Idiosyncratic Volatility and Cross-section of Stock Returns: Evidences from India

Transcription

1 Asian Journal of Finance & Accouning Idiosyncraic Volailiy and Cross-secion of Sock Reurns: Evidences from India Prashan Sharma Assisan Professor and Area Chair (Finance and Accouns) Jaipuria Insiue of Managemen, Jaipur, India Brajesh Kumar Assisan Professor, Deparmen of Economics Naional Insiue of Financial Managemen, Faridabad, Haryana, India Received: Jan. 19, 2016 Acceped: Feb. 22, 2016 Published: June 1, 2016 doi: /ajfa.v8i URL: hp://dx.doi.org/ /ajfa.v8i Absrac The presen sudy examines he cross-secional pricing abiliy of idiosyncraic volailiy (IV) in Indian sock marke and invesigaes he relaionship amongs expeced idiosyncraic volailiy (EI), unexpeced idiosyncraic volailiy (UI), and cross-secion of socks reurns. The sudy uses ARIMA (2, 0, 1) model o IV ino EI and UI. The socks reurns are regressed on IV, EI and UI using Newey-Wes (1987) correcions, in order o invesigae heir empirical relaionship. The sudy finds ha IV is posiively relaed wih sock reurns. Furher he IV significanly explains he cross-secion of sock reurns in Indian conex. Afer imposing conrol over UI, as i is highly correlaed wih unexpeced reurns, he iner-emporal relaionship beween EI and expeced reurns urns ou o be posiive. Keywords: idiosyncraic risk, asse pricing, Fama-French facor model, Newey-Wes saisics, arima JEL Classificaion: C30, G11, G12 1

2 Asian Journal of Finance & Accouning 1. Inroducion Asse pricing heories focus on he iner-emporal relaionship beween risk and reurn. The radiional heories focus majorly on he sysemaic risks bu no on idiosyncraic risk, as i was assumed ha perfec diversificaion in he porfolio can eliminae he idiosyncraic risk (Markowiz, 1959; Sharpe, 1964; Treynor, 1961; and Linner, 1965). Bu, in real marke scenario, i is very hard o diversify he porfolio perfecly. As menioned by Goyal and Clara (2003), he reasons for no aaining fully diversified porfolios are ransacion coss, axes, concenraion exposure ha resric he capaciy of employees o sell heir holdings received under employee compensaion plans, privae informaion abou individual socks, prone o inves in familiar socks and irraionaliy of invesors. To overcome such issue, in pas wo decades, he researchers have paid considerable aenion o he role of IV in deermining he excess reurns. Considering he imporance of IV in asse pricing heory, Meron (1987), in his heoreical model (assuming invesor s under-diversified porfolio) emphasized ha i can have significan role in deermining excess reurns. Following he heoreical model of Meron (1987), numerous works had been conduced o see he iner-emporal relaionship beween IV and excess reurns, which can be divided majorly ino hree caegories; firs caegory focusing on he ime series rend ofiv in asse pricing process; second, emphasizing on he iner-emporal relaionship beween idiosyncraic volailiy and fuure reurns of socks; and he hird is on he ime series associaion and predicing power of idiosyncraic volailiy and cross-secion of sock s excess reurns. The sudy conduced by Campbell e. al., (2001) was in suppor of firs branch of lieraure which focused o analyze he ime series rends in idiosyncraic volailiy. They divided oal volailiy ino wo i.e., firm volailiy and he marke volailiy. Employing daa for period of , he resuls showed ha he firm level volailiy had increased over a period of ime relaive o marke volailiy and as resul of ha he explanaory power of marke models had been declined. Apar from his, he number of socks needed for achieving a given level of diversificaion had increased. In line wih second branch of lieraure, he predicabiliy of sock reurns wih differen risk measures was esed by Goyal and Clara (2003) for period of July 1962 o December 1999 and showed ha here is significan posiive relaionship beween average sock variance (largely idiosyncraic risk ) and marke reurns.these resuls were robus afer conrolling for various macroeconomic risk indicaors i. These empirical evidences indicae he significan role of IV in asse pricing heory. The sudy conduced by Ange. al., (2006), provides sysemaic invesigaion of pricing of IV in US conex using he daa from January 1986 o December This sudy examines he cross-secional pricing abiliy of IV and provides a puzzle which is commonly known as idiosyncraic risk puzzle, and documened a negaive relaionship beween IV and sock reurns. These findings were robus afer conrolling for various firm characerisics ii. The focus of our sudy is on he second and hird branch of lieraure; focusing on he iner-emporal relaionship associaion beween IV and sock s excess reurns; and he cross-secional pricing abiliy of IV in Indian sock marke. The relaionship beween IV and cross-secion of sock reurns have shown mixed oucomes, some sudies repored he significanly posiive relaionship while ohers have documened 2

