Idiosyncratic Volatility, Stock Returns and Economy Conditions: The Role of Idiosyncratic Volatility in the Australian Stock Market


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1 Idiosyncraic Volailiy, Sock Reurns and Economy Condiions: The Role of Idiosyncraic Volailiy in he Ausralian Sock Marke Bin Liu Amalia Di Iorio RMIT Universiy Melbourne Ausralia Absrac This sudy examines he imporance of idiosyncraic volailiy in asse pricing for Ausralian sock reurns from 1993 o We form an idiosyncraic volailiy mimicking facor. In he presence of he FamaFrench hreefacor we find ha he idiosyncraic volailiy mimicking facor is priced in Ausralian sock reurns over he sample period, implying ha his ype of volailiy is significan in he pricing of Ausralian socks. Furher, we find ha idiosyncraic volailiy is priced during boh economy expansions and conracions and our model capures greaer variaions in Ausralian sock reurns during expansions han conracions. JEL Classificaion: G12 Key words: idiosyncraic volailiy; asse pricing; sock reurns; business cycles Conac Auhors: Bin Liu, School of Economics, Finance and Markeing, RMIT Universiy, phone: , fax: , Amalia Di Iorio, Graduae School of Business and Law, RMIT Universiy, phone: , fax: ,
2 1. Inroducion The Capial Asse Pricing Model (hereafer CAPM) of Sharpe (1964) and Linner (1965) suggess ha only sysemaic risk is priced. This implies ha idiosyncraic risk/volailiy has no role in explaining asse reurns. Specifically, given he assumpions of CAPM, idiosyncraic volailiy is diversified away since invesors hold a proporion of he welldiversified marke porfolio. In realiy, however, his is no always he case. Several sudies have idenified ha for various reasons invesors do no always hold welldiversified porfolios (see example Malkiel and Xu, 2002; Goezmann and Kumar, 2004), and herefore sysemaic risk is no necessarily he only risk facor o be priced. In some cases idiosyncraic volailiy has also been found o be priced. Unil recenly, he role of idiosyncraic volailiy in asse pricing has been ignored in he lieraure. Idiosyncraic volailiy should play no role in asse pricing because under assumpions of CAPM idiosyncraic volailiy is perfecly diversified away However, invesors do no always hold well diversified porfolios and Meron (1987) suggess ha invesors are compensaed for he holdings of underdiversified porfolios. Therefore, idiosyncraic volailiy has araced researcher s aenions. Indeed, several sudies have found significan relaionships beween reurns and idiosyncraic volailiy ha have creaed some ineres, as well as some conroversy. For example, Malkiel and Xu (1997, 2002), Goyal and SanaClara (2003) and Fu (2009) find idiosyncraic volailiy is significanly and posiively relaed o sock reurns in he US. Conversely, Ang, Hoddrick, Xing and Zhang (2006) find a negaive relaionship beween lagged idiosyncraic volailiy and fuure average reurns in he US. Furher, Ang, Hoddrick, Xing and Zhang (2009) find ha he negaive relaionship beween lagged idiosyncraic volailiy and fuure average reurns is significan in he larges seven equiy marke. Ineresingly, alhough he repored empirical resuls are mixed, mos suppor ha idiosyncraic volailiy is an omied pricing facor by CAPM. 2
3 In his paper, we examine he role of idiosyncraic volailiy in pricing of Ausralian socks. We follow Fama and French (1993) and Drew, Naughon and Veeraraghavan (2004) o consruc an idiosyncraic volailiy mimicking facor (hereafer idiosyncraic volailiy facor). Our objecive is o es wheher his idiosyncraic volailiy facor is priced in he presence of he Fama and French hreefacor. Furher, we examine he pricing abiliy of he idiosyncraic volailiy facor in economy expansions and conracions. This is moivaed by Campbell e al. (2001) and Ooi e al (2009) who sugges ha he behaviour of idiosyncraic volailiy is asymmeric during differen marke condiions. This sudy conribues o he lieraure in several ways. Firs, we follow Drew, Naughon and Veeraraghavan (2004) by consrucing an idiosyncraic volailiy facor. However, unlike Drew e al (2004) who define he idiosyncraic volailiy as he difference beween oal risk and he sysemaic risk of a sock, we define idiosyncraic volailiy as he sandard deviaion of he regression residual of he Fama and French hreefacor model. This definiion has been implemened in several oher sudies, for example Ang, Hoddrick, Xing and Zhang (2009) and Fu (2009). In addiion, we examine he pricing abiliy of he idiosyncraic volailiy facor in presence of he Fama and French hreefacor model. Second, we explore he sabiliy of he idiosyncraic volailiy facor enhanced model in differen phases of business cycles. This is moivaed by a number of sudies in he asse pricing lieraure. For example, Campbell e al. (1997) repor ha idiosyncraic volailiy increases during economic downurns, hus suggesing ha he pricing abiliy of idiosyncraic volailiy may no be sable. Leau and Ludvigson (2001) find ha sock reurns vary in he differen phases of business cycles and herefore argue ha he pricing abiliy of idiosyncraic volailiy facor may be affeced. Ooi e al. (2009) also repor ha idiosyncraic volailiy increases significanly during bad marke cycles bu decreases slighly during good marke imes. This evidence of he asymmeric behaviour of idiosyncraic volailiy moivaes us o explore he pricing abiliy of idiosyncraic volailiy in differen phases of he business cycle. 3
