CAN THE CONSUMPTION-FREE NONEXPECTED UTILITY MODEL SOLVE THE RISK PREMIUM PUZZLE? AN EMPIRICAL STUDY OF THE JAPANESE STOCK MARKET

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1 Discussion Paper No. 783 CAN THE CONSUMPTION-FREE NONEXPECTED UTILITY MODEL SOLVE THE RISK PREMIUM PUZZLE? AN EMPIRICAL STUDY OF THE JAPANESE STOCK MARKET Myong-Il Kang June 00 The Insiue of Social and Economic Research Osaka Universiy 6- Mihogaoka, Ibaraki, Osaka , Japan

2 Can he Consumpion-Free Nonexpeced Uiliy Model Solve he Risk Premium Puzzle? An Empirical Sudy of he Japanese Sock Marke Myong-Il Kang Korea Universiy June 7, 00 Correspondence: M Kang, Assisan professor, Deparmen of Business Adminisraion, Korea Universiy, -700 Ogawa-cho, Kodaira, Tokyo , JAPAN. Tel: Fax: mkang@korea-u.ac.jp. This paper is a par of he visiing research of he Insiue of Social and Economic Research, Osaka Universiy. My special hanks go o S. Ikeda for helpful commens, and I am also graeful o Y. Fukua, K. Hiraa, K. Kuboa, H. Nakaoa, K. Nishina, M. Ohnishi, F. Ohake, K. Oya, Y. Tanigawa, and paricipans a he 004 Annual Meeing of he Japanese Economic Associaion, Okayama Universiy, for beneficial discussions. I acknowledge a financial suppor by he Gran-in-Aid for JSPS Fellows (88689), he Minisry of Educaion, Culure, Spors, Science and Technology.

3 Absrac This paper invesigaes wheher he consumpion-free wo-bea ineremporal capial asse-pricing model developed by Campbell and Vuoleenaho (004) is able o solve he risk premium puzzle in he Japanese sock marke over he period Using he cash flow and discoun rae beas as risk facors, he model is able o explain abou half of he marke reurns by selecion of suiable vecor auoregression variables. On his basis, he model proposed solves he risk premium puzzle in Japan, hereby suggesing ha Japanese invesors are less risk averse han US invesors. However, a model including only he cash flow bea beer explains reurns han a model wih boh beas. The analysis also ess and rejecs he simple capial asse-pricing model in Japan. Key words: Risk premium puzzle, Nonexpeced uiliy, CAPM JEL classificaion: G

4 . Inroducion Since Mehra and Presco (985) firs idenified he risk premium puzzle, many researchers have invesigaed wheher he Lucas (978) and Breeden (979) form of he consumpion-based capial asse-pricing model (C CAPM) is compaible wih he Japanese sock marke. Using Hansen s (98) Generalized Mehod of Momens, Hamori (99) showed ha he power uiliy ype C CAPM exhibis good performance wih low-risk parameers while Hamori (994) verified ha he Epsein and Zin (989, 99) nonexpeced uiliy ype C CAPM explains reurns beer in he Japanese equiy marke. Conversely, Tanigawa (994) and Hori (996) reesed hese models using he Hansen and Jagannahan (99) bound es and rejeced boh. Nakano and Saio (998) also applied hese models o hree Japanese markes sock, land, and bonds and verified heir poor performance. Imporanly, all of hese models explicily conain a consumpion variable in he pricing kernel, and hus could no avoid he harmful effecs arising from he use of aggregae consumpion daa: ofen incriminaed as he cause of he risk premium puzzle because of aggregaion bias, he infrequen reporing of consumpion, sampling error, and smoohing associaed wih seasonal adjusmen. To avoid hese problems wih he use of aggregae consumpion daa, Campbell and Vuoleenaho (004) develop a consumpion-free ineremporal capial asse-pricing model (hereafer, CV model) assuming Epsein Zin nonexpeced uiliy. They solve he discree-ime version of Meron s ICAPM by using a dividend raio model (Campbell, 988a) and reurn decomposiion (Campbell, 99). The induced model includes wo risk facors, he cash flow bea and he discoun rae bea, boh of which are endogenously deermined. The former measures he correlaion beween asse reurns and unexpeced flucuaions in fuure cash flows (cash flow news) while he laer measures fuure discoun raes (discoun rae news). Campbell and Vuoleenaho (004) decompose unexpeced marke reurns ino wo componens by assuming ha he marke variables follow a firs-order vecor auoregression (VAR) process, and find ha he model empirically solves he risk premium puzzle wih a low-risk aversion parameer in he US sock marke. The focus of his paper is wheher he CV model also solves he risk premium puzzle in Japan. For his purpose, we empirically invesigae he validiy of he CV model for Japanese sock reurns, and 3

