reurns. In his subsecion, we provide he change in he persisence for size-sored porfolios and is implicaions for he sock price variaion generaed from he discoun rae channel. Table.4 shows ha he persisence of expeced reurns declines wih he use of price-oal payou raio for medium and large cap porfolios as well as for he aggregae marke index. For he annual aggregae marke index, he persisence of expeced reurns falls from 0.92 o 0.83, which is ranslaed as a 4.8%p smaller sock price change in a response o an % expeced reurn shock. Alhough he persisence of expeced reurn in small cap porfolio rises slighly from o 0.939, an expeced fall in he sock price of small-sized firms in a response o a % discoun rae shock ges smaller since he decrease in value of r offses he effec of he sligh increase in he persisence of expeced reurn for small cap porfolio.

25 .4.4 Role of Cash Flow and Discoun Rae in Marke Variaion 2 Mos of he exising sudies claim ha cash flow growh conribues lile o he variaion of sock prices and reurns, while mos of he sock price variaion is a resul of ime-varying discoun raes. We reassess he validiy of his dominaing claim in his subsecion by incorporaing sock repurchases ino he oal cash flow. In Table.5, we provide he variance decomposiions of sock prices and unexpeced reurns for aggregae marke index and size-sored porfolios, based on he Binsbergen-Koijen model. As in he exising view, only a small porion of he variaions in sock prices and reurns are explained by he cash flow channel excep for unexpeced reurns of small-sized firms wihou any consideraion of sock repurchases. Wih he inroducion of sock repurchases, however, cash flow accouns for 25% and 72% of annual variaions in price-oal payou raio and unexpeced reurns of aggregae marke index, respecively, much higher han in he case wihou sock repurchases considered (6% and 35%, respecively). The increase in he role of cash flow is mainly valid in large cap porfolio, while boh small and medium cap porfolios do no show a sronger role of cash flow in sock marke variaions. Table.6 shows ha our resul from he annual sample in he Binsbergen-Koijen model also holds in boh annual and quarerly samples in he Cambell-Ammer model. From he full annual sample ( ), he variaion of cash flow accouns for more han 50% of unexpeced reurn wih he use of price-oal payou raio, much higher han 8% when using price-dividend raio. From he full quarerly sample (952.Q-205.4Q), he share of cash flow variaion in unexpeced reurn variaion rises from 50% o 73%, while he conribuion of discoun rae channel does no change significanly. We can also observe a sronger role of cash flow channel

26 3 in sock marke wih he incorporaion of sock repurchases from all of hree differen annual and quarerly sample periods in Table.6. To check he robusness of our resuls o he choice of sample periods, we depics dynamic changes in he shares of cash flow and discoun rae channels in he oal variaion of sock reurn, by changing he las year of annual samples from 988 o 205, based on recursive esimaion of he Cambell and Ammer model. Figure.4 shows ha he increase in he conribuion of cash flow channel o he marke variaion, when we consider sock repurchase, is no affeced by he choice of sample periods..5 CONCLUSION Recenly, sock repurchases are being enrenched as a more popular way of disribuing cash flow from firms ino heir shareholders han he radiional ype of dividends. Therefore, he failure o accoun for sock repurchases could disor empirical resuls for he join dynamics of expeced reurn and cash flow growh. We reveal ha he use of he radiional predicor of sock reurn price-dividend raio can undermine he in-sample goodness of fi for he laen variables approach, overesimae he persisence of expeced reurns, and undersae he role of cash flow channel in he sock marke variaions. By using a ruer measure of cash flow priceoal payou raio insead of price-dividend raio, we can show ha he fundamenals of he U.S. economy or he profiabiliy of he U.S. corporae secor is a non-negligible facor o explain he variaion of he U.S. sock marke as well as he senimens of he marke paricipans. Our empirical resuls are also robus o he choice of sample periods. So far, we have implicily assumed ha he non-saionariy of price-dividend raio is mainly aribuable o he recen increase in sock repurchases. However, recen sudies provide various

27 4 possible reasons for he declining dividend-price raio oher han sock repurchases. Jank (203) claims ha he main culpri behind he non-saionary dividend-price raio is he change in he composiion of firms due o he deregulaion of he requiremens for lised companies. Leau, Ludvigson, and Wacher (2008) pay aenion o a persisen decline in consumpion volailiy as a source of he change in he sable relaionship beween dividend and price. If ha is he case, he incorporaion of sock repurchases could no provide a saifacory soluion for he empirical issues ha sem from he non-saionariy of price-dividend raio. We leave his subjec for our fuure research.