4 Our resuls reveal several ineresing findings. Firs, he idiosyncraic volailiy facor is priced for he reurns of Ausralian socks from 1993 o Second, he pricing abiliy of he idiosyncraic volailiy remains srong even in he presence of he Fama and French hreefacor. Third, we find ha he Fama and French size facor is highly correlaed wih he idiosyncraic volailiy facor. This may sugges ha boh facors capure similar informaion and herefore he idiosyncraic facor could replace he size facor in he hreefacor model. This asserion is suppored by he our hreefacor model (he marke risk facor, he bookomarke facor and he idiosyncraic volailiy facor) as our hreefacor model produces less mispricing han he Fama and French hreefacor model over he sample period. Fourh, we find he idiosyncraic volailiy facor is priced in boh economy expansions and conracions, bu our model capures greaer variaions of he sock reurns during expansion han conracions. Our empirical findings have several pracical implicaions for he invesor. Firs, idiosyncraic volailiy should no be ignored when esimaing he required rae of reurn and he cos of capial. Second, invesors should mach he idiosyncraic volailiy of heir porfolios wih he benchmark porfolio when evaluaing he performance of he porfolios. Third, due o he asymmeric naure of idiosyncraic volailiy, invesors should rebalance heir porfolios according o differen phases in he business cycle since changes in idiosyncraic volailiy will affec he level of diversificaion of heir porfolios. The reminder of his paper is organized as follows. Secion 2 oulines previous lieraure. The mehods employed in his sudy are found in secion 3. Secion 4 describes he daa. Secion 5 presens he empirical es resuls. Finally, secion 6 provides he conclusion. 4
5 2. Lieraure Review According o he CAPM of Sharpe (1964) and Linner (1965), only sysemaic risk is priced. Idiosyncraic risk is no priced because i is diversifiable. However, many researchers sugges ha CAPM fails in is pracical applicaion, for example, Samean (1980) finds ha socks wih high bookomarke equiy raio generae higher average reurns ha CAPM fails o capure. Basu (1981) finds small socks earn higher reurns han esimaed by CAPM, while Rosenberg, Reid and Lansein (1985) find ha he bookomarke equiy raio explains expeced reurns. Chan, Hamao and Lakonishok (1991) find ha he bookomarke equiy raio also explains he average reurns on Japanese socks. These sudies do no suppor CAPM empirically, and provide he impeus o invesigae addiional risk facors. Fama and French (1992) repor ha size, and he bookomarke equiy raio are pricing facors for reurns. This evidence suggess ha hese variables proxy differen dimensions of sock risks and subsequenly led o he developmen of he Fama and French (1993) hreefacor model. Specifically, Fama and French (1993) find ha risk mimicking facors for size and bookomarke equiy raio plus he marke risk facor capure he variaion in he sock reurns, suggesing he risk mimicking facors of size and bookomarke equiy raio are firmspecific risks omied by he marke risk facor. Fama and French (1996, 1998) have confirmed and consolidaed hese findings. The success of he Fama and French hreefacor model indicaes ha unsysemaic risk facors omied by he CAPM could have significan explanaory power o he asse reurns. Meron (1987) suggess ha idiosyncraic risk should be priced if invesors hold underdiversified porfolios. In realiy, individual invesors are no likely o hold welldiversified porfolios due o a number of reasons, for example, ransacion coss, informaion coss and choice of invesmen syle. Specifically, individual invesors are relucan o increase he level of diversificaion of heir porfolios if hey believe he ransacion coss be greaer han he benefis associaed wih furher 5
6 diversificaion. Moreover, informaion is cosly, so i is impossible for individual invesors and even insiuional invesors o collec and analyse all informaion abou all securiies in he marke in a imely manner. Consequenly, invesors only have informaion for a subse of all securiies and hey subsequenly consruc porfolios heavily weighed in hese securiies. The oucome is ha hey herefore hold underdiversified porfolios. In some cases, invesors are speculaors who are willing o speculae on forhcoming informaion. These invesors deliberaely hold underdiversified porfolios as hey expec high fuure reurns o compensae he high idiosyncraic risk hey assume. Finally, invesmen syle may also lead o invesors holding less han fully diversified porfolios. Campbell, Leau, Malkiel and Xu (2001), for example, sugges ha many individual invesors hold a few socks due o he resricions of he corporae compensaion plan. Goezmann and Kumar (2004) repor ha more ha 25% of invesors hold only one sock and less han 10% of he invesors hold more han 10 socks, while Campbell, Leau, Malkiel and Xu (2001) sugges ha in order o achieve diversificaion invesors mus hold a leas 50 randomly seleced socks in heir porfolio. These sudies suppor ha noion ha many invesors do no hold well diversified porfolios and unsysemaic risk is no fully diversified. Therefore, idiosyncraic risk should be priced. The imporan role of idiosyncraic risk in asse pricing was firs repored in he 1990 s. Since hen idiosyncraic volailiy has drawn he aenion of a number of researchers. For example, Malkiel and Xu (1997) find ha idiosyncraic volailiy is priced for U.S. socks reurns. They sugges ha porfolio managers may be forced by he board of direcors o buy or sell socks when hey dropping in price, so hese porfolios managers require higher reurns in order o compensae for he addiional idiosyncraic risk hey have assumed. Campbell e al. (2001) repor ha idiosyncraic volailiy increased from 1962 o They sugges ha he number of socks o achieve given level of diversificaion has increased over he sample period. They also sugges ha idiosyncraic volailiy increases during economic downurns. The implicaion is ha invesors mus increase he number of socks hey are holding in heir porfolios in order o mainain he same level of 6