5 compare i wih a facor model and he simple capial asse-pricing model (CAPM). We selec five variables as VAR sae variables suiable for he Japanese daa and esimae wo beas as risk facors. The main conribuion is ha we demonsrae ha he CV model is valid in Japan wih high adjused R-squared values (5.% and 4.6%), and solve he risk premium puzzle wih low values of he relaive risk aversion (RRA) parameer (.80 and.05). Given ha he esimaed RRA is lower han in he US, we conjecure ha Japanese invesors are less risk averse han invesors in he US. We also find ha a single-facor model only including a cash flow bea can successfully explain Japanese sock reurns and rejec he CAPM. The remainder of he paper is organized as follows. Secion inroduces he CV model. Secion 3 discusses he variables used as sae variables in he VAR, generaes daa on he wo news variables, and esimaes heir beas. We also empirically analyze he Japanese sock marke by comparing he CV model wih he facor model and he CAPM, and esimae he RRA coefficien. Secion 4 provides he conclusion.. Model Consider a sock ha pays dividends D a he end of he period. Leing P denoe he price of he sock a ime, reurns R are: R P D. () P Taking logarihms of boh sides of equaion () and using a Taylor expansion, he log of R, r, can be expressed approximaely as linear in he logs of P and D : r k p ( ) d p, () where /( exp ( d p )) ; k ln( ) ( )ln(/ ) ; and p and d denoe he logarihms of P and D, respecively. We solve equaion () forward ieraively. By aking expecaions and subracing d from boh sides, we obain he familiar Campbell and Shiller (988a) formula: p d k E j0 j d j r j, (3) 4

6 where d ( d d ) denoes he log of dividend growh. This formula explains ha he log of he price dividend raio a ime depends on expecaions a ime of he discouned sum of fuure dividend growh minus he discoun rae. We follow Campbell (99) in decomposing unexpeced reurns ino wo of is componen pars by using (3). Subsiuing equaion (3) for p and p in () and rearranging obains: j Er ( E E ) d j ( E E ) j0 j r CF, DR, r j j N N, (4) where N CF, ( j ( E E ) d j ) denoes news abou fuure cash flows and j0 N DR, ( ( E ) j E r ) denoes news abou fuure discoun raes. Equaion (4) implies ha j j unexpeced reurns are composed of wo pars: changes during he period from o + in expecaions of fuure cash flows j j0 d and discoun raes r j j. Le period over he risk-free rae on he marke porfolio. We define he beas as follows: r, represen he excess reurn in e M Cov( ri,, NCF, ) i, CF and e e Var( r E r ) M, M, Cov( ri,, N DR, ) i, DR. (5) e e Var( r E r ) M, M, Because discoun rae news has a negaive sign, he sum of he wo beas equals he marke bea: i, M i, CF i, DR. (6) Campbell and Vuoleenaho (004) refer o i, CF as he cash flow bea and i, DR as he discoun rae bea. Equaion (6) indicaes ha we can decompose he marke bea ino he cash flow and discoun rae beas. We close he model by specifying he uiliy-maximizing behavior of consumers. Consider an News is used o describe he revision of expecaions during he wo periods. Campbell and Vuoleenaho (004) also refer o he cash flow bea as he bad bea and he discoun rae bea as he good bea. 5

7 infiniely lived represenaive consumer. He or she chooses he sochasic process of consumpionc. Assume ha he nonexpeced uiliy funcion U proposed by Epsein and Zin (989, 99) gives consumer preferences, U ( C, E ( U )) ( ) C ( E ( U )), (7) where saisfies ( ) /( ), represens he relaive risk aversion (RRA) coefficien, he elasiciy of ineremporal subsiuion (EIS), and he ime discoun facor. Leing W denoe wealh holding a ime, he budge consrain is given by W R )( W C ) ( p,. The represenaive consumer maximizes (7) subjec o he budge consrain. The firs-order condiion is given by he Euler equaion, E p, C i,. (8) C ( R ) ( ) ( ) ( R ) In equaion (8), he pricing kernel or ineremporal marginal rae of subsiuion (IMRS) is given C ( C ( R ( ) by ) p, ), and is shown o depend on wo facors, consumpion growh and marke reurns. The resuling wo-facor srucure enables us o examine he asse pricing implicaions of boh news iems ( N CF and N DR ). Noe ha in he case of =, he pricing kernel depends solely on marke reurns, i.e., he model reduces o CAPM, whereas when = /, he pricing kernel depends solely on consumpion growh, so ha he C CAPM holds. 3 By assuming ha consumpion growh and asse reurns follow a join lognormal disribuion, he logarihmic Euler equaion is obained from (8) as follows: i, E ( ri, ) rf, Cov ( ri,, rp, Erp, ) ( ) Cov ( ri,, N p, DR, ). (9) Subsiuing (4) ino (9) yields: 3 Wih Epsein Zin preferences, we can generally express he pricing kernel as he weighed produc of consumpion growh and marke reurns. 6

