Predictive Ability of Three Different Estimates of Cay to Excess Stock Returns A Comparative Study for South Africa and USA

Transcription

1 European Research Sudies, Volume XVII, Issue (1), 2014 pp Predicive Abiliy of Three Differen Esimaes of Cay o Excess Sock Reurns A Comparaive Sudy for Souh Africa and USA Noha Emara 1 Absrac: The resuls of Leau and Ludvigson (2001) show ha Cay-LL has a significan predicive power boh in he in-sample and he ou-of-sample forecas of excess reurn. Our sudy depars from Leau and Ludvigson (2001) in adding and comparing oher wo esimaes of cay namely cay-ols and cay-dls besides cay-ll for forecasing excess reurn in boh he Unied Saes and Souh Africa. Using quarerly daa over he period 1988:1 o 2012:2, he resuls for he Unied Saes sugges ha he hree alernaive measures of cay have posiive significan predicing abiliy for he in-sample and ou-of-sample forecasing models. Furhermore, and in line wih he resuls of Leau and Ludvigson (2001), cay-ll has he leas mean squared forecasing errors. For he case of Souh Africa, lagged excess reurn and dividend yield bea he hree alernaive measures of cay in forecasing excess reurn. The resuls sugges ha for he case of Souh Africa, he rend deviaions of he macroeconomic variables is no a srong predicor of he excess sock reurns over a reasury bill rae, and canno accoun for a saisical significan variaion in fuure excess reurns. Key Words: Forecas; Excess Reurn; In-sample; Ou-of-sample; Nesed Forecas JEL Classificaion : 1 Economic Deparmen Rugers Universiy, nemara@camden.rugers.edu

2 4 European Research Sudies, XVII (1), 2014 N. Emara 1. Inroducion Financial economiss discuss wheher excess reurns are acually predicable as an overarching quesion. The sudy by Campbell and Shiller (1988) ess marke efficiency based on sock price indexes by exploring wheher sock prices relaive o dividends predic he sock s dividend changes ino he fuure. Through research, hey find ha real earnings variable is a srong predicor of fuure real dividend changes. They also find ha he raio of real earnings o curren price of sock parially predics forecasing sock reurn. Campbell and Mankiw (1989) were he firs economiss o use wealh and asse reurns o deermine he curren level of consumpion. In heir paper, hey find an associaion beween he log consumpion-wealh raio and fuure consumpion growh and he fuure rae of reurn on invesed wealh. Building upon heir logic, Leau and Ludvigson (2001) add four addiional assumpions for his raio including ha he raio is held ex-ane, wealh is he sum of asse holdings and human capial, aggregae labor income also describes unobservable human capial, and log consumpion is a consan muliple of nondurables and services. Furhermore, Leau and Ludvigson (2001), argue ha macroeconomic variables play a key role in forecasing excess reurns. Thalassinos e al. (2014) and Thalassinos (2014) argue ha besides macroeconomic financial variables as well play a key role in forecasing CDS spreads. However, in conras o Campbell and Shiller (1988), Leau and Ludvigson show ha he dividend price raio does no adequaely predic excess reurns hrough he inroducion of he macroeconomic variable named cay : he consumpion wealh raio. They sudy he effec of flucuaions of he consumpion-wealh raio on boh he real sock reurns and excess sock reurns over a Treasury bill rae. The impossibiliy of observing he consumpion wealh raio presens a key problem wih heir approach. Leau and Ludvigson provide a soluion by defining cay in erms of hree inegraed variables: consumpion, asse holdings and labor income. Leau and Ludvigson (2001) have shown he rend deviaions of hese macroeconomic variables srongly predics he excess sock reurns over a reasury bill rae, and can accoun for a subsanial fracion of he variaion in fuure excess reurns. The variable cay reflecs he assumpion ha aggregae consumpion carries informaion abou fuure reurns. Brennan and Xia (2005), neverheless, criicize he growh of he consumpion-wealh raio as a predicor. They argue ha he predicive power of cay resuls from a look ahead bias, since he informaion in Leau and Ludvigson (2001) sudy uses informaion unavailable a he ime of rade. The coinegraion of he variables, which Leau and Ludvigson (2001) analysis