7 diversificaion during economic conracions. Goyal and SanaClara (2003) find a posiive relaionship beween idiosyncraic volailiy and porfolio reurns on he NYSE/AMEX/NASDAQ socks. Bali, Cakici, Yan and Zhang (2005) replicaed he sudy by Goyal and SanaClara (2003). They show ha he posiive relaionship beween idiosyncraic volailiy and reurns is driven by small socks on he NASDAQ. The posiive relaionship does no hold for NYSE socks. Fu (2005, 2009) repor a posiive relaionship beween expeced idiosyncraic volailiy and reurns. However, conrary resuls are found by Ang e al. (2006, 2009). Their findings indicae ha realized idiosyncraic volailiy is negaively relaed o he sock reurns in he U.S. and oher developed counries. They sugges ha here is an unidenified economic source which is driving he relaionship beween idiosyncraic volailiy and reurn. While a number of previous sudies focus on he U.S. marke, here are only a few research papers published ha invesigae he effec of idiosyncraic volailiy on he pricing of Ausralian asses. Bollen, Skonicki and Veeraraghavan (2009) follow he idiosyncraic volailiy esimaion mehod of Campbell e al. (1997) and find ha idiosyncraic volailiy is no priced in Ausralian sock marke. Brockman e al. (2009) followed idiosyncraic volailiy esimaion mehod of Fu (2009), and examined idiosyncraic volailiy in pricing of socks in 44 counries including Ausralia. They repor a significan posiive relaionship beween expeced idiosyncraic volailiy and Ausralian sock reurns. We consruc a 4facor model by adding a risk mimicking facor for idiosyncraic volailiy o he Fama and French (1993) 3facor model. Our approach o consruc he idiosyncraic volailiy mimicking facor is similar o ha implemened by Drew, Naughon and Veeraraghavan (2004), alhough we define idiosyncraic volailiy differenly. Following Xu and Malkiel (2003), Drew e al (2004) define idiosyncraic volailiy as he difference beween oal risk and sysemaic risk. We, on he oher hand, define idiosyncraic volailiy as he sandard deviaion of he regression 7
8 residual of he Fama and French (1993) hreefacor model: r r ) f ( rm rf s SMB h HML, where rf r is he excess reurn of individual socks, r r is he excess reurn of he marke porfolio, SMB is he difference beween reurns m f of small socks porfolio and large socks porfolio, HML is he difference beween reurns of high bookomarke equiy raio socks and low bookomarke equiy raio socks. Our definiion of idiosyncraic volailiy is commonly used and widely acceped in many published research papers, for example Ang e al. (2006, 2009), Fu (2005, 2009) and Ooi e al. (2009). We consruc a risk mimicking facor for idiosyncraic volailiy. The idiosyncraic volailiy mimicking facor HIMLI is he difference in reurns beween high idiosyncraic volailiy porfolio and low idiosyncraic volailiy porfolio. This idiosyncraic volailiy mimicking facor is esed in he asse pricing models. This sudy is also moivaed by empirical evidence ha he HML facor of he Fama and French hree facor model has weak explanaory power when implemened o es Ausralian sock reurns. Previous sudies sugges ha he book o marke equiy raio mimicking facor may no conribue as much as he size mimicking facor in explaining realized reurns in Ausralia. For example, Gaun (2004) repors 14 ou of 25 significan HML facors and 21 ou of 25 significan SMB facors. Faff (2004) suppors hese findings by reporing only 14 ou of 24 significan cases of HML facors and 18 ou of 24 significan SMB facors in his invesigaion of Ausralian indusry porfolios. These sudies sugges ha for Ausralian socks, he Fama and French hreefacor model capures he variaons in he reurns for Ausralian socks, bu he pricing abiliy of he Fama and French hreefacor model is weaker for Ausralian socks han U.S. socks when compare hese Ausralian empirical resuls o he resuls of Fama and French (1993, 1996). The weaker pricing abiliy of he Fama and French hreefacor model for Ausralian socks may be resuled by a missing pricing 8
9 facor in he Fama and French hreefacor model for Ausralian socks. Hence, we are moivaed o invesigae wheher or no he idiosyncraic volailiy mimicking facor is a missing pricing facor in he Fama and French hreefacor model for Ausralian socks. Moreover, we furher invesigae he sabiliy of our idiosyncraic volailiy mimicking facor in he pricing of socks over business cycles during he sample period. Previous sudies sugges ha he behaviour of idiosyncraic volailiy is asymmeric, for example Ooi e al. (2009) sugges ha idiosyncraic volailiy increases significanly during bad marke imes, bu decreases slighly during good marke imes. Campbell e al. (2001) also sugges ha idiosyncraic volailiy is high during economy recessions. Due o he differen behaviour of idiosyncraic volailiy during differen marke imes, he pricing abiliy of idiosyncraic volailiy mimicking facor may be affeced. Thus, we examine he pricing abiliy of he idiosyncraic volailiy mimicking facor over he business cycles. 3. Mehod 3.1. Consrucing Daily Fama and French Risk Mimicking Porfolios and Esimaing Idiosyncraic Volailiy We follow Fama and French (1993) o consruc daily SMB and HML porfolios. Companies are divided ino wo size porfolios and hree bookomarke equiy raio porfolios. The wo size porfolios consis of (i) he op 50% of companies (big) by marke capializaion, and (ii) he boom 50% companies (small) by marke capializaion. The hree bookomarke equiy raio porfolios consis of (i) 1/3 high bookomarke equiy raio companies, (ii) 1/3 medium bookomarke equiy raio companies, and (iii) 1/3 low bookomarke equiy raio companies. Every year, he companies are ranked and sored ino porfolios according o heir size and bookomarke equiy raio a December of year 1. The daily SMB is calculaed as he reurns of he big size porfolio minus he reurns of he small size porfolio. Daily HML is calculaed as he reurns of he high 9