8 i, E ( ri, ) rf, Cov ( ri,, N p, CF, ) Cov ( ri,, N p, DR, ), (0) which in urn can be rewrien using (6) as:. () i, E ( ri, ) r f, p, i, CF p, p, i, DR p, Equaion () indicaes ha wo risk facors, he cash flow bea and he discoun rae bea, deermine he equiy risk premium i. The risk price of he cash flow bea is and he risk price for he discoun p, rae bea is p,. The risk price of he cash flow bea is hus larger han he discoun rae bea when he RRA coefficien is greaer han one. 3. Empirical analysis In his secion, we use Japanese sock marke daa o examine: (i) wheher he CV model is valid in he Japanese sock marke compared wih he facor model and he CAPM, and (ii) how large he RRA is in Japan. We conduc he empirical asks as follows. Firs, we generae daa on he cash flow and discoun rae news by esimaing a VAR model. We also show ha he VAR variables used in his sudy are more suiable for explaining Japanese economic daa han hose used by Campbell and Vuoleenaho (004) in he US. Second, using he news daa, we esimae he cash flow and discoun rae beas for various porfolios. Third, we regress porfolio reurns on hese beas o es he empirical validiy of he models and o esimae he value of he RRA coefficien. 3.. Daa descripion and news and bea esimaion To consruc daa on cash flow and discoun rae news, we esimae a VAR model as follows: z a, () z where z denoes an m sae vecor, he firs elemen of which is marke porfolio reurns wih he oher elemens being specified laer, a is an m consan vecor, is an m m VAR coefficien 7

9 marix, and is he m error erm or shock vecor. Upon esimaion of he VAR process, he news daa N, ( CF e e ) and N e are consruced as affine ransformaions of he shock vecor : DR, N CF, ( e e ) and N, DR e, (3) where ( I ) maps VAR shocks o news, I denoes he m m ideniy marix, and e is an m vecor wih one in he firs elemen and zero oherwise. For he VAR variables in z, we firs ry four variables; he excess reurns on he marke index (ER), he erm yield spread (YS), he price book value raio (PBR), and he value yield spread of small socks (VS). We consruc ER by aking he difference in sock reurns and he risk-free rae. For sock reurns, we use he Toal Index of he DAIWA Sock Index (DSI, hereafer) from he websie of he Daiwa Insiue of Research Ld. For he risk-free rae, we use he monhly GENSAKI Raes (he rae in he repurchase agreemen marke) from he Financial and Economic Saisics Monhly published by he Research and Saisics Deparmen of he Bank of Japan. 4 YS is he difference beween shor- and long-erm yields on he Nikkei Bond Indices a he end of he monh. PBR is he average value of he price book value raios compued from all lised companies on he Firs Secion of he Tokyo Sock Exchange. This daa are from he Monhly Saisics Repor published by he Tokyo Sock Exchange. The raio is log ransformed. VS is he difference in small index reurns for value and growh socks from he DSI. The daa series span he period 984: 00:. Table provides descripive saisics for he sae variables. Table 3 repors he resuls of he VAR esimaion using he four variables. Alhough TY and YS 4 The reference base for he DSI indices is he end of December 983. There are four major DSI indices: () a Toal Index ha includes all securiies lised on six markes (Tokyo, Osaka, and Nagoya Sock Exchanges, JASDAQ, TSE Mohers, and Hercules); () Syle Indices, including large, small, value, and growh indices; (3) Secor Indices ha correspond o various indusrial secors; and (4) Oher Indices, which include sock indices for large nonfinancials and financials, and a nonfinancials oal index. All of hese indices are derived by weighing he oal reurns of composie socks by heir marke. All of hese indices have wo ypes, DSI and DSI : he former is based on floaing shares and laer on all lised shares. For more deails, see he Web sie of Daiwa Capial Marke Indices a hp:// 8