3 Predicive Abiliy of Three Differen Esimaes of Cay o Excess Sock Reurns A Comparaive Sudy for Souh Africa and USA 5 relies on hroughou, causes he parameers of he regression o be esimaed insample. The broader conex of forecasing models affec Leau and Ludvingson (2001) ideas abou cay esimaion and paricularly heir analysis of he join rend beween aggregae consumpion, asse wealh, and labor income. In order o undersand he evaluaions of hese models, Harvey, Leybourne, and Newbold (1998) address Leau and Ludvingson (2001) conenion ha he univariae indicaor, consiued by a sudy of he shared rend beween aggregae consumpion, asse wealh, and labor income, srongly predics excess reurns while each variable individually caries lile predicive power. The auhors consider a siuaion in which wo forecass of he same variable are available, raising he possibiliy ha of a combined forecas as a weighed average of boh will achieve a more valuable combined forecasing model. Harvey, Leybourne, and Newbold (1998) address his possibiliy by invesigaing he opposie as hey describe i, an individual forecas can encompass he oher, meaning ha one forecas should opimally receive he enire weigh. The auhors deermine such an encompassing forecas is no robus ha few forecass will reflec his exreme scenario and ha he join forecas model offered by Leau and Ludvingson (2001) meris furher invesigaion and discussion. Diebold and Mariano (1995) presen anoher rubric for evaluaing forecasing models. Diebold and Mariano boh propose and invesigae ess for he null hypohesis of no difference in accuracy beween wo models, a useful exercise which informs any evaluaion of a forecasing model somehing which is inheren o any specific sudy of cay esimaion, paricularly as i perains o oher mehods of cay esimaion and even more broadly o oher forecasing models, such as hose described in earlier research. Clark and McCracken (1999) also aid in our evaluaion of forecasing models and accuracy, again addressing he issue of forecas encompassing invesigaed by Harvey, Leybourne, and Newbold (1998). Clark and McCracken (1999) offer furher breadh and perspecive o our undersanding of possible ways o appraise forecasing models, a cenral ask in any aemp o examine he value of cay esimaion as a forecasing model. McCracken (1999) offers addiional help in he form of his manuscrip, Asympoics for Ou of Sample Tess of Causaliy, which as he ile suggess conribues a mehod of assessing forecasing models by heir abiliy o predic esing ou-of-sample. This sudy presens hree differen ways of esimaing his rend deviaion in he Unied Saes and Souh Africa over he period 1988:1 o 2012:2. The variables are called cay-ols, cay-dls and cay-ll referring o esimaing he macroeconomic

4 6 European Research Sudies, XVII (1), 2014 N. Emara rend deviaions using he ordinary leas square mehod, dynamic leas square mehod, and Ludvigson and Leau (2001) mehod, respecively. This aricle includes he following analysis: (1) A comparison of he abiliy of hese hree variables besides oher radiional variables such as lagged excess reurn, dividend raio, and payou raio o predic in-sample excess sock reurn over Treasury bill rae in boh Souh Africa and U.S. (2) An esimaion of he ou-of sample forecas of cay-ols, cay-dls and cay-ll using recursive esimaion scheme for he period 2002:1 o 2012:1 for boh counries. (3) A es of he abiliy of he unresriced model (he one includes he variable cay) o hold all he informaion conained by he resriced model, or encompass he resriced model, using he mean squared error (MSE) F-es. (4) A comparison of he ou-of sample forecas of alernaive nesed models using he McCracken (1999) es. (5) A es of he equivalence accuracy of wo non-nesed models under comparison using he Diebold and Mariano (1995) es. The paper is organized as follows: Secion I explains hree ways of esimaing he rend relaionship among consumpion, labor income, and asse holdings. Secion II explains he asse reurn daa and he correlaion marix. Secion III explains quarerly in-sample forecasing regressions. Secion IV explains Ou-of- Sample Nesed forecasing regression. Secion V explains Ou-of-Sample Non- Nesed forecasing regression. Secion VI concludes he analysis of he differen esimaes of cay using he hree differen mehodologies for he wo counries. 2. Daa The esimaion reflecs quarerly, seasonally adjused, per capia variables, over he period of he firs quarer 1988 o he firs quarer of 2012 for he Unied Saes and Souh Africa. Consumpion daa here refers o non-durables consumpion and services; his sock marke capializaion daa provides a proxy for asse wealh in boh counries. Finally he daa for gross naional income serves as a proxy for labor income. All he daa for Souh Africa and he Unied Saes have been colleced from he daabases of he Global Finance and Inernaional Financial Saisics. Table 1: Correlaion Marix Panel A: Souh Africa DIV P / e Cay LL cay Ols cay Dls DIV P / e cay - LL