10 bookomarke equiy raio porfolio minus he reurns of he low bookomarke equiy raio porfolio. The porfolios are rebalanced on an annual basis. Then, following Ang e al (2009), we define idiosyncraic volailiy as he sandard deviaion of regression residuals of he Fama and French (1993) hreefacor model. Over he sample period, daily excess reurns of sock i are regressed on he daily Fama and French (1993) hree facors. The regression equaion is he following: r r ( r r ) s SMB h HML (1) f m f Where r is he daily reurns of sock i, r f is he daily 90day bank accepable bill rae, r m is he daily reurns of S&P/ASX All Ordinary Index, SMB and HML are he daily reurns of Fama and French (1993) risk facor mimicking porfolios for size and bookomarke raio. Idiosyncraic volailiy is esimaed as he sandard deviaion of regression residual afer regressing equaion (1). Subsequenly he sandard deviaion of daily regression residuals is ransformed o a monhly value by muliplying he square roo of he number of rading days in he monh Consrucing Monhly Risk Mimicking Porfolios for Size, BookoMarke Equiy Raio and Idiosyncraic Volailiy We follow Fama and French (1993) o consruc monhly SMB and HML. The monhly SMB is calculaed as he reurns of he big size porfolio minus he reurns of he small size porfolio. The monhly HML is calculaed as he reurns of he high bookomarke equiy raio porfolio minus he reurns of he low bookomarke equiy raio porfolio. The porfolios are rebalanced on an annual basis. Then, following Drew, Naughon and Veeraraghavan (2006), we consruc he risk mimicking porfolio HIMLI for idiosyncraic volailiy. Three idiosyncraic volailiy porfolios consis of 1/3 10
11 high idiosyncraic volailiy companies, 1/3 medium idiosyncraic volailiy companies and 1/3 low idiosyncraic volailiy companies. Every year, he companies are ranked and sored ino porfolios according o heir idiosyncraic volailiy a December of year 1. Monhly HIMLI is calculaed as he reurn of high idiosyncraic volailiy porfolio minus reurn of low idiosyncraic volailiy porfolio. As wih he SMB and HML porfolios, he HIMLI porfolio is rebalanced on annual basis Idiosyncraic Volailiy Enhanced Asse Pricing Models The base model is idiosyncraic volailiy enhanced wofacor model. The regression equaion is he following: r r ( r r ) i HIMLI (2) f m f The explanaory power of he risk mimicking porfolio for idiosyncraic volailiy HIMLI is esed in presence of size premia The regression equaions are he followings: SMB or book o marke equiy premia HML and he marke risk facor. r r ( r r ) s SMB i HIMLI (3) f m f r r ( r r ) s HML i HIMLI (4) f m f The regression equaion of an idiosyncraic volailiy enhanced Fama and French hreefacor model is he following: r r ( r r ) s SMB h HML i HIMLI (5) f m f where r r is he monhly reurns of sock i, f is he monhly 90day bank accepable bill rae, r m is he monhly reurn of S&P/ASX All Ordinary Index, SMB and HML are Fama and French risk facor mimicking porfolios for size and bookomarke raio and risk mimicking porfolio for idiosyncraic volailiy. HIMLI is he monhly reurns of 11
12 3.4. Idiosyncraic Volailiy Enhanced Asse Pricing Model Over Business Cycles Campbell e al. (2001) find ha idiosyncraic volailiy increases during economic downurns. In differen saes of business cycle, he idiosyncraic volailiy enhanced models are: r r f D ( r r i D HIMLI (6) exp ansion m f ) exp ansion r r D ( r r ) i D HIMLI (7) f conracion m f conracion where r r is he monhly reurns of sock i, f is he monhly 90day bank accepable bill rae, r m is he monhly reurn of S&P/ASX All Ordinary Index, HIMLI is a risk facor mimicking porfolios for idiosyncraic volailiy. Alpha is he inercep of he regression model. D exp ansion is a dummy variable which akes a value of uniy in an expansionary phase of he business cycle 1 and a value of zero oherwise. D conracio n is a dummy variable which akes a value of uniy in a conracion phase of he business cycle and a value of zero oherwise. Table 9 shows he phases of business cycles over he sample period. [Inser Table 9 here] 3.5. Ten Equally Weighed Porfolios A January of each year, we consruc en porfolios of socks based on idiosyncraic volailiy a December of year 1 wih each porfolio comprising of an equal number of socks. We hold he porfolios for one year, and rebalance hem in January of year +1. This provides a ime series of monhly reurns on each porfolio from 1993 o The business cycle classificaion is in accordance o he definiions provided by he Melbourne Insiue of Applied Economics and Social Research on is websie a hp://melbourneinsiue.com/macro/repors/bcchronology.hml 12
13 4. Daa Ausralian sock reurn daa are obained from Daasream for he period of January 1993 o December The 90day Ausralian Bank Acceped Bill Rae is obained from he websie of he Reserve Bank of Ausralia o represen a proxy for he risk free rae in Ausralia. We use oal reurn indices of he socks o calculae he average reurns of he socks. We use ASX All Ordinaries Toal Reurn Index o calculaed average reurn of he marke proxy. The oal reurn index is he accumulaion reurn index adjused for dividends and oher capial issues. Finally we use monhly marke capializaion daa o represen he size of socks, and monhly marke o book values o calculae he relevan book o marke raios. The iniial sample included acive and dead companies lised on Ausralian Securiies Exchange (hereafer ASX) during he sample period. In order o esimae monhly idiosyncraic volailiy, daily reurn index for he socks and he marke proxy are obained. Two filers were applied o obain he final sample: 1. Following Guan (2004), only socks ha have a leas one rade in a monh were included o avoid any possible hin rading effecs; and 2. Only socks ha had he following available daa were included: daily and monhly oal reurn index, monhly marke capializaion and monhly marke o book value. Table 1 provides he number of socks in he final sample and heir equallyweighed average reurns, equallyweighed average size, equallyweighed average bookomarke equiy raio and equallyweighed average idiosyncraic volailiy during he sample period. Equallyweighed averages are used raher han valueweighed averages, since small socks have high idiosyncraic volailiies (Bali, Cakici, Yan and Zhang (2005)), and herefore equallyweighed averages allow he idiosyncraic volailiy effec of small socks o be equally pronounced.. The smalles conribuion of 13