3 Asian Journal of Finance & Accouning ha eiher here is no relaionship or negaive relaionship. The sudies conduced by Goyal and Clara (2003) and Spiegal and Wang (2005) presened significan posiive relaionship beween IV and sock reurns. The findings of Goyal and Clara (2003) were opposed by Bali e. al., (2005), as hey argued ha he resuls were driven by small socks raded on NASDAQ, and was in par due o a liquidiy premium. There were no evidences of relaionship beween value-weighed porfolio reurns and he median value-weighed average sock volailiy. The recen sudies conduced by Fu (2009), Boehme e. al., (2009), Chua e. al., (2010)and Marcelo e. al., (2012) emphasized on he significan posiive relaionship beween IV and cross-secion of socks reurns while he sudies of Ange. al., (2006, 2009), Guo and Savickas (2010) and Bley and Saad (2012) documened he negaive relaionship. Some oher sudies by Bali e. al., (2005) and Bali and Cakici (2008) repored no significan relaionship beween IV and cross-secion of sock reurns. The relaionship beween cross-secion of sock reurns and IV are sensiive o model specificaion and he sample daa used o measure he idiosyncraic risk and hese mixed evidences are mainly due o lack of consisency choice of variable used o esimae idiosyncraic volailiy. Some of he exising sudies have considered he oal IV and while ohers have used he EI. Fu (2009) addressed his issue and emphasized on he use of EI deermined ex-ane, no he oal idiosyncraic volailiy, since he objecive is o examine is relaionship wih expeced reurns. In addiion, French, Schwer and Sambaugh (1987) indicaed ha he use of oal volailiy may presen some obscure relaionship beween he marke reurns and marke volailiy, and suggesed o decompose he oal volailiy o predicive and un-predicive componens. Following his decomposiion approach, Chua e. al., (2010) decomposed he IV ino wo, EI and UI and repored ha UI conrols for unexpeced componen of reurns. The EI explains cross-secion of sock reurns significanly and have a posiive relaionship wih reurns. As discussed above, numerous evidences on relaionship beween idiosyncraic volailiy and cross-secion of socks reurns exis in global conex, bu here is dearh of lieraure in Indian conex. In his background, he presen sudy has been designed o: examine he cross-secional pricing abiliy of idiosyncraic risk in Indian conex; and invesigaes he empirical relaionship amongs EI, UI, and socks excess reurns. The presen sudy conribues in he exising body of lieraure by improving he inernaional evidences wih he exclusive in-dephanalysis of he Indian marke which is relaively less explored. The sudy follows he approach of Chua e. al., (2010) for esimaion of idiosyncraic volailiy. Similar o French, Schwer and Sambaugh (1987), he sudy employs ARIMA (2, 0, 1) or ARMA (2, 1) model for decomposiion of IV ino EI and UI. The sudy employs monhly daa from 2001 (FY) o 2012 (FY) of non banking and financial companies of BSE 500 index. For esimaion of IV, he monhly Fama French (1993) facors iii are regressed on monhly reurns of he individual sample firms. The square of he resuling regression residuals are reaed as IV of he paricular firm. Addiionally, for decomposiion of IV, ARMA (2, 1) model is pressed ino service for each company and he fied values are ermed as he EI and he residuals are ermed as UI. In order examine he cross-secion pricing abiliy of IV, EI and UI, he cross-secional regression analysis are conduced wih he esimaion of Newey-Wes (1987) -saisics. The robusness of he 3