28 5.6 TABLES AND FIGURES Table.: Persisence of Price-Dividend Raio and Price-Toal Payou Raio (Aggregae Marke Index) Price-Dividend Price-Toal Payou Price-Dividend Price-Toal Payou Persisence (Sandard Error) (0.066) (0.086) (0.055) (0.092) Table.2: Parameer Esimaes: Binsbergen-Koijen Model ( : Aggregae Marke Index) Parameer Price-Dividend Raio Price-Toal Payou Raio Esimae Sandard Error Esimae Sandard Error d (0.04) 0.02 (0.07) g (0.0) (0.06) d 0.92 (0.043) (0.069) g (0.9) (0.9) s m 0.06 (0.007) 0.03 (0.02) s g (0.006) 0.20 (0.00) s d 0.00 (0.008) (0.007) r dm (0.069) 0.94 (36.300) r mg (0.44) (0.45)

29 6 2 Table.3: In-Sample Goodness of Fi: Binsbergen-Koijen Model ( R : ) Sock Reurn Cash Flow Growh Toal Small Medium Large Toal Small Medium Large Price- Dividend 9.% 3.6% 7.5% 9.3% 7.0% 22.0% 8.0% 5.7% Price-Toal Payou 0.6% 3.2% 9.5% 0.9% 22.4% 22.5% 20.0% 2.2% Noe: Toal, Small, Medium, and Large refer o aggregae marke index, small cap porfolio, medium cap porfolio, and large cap porfolio, respecively. Table.4: Expeced Reurn Persisence and Price Effec: Binsbergen-Koijen Model ( ) Persisence of Expeced Reurns Sock Price Change from % Expeced Reurn Shock Toal Small Medium Large Toal Small Medium Large Price- Dividend 0.92 (0.043) (0.039) (0.055) 0.92 (0.043) -9.4% -.6% -6.7% -9.4% Price-Toal Payou (0.069) (0.056) 0.89 (0.079) (0.068) -4.6% -9.8% -4.5% -4.6% Noe: Toal, Small, Medium, and Large refer o aggregae marke index, small cap porfolio, medium cap porfolio, and large cap porfolio, respecively.

30 7 Table.5: Variance Decomposiion of Price and Reurn: Binsbergen-Koijen Model ( ) Toal Small Medium Large PD PP PD PP PD PP PD PP CF 6.3% 24.6% 7.6%.% 4.5% 4.6% 6.% 25.% Price-Payou Raio DR 00.5% 99.4% 97.6% 96.8% 00.5% 93.9% 0.% 00.7% Cov -6.9% -24.% -5.3% -8.0% -5.0% -8.5% -7.2% -25.8% CF 35.4% 72.2% 73.% 59.% 48.7% 4.3% 35.2% 75.3% Unexpeced Reurn DR 93.8% 93.3% 50.6% 57.9% 8.8% 87.3% 97.7% 97.0% Cov -29.2% -65.5% -23.7% -7.0% -30.5% -28.6% -32.9% -72.3% Noe: Toal, Small, Medium, and Large refer o aggregae marke index, small cap porfolio, medium cap porfolio, and large cap porfolio, respecively. CF, DR, and Cov refer o variance of cash flow, variance of discoun rae, and covariance beween cash flow and discoun rae, respecively. PD and PP refers o price-dividend raio and price-oal payou raio, respecively.

31 8 Table.6: Variance Decomposiion of Unexpeced Reurn: Campbell-Ammer Model Aggregae Marke Index, Annual, VAR() Price- Dividend Price-Toal Payou Price- Dividend Price-Toal Payou Price- Dividend Price-Toal Payou Var(CF) 4.8% 83.9% 4.5% 5.6% 8.2% 5.6% Var(DR) 5.7% 20.8% 66.0%.4% 58.4% 68.6% VAR(IR) 8.2%.9% 4.5% 6.% 4.2% 5.7% Cov(CF,DR) -44.5% % 7.0% -66.8% 6.9% -5.9% Cov(CF,IR) -7.2% -46.5% -0.7% -3.9%.9% -9.0% Cov(DR,IR) 3.0% 60.0% -.2%.6% 0.3% -.%