5 Predicive Abiliy of Three Differen Esimaes of Cay o Excess Sock Reurns A Comparaive Sudy for Souh Africa and USA 7 cay Ols cay Dls 1 Panel B: U.S. DIV P / e cay - LL cay Ols cay Dls 1 Table (1) presens he correlaion marix beween he financial quarerly daa including he hree differen esimaes of cay. Panel A shows he correlaion marix in Souh Africa, while panel B shows he corresponding values in he Unied Saes. This able shows he posiive correlaion beween he hree esimaes of cay and he excess reurn for boh Souh Africa and he Unied Saes However, he Unied Saes shows a much higher esimaed correlaion for he hree differen mehods of cay. 3. Three Ways of Esimaing he Trend Relaionship Among Consumpion, Labour Income and Asse Holdings Leau and Ludvigson (2001) showed ha cay can be a good proxy for marke expecaions of fuure asse reurns as long as expeced fuure reurns on human capial and consumpion growh are no oo volaile, or as long as hese variables correlae srongly wih expeced reurns on asses. All he erms on he righ-hand side of equaion (1) are presumed saionary such ha c,a, and y are coinegraed, and he lef side of (1) gives he deviaion in he common rend of c, a, y. This rend deviaion erm c a ( 1 ) y will be denoed as cay. i ( 1) y E {[ ra, i (1 ) rh, i ] c i} (1 ) z (1) i1 c a In his sudy we will presen hree differen ways of esimaing his rend deviaion. A descripion of he esimaion follows. Mehod 1: dynamic leas squares (DLS) echnique The firs mehod used o esimae he erm cay is he DLS. This mehod follows a single equaion aking his form: c k k n aa y y ba iai by yi (2),,, ik ik

6 8 European Research Sudies, XVII (1), 2014 N. Emara where denoes he firs difference operaor. This mehod generaes opimal esimaes of he coinegraing parameers in a mulivariae seing. The DLS specificaion adds leads and lags of he firs difference o he righ-hand side variables o a sandard OLS regression of consumpion on labor income and asse holdings o eliminae he effecs of he regressor endogeneiy on he disribuion of he leas square esimaor. The residual of equaion (2) will be he esimaed rend deviaion, denoed as cay-dls. Mehod 2: Ordinary Leas Square (OLS) Technique The second mehod of esimaing he rend deviaions is he OLS. This mehod esimaes Equaion (2) wih only he lags of asse wealh and labor income included. cay is hen serves as he residual of he significan regression. The cay under his second mehod will be denoed as cay-ols. Mehod 3: Leau and Ludvigson (2001) Technique This mehod esimaes cay following he mehod of Leau and Ludvigson (2001). In heir paper, hey esimae cay by he dynamic leas square echnique as in equaion (2), aking he coefficiens of asse wealh and labor income of he significan regression. 2 cay is hen calculaed as follows: cayˆ c ˆ a ˆ, y n The esimaed cay under his mehod will be denoed as cay-ll. The poin esimaes for he parameers of consumpion, labor income and asses for Souh Africa is c n, = a y (2) (56.19) (3.22) (47.87) and he poin esimaes for he equivalen model for he Unied Saes is cn, a y (3) (-7.3) (3.5) (37.18) where he -saisics appear in parenheses below he coefficien esimaes. 4. Quarerly In-Sample Forecasing Regressions This secion presens esimaes of he forecasing power of differen variables for he quarerly excess sock reurn. Table (2) presens he in-sample forecas of he U.S. excess sock reurn. Again he AR(1) model presened in regression one shows a 2 The significan regression was chosen based on he AIC measure. a y (3)