4 Asian Journal of Finance & Accouning relaionship is esed afer conrolling for various firm characerisics such as marke capializaion and book o marke equiy raio. The sudy finds a significan posiive relaionship beween EI and socks expeced reurns, ha is consisen wih sudies of Meron (1987), Fu (2009) and Chua e. al., (2010) which repored he significan robus relaionship beween EI and expeced reurns. Our resuls are differen wih he sudies of Ange. al., (2006, 2009) indicaing negaive relaionship beween he wo, wherein Bali and Cakici (2008) found no significanly robus relaionship beween IV and expeced reurns. The sudy has been srucured in following secions. Secion 2 presens he daa and empirical mehodology for esimaion of IV and secion 3 presens he empirical resuls and findings of he sudy and we conclude wih secion Daa and Mehodology for Esimaion of Volailiy The sudy employs monhly daa on socks reurns, marke reurns, 91 days-bills raes, SMB and HML of BSE 500 companies (excep banking and financial insiuions) from 2001(FY) o 2012 (FY). The daa are colleced from CMIE (Cener for Monioring Indian Economy) PROWESS 4.0 daa base and he Indiasadsaabase. In order o mainain he consisency in he daa, only hose firms are considered which are having daa for full sample period; his number urns ou o be 273 firms. The daa on variables; sock excess reurns and marke excess reurns are derived by subracing he 91 days -bills raes from individual firmreurns and marke reurns series. The facors SMB, HML are consruced using Fama-French (1992) mehodology. 2.1 Consrucion of Fama-French (1992) Facors The facors SMB and HML are consruced from a wo-by-hree sor on size and book-o-marke value. A he end of March of each year from 2001 o 2011, all socks are ranked on marke capializaion (or size) and book o marke value. The median value of he size is used as a size break poin o spli all socks ino wo groups, small (S) and big (B). The socks shored on book o marke value are divided ino hree book-o-marke groups based on he break poins for he boom 30% (L), middle 40% (M), and op 30% (H). Monhly equally-weighed reurns on he six porfolios are calculaed from April of year y o March of year y+1. SMB is he difference, each monh, beween he simple average of he reurns on he hree small porfolios (S/L, S/M, and S/H) and he simple average of he reurns on he hree big socks (B/L, B/M, and B/H). HML is he difference, each monh, beween he simple average of he reurns on he wo high book o marke porfolios (S/H and B/H) and he simple average of he reurns on he wo low book o marke porfolios (S/L and B/L). 2.2 Idiosyncraic Volailiy: Definiion and Esimaion To esimae he idiosyncraic volailiy, Fama-French (1993) regression is conduced using he monhly reurns of all socks. r = α + β Rm + β 2SMBi, + β 3HMLi, + ε 4 (1)

5 Asian Journal of Finance & Accouning Where r, represens he monhly excess reurns on sock i on monh. Similarly i Rm i, represens he monhly excess reurns of BSE 500 index, SMB i, is he reurn difference on size facor and HML i, is he reurn difference on value facor. i, α is coefficien and β i, are parameers for each facors. Following he Ange. al., (2006) and Chua e. al., (2010) mehodology, he idiosyncraic volailiy of sock i in monh is defined as; IV i, = ε 2 i, (2) Where IV i, is he idiosyncraic volailiy measure for firm i in monh which is he square of he Fama-French regression residuals ( ε 2 ). To decompose he idiosyncraic volailiy ino expeced and unexpeced componens, ARMA (2, 1) model is used. For each sock, using monhly daa, he following ime series regression is performed; IV = θ 0 + θ 1IV 1 + θ 2IV 2 φ 1ξ 1 (3) Here IV 1 andivi, 2 are he lagged auo-regressive erms of order one and order wo and ξ 1 is moving average erms of firs order. Following Chua e. al., (2010), he fied values of regression equaion 3 are defined as EI and he residuals are ermed as UI. 2.3 Descripive Saisics Table 1. Descripive Saisics IV EI UI Mean Median Sd. Dev Skewness Kurosis Noe: The sample is from June 2001 o March A every monh, for each firm, he IV (idiosyncraic volailiy) is calculaed by following equaion 2 and EI (expeced idiosyncraic 5

6 Asian Journal of Finance & Accouning volailiy) and UI (unexpeced idiosyncraic volailiy) are esimaed using equaion 3. In order o provide poin esimae, he cross-secional averages of IV, EI and UI are repored. Table 1 repors he summary saisics; mean, median, sandard deviaion, skewness and kurosis of he cross-secional series of IV, EI and UI. The cross-secional mean of IV in Indian sock marke is and he sandard deviaion is The mean IV of Indian marke is higher han hose repored for US conex; while sandard deviaion is lower (see Chua e. al., 2010, Zang 2004); indicaing ha IV is less volaile in Indian conex. The mean of EI is which is near o IV mean bu EI is less volaile han IV since is sandard deviaion UI is having very low mean value of wih sandard deviaion of 0.03, showing less volaile behavior. 3. Resuls and Discussions 3.1 Cross-secional Regression of Reurns on IV Following regression is performed o invesigae he relaionship beween cross-secion of sock reurns and idiosyncraic volailiy. r = σ 0 + σ 1IV + η (4) Table 2. Cross-Secional Regression of Reurns on IV and Conrol Variables (Size and Value) Variable Model 1 Model 2 Parameer -saisics Parameer -Saisic C IV * * LNBEME LNMCAP ** R-squared Noe: The sample is from June 2001 o March A each monh, he cross-secion of reurns is regressed on cross-secion of IV of 273 sample firms of BSE 500. The able repors he ime-series average of parameers and he Newey-Wes (1987) adjused -saisics. The 6