32 9 Aggregae Marke Index, Quarerly, VAR(4) 952.Q-988.4Q 952.Q Q 952.Q-205.4Q Price- Dividend Price-Toal Payou Price- Dividend Price-Toal Payou Price- Dividend Price-Toal Payou Var(CF) 25.3% 43.6% 44.6% 53.3% 49.5% 73.3% Var(DR) 80.8% 8.3% 50.3% 42.5% 28.6% 30.% VAR(IR) 5.9% 7.4% 4.9% 4.7% 4.% 4.4% Cov(CF,DR) -2.% -32.% 2.3% 3.2% 7.0% 2.5% Cov(CF,IR) -7.0% -20.9% -2.5% -3.2% 0.% -2.9% Cov(DR,IR) 7.2% 20.7% 0.4% -0.5% 0.7% 2.5% Noe: Var(CF), Var(DR), Var(IR), Cov(CF,DR), Cov(CF,IR), and Cov(DR,IR) refer o variance of cash flow, variance of discoun rae, variance of ineres rae, covariance beween cash flow and discoun rae, covariance beween cash flow and ineres rae and covariance beween discoun rae and ineres rae, respecively.

33 20 Figure.: Price-Dividend Raio and Price-Toal Payou Raio 4.7 Aggregae Marke Index 5.5 Small Cap Porfolio 4.2 Price-Dividend Raio Price-Toal Payou Raio Medium Cap Porfolio 4.7 Large Cap Porfolio

34 Figure.2: Filered Series of Sock Reurn: Binsbergen-Koijen Model Case of Price-Dividend Raio Realized Reurn Filered Expeced Reurn Case of Price-Toal Payou Raio Realized Reurn Filered Expeced Reurn

35 Figure.3: Filered Series of Cash Flow Growh: Binsbergen-Koijen Model Case of Price-Dividend Raio Realized Cash Flow Growh Filered Expeced Cash Flow Growh Case of Price-Toal Payou Raio Realized Cash Flow Growh Filered Expeced Cash Flow Growh

36 Figure.4: Variance Decomposiions of Unexpeced Excess Reurn (Recursive Esimaion, Campbell-Ammer Model, Annual, VAR()) Share of Variance of Cash Flow News Price-Dividend Raio Price-Toal Payou Raio Share of Variance of Discoun Rae News Price-Dividend Raio Price-Toal Payou Raio Noe: The recursive esimaion is conduced from 952 o he year specified on he horizonal axis.

37 Chaper 2. WHAT MOVES THE STOCK MARKET IN THE 24 PRESENCE OF REGIME SHIFTS? 2. INTRODUCTION Since Campbell and Shiller (988) formulaed price-dividend raio as a linear relaion beween he economic agen s expecaion on fuure dividend growh and expeced fuure reurn hrough heir presen value framework, price-dividend raio has received a lo of aenion in he finance lieraure as a predicor of reurn and cash flow. As long as price and dividend mainain a sable one-o-one long-run relaionship beween each oher, a higher price-dividend raio han is longrun mean should predic a lower fuure reurn or a higher dividend growh or a combinaion of hem since he higher-han-normal price-dividend raio is desined o rever o is long-run mean. Alhough a lo of empirical evidence has been uncovered showing ha sock reurns are predicable by price-dividend raio, recen empirical sudies documen evidence of is srong persisence and non-saionariy, which undermine he validiy of price-dividend raio as an insrumen o capure he join dynamics of sock reurn and cash flow growh. Sambaugh (986a, 999), Hodrick (992) and Nelson and Kim (993) poin ou ha he saisical significance of reurn predicabiliy could be weaker when he saisical ess are adjused in consideraion of high persisence or near-uni roo propery of price-dividend raio. They show ha a ypically high persisence in price-dividend raio, coupled wih a srong negaive correlaion beween error erms in price-dividend raio and sock reurn, makes convenional - saisics unreliable since he poin esimaes may be biased and he OLS sandard errors incorrec. Koijen and van Nieuwerburgh (20) documen a srong insabiliy of reurn and dividend growh predicabiliy by price-dividend raio over ime, while Park (200a) aribues