7 Predicive Abiliy of Three Differen Esimaes of Cay o Excess Sock Reurns A Comparaive Sudy for Souh Africa and USA 9 saisical significan abiliy o predic excess sock reurn. Adding he differen esimaes of cay, regressions five hrough seven, slighly improves he significance of he model, bu he hree differen esimaes of cay are no saisically significan. Adding dividends yield and payou raio o he model, as shown in regression five hrough seven, he hree alernaive measures of cay, cay-ols, cay-dls, and cay- LL, show an expeced posiive saisical significan effec on excess reurn. The cay-dls is also posiive bu only significan a he 15 percen level of significance. As expeced, he signs of he alernaive measures of cay where he deviaions in he long-erm rend among consumpion, income, and asse holdings posiively relae o fuure sock reurn. Furhermore, dividends yield shows an insignifican impac on excess reurn while he payou raio was expecedly posiive and saisically significan ** (2.160) ** (2.101) ** (2.02) 0.72*** (0.091) 0.75*** (0.082) 0.75*** (0.078) 19.8* (11) Table 2: In-Sample Forecas U.S. # Consan ER Cay- OLS *** (0.093) (37.9) *** 5.99 (0.085) (28.5) (6.240) *** (0.083) (29.8) *** (0.085) (29.2) Cay- DLS 6.28 (6.901) 15.64* (9.53) Cay- LL 5.02 (5.229) 15.06* (8.366) Div p/e Adj- 2 R (0.6) -034 (0.68) (0.6) 2.24*** (8.896) 2.15*** (0.977) 2.15*** (1.02) Noe: *, **, and *** refers o he 10%, 5%, and 1% level of significance, respecively. Similarly, Table (3) repors esimaes from OLS regressions of excess sock reurns on lagged values for he differen esimaes of cay and financial variable in Souh Africa. The regression resuls sugges a saisically significan AR(1) model for excess sock reurn in Souh Africa. Adding he hree differen esimaes of cay, rows 2 hrough 4, does no show an improvemen in he explanaion of he model.

8 10 European Research Sudies, XVII (1), 2014 N. Emara Table 3: In-Sample Forecas Souh Africa # Consan ER Cay- OLS Cay- DLS Cay- LL *** (0.053) *** (0.111) (0.057) (3.308) *** (0.112) (0.058) (6.165) *** (3.361) (0.053) (0.228) *** ** (0.051) (4.872) (0.444) * (0.465) (2.706) 0.856*** (0.052) 0.857*** (0.046) (5.910) (0.188) Div p/e Adj- 2 R *** (0.076) *** (0.077) *** (0.075) 0.071*** (0.034) 0.062* (0.035) 0.063** (0.028) Noe: *, **, and *** refers o he 10%, 5%, and 1% level of significance, respecively. On he oher hand, adding he financial variables represened by dividends yield and payou raio in regressions 5-7 increases he explanaion of he model. I also shows a posiive, saisically significan impac of financial variables in predicing excess reurn. Again, he hree esimaes of cay do no predic excess reurn wih saisical significance. 5. Ou-of-Sample Nesed Forecasing Regression The resuls of he in-sample forecas, especially he case of Souh Africa, imply ha he hree esimaes of cay do no significanly predic excess sock reurn over he reasury-bill reurn. However, a possible esimaion bias arises from he fac ha hese esimaes of cay use he coefficien of he whole sample. An alernaive model using an ou-of-sample nesed forecas eliminaes his. The sample is spli ino wo subsamples, an in-sample period ha sars from he firs quarer of 1988 o he fourh quarer of 2001 and an ou-of-sample ha sars from he firs quarer of 2002 o he firs quarer of 2012.