10 have large values of adjused R-squared, he sysem overall has only a few significan coefficiens. More imporanly, ER has a negaive adjused R-squared and no significan coefficiens. The poor performance of he VAR esimaion clearly indicaes ha hese four VAR variables are unable o capure he expecaions among marke paricipans and may be inappropriae for he purposes of our analysis. To improve he performance of he VAR, we add he following wo variables insead of VS: he growh rae of business failure (DEF) and bond yields (BY). DEF is he year-on-year growh rae of business failures obained from Tokyo Syoko Research (TSR). BY are he hree-monh GENSAKI raes a monh end for hree-monh conracs. These are from he monhly repor published by he Japan Securiies Dealers Associaion, hen ransformed ino real erms and aking he hree-monh moving average. Table 4 shows he resuls of he VAR using hese five variables. By adding new wo variables, he number of significan coefficiens and he value of he adjused R-squared boh improve. In paricular, ER now has hree significan coefficiens and a posiive adjused R-squared of.69. We can compue he residuals using he esimaed VAR coefficiens and hen decompose hem ino cash flow and discoun rae news. Tables 5 and Table 6 provide descripive saisics for he news calculaed wih he four-variable and five-variable VARs, respecively. Using he news daa calculaed above, we can compare he performance of he four-variable and five-variable VARs. Because cash flow news is he sum of discoun rae news and he residuals of RP according o equaion (3), he larger he VAR unpredicabiliy, he greaer he magniude of he RP residuals and, as a consequence, he larger he cash flow news. Table 7 presens a comparison of he absolue sum, absolue average, and squared sum of boh news calculaed using four and five variables. As cash flow news for four variables is much larger han for five variables, we suspec ha he four sae variables have poorer predicion performance han he five sae variables. Using Equaion (3), we decompose he variance of reurns ino hree erms as follows: Var( r Er ) Var( N CF, ) Var( N DR, ) Cov( N CF,, N DR, ). (4) This expression indicaes ha we can decompose he variance of expeced reurns, i.e., variance of oal news, ino variance and covariance of boh ypes of news. Table 8 provides a comparison of boh VARs using he variance decomposiion of news. In he case of four variables, he variance of cash flow news and covariance of news unnaurally consiss of a greaer porion of oal news, while wih five variables, oal 9

11 news decomposes well ino boh ypes of news. Accordingly, we use he news esimaed by applying he VAR wih five variables. Nex, we esimae he cash flow and discoun rae beas. From definiion (5) of he beas, hese are esimaed using he following equaions: ˆ ˆ ˆ Cov( ri,, N CF, ) i, CF and Var ˆ ( Nˆ Nˆ ) CF, DR, ˆ ˆ ˆ Cov( ri,, N DR, ) i, DR (5) Var ˆ ( Nˆ Nˆ ) CF, DR, We use 43 DSI indices for he asse reurn daa: 33 secor indices, 7 Daiwa secor indices, and 3 oher indices. 5 We esimae he beas for hese asses using he news daa obained above. The resuls are included in Table 9. On average, he discoun rae bea is larger han he cash flow bea, and he correlaion coefficien beween he beas akes a posiive and low value of These feaures are similar o he US findings in Campbell and Vuoleenaho (004). 3.. Tess for asse-pricing models Using hese beas, we empirically compare hree asse-pricing models: he facor model, he CV model, and he CAPM. Following Campbell and Vuoleenaho (004), we assume hree assumpions for equaion (). Firs, simple reurns R R E are used insead of log-reurns on he lef-hand side. i, f, Second, he momens are invarian hroughou ime, so ha uncondiional momens can replace condiional momens. Finally, he sock porfolio is a proxy for he marke porfolio. 6 Equaion () can hen be rewrien as follows: R i R f M i, CF M M i DR M E,. (6) Using he esimaed beas as explanaory variables, we represen he regression equaion for he CV model as: R e i ˆ ˆ e, (7) g0 g i, CF g i, DR i 5 See Foonoe 4 for a shor descripion of hese indices. 6 For explici expression of he hird assumpion, we inser subscrip p ino M. 0