38 25 he difference in is predicive power beween sample periods o a change in he saionariy of price-dividend raio, claiming ha reurn is more predicable when price-dividend raio follows an I(0) process while is predicive power weakens when price-dividend raio follows an I() process. Some sudies pay aenion o he change in he dividend payou policy by firms as a source of he srong persisence in price-dividend raio. Boudoukh, Michaely, Richardson, and Robers (2007) and Roberson and Wrigh (2006) recognize ha alhough price-dividend raio shows a srong persisence especially during he 990s, price-oal payou (dividends plus repurchases) raio exhibis a relaively saionary dynamics during he periods. They achieve improved ou-ofsample reurn predicabiliy by employing price-oal payou raio insead of price-dividend raio. Kim and Park (203) aemp o incorporae he effec of a recen decrease in firms wih a radiional dividend-payou policy on price-dividend raio and repor ha he predicive regression model ha employs he adjused price-dividend raio as a regressor ouperforms he random-walk model. Lee (207) incorporaes sock repurchases ino boh a more radiional VAR approach of Campbell and Ammer (993) and a newer laen variables approach of Binsbergen and Koijen (200) o sress he role of cash flow channel in sock marke variaion. While a group of sudies regard he recen increase in sock repurchases as a main culpri behind he non-saionariy of price-dividend raio, oher sudies reveal anoher sources of he srong persisence in price-dividend raio. Jank (203) claims ha he change in he composiion of firms due o he deregulaion of he requiremens for lised companies makes he relaionship beween sock prices and dividends more unsable. Leau, Ludvigson, and Wacher (2008) pay aenion o a persisen decline in consumpion volailiy as a source of he excepionally high sock valuaion in he lae 990 s. Abel (2003) and Park (200b) look for he cause of he U.S.

39 26 sock marke boom from a change in he demographic srucure, while Jermann and Quadrini (2003) model he sock price rise from a persisen increase in U.S. produciviy growh. If hese sources accoun for a significan porion of he non-saionary dynamics of price-dividend raio, he incorporaion of sock repurchases is no enough o provide a saisfacory soluion for he empirical issues ha sem from he saisical propery of price-dividend raio, since hey could affec price-oal payou raio in a non-negligible manner as well as price-dividend raio. We find a feasible soluion o accoun for oher possible sources of he non-saionariy in price-dividend raio, ypically no easy o quanify hrough observable daa, from he incorporaion of regime shifs in he mean of price-oal payou raio. Leau and van Nieuwerburgh (2008) and Choi, Kim, and Park (207) accoun for srucural shifs in he mean of price-dividend raio o provide a beer explanaion of reurn predicabiliy and join dynamics beween expeced reurn and expeced dividend growh. Alhough he consideraion of regime shifs in price-dividend raio can capure a par of he change in dividend payou policy, i does no fully accoun for he effecs of sock repurchases on he sock marke dynamics. Alhough Lee (207) provides a beer illuminaion of he role of sock repurchases on he sock marke by applying price-oal payou raio o he exising models, i does no ake oher facors affecing price-dividend raio ino full accoun. We find hese wo approaches as muually complemenary o each oher and hus combine hem by incorporaing regime shifs in he mean of price-oal payou raio ino he models of Binsbergen and Koijen (200) and Campbell and Ammer (993). Compared o he resul of Lee (207) which implicily assumes a consan mean of priceoal payou raio, we achieve i) a beer in-sample goodness of fi for reurn, cash flow growh, and ineres rae from boh of he models, ii) a lower persisence and higher volailiy of expeced reurn from aggregae marke index and medium and large cap porfolios, and iii) a sronger