9 Predicive Abiliy of Three Differen Esimaes of Cay o Excess Sock Reurns A Comparaive Sudy for Souh Africa and USA 11 Using recursive esimaion scheme, he analysis below compares nesed forecas models based on he mean-squared forecasing error from an unresriced model, including he hree esimaes of cay each one in a urn, o a resriced benchmark model. Two alernaive benchmark models, a consan and a random walk, cause he unresriced model o nes he benchmark model. Table (4) below presens he mean squared forecas errors for nesed models using alernaive benchmark models. Panel A of he able presens he resuls for he resriced model conaining he consan expeced reurns as he only explanaory variable and he unresriced model conaining he alernaive esimaes of cay besides he consan erm. The resuls sugges ha, wih he excepion of cay-ols, he mean squared forecas error of he oher wo esimaes cay exceed he consan benchmark. This resul applies for boh Souh Africa and he Unied Saes. Similarly, panel B of he same able presens he mean squared forecas error for he random walk benchmark wih he hree alernaive esimaes for cay. For he case of Souh Africa, he hree differen esimaes of cay produce mean squared forecas error higher han he random walk benchmark. On he oher hand, for he case of he Unied Saes he unresriced Cay-DLS model shows he leas when compared wih he oher wo alernaive esimaes for cay. Table 4: Mean Squared Forecas Errors Nesed Models Panel A Benchmark Unresriced Models Consan Cay-OLS Cay-DLS Cay-LL Unied Saes Souh Africa Unied Saes Souh Africa Panel B Benchmark Unresriced Models Random walk Cay-OLS Cay-DLS Cay-LL To formally compare beween models, Table (5) repors he McCracken (1999) nesed ou-of sample F-es, or MC from here onwards, wih a null hypohesis of equal predicive accuracy for he resriced and he unresriced models. The

10 12 European Research Sudies, XVII (1), 2014 N. Emara calculaed es saisics is compared wih he abulaed values for recursive scheme provided by McCracken (1999). 3 The F-es is calculaed as follows P P where 1 T R L uˆ ) P cˆ T 1 ( L( uˆ 1, 1 2, 1 R T 1 c P uˆ 2, 1 R ) ˆi, 1 i, 1 ˆ and u L( uˆ ) i = 1, 2, where 1 refers o he resriced model and 2 refers o he unresriced model. The resuls for he Unied Saes sugges ha he hree alernaive esimaes of cay do no significanly bea he consan benchmark model. Using he random walk as he benchmark model, he cay-ll beas he random walk model. The oher wo alernaive esimaes of cay, cay-ols and cay-dls, show a higher mean squared error han he resriced random walk model. The resuls of he random walk benchmark confirm he findings for he significance cay-ols and cay-ll for he insample forecas for excess reurn. Only when compared wih he random benchmark model are nesed models ha include cay-ols, cay-dls or cay-ll significan. Table 5: Nesed Models Mean Squared Error and he McCracken F-Tes Unied Saes Souh Africa Row Comparison MSE u / MSE r McCracken MSE u / MSE r McCracken Saisic Saisic 1 Cay-OLS vs consan 2 Cay-DLS vs. consan ** 3 Cay-LL vs ** consan 4 Cay-OLS vs ** * random walk 5 Cay-DLS vs *** random walk 6 Cay- LL vs. random walk *** * (4) 3 Table (1) of McCracken (1999)