12 where R e i Ri R is he simple mean of excess reurns on asse i and he slope parameers f g and g are he prices of he risk facors. From equaion (7), he raio g g equals he RRA coefficien. Following Campbell and Vuoleenaho (004), each model is esimaed in wo differen regression forms: he firs wih an unresriced zero bea, and he second wih a resricion ha zero bea equals he GENSAKI rae. Each model includes Whie s heeroskedasiciy consisen covariances. We also repor he 95% criical value of a boosrap using,500 simulaed realizaions. We sar by esimaing he wo-facor model wih he cash flow and discoun rae beas. We do his by regressing asse reurns on boh beas wihou imposing any resricions on he risk prices. The resuls of hese esimaions are in he second and hird columns of Table 0. The risk price of he cash flow bea is significanly posiive whereas he risk price of he discoun rae bea is insignifican wih a large adjused R-squared. Based on hese resuls, we doub ha we could explain asse reurns beer using he single-facor model wih a cash flow bea, so we regress reurns on he cash flow and discoun rae beas separaely. Table shows he resuls. In he single-facor specificaion, he cash flow bea is sill significan and exhibis a value of adjused R-squared larger han even he wo-facor cases. In conras, he discoun rae bea remains insignifican. These findings sugges ha only he cash flow bea significanly explains asse reurns. We nex examine he CV model by running a regression wih a resricion on he risk price of he discoun rae bea, g = M. 7 The resuls are included in he fourh and fifh columns of Table 0. The esimaed slope parameer g, which is he risk price of he cash flow bea, is significanly posiive, implying ha he CV model significanly predics asse reurns. The las row of Table 0 provides he RRA coefficien calculaed by = g g. This is.80 wih an unresriced zero bea and.05 wih a resriced zero bea. These values are lower han in he US case and indicae ha Japanese invesors may be less risk averse han US invesors. 8 I is also noeworhy ha we could solve he risk premium puzzle wih his low-risk aversion parameer by applying he model o Japanese daa. The resuls lead us o he conclusion ha he CV model is useful for solving he risk premium puzzle in he Japanese sock marke. 7 This resricion is from equaion (). In our daa ses, M = compued from DSI. 8 In he US case in Campbell and Vuoleenaho (004), RRA equals 8.6 and 7.0, respecively.

13 Lasly, we examine he CAPM wih he resricion ha boh risk prices are equal, g g. 9 The sixh and sevenh columns of Table 0 repor he resuls. Alhough he esimaed coefficien is significanly posiive, he value far exceeds average marke porfolio reurns; ha is, he esimaed risk price is significanly higher han ha required by he CAPM specificaion. 0 Accordingly, we conclude ha a single-facor model wih a marke bea only marginally explains asse reurns. 4. Conclusion This paper invesigaes wheher he consumpion-free CV model beer explains Japanese sock reurns han he facor model and he radiional CAPM, and wheher we can solve he risk premium puzzle, a leas in Japan, using his model. In he analysis, we seleced five VAR sae variables (RP, YS, PBR, DEF, and BY) as being more suiable for Japanese daa han he four variables used in he comparable US sudy. Using he esimaed VAR coefficiens, we decomposed unexpeced reurns ino wo componens, and esimaed he cash flow bea and he discoun rae bea. We found he discoun rae bea o be larger, on average, han he cash flow bea, and heir low and posiive correlaion coefficien is consisen wih he US case. We hen esed hree ypes of asse-pricing models: a wo-facor model wih wo beas, he CV model, and he radiional CAPM. The resuls of his analysis are as follows. Firsly, he single-facor model including only he cash flow bea beer explained Japanese sock reurns raher han a wo-facor model including boh beas. Second, he CV model is valid in he Japanese sock marke, hough wih a somewha lower adjused R-squared han ha found wih he single-facor model. On his basis, we can solve he risk premium puzzle as he risk aversion parameer lies below hree. Moreover, as he value of RRA is smaller han in comparable US sudies, he implicaion is ha Japanese invesors are less risk averse han US invesors. These resuls suppor previous findings by Hamori (99, 994) ha he risk premium puzzle does no arise in Japan. Third, consisen wih many previous sudies, we rejec he CAPM. 9 This resricion is from CAPM heory and he definiion of beas in Equaion (5). 0 The average of he excess marke porfolio reurns is in our daa se.