40 conribuion of cash flow channel o he marke variaion from boh of he models, by using annual samples from 946 o 205. The main findings can be summarized as follows: Firs, he incorporaion of regime shifs in he mean of price-oal payou raio ino he models of Binsbergen and Koijen (200) and Campbell and Ammer (993) improves he insample goodness of fi for reurn, cash flow growh, and ineres raes. For he aggregae marke index of he full sample period, 27 2 R slighly rises from 0.6% o.4% for sock reurn and from 22.4% o 24.9% for cash flow growh. The improvemen in he explanaory power is more eviden from Campbell-Ammer model wih regime shifs. The variaions in excess sock reurn and ineres rae are significanly beer capured wihin he model as evidenced by higher values for hree differen sample periods. Second, by accouning for regime shifs in he mean of price-oal payou raio, he Binsbergen-Koijen model produces a lower persisence and higher volailiy of expeced reurns. For he annual aggregae marke index, he persisence of expeced reurns declines from 0.83 o 0.62, which is ranslaed as a 2.3%p smaller sock price change in a response o an % expeced reurn shock, while he volailiy of expeced reurn rises from 0.03 o The lower persisence in expeced reurns is observed from all size-sored porfolios, while medium-sized firms show a greaer decrease in expeced reurn persisence han firms of oher sizes. Third, we find a furher increase in he role of cash flow channel in explaining sock marke variaion by accouning for regime shifs ino boh of he models. Lee (207) reveal ha correcing for he measuremen error of cash flow enables he cash flow channel o capure a sizable share of marke variaion. We show ha he incorporaion of oher facors ino he correcly measured cash flow can furher srenghen he role of cash flow in he sock marke. In he Binsbergen-Koijen model, he cash flow channel can accoun for 6% and 86% of annual 2 R

41 28 variaions in price-oal payou raio and unexpeced reurns, respecively, much higher han when we assume ha he mean of price-oal payou raio is consan (25% and 72%, respecively), alhough he discoun rae channel sill ac on he sock marke srongly. We can also observe a similar increase in he share of cash flow channel in he sock marke variaions from hree differen sample periods. The remainder of his chaper is organized as follows. Secion 2.2 specifies how o incorporae he regime shifs in he mean of price-oal payou raio ino he models of Binsbergen and Koijen (200) and Cambpell and Ammer (993). Secion 2.3 explains he daa and Bayesian esimaion mehodology applied o he Campbell-Ammer model wih regime shifs. Secion 2.4 provides he empirical resuls and heir implicaions for persisence of expeced reurns and sock marke variaions. Secion 2.5 concludes. 2.2 SPECIFICATION OF MODELS In his secion, we describe wo models ha we employ o derive empirical implicaions for sock marke variaions, using price-oal payou raio. One model is proposed by Choi, Kim, and Park (207) which accouns for regime shifs in he mean of price-dividend raio ino Binsbergen and Koijen s (200) laen variables approach, based on he presen value framework of Campbell and Shiller (988). We provide a review of heir model in subsecion Addiionally, we propose an exension of he model of Campbell and Ammer (993) so ha he means of sae variables in heir VAR seing follow a wo-sae, firs-order Markov swiching process. The inroducion of he proposed model is provided in subsecion

42 2.2. A Review of Choi, Kim, and Park s (207) Model 29 Following he Binsbergen-Koijen s specificaion of reurn and dividend growh, hey specify reurn r + and dividend growh rae D d + as: r = m + e (2.) r + + D d = g + e (2.2) d + +, where m + j º E( r + j + I + j ), g+ j º E( D d+ j+ I+ j ), and I + j is informaion available up o ime +j. While he Binsbergen-Kojine s model assume ha expeced reurn m + j and expeced dividend growh g + j follow a saionary AR() process wih ime-invarian means, hese means are subjec o regime shifs, governed by a laen regime indicaor variable S + j, which follows a wo-sae, firs-order Markov chain where he ransiion probabiliies beween one regime a ime and he coniguous regime a ime + are fixed and conained in a 2 2 ransiion marix P : Pr[ S = j S = + i] º p, ij å pij =, i, j Î {0,}, j= 0 P é p p ù 00 0 º ê p0 p ú ë û (2.3) S = l + l S + n, S+ - p = l ( S - p ) + n + (2.4) p00, where l 0 = - p00, l = p + p00 -, and p º E( S+ ) =. 2 - p - p 00 They specify he regime-dependen means for sock reurns and dividend growh rae as: d º E( r S ) = d + ( d - d ) S (2.5) 0, S+ j + j + j 0,0 0, 0,0 + j g º E( D d S ) = g + ( g -g ) S 0, S+ j + j + j 0,0 0, 0,0 + j (2.6)