7 Asian Journal of Finance & Accouning adjused R 2 value is also repored. Laer on his regression were performed afer conrolling for LNMCAP (size) and LNBEME (value) effec. * represen significan a 1% level of significance and ** for 5% level of significance. Model 1 of able 2 repors he ime series means of parameers and Newey-Wes (1987) -saisics for regression of reurns on IV. The coefficien of IV is which is very low and insignifican while he parameer of IV is 0.48 which is posiive and significan a 1% level of significance. This indicaes ha in Indian sock marke, he IV is having significan explanaory power o predic he sock reurns. The exising asse pricing lieraure had documened ha he anomaly facors; marke capializaion and book o marke raio (Fama French, 1992) had significan explanaory power of explaining variaion in he cross-secion of sock reurns. In order o es he robusness of he resuls repored in model 1 of able 2, cross-secion of reurns is regressed on IV afer conrolling for variables i.e., he logarihmic value of marke capializaion and book o marke raio of individual firms. r = σ + σ IV + σ lnbeme + σ lnmcap + η (5) The resuls are repored in he model 2 of able 2. The parameer of IV, afer conrolling for conrol variables, is 0.62 which is higher han hose repored in model 1. I is significan a 1% level of significance, and he explanaory power (adjused R 2 ) of his model has improved afer conrolling for anomaly facors. This clearly indicaes ha IV is having significan explanaory power o explain cross-secional variaion in sock s reurns and he impac of IV is posiive and significan. Recen lieraure on he relaionship beween idiosyncraic volailiy and sock reurns advocaes he decomposiion of IV ino EI and UI. Fu (2009) addressed his issue and emphasized he use of EI deermined ex-ane and no he oal idiosyncraic volailiy. 3.2 Cross-Secional Pricing Abiliy of EI and UI To invesigae he relaionship of EI, UI and reurns, he reurns of companies are regressed on EI using following cross-secional regression; r = ϑ + ϑ EI + η i, 0 1 i, i, (6) 7

8 Asian Journal of Finance & Accouning Table 3. Cross-Secional Regression of Sock Reurns on EI and Boh EI and UI Model 3 Model 4 Variable Parameer -Saisic Parameer -Saisic C EI ** ** UI * Adjused R Noe: The sample is from June 2001 o March A each monh, he cross-secion of reurns is regressed on EI of 273 sample firms of BSE 500. The able repors he ime-series average of parameers and he Newey-Wes (1987) adjused -saisics. The adjused R 2 value is also repored. Laer on his regression were performed afer conrolling for UI. * represen significan a 1% level of significance and ** for 5% level of significance. Model 3 of able 3presens he mean of cross-secional regression resul of reurns on EI. The parameer of EI is 0.26, which is saisically significan a 5% significance level. This indicaes ha EI is having significan explanaory power o explain cross-secional variaion in expeced sock reurns, bu EI doesn ouperform in comparison o IV. Furher he relaionship of EI and reurns is explored afer conrolling for UI and following cross-secional regression equaion is used; r = ϑ + ϑ EI + ϑ UI + η i, (7) Model 4 of able 3 represens he resuls of he cross-secional regression of reurns on EI and UI. The parameer of UI is which is significan a 1% level of significance, suppors he findings of Chua e. al., (2010), who repored ha UI conrols for unexpeced variaion in he fuure sock reurns. The Parameer of EI is 0.24 a 5% level of significance. This parameer value is marginally lower han he parameer of EI (when here was no conrol over UI). These resuls sugges ha in Indian conex, EI s explanaory power for explaining cross-secion of expeced reurns, susains afer UI conrolling for unexpeced componen of fuure socks reurns. The resuls also sugges ha he impac of EI on reurns is economically significan. A 1% increase in he EI will lead o 0.24% increase in he expeced sock reurns. The relaionship of EI and reurns is posiive, which is in line wih he exising lieraure. Afer conrolling for unexpeced reurns, he EI s explanaory power should increase bu we don find any evidences in Indian conex. In order o re-examine and es he robusness of 8