14 References Breeden, D. T, 979. An ineremporal asse-pricing model wih sochasic consumpion and invesmen opporuniies. Journal of Financial Economics 7, Campbell, J. Y, 99. A variance decomposiion for sock reurns. Economic Journal 0, Campbell, J. Y, 993. Ineremporal asse pricing wihou consumpion daa. American Economic Review 83, Campbell, J. Y, 996. Undersanding risk and reurn. Journal of Poliical Economy 04, Campbell, J. Y., A. W. Lo, and A. C. Mackinlay, 996. The Economerics of Financial Markes (Princeon Universiy Press). Campbell, J. Y. and J. Mei, 993. Where do beas come from? Asse price dynamics and he source of sysemaic risk. Review of Financial Sudies 6, Campbell, J. Y. and R. J. Shiller, 988a. The dividend-price raio and expecaions of fuure dividends and discoun facors. Review of Financial Sudies, Campbell, J. Y. and R. J. Shiller, 988b. Sock price, earnings, and expeced dividends. Journal of Finance 43, Campbell, J. Y, and L. M. Viceira, 997. Sraegic asse allocaion (Oxford Universiy Press). Campbell, J. Y. and T. Vuoleenaho, 004. Bad bea, good bea. American Economic Review 94, Epsein, L. and S. Zin, 989. Subsiuion, risk aversion, and he emporal behavior of consumpion and asse reurns: A heoreical framework. Economerica 57, Epsein, L. and S. Zin, 99. Subsiuion, risk aversion, and he emporal behavior of consumpion and asse reurns: A empirical invesigaion. Journal of Poliical Economy 99, Fama, E. F. and K. R. French, 99. The cross-secion of expeced sock reurns. Journal of Finance 47, Fama, E. F. and K. R. French, 993. Common risk facors in he reurns on sand bonds. Journal of Financial Economics 33, Hamori, S, 99. Tes of C-CAPM for Japan: Economics Leers, 38,

15 Hamori, S, 994. The non-expeced uiliy model and asse reurns: Some evidence from Japan. Japanese Journal of Financial Economics,, Hansen, L. P. and R. Jagannahan, 99. Implicaions of securiy marke daa for models of dynamic economies. Journal of Poliical Economy 99, 5 6. Hori, K, 996. C-CAPM in Japanese asse marke: Reexaminaion (in Japanese). Osaka Economic Papers, 45, Linner, J, 965. The valuaion of risky asses and he selecion of risky invesmens in sock porfolios and capial budges. Review of Economics and Saisics 47, Lucas, R. E. Jr., 978. Asse prices in an exchange economy. Economerica 46, Mehra, R. and E. C. Presco. 985, The equiy premium: A puzzle. Journal of Moneary Economics, 5, Meron, R. C, 973. An ineremporal capial asse pricing model. Economerica 4, Nakano, K. and M. Saio, 998. Communicaion: Asse pricing in Japan. Journal of he Japanese and Inernaional Economies, Roll, R, 977. A criique of he asse pricing heory s es; par I: On pas and poenial esabiliy of he heory. Journal of Finance 49, 0. Sharpe, W, 964. Capial asse prices: A heory of marke equilibrium under condiions of risk. Journal of Finance 9, Tanigawa, Y, 994. Syouhi daa wo moiia sisankakaku no jissyou bunseki (in Japanese). Okayama Economic Review, 5,

16 Table Descripive saisics of he four VAR sae variables ER YS PBR VS Mean Serr Median Sdev Variance E Kurosis Skewness Range Min Max Sum Noe: This able shows he descripive saisics of he VAR sae variables. The sample period 984:0 00: comprises 8 monhly daa poins. ER is he excess reurn on he DSI oal sock index wih all lised socks. YS is he erm yield spread of he Nikkei Index of Bond Yields. PBR is he average value of he price o book value raio (in logs) of all socks rading in he Firs Secion of he Tokyo Sock Exchange. VS is he value yield spread of small socks, which is he difference beween he DSI small-value and small-growh indexes. Serr. is he sandard error and Sdev. is he sandard deviaion. 5

17 Table Descripive saisics of he five VAR sae variables ER YS PBR DEF BY Mean Serr Median Sdev Variance E Kurosis Skewness Range Min Max Sum Noe: This able shows he descripive saisics of he VAR sae variables. The sample period 984:0 00: comprises 8 monhly daa poins. ER is he excess reurn on he DSI oal sock index wih all lised socks. YS is he erm yield spread of he Nikkei Index of Bond Yields. PBR is he average value of he price o book value raio (in logs) of all socks rading in he Firs Secion of he Tokyo Sock Exchange. DEF is he growh rae of business failures calculaed as he year-on-year rae. BY is he bond yield rading wih repurchase agreemen a monh-end, wih a erm o mauriy of hree monhs, ransformed ino real erms and a hree-monh moving average. Serr. is he sandard error and Sdev. is he sandard deviaion. 6