11 Predicive Abiliy of Three Differen Esimaes of Cay o Excess Sock Reurns A Comparaive Sudy for Souh Africa and USA 13 Noe: *, **, and *** refers o he 10%, 5%, and 1% level of significance, respecively. On he oher hand, using he consan benchmark, he resuls of Souh Africa sugges ha cay-dls beas he consan benchmark wih a saisically significan MC es saisic. The cay-ols is, however, no saisically significan while he cay-ll does no bea he consan benchmark. In addiion, using he random walk benchmark, he mean squared forecas errors of he models including he hree alernaive measures of cay are higher han he benchmark model. This means ha he hree measures of cay have less predicive abiliy o forecas excess reurn over he benchmark model. The MC es confirms hese resuls for all models excep he cay-dls versus he random walk model. I is worh noing ha, despie he fac ha none of he hree alernaive measures of cay show any saisically significan in-sample predicions for excess reurns for he case of Souh Africa, using he random walk excess reurn as he benchmark model shows a saisically significan impac for he ou-of-sample forecas. 6. Ou-of-Sample Non-Nesed Forecasing Regression A comparison of a se of non-nesed models provides a furher check of he predicive power of alernaive esimaes of cay and financial variables wih respec o excess reurn in he Unied Saes and Souh Africa. The lagged value of he hree alernaive mehods esimaes of esimaing cay is he sole predicive variable for hese models. Analysis below shows each alernaely compared wih compeior models wih a sole predicive variable of eiher he lagged excess reurn, lagged dividend yield, or lagged payou raio. Using he Diebold and Mariano (DM) es for ou-of-sample forecas of equal predicive accuracy of wo non-nesed model. The null under DM es is as follows, H H 1 2 : E( g( ) g( )) : E( g( ) g( )) 0 0 A where refers o he quadraic loss funcion of model i, such ha 1 refers o he resriced model and 2 refers o he unresriced model. Under he null hypohesis of equal predicive abiliy, he DM es has an asympoically sandard normal disribuion and is calculaed as follows 4 4 more deails are available in he paper Diebold (1995)

12 14 European Research Sudies, XVII (1), 2014 N. Emara dˆ p P 1/ 2 ( d ) P ˆ p 1/ 2 d P ˆ 1 p P 1/ 2 d ˆ 1 p P T 1 1/ 2 Rh1 ( g( ˆ 1 h ˆ ) g( ˆ p 2 h )) where and he equaion represens he sample esimae of Table (6) repors he resuls of he DM es saisic for he ou-of-sample forecas of hireen compeing non-nesed models for he Unied Saes. As he resuls of rows 1 hrough 3 show, cay-ols significanly beas he hree differen financial variables in predicing excess reurn. For example, row 1 shows ha he mean squared forecas error of he regression including cay-ols as he sole predicor for excess reurn is smaller han he mean square forecas error of an AR(1) model. This resul is significan a he 5 percen level of significance. Similarly, rows 7 hough 9 confirm ha cay-dls beer predics financial variables, and again he resuls were saisically significan. Finally, and in line wih Leau and Ludvigson (2001), rows 11 hrough 13 show ha Cay-LL significanly beas abiliy of financial variables o predic excess sock reurn. Table 6: Diebold and Mariano Tes Non-nesed comparison - Unied Saes # Model 1 vs. Model 2 MSE1/MSE2 DM 1 Cay-OLS vs. ER ** 2 Cay-OLS vs. DIV *** 3 Cay-OLS vs. P/E ** 5 Cay-OLS vs. Cay-DLS Cay-OLS vs. Cay-LL Cay-DLS vs. ER ** 8 Cay-DLS vs. DIV *** 9 Cay-DLS vs. P/E ** 10 Cay-DLS vs. Cay-LL Cay-LL vs. ER *** 12 Cay-LL vs. DIV *** 13 Cay-LL vs. P/E ** Noe: *, **, and *** refers o he 10%, 5%, and 1% level of significance, respecively.