43 Addiionally, hey assume ha he economic agen observes he curren sae by he end of he curren period. Therefore, he economic agen s informaion se Y + j conains he curren sae S + j as well as he economerician s informaion se I + j. Then, hey specify he AR() dynamics for de-meaned expeced reurn and expeced dividend growh as: m m º m - d = d m + e (2.7) + j + j 0, S+ j + j- + j g g º g - g = g g + e (2.8) + j + j 0, S+ j + j- + j They incorporae he regime shifs in he means of sock reurn and dividend growh in he presen value ideniy of Campbell and Shiller (988): 30 k pd E d E r j j = + r D + + j - r + + j r j= 0 j= 0 - å å (2.9) k pd E[ d I, S ] E[ r I, S ] j j = + å r D + + j -å r + + j - r j= 0 j= 0 k = + å [, ]-å [, ] - r j j r E g+ j I S r E m+ j I S j= 0 j= 0 k + g 0,0 - d0,0 + p{( g 0, -g 0,0) - ( d0, -d0,0)} ( S+ -p ){( g 0, -g 0,0) - ( d0, -d0,0)} ² = + + g ² + - m+ - r - rl - rg - rd = pd - B m + B g (2.0) S An Exension of Campbell and Ammer s (993) Model Alhough Campbell and Ammer (993) assume ha he mean of he vecor sae variables Z + is ime-invarian, we assume ha hey are subjec o regime shifs, governed by a laen regime indicaor variable S +, whose dynamics is he same as equaions (2.3) and (2.4): ( ) ' Z º e i rb pp (2.)

44 * + + S 3 Z = Z + Z + (2.2) Z = Z + ( Z - Z ) S (2.3) S , where e + is he excess sock reurn, i + is he ineres rae, pp + is price-oal payou raio, and rb + is he relaive bill rae, defined as he level of he shor rae relaive o a -year backwards moving average of shor raes. We assume ha he de-meaned vecor of sae variables follows a VAR() process: * * Z+ = BZ + u+, u ~ (0, ) + N S (2.4) Solving he recursive dynamics for he laen regime indicaor in equaion (2.4) j-period forward, we can obain he effec of a shock o he expecaion on he curren sae on he expecaion on j-period forward regime-dependen mean of he vecor of sae variables: ( E - E ) Z = ( Z - Z ) l h (2.5) j + S+ j+ 0 +, where h + º ( E + - E ) S +. Following Choi, Kim, and Park (207), we also assume ha he economic agen observes he curren sae by he end of he curren period: h º ( E - E ) S = S -{ p + l ( S - p )} (2.6) Therefore, he revision of expecaion on j-period forward values of he sae variables can be expressed as: ( E - E ) Z = ( E - E ){ Z + Z } = B u + ( Z - Z ) l h (2.7) * j j + + j+ + + j+ S 0 + j+ + +, where, in he righ-hand side, he firs erm akes he same form as in he Campbell-Ammer model, which delivers he innovaion o curren de-meaned sae variables ( u + ) o j-period forward de-meaned sae variables, while he second erm ha does no appear in he Campbell-

45 Ammer model plays he role of ransmiing he curren shock o regime probabiliies ( h + ) o j- period forward means of sae variables. Using he dynamics for Z + componens as follows:, we can obain he analyical soluion for each of news 32 N º ( E - E ) s Z = s u + s ' ( Z - Z 0) h + (2.8) ' ' R, ' j j ' ' DR, + º ( + - ) r + = + + ( - 0) dh + j= N E E s å B u s Qu s Z Z (2.9) ' j j ' ' IR, + º ( + - ) 2 r + = 2( 4 + ) + + 2( - 0)( + d ) h+ j= 0 N E E s å B u s I Q u s Z Z (2.20) N = N + N + N (2.2) CF, + R, + DR, + IR, + -, where Q º rb( I - rb) is he marix of he long-run responses, s n is an n indicaion 4 vecor wih he n h elemen equal o uniy and he remaining elemens equal o zero, I N is an N rl N ideniy marix, and k º is he consan of he long-run responses from he shock o - rl regime probabiliies. 2.3 DATA AND ESTIMATION 2.3. Daa We use annual daa from 946 o 205 for he Binsbergen-Koijen model wih regime shifs and from 952 o 205 for he Campbell-Ammer model wih regime shifs. We collec aggregae sock reurn and price-dividend raio from monhly reurns wih dividend and wihou dividend on he value-weighed porfolio of all NYSE, AMEX, NASDAQ, and ARCA socks in he CRSP daa. We consruc monhly sock price afer normalizing he iniial sock price o one and