18 Table 3 VAR parameer esimaes using four variables ER YS PBR VS ER( ) (0.507) (0.4495) (.7987) ( ) YS( ) *** (.07960) (60.004) (0.6069) (0.3657) PBR( ) *** (0.439) ( ) ( ) (0.36) VS( ) *** ( ) ( 0.90) (0.86) (3.8365) C ( ) (0.9775) ( ) (0.50) Adj. R-squared 0.69% 94.70% 97.94% 4.69% Noe: This able provides he OLS parameer esimaes for a firs-order VAR model including a consan erm (C), he risk premium (ER), he erm yield spread (YS), he price book value raio (PBR), and he value yield spread of small socks (VS). The sample periods for he dependen variables 984:0 00: comprise 7 monhly daa poins. (-) is he explanaory variable of he VAR and denoes a lag of one period. Adj. R-squared denoes he adjused R-squared. The firs row for each variable is he esimaed coefficiens. The values in parenheses are -values. *** denoes significance a he % level, ** a he 5% level, and * a he 0% level. 7

19 Table 4 VAR parameer esimaes using five variables ER YS PBR DEF BY ER ( ) [0.4459] [ ] [.09] [0.4599] [.5694] YS ( ) *** ** [0.8570] [ ] [ ] [.300] [.404] PBR ( ) *** [.49368] [.0993] [ ] [ ] [0.080] DEF ( ) ** ** 0.960*** [.304] [.589] [.043] [30.569] [ ] BY ( ) 7.536** * *** [.3043] [.93038] [.6357] [ ] [ ] C ** [ ] [0.8377] [0.0665] [.8] [.07685] Adj. R-squared.69% 94.86% 97.98% 83.55% 93.09% Noe: The able provides he OLS parameer esimaes for he firs-order VAR model including a consan erm (C), he risk premium (ER), he erm yield spread (YS), he price book value raio (PBR), he growh rae of business failure (DEF), and he bond yields (BY). The sample periods for he dependen variables 984:0 00: comprise 7 monhly daa poins. (-) is he explanaory variable of he VAR and denoes a lag of one period. Adj. R-squared denoes he adjused R-squared. The firs row for each variable is he esimaed coefficiens. The values in parenheses are -values. *** denoes significance a he % level, ** a he 5% level, and * a he 0% level. 8

20 Table 5 Descripive saisics for cash flow and discoun rae news as generaed by he four-variable VAR DR news CF news Mean Mean Serr Serr Median Median Sdev Sdev Variance Variance Kurosis.0748 Kurosis Skewness Skewness Range Range Min Min Max Max Sum Sum Noe: This able provides descripive saisics for he cash flow (CF) and discoun rae (DR) news generaed from he four-variable VAR wih elemens RP, YS, PBR, and VS. Serr. is he sandard error and Sdev. is he sandard deviaion. 9

21 Table 6 Descripive saisics for cash flow and discoun rae news generaed by he five-variable VAR DR news CF news Mean Mean Serr Serr Median Median Sdev Sdev Variance Variance Kurosis Kurosis Skewness Skewness Range Range 0.04 Min Min Max Max Sum Sum Noe: The able provides descripive saisics for cash flow (CF) and discoun rae (DR) news generaed from he five-variable VAR wih elemens RP, YS, PBR, DEF, and BY. Serr. is he sandard error and Sdev. is he sandard deviaion. 0

22 Table 7 Absolue sum, absolue average, and sum of squares of news CF news DR news Four variables Five variables Four variables Five variables Absolue sum Absolue average Sum of squares Noe: The able provides he absolue sum, absolue average, and sum of squares for news generaed by he four and five-variable VARs, respecively. Absolue sum is he sum of he absolue value of news; absolue average is he average of he absolue value of news; sum of squares is he sum of he squared value of news.

23 Table 8 Variance decomposiion of reurns Four variables Var(oal news) Var(CFN) Var(DRN) Cov(CFN.DRN) Real value Raio Five variables Var(oal news) Var(CFN) Var(DRN) Cov(CFN.DRN) Real value Raio Noe: The able provides he variance decomposiion for unexpeced sock reurns, i.e., oal news, using four- and five-var sae variables, respecively. Each column Real value, i.e., Var (oal news), Var (CFN), Var (DRN), and Cov (CFN, DRN), are given as each erms of equaion Var (r + - E r + ) = Var (N CF,+ ) + Var (N DR, + ) - Cov (N CF, +, N DR, + ). Dividing Real value by he variance of oal news gives Raio (by definiion sums o one).