9 Asian Journal of Finance & Accouning his relaionship, he sudy uses he marke capializaion and book o marke raio (Fama French, 1992) as conrol variables. 3.3 Conrol Variable and Relaionship of EI, UI and Reurns To es he robusness of he relaionship of EI and reurns, hese facors (marke capializaion and book o marke raio) are inroduced in following cross-secional regression equaion; r = ϑ + ϑ EI + ϑ UI + ϑ lnmcap + ϑ lnbeme + η (8) Table 4. Cross-secional Regression wih Conrol Variables (Size and Value) Variable Parameer -Saisic C EI ** UI * LNBEME LNMCAP ** Adjused R-squared Noe: The sample is from June 2001 o March A each monh, he cross-secion of reurns is regressed on EI afer conrolling for UI, marke capializaion and book o marke raio of 273 sample firms of BSE 500. The able repors he ime-series average of parameers and he Newey-Wes (1987) adjused -saisics. The adjused R 2 value is also repored. * represen significan a 1% level of significance and ** for 5% level of significance. Table 4 repors he mean of parameers and Newey Wes (1987) -saisics of he cross-secional regression of reurns on EI, afer conrolling for UI, marke capializaion and book o marke equiy raio. The parameer of EI is 0.55, which is significanly higher han he parameer (0.24) repored in model 4 of able 3, where no conrol were imposed on he relaionship beween reurns and EI excep UI. Afer conrolling for UI along wih marke capializaion and book o marke raio, he explanaory power of EI has significanly improved. The parameer is saisically significan a 5% level of significance level; clearly 9

10 Asian Journal of Finance & Accouning indicaes ha he EI explain he cross-secion of sock reurns significanly in Indian marke. These findings are consisen wih Fu (2009) and Chua e. al., (2010). 4. Conclusion The sudy aims o examine he relaionship of IV and cross-secion of sock reurns in Indian sock marke. The exising lieraure suggess wo approaches o invesigae he relaionship beween idiosyncraic volailiy and reurns; firs o regress sock reurns on IV and second is o decompose he IV ino expeced and unexpeced componens and hen find he resuling relaionship. Considering he second approach, he IV is decomposed ino EI and UI, as Fu (2009) emphasized he use of EI deermined ex-ane and no he oal IV o examine is impac on cross-secion of sock reurns. The findings of he sudy sugges ha IV and EI explain he cross-secion of sock reurns significanly in Indian conex. The explanaory power of EI doesn improve afer conrolling for UI, bu when we conrol for he Fama French (1992) facors i.e., marke capializaion and book o marke equiy, he explanaory power of EI improves significanly and hen explains 55% of cross-secional variaion in expeced sock reurns. The relaionship is posiive, indicaes ha a 1% increase in EI will lead o 0.55% increase in expeced sock reurns. The resuls are consisen wih he sudy of Spiegel and Wang (2005), Fu (2009) and Chua e. al., (2010), as hey documened a significan posiive relaionship beween expeced reurns, EI and UI. The findings don suppor Ange. al., (2006, 2009) and Bali and Cakici (2008)because he former have documened negaive relaionship while laer repored no significan relaionship beween IV and expeced reurns. The sudy concludes wih a noe ha along wih he sysemaic risk, he idiosyncraic risk should also be considered while deermining he asse prices in Indian sock marke. References Ang, A., Hodrick, R., Xing, & Y., Zhang, X. (2006). The Cross-Secion of Volailiy and Expeced Reurns. Journal of Finance, 61, hp://dx.doi.org/ /j x Ang, A., Hodrick, R.J., Xing, Y., & Zhang, X. (2009). High Idiosyncraic Volailiy and Low Reurns: Inernaional and Furher U.S Evidence. Journal of Financial Economics, 91, pp hp://dx.doi.org/ /j.jfineco Bal T., & Cakic N. (2008). Idiosyncraic Volailiy and he Cross-Secion of Expeced Reurns?. Journal of Financial and Quaniaive Analysis, 43, hp://dx.doi.org/ /s x Bal T., Cakic N., Yan, X.,& Zhang, Z. (2005). Does Idiosyncraic Risk Really Maer? Journal of Finance, 60, hp://dx.doi.org/ /j x Bley, J., Saad, M. (2012). Idiosyncraic Risk and Expeced Reurns in Fronier Markes: Evidence from GCC. Journal of Inernaional Financial Markes, Insiuions & Money, 22, hp://dx.doi.org/ /j.infin