14 iniial sample o he final sample is in 1993 (422 socks), and he larges conribuion is in 2008 (1773 socks). [Inser Table 1 here] Table 2 presens he descripive saisics of he relevan variables used in he regression equaions. We observe ha (i) he average marke reurn is 0.95% per monh from 1993 o 2010, and (ii) he monhly average excess reurn of he marke proxy, average reurn of size mimicking porfolio, bookomarke equiy raio mimicking porfolio and idiosyncraic volailiy mimicking porfolio are 0.49%, 1.24%, 1.88% and 1.61% respecively. [Inser Table 2 here] The monhly sock reurns are ranked by idiosyncraic volailiy in December and sored ino 10 idiosyncraic volailiy ranked porfolios wih an equal number of socks in each porfolio. These porfolios are held for one year and rebalanced in he following year. Porfolio 1 comprises he socks wih highes idiosyncraic volailiy and porfolio 10 comprises he socks wih lowes idiosyncraic volailiy. Table 3 repors he summary saisics of 10 idiosyncraic volailiy porfolios. Overall, i shows ha monhly excess reurns decrease monoonically when moving from high idiosyncraic volailiy porfolio (porfolio 1) o low idiosyncraic volailiy porfolio (porfolio 9). The sandard deviaion also decreases monoonically when moving from high idiosyncraic volailiy porfolio (porfolio 1) o low idiosyncraic volailiy porfolio (porfolio 9). Moreover, he average size is noed o increase when moving from he high idiosyncraic volailiy porfolio (porfolio 1) o he low idiosyncraic volailiy porfolio (porfolio 9). This finding is consisen wih ha repored by Bali, Cakici, Yan and Zhang (2005) who sugges ha small companies have high 14
15 idiosyncraic volailiy. There is no such paern in he BE/ME variable when moving from he high idiosyncraic volailiy porfolio o he low idiosyncraic volailiy porfolio. [Inser Table 3 here] Figure 1 shows he variaion of he average idiosyncraic volailiy over he sample period. We make several observaions. Firs, he idiosyncraic volailiy was high a he end of Following a 4 year downward drif, he volailiy again reached a peak a he end of In 1997, Asian Financial Crisis caused a global sock marke crash. This paern was repeaed wo more imes unil he idiosyncraic volailiy reached he highes peak in he end of This highes peak resuled by he Globe Financial Crisis which is he wors financial crisis since he Grea Depression of 1930 s [Inser Figure 1 here] Figure 2 shows he variaion hrough ime of he average idiosyncraic volailiy and he marke reurn over he sample period. In his case we noe ha he idiosyncraic volailiy increases significanly when he marke reurn drops bu decreases slighly when he marke reurn increases. This finding is consisen wih Ooi, Wang and Webb (2009), who repor ha idiosyncraic volailiy increases dramaically during bad marke imes and decreases marginally during good marke imes. From Figure 1 and 2, i is obvious ha idiosyncraic volailiy increased rapidly when here are sudden collapses in he sock marke. The imporan implicaion of hese resuls for an invesmen perspecive is ha he opimal level of porfolio diversificaion changes over differen marke condiions and invesors mus ake his ino consideraion when rebalancing heir porfolios. [Inser Figure 2 here] 15
16 5. Empirical resuls This secion repors he resuls of he crosssecional regression analysis. In secion 5.1, we provide he resuls over he whole sample period. Firs, we repor and analyse he resuls of a wofacor model: a marke risk facor plus an idiosyncraic volailiy mimicking facor. Second, we discuss wo hreefacor models: firs model comprises a marke risk facor, a size facor and an idiosyncraic volailiy facor, second model comprises a marke risk facor, a bookomarke facor and an idiosyncraic volailiy facor. Third, we presen he resuls of Fama and French hreefacor model and a fourfacor model. The resuls provide an insigh ino he pricing abiliy of he idiosyncraic volailiy mimicking facor in Ausralia from 1993 o In secion 5.22, we provide resuls of an analysis of he behaviour of idiosyncraic volailiy during economy expansions and conracions Is Idiosyncraic Volailiy Priced in Ausralian Socks Reurns? Table 4 repors he resuls of a wofacor model. This wofacor model comprises a marke risk facor and an idiosyncraic volailiy facor. Firs, we observe ha he inerceps are saisically significan in 3 ou of 10 cases and all have posiive signs. A significan inercep indicaes ha here is a pricing error caused by he asse pricing model. Therefore our findings indicae ha he highes (Porfolio 1) and lowes idiosyncraic volailiy porfolios (Porfolios 9 and 10) produce large posiive abnormal reurns. Second, all facor loadings of he marke risk facor are saisically significan and posiive as expeced. The facor loadings do no, however, demonsrae a paern when moving from high idiosyncraic volailiy porfolios o low idiosyncraic volailiy porfolios. Third, he coefficiens of idiosyncraic volailiy facor decrease monoonically when moving from he high idiosyncraic volailiy porfolio o he low idiosyncraic volailiy porfolio. This suggess ha he higher he idiosyncraic volailiy of he porfolio, he more sensiive he changes in reurn o changes in he idiosyncraic volailiy facor. The reurns of he idiosyncraic volailiy porfolios are srongly and posiively relaed o he idiosyncraic volailiy facor excep porfolio 10. This 16