13 Predicive Abiliy of Three Differen Esimaes of Cay o Excess Sock Reurns A Comparaive Sudy for Souh Africa and USA 15 Comparing he predicive abiliy of he hree alernaive esimaes of cay, he resuls of row 5 could no confirm he saisical significance of he beer predicing abiliy of he cay-ols over cay-dls. Furhermore, he resuls of rows 6 and 10 could no confirm ha cay-ols and cay-dls beer forecas excess reurn when compared wih Cay-LL. Finally, comparing he relaive mean squared forecas errors of he 13 compeing models, cay-ll has he leas predicive errors when compared he wo oher esimaes of cay and he hree financial variables. Similarly, Table (7) shows he non-nesed comparison of he hireen models in Souh Africa. As he resuls show, he predicive abiliy of he hree alernaive measures of cay could no bea he predicive abiliy of he lagged excess reserves or he dividends raio. The resuls of rows 1, 7, and 11 show ha cay-ols, cay-dls, and cay-ll, respecively, have a higher mean squared forecas error han he random walk benchmark model. The Diebold and Mariano es confirm he significance of his resul by rejecing he null of equal predicive accuracy beween he model using a measure of cay and a model using he random walk o predic excess sock reurn. Similarly, rows 2, 8, and 12 show ha he models ha use he hree measures of cay as predicors for excess sock reurn have smaller mean squared forecas errors han he model ha uses he dividends raio as he sole predicor of excess reurn. Again, he DM es confirms ha he null hypohesis is rejeced and ha he compeing models do no have equal predicive accuracy. Table 7: Diebold and Mariano Tes Non-nesed comparison- Souh Africa # Model 1 vs. Model 2 MSE1/MSE2 DM 1 Cay-OLS vs. ER *** 2 Cay-OLS vs. DIV *** 3 Cay-OLS vs. P/E Cay-OLS vs. Cay-DLS Cay-OLS vs. Cay-LL Cay-DLS vs. ER *** 8 Cay-DLS vs. DIV *** 9 Cay-DLS vs. P/E Cay-DLS vs. Cay-LL Cay-LL vs. ER *** 12 Cay-LL vs. DIV ** 13 Cay-LL vs. P/E Noe: *, **, and *** refers o he 10%, 5%, and 1% level of significance, respecively.

14 16 European Research Sudies, XVII (1), 2014 N. Emara Unlike he U.S. resuls, as shown in rows 5, 6, and 10, in Souh Africa he null hypohesis of equal predicive accuracy beween he hree differen mehods of esimaing cay is rejeced. The resuls also sugges ha, unlike for he Unied Saes, he null hypohesis of equal predicive accuracy beween he hree alernaive measures of cay (rows 3, 9, and 13) and he payou raio canno be rejeced. 7. Conclusion The resuls of Leau and Ludvigson (2001) show ha Cay-LL has a significan predicive power boh in he in-sample and in he ou-of-sample forecas of excess sock reurn. Our sudy depars from Leau and Ludvigson (2001) in adding and comparing wo oher esimaes of cay, namely cay-ols and cay-dls, besides cay- LL in forecasing excess reurn in boh he Unied Saes and Souh Africa over he period 1988:1 o 2012:1. Our resuls show ha for he case of he Unied Saes, for he in sample forecas, he hree alernaive measures of cay show a posiive saisical significan impac in predicing excess sock reurn. In addiion, he magniude of he effec was similar in each case. Furhermore, using ou-of-sample forecas nesed models wih a consan benchmark, he resuls shows ha he hree alernaive measures of cay could no significanly predic he excess sock reurn. However, using he random walk model as he benchmark, he resuls of he McCracken (1990) es saisic sugges ha he hree measures of cay do no have equal predicive accuracy wih he benchmark model. However, and in line wih Leau and Ludvigson (2001), cay-ll has he leas mean squared forecasing errors. In addiion, using he ou-of-sample non-nesed models comparisons, he resuls of he Diebold and Mariano (1995) es show ha he hree measures of cay bea he financial variables, and, again, cay-ll has he leas mean squared errors. On he oher hand, our resuls also show ha for he case of Souh Africa, he hree esimaes of cay are saisically insignifican in he in-sample forecas of excess sock reurn. Using he consan benchmark wih ou-of-sample nesed models comparisons, cay-dls is he only measure of cay ha significanly beas he benchmark model. In addiion, using he random walk model as he benchmark model, boh mean squared errors of he wo models including cay-ols and cay-ll are higher han he benchmark model. This resul is confirmed by he saisically significan McCracken (1990) es. Furhermore, he ou-of-sample forecas of he non-nesed models shows ha he lagged excess reserves and he dividend yield bea he hree alernaive measures of cay for predicing excess sock reurn. The Dieblod Mariano (1995) confirms his resul.