11 Asian Journal of Finance & Accouning Boehme, R., Danielsen, B., Kumar, P., & Sorescu, S.(2009). Idiosyncraic Risk and he Cross Secion of Sock Reurns: Meron (1987) mees Miller (1977). Journal of Financial Markes, 12, hp://dx.doi.org/ /j.finmar Campbell, J., Leau, M., Malkiel, B., & Xu, Y. (2001). Have Individual Socks Become More Volaile? An Empirical Exploraion of Idiosyncraic Risk. Journal of Finance, 56, hp://dx.doi.org/ / Chua, C., Goh, J., & Zhang, Z. (2010). Expeced Volailiy, Unexpeced Volailiy and he Cross Secion of Sock Reurns. Journal of Financial Research, 33(2), hp://dx.doi.org/ /j x Fama, E., & French, K. (1992). The Cross-secion of Expeced Sock Reurns. Journal of Finance, 48, hp://dx.doi.org/ /j b04398.x Fama, E., & French, K. (1993). Common Risk Facors in he Reurns on Socks and Bonds. Journal of Financial Economics, 33, hp://dx.doi.org/ / x(93) French, K., Schwer, G., & Sambaugh, R. (1987). Expeced Sock Reurns and Volailiy. Journal of Financial Economics, 19, hp://dx.doi.org/ / x(87) Fu, F.(2009). Idiosyncraic Risk and he Cross-Secion of Expeced Sock Reurns.Journal of Financial Economics,Vol. 91, pp hp://dx.doi.org/ /j.jfineco Goyal, A., & Sana-Clara, P.(2003). Idiosyncraic Risk Maers!. Journal of Finance, 58, hp://dx.doi.org/ / Guo, H., & Savickas, R. (2010). Relaion beween Time-Series and Cross-Secional Effecs of Idiosyncraic Variance on Sock Reurns. Journal of Banking and Finance, 34(7), hp://dx.doi.org/ /j.jbankfin Jegadeesh, N., & Timan, S. (2001). Profiabiliy of Momenum Sraegies: An Evaluaion of Alernaive Explanaions. Journal of Finance, 56, hp://dx.doi.org/ / Linner, J. (1965). The Valuaion of Risk Asses and he Selecion of Risky Invesmens in Sock Porfolios and Capial Budges. Review of Economics and Saisics, 47, hp://dx.doi.org/ / Marcelo, J. L. M., Quirós, M. M. M., & Quirós, J. L. M. (2012). Asse Pricing wih Idiosyncraic Risk: The Spanish Case. Inernaional Review of Economics and Finance, 21, hp://dx.doi.org/ /j.iref Markowiz, H. (1959). Porfolio Selecion: Efficien diversificaion of Invesmens. New York: Wiley. Meron, R. (1987). A Simple Model of Capial Marke Equilibrium wih Incomplee Informaion. Journal of Finance, 42, hp://dx.doi.org/ /j b04565.x 11

12 Asian Journal of Finance & Accouning Newey, W.K., & Wes K.D. (1987). A Simple, Posiive-Definie, Heeroskedasiciy and Auocorrelaion Consisen Covariance Marix. Economerica, 55, hp://dx.doi.org/ / Sharpe, W. (1964). Capial Asse Prices: A Theory of Marke Equilibrium. Journal of Finance, 19, hp://dx.doi.org/ /j b02865.x Spiegel, M., & Wang, X. (2006). Cross-secional Variaion in Sock Reurns: Liquidiy and Idiosyncraic Risk. Unpublished working paper, Yale Universiy. Treynor, J. L. (1961). Toward a Theory of Marke Value of Risky Asses. Mimeo, subsequenly published in Korajczyk, Rober A. 1999, Asse Pricing and Porfolios Performance: Models, Sraegy and Performance Merics London: Risk Books. i Macroeconomic indicaors used as conrol variable by Goyal and Clara (2003) were dividend price raio, hree-monh Treasury bill rae, erm Spread and defaul Spread. ii Firm characerisics i.e. size, value, volume, liquidiy, momenum, analys forecas dispersion and marke condiions. iii The facors (SMB, HML and ERm) were calculaed using he Fama French (1993) mehodology which is described in secion 2.1 of he sudy. 12