17 indicaes ha he idiosyncraic volailiy facor capures variaion in sock reurns ha is missed by he marke risk facor and, herefore suggess ha he marke facor alone canno explain he variaion in he sock excess reurns. The adjused Rsquared also exhibis a decreasing paern from he high idiosyncraic volailiy porfolio o he low idiosyncraic volailiy porfolio. The adjused Rsquared is above 50% for all porfolios excep porfolio 10. This indicaes ha he wo facor model capures large proporions of variaion in reurns from porfolio 1 o 9, wih he only excepion being he lowes idiosyncraic volailiy porfolio. [Inser Table 4 here] Table 5 and Table 6 show he resuls of wo hreefacor models. In able 5, he hreefacor model comprises a marke risk facor, a size facor (Fama and French SMB), and an idiosyncraic volailiy facor. Table 5 shows he facor loading of his hreefacor model and several imporan findings are observed. Firs, in 7 ou of 10 cases, he inerceps are significan and 5 of hese have negaive signs. This indicaes ha high idiosyncraic volailiy porfolios produce abnormal reurns. Second, as expeced, all facor loadings of he marke risk facor are posiive and significan and do no exhibi any paern. The facor loadings of he marke risk facor for porfolio 2 o 8 are very close o 1and porfolio 1 and 10 have smaller facor loadings han oher porfolios. Third, he facor loadings of he size facor are posiive and significan. There is a monoonically decreasing paern in he facor loadings from porfolio 3 o porfolio 8 and porfolios 1 and 2 have bigger facor loadings han porfolio 10. This indicaes ha excess reurns of he high idiosyncraic volailiy porfolios are more sensiive o he changes in he size facor han low idiosyncraic volailiy porfolios. Fourh, in 8 ou of 10 cases, he idiosyncraic volailiy facor has significan and posiive facor loadings. A monoonically decreasing paern in he facor loading is eviden when moving from high idiosyncraic volailiy porfolios o low idiosyncraic volailiy porfolios, and he lowes idiosyncraic volailiy porfolios have negaive facor loadings. This indicaes ha he idiosyncraic 17
18 volailiy facor is priced in his hree facor model and i capures he grea variaions in he excess reurns of he idiosyncraic volailiy porfolios. The adjused Rsquared shows a decreasing paern again, bu he values of adjused Rsquared of his hreefacor model are greaer han he adjused Rsquared values of he wofacor model. This indicaes ha here is an increase in he proporion of variaion explained by he hreefacor model. [Inser Table 5 here] Table 6 shows he facor loadings of a hreefacor model ha comprises a marke risk facor, a bookomarke equiy facor and an idiosyncraic volailiy facor. Firs, surprisingly, he highes and lowes idiosyncraic volailiy porfolios have significan posiive inerceps which indicae abnormal reurns are only available on wo exreme cases. Second, as expeced, he facor loadings of he marke risk facor are significan and posiive. There is no paern when moving from he high idiosyncraic volailiy porfolio o he low idiosyncraic volailiy porfolio. Third, in 3 ou of 10 cases, he bookomarke equiy facor has a posiive and significan facor loading. Fourh, again, he idiosyncraic volailiy facor has a significan and posiive facor loading excep in he case of porfolio 10. There is a monoonically decreasing paern in he facor loadings. The adjused R squared is above 50% excep porfolio 10 which indicaes ha a large proporion of variaion is explained by he model. The resuls from Table 5 and 6 sugges ha he idiosyncraic volailiy facor is priced in excess reurns of Ausralian socks. [Inser Table 6 here] Table 7 repors he resuls of he Fama and French hreefacor model (Panel A) and a fourfacor model (Panel B). The fourfacor model comprises he welldocumened Fama and French hree facors and an addiional idiosyncraic volailiy facor. Firs, in panel A of able 7 we noe ha in 6 18
19 of 10 cases he inercep is significan and he highes and lowes idiosyncraic volailiy porfolios (Porfolio 1 and Porfolio 10 respecively) have he larges posiive abnormal reurns. Porfolios 4 o 7 show negaive abnormal reurns. Second, he facor loadings of he marke risk facor show consisency as hey are significan, posiive, and here is no paern. In 8 ou of 10 cases, he facor loadings of he marke risk facor are close o 1, a finding ha is consisen wih many previous sudies, including Gaun (2004). Third, he size facor has significan and posiive loadings, and we observe a monoonically decreasing paern when moving from porfolio 1 o porfolio 10. This indicaes ha he size facor capures he variaion in excess reurns of he porfolios. Fourh, he explanaory power of HML is once again low. In 4 ou of 10 cases, he facor loadings are significan wih a negaive facor loading for he high idiosyncraic volailiy porfolio. The Adjused Rsquared values are high excep for porfolio 10. Consisen wih he resuls of he Fama and French hreefacor model, he fourfacor model explains a greaer proporion of he variaion in he excess reurn of he porfolios. This is evidenced by high adjused Rsquared values. The inerceps, facor loadings of he marke risk facor, size facor values and bookomarke equiy facor values exhibi similar resuls as he Fama and French hreefacor model. The ineresing finding is ha he idiosyncraic volailiy facor is priced in his fourfacor model and here is a monoonically decreasing paern in he facor loadings when moving from highes idiosyncraic volailiy porfolio (Porfolio 1) o he lowes idiosyncraic volailiy porfolio (Porfolio 10). Boh he loading of he size facor and he idiosyncraic volailiy facor show monoonically decreasing paerns and hese wo facors capure mos of variaions of excess reurns. The excess reurns of high idiosyncraic volailiy porfolios are posiively relaed o he idiosyncraic volailiy facor, while excess reurns of he boom wo porfolios are negaively relaed o he idiosyncraic volailiy facor. 19