15 Predicive Abiliy of Three Differen Esimaes of Cay o Excess Sock Reurns A Comparaive Sudy for Souh Africa and USA 17 Our resuls confirm he general predicions of Leau and Ludvigson (2001) for he Unied Saes. However, he daa for Souh Africa show ha he resuls of Leau and Ludvigson (2001) canno be applied o an emerging economy such as Souh Africa. In such an economy, he financial rend deviaions of hese consumpion, income, and asse holdings variables are no a srong predicor of he excess sock reurns over a reasury bill rae, and canno accoun for a saisical significan variaion in fuure excess reurns. References Campbell, Y.J., and Cochrane, H.J. (1999), By Force of Habi: A consumpion Based Explanaion of Aggregae Sock Marke Behaviour, J.P.E 107, pp Campbell, J. Y., and R. J. Shiller (1988), The Dividend-Price Raio and Expecaions of Fuure Dividends and Discoun Facors, Review of Financial Sudies, 1, pp Campbell, John, and N. Gregory Mankiw (1989), Consumpion, Income and Ineres Raes: Reinerpreing he Time Series Evidence, Naional Bureau of Economic Research 4 (1989), pp Clark, Todd and Michael McCracken (1999), Tess of Equal Forecas Accuracy and encompassing for nesed models, Working paper, Federal Reserve Bank of Kansas Ciy. Diebold, F.X. and R. Mariano (1995), Comparing Predicive Accuracy, Journal of Business and Economic Saisics, 13, pp Harvey, David, Sephen Leybourne, and Paul Newbold (1998), Tess for Forecas Encompassing, Journal of Business and Economic Saisics 16, pp Leau, Marin, and Ludvigson, Sydney (2001), Consumpion, Aggregae Wealh, and Expeced Sock Reurns, J. Finance 56, Michael W. McCracken (1999), Asympoic for ou of Sample Tess of Causaliy, Unpublished manuscrip, Louisiana Sae Universiy. Michael J. Brennan and Yihong Xia (2005), Tay s as good as cay, Finance Research Leers 2, pp Thalassinos, I.E. and Pociovaliseanu, D.M. (2007), A Time Series Model for he Romanian Sock Marke, European Research Sudies Journal, Vol. X(3-4), Thalassinos, I.E., Samaopoulos, Th. and Thalassinos, E.P. (2014) The European Sovereign Deb Crisis and he Role of Credi Swaps, Chaper book in The WSPC Handbook of Fuures Markes (eds) W. T. Ziemba and A.G. Malliaris, in memory of Lae Milon Miller (Nobel 1990) World Scienific Handbook in Financial Economic Series Vol. 5. Thalassinos, E.P., (2014), Credi Defaul Swaps and Sovereign Deb in Eurozone, Chaper book in, Risk Managemen: Sraegies for Economic Developmen and Challenges in he Financial Sysem, (eds), D. Milos Sprcic, Nova Publishers, ISBN: , , NY, USA.

16 18 European Research Sudies, XVII (1), 2014 N. Emara