24 Table 9 Bea of each index Indices Porfolio classificaion CF β DR β Toal β 33 secors Fishery, Agriculure & Foresry Mining Consrucion Foods Texiles Pulp & Paper Chemicals Pharmaceuical Oil & Coal Producs Rubber Producs Glass & Ceramic Producs Iron & Seel Nonferrous Meals Meal Producs Machinery Elecric Appliances Transporaion Equipmen Precision Insrumens Oher Producs Elecric Power & Gas Land Transporaion Marine Transporaion Air Transporaion Warehousing & Harbor Informaion & Communicaion Wholesale Trade Reail Trade Banks Securiies Insurance Oher Finance Real Esae Services

25 Table 9 Bea of each index coninued Indices Porfolio classificaion CF β DR β Toal β Daiwa 7 secors Maerial Manufacuring Miscellaneous Manufacuring Transporaion & Uiliy Services Miscellaneous Non-Manufacuring Financial Ohers Large Non-Financials Large Financials Non-Financials Toal Index Average Correlaion coef Noe: The able provides he value of he beas for each index. CF β denoes he cash flow bea and DR β denoes he discoun rae bea. Toal β denoes he sum of he wo beas. Correlaion coef. denoes he correlaion coefficien of he wo beas. 4

26 Table 0 Regression ess for he hree asse-pricing models Facor Model CV model CAPM g *** NA 0.005*** NA 0.005** NA Sd.error [ ] NA [0.0005] NA [ ] NA 95% BS inerval Upper NA NA NA Lower NA NA NA g 0.00*** *** 0.009*** *** *** 0.003*** Sd.error [ ] [0.006] [ ] [0.003] [ ] [ ] 95% BS inerval Upper Lower g *** 0.003*** Sd.error [ ] [ ] NA NA [ ] [ ] 95% BS inerval Upper NA NA Lower NA NA Adj. R-squared 70.8% 60.08% 5.7% 4.55% 8.4%.4% RRA coef. NA NA NA NA Noe: The able shows esimaed risk prices for he facor model wih wo beas, he CV model, and he CAPM. g 0, g, and g are regression esimaes of he consan erm, he risk price of he cash flow bea, and he risk price of he discoun rae bea, respecively. All regressions include Whie Heeroskedasiciy Consisen Covariances. The facor model is regressed wih no resricion, he CV model wih g = , and he CAPM wih g = g. The able repors wo regressions for each model, wih and wihou a consan. Sd. error denoes he sandard error of esimaed coefficien. 95% BS inerval denoes he 95% confidence inerval wih boosrap from,500 simulaed realizaions. Upper is he upper criical value and Lower is he lower criical value. Adj, R-squared is he adjused R-squared of he regression. RRA coef. is he relaive risk aversion coefficien calculaed as γ = g /g. NA no applicable. *** denoes significance a he % level, ** a he 5% level, and * a he 0% level. 5

27 Table Regression ess wih individual beas Cash flow bea Discoun rae bea g *** NA NA Sd.error [0.0004] NA [ ] NA 95% BS inerval Upper NA NA Lower NA NA g 0.004*** *** NA NA Sd.error [ ] [0.000] NA NA 95% BS inerval Upper NA NA Lower NA NA g NA NA Sd.error NA NA [ ] [0.0008] 95% BS inerval Upper NA NA Lower NA NA Adj. R-squared 7.4% 60.43%.4% 3.6% Noe: The able shows esimaed risk prices for he single facor model wih each bea. g 0, g, and g are regression esimaes of he consan erm, he risk price of he cash flow bea, and he risk price of he discoun rae bea, respecively. All regressions include Whie Heeroskedasiciy Consisen Covariances. Cash flow bea is he single-facor model wih only he cash flow bea, and discoun rae bea only includes he discoun rae bea. The able repors wo regressions for each model, wih and wihou a consan. Sd. error denoes he sandard error of esimaed coefficien. 95% BS inerval denoes he 95% confidence inerval wih boosrap from,500 simulaed realizaions. Upper is he upper criical value and Lower is he lower criical value. Adj, R-squared is he adjused R-squared of he regression. NA no applicable. *** denoes significance a he % level, ** a he 5% level, and * a he 0% level. 6