20 Given hese resuls, our findings sugges ha idiosyncraic volailiy was priced for Ausralian sock reurns from 1993 o High (low) idiosyncraic volailiy socks are small (big) by size, have big (small) facor loadings on he size facor and idiosyncraic volailiy facor. The bookomarke equiy facor has weaker explanaory power han he size facor and he idiosyncraic volailiy facor o he reurns of Ausralian socks. [Inser Table 7 here] 5.2. A ThreeFacor Model for Ausralian Sock Marke From Tables 4 o 7, which presen he findings of our examinaion of explanaory power of idiosyncraic volailiy in (i) he wofacor model (ii) he hreefacor models and (iii) he fourfacor model respecively, we find ha he idiosyncraic volailiy facor exhibis consisen explanaory power in relaion o variaion in he excess reurns of he socks. However, we noe a sronger significan inercep when he size facor appears in he asse pricing model. This suggess ha he size facor may cause a greaer pricing error in he asse pricing model han does idiosyncraic volailiy. For example here are 7 significan inerceps in Table 5 which repors he regression resuls of Equaion 3 compared wih 2 significan inerceps in Table 6 ha presens he regression resuls of Equaion 4. Our analysis is based on porfolios, specifically size porfolios where he reurns of small socks minus he reurns of big sock and idiosyncraic volailiy as he reurns of high idiosyncraic volailiy socks minus reurn of low idiosyncraic volailiy socks. However, Table 3 shows ha high idiosyncraic volailiy socks are small socks, so he idiosyncraic volailiy facor may capure similar informaion as ha capured by he size facor. Table 8 shows he correlaion coefficiens beween he explanaory variables. The correlaion beween he size facor and he idiosyncraic volailiy facor is significanly high a 67%. The high correlaion beween hese wo 20
21 explanaory variables indicaes a close bu no exac relaionship beween hem and may sugges ha he saisics are unreliable. A simple soluion o his mulicollineariy problem is o omi one of wo explanaory facors from he regression funcion. Consequenly, we compared he resuls of Fama and French hreefacor model presened in able 7 and he regression resuls of he hreefacor model repored in able 6. We find ha boh models capure a large proporion of variaions in he excess reurns of sock porfolios, bu he hreefacor model of Equaion 4 is favourable over he Fama and French hreefacor model due o he fac ha here are fewer missing pricing for he hreefacor model of Equaion 4. [Inser Table 8 here] 5.3. Is Idiosyncraic Volailiy priced condiional on Business Cycles? Previous sudies have invesigaed he behaviour of idiosyncraic volailiy in differen marke cycles. The empirical findings have been mixed. For example, Campbell e al. (2001) find ha idiosyncraic volailiy decreases during economy downurns, while Ooi e al (2009) repor ha idiosyncraic volailiy increases dramaically during bad marke imes bu decreases marginally during good marke imes. Nowihsanding hese conflicing resuls, i is eviden ha differences in behaviour of idiosyncraic volailiy during differen business cycles may affec he pricing abiliy of he idiosyncraic volailiy facor. Therefore, we exend our analysis in his paper o invesigae he pricing abiliy of he idiosyncraic volailiy facor during marke expansions and conracions.. Our classificaion of Business Cycle phases in he Ausralian marke is based on he definiions produced by he Melbourne Insiue of Applied Economic and Social Research. Table 9 shows a summary of hese phases over he sample period. There is a oal of 144 monhs of expansion and 72 21
22 monhs of recession. We creae an expansion dummy variable and a conracion dummy base on he informaion provided by Table 9 and we use a wofacor model o es he sabiliy of he pricing abiliy of he idiosyncraic volailiy facor. The wofacor model comprises a marke risk facor and an idiosyncraic volailiy facor. The wofacor model is seleced among all he models used in his sudy because he marke risk facor is he mos sable pricing facor. Table 10 repors he facor loadings for he wofacor model during expansions and conracions. During expansions, here is evidence of hree mispricings by he wofacor model. The abnormal reurns are posiive and large abnormal reurns were eviden for he highes and lowes idiosyncraic volailiy porfolios. There is no paern in he facor loadings of he marke risk facor and hey are all significanly differen from zero. In 9 ou of 10 cases, he facor loadings of he idiosyncraic volailiy facor are significan and posiive, excep he facor loading for porfolio 10. We observe a monoonically decreasing paern in he facor loadings which suggess ha he idiosyncraic volailiy facor is priced and capures he variaion in he excess reurns of he porfolios during expansions. The adjused Rsquared values are lower han hose presened in Table 4, bu hey are all above 30% excep Rsquared for porfolio 10 (wha is he R squared here?) which suggess ha he wofacor model capures he variaions in he excess reurns. [Inser Table 10 here] During conracions, here are 9 significan inerceps. Hence, he wofacor model exhibis greaer mispricing during conracions han during expansions. All he facor loadings of he marke risk facor are significan and posiive. There is no paern in he facor loadings of he marke risk facor. The facor loadings of he idiosyncraic volailiy facor show a monoonically decreasing paern from porfolio 1 o porfolio 7. The adjused Rsquared values are much lower han hose of he wofacor model during expansions. Based on he resuls provided in Table 10, we conclude ha he 22
23 idiosyncraic volailiy facor is priced in boh expansions and conracions, bu here is more mispricing produced by he wofacor model during conracions. 6. Conclusion Invesors do no always hold welldiversified porfolios. This could be due o a number of reasons, including high ransacion coss, and lack of informaion. Therefore, idiosyncraic risk is no fully diversified so invesors should be compensaed for he idiosyncraic risk. Hence, idiosyncraic volailiy should be priced in he asse pricing models. This sudy examines he role of idiosyncraic volailiy in he pricing of Ausralian socks from 1993 o We find ha he idiosyncraic volailiy mimicking facor capures informaion omied by he Fama and French hreefacor model. Furher, we show ha he idiosyncraic volailiy mimicking facor is priced in differen business cycle phases. Our main findings are summarized as follows. Firs, we show ha he idiosyncraic volailiy mimicking facor is priced for Ausralian sock reurns from 1993 o There are paerns in he facor loadings of he idiosyncraic volailiy mimicking facor when moving from high idiosyncraic volailiy porfolios o low idiosyncraic porfolios which suggess ha he idiosyncraic volailiy mimicking facor capures variaions in he reurn of he porfolios. The facor loadings of he marke risk facor and he Fama and French size facor are posiive, significan and consisen wih previous findings in he lieraure. The pricing abiliy of he Fama and French bookomarke equiy facor is weaker han oher pricing facors in our asse pricing models. Second, we provide evidence o show ha he idiosyncraic volailiy mimicking facor is a sronger pricing facor han he Fama and French size facor for Ausralian sock reurns due o he fac ha our hreefacor model comprising a marke risk facor, a bookomarke equiy facor and an idiosyncraic volailiy facor ha capure large proporion of variaion in Ausralian sock reurns 23
24 and our hreefacor model produces fewer mispricing han he Fama and French hreefacor model over he same sample period. Third, we also show ha he idiosyncraic volailiy mimicking facor is priced during economy expansions and conracions. However, our wofacor model produces more mispricing during conracions han expansions. The main goal of his paper is o explore he pricing role of he idiosyncraic volailiy, so furher work is needed o explain he asymmeric behaviour of idiosyncraic volailiy during good and bad economic cycles. The findings of his sudy provide a number of imporan implicaions for invesors. Firs, invesors should consider he level of idiosyncraic volailiy remaining in heir porfolio if hey are no welldiversified when esimaing he required rae of reurn and/or evaluaing he performance of hese porfolios. Second, invesors should rebalance heir porfolios during differen economic phases, specifically expansions and conracions. This is due o he asymmeric behaviour of he idiosyncraic volailiy. Holding a consan number of socks in differen phases of business cycle may resul in underdiversificaion of he porfolio as idiosyncraic volailiy increases significanly during bad imes. 24
25 References Ang, A., R. J. Hodrick, e al. (2006). The cross secion of volailiy and expeced reurns. The Journal of Finance, 61(1): Ang, A., R. J. Hodrick, e al. (2009). High idiosyncraic volailiy and low reurns: Inernaional and furher US evidence. Journal of Financial Economics, 91(1): Bali, T. G., N. Cakici, e al. (2005). Does idiosyncraic risk really maer? The Journal of Finance, 60(2): Basu, S. (1977). Invesmen performance of common socks in relaion o heir priceearnings raios: A es of he efficien marke hypohesis. The Journal of Finance, 32(3): Bollena, B., A. Skonickia, e al. (2009). Idiosyncraic volailiy and securiy reurns: Ausralian evidence. Applied Financial Economics, 19(19): Brockman, P., Schue, M. G., & Yu, W (July 11, 2009). Is idiosyncraic risk priced? The inernaional evidence. Working paper. SSRN: hp://ssrn.com/absrac= Campbell, J. Y., M. Leau, e al. (2001). Have individual socks become more volaile? An empirical exploraion of idiosyncraic risk. The Journal of Finance, 56(1): Chan, L. K. C., Y. Hamao, e al. (1991). Fundamenals and sock reurns in Japan. Journal of finance: Drew, M. E., T. Naughon, e al. (2004). Is idiosyncraic volailiy priced? Evidence from he Shanghai Sock Exchange. Inernaional Review of Financial Analysis, 13(3): Faff, R. (2004). A simple es of he Fama and French model using daily daa: Ausralian evidence. Applied Financial Economics, 14(2): Fama, E. F. and K. R. French (1992). The crosssecion of expeced sock reurns. The Journal of Finance, 47(2): Fama, E. F. and K. R. French (1993). Common risk facors in he reurns on socks and bonds. Journal of financial economics, 33(1): Fama, E. F. and K. R. French (1996). Mulifacor explanaions of asse pricing anomalies. The Journal of Finance, 51(1): Fama, E. F. and K. R. French (1998). Value versus growh: The inernaional evidence. The Journal of Finance, 53(6): Fu, F. (2005). Idiosyncraic risk and he crosssecion of expeced sock reurns, Working paper, Universiy of Rocheser. Fu, F. (2009). Idiosyncraic risk and he crosssecion of expeced sock reurns. Journal of Financial Economics, 91(1):
26 Gaun, C. (2004). Size and book o marke effecs and he Fama French hree facor asse pricing model: evidence from he Ausralian sock marke. Accouning & Finance, 44(1): Goezmann, W. N. and A. Kumar (2004). Why do individual invesors hold underdiversified porfolios. Yale Universiy and Universiy of Nore Dame Working Paper. Goyal, A. and P. SanaClara (2003). Idiosyncraic risk maers! Journal of finance, 58: Leau, M. and S. Ludvigson (2001). Resurrecing he (C) CAPM: A crosssecional es when risk premia are imevarying. Journal of Poliical Economy, 109: Linner, J. (1965). The valuaion of risk asses and he selecion of risky invesmens in sock porfolios and capial budges. The Review of Economics and Saisics, 43: Malkiel, B. G. and Y. Xu. (2002). Idiosyncraic risk and securiy reurns. Universiy of Texas a Dallas (November 2002). Malkiel, B. G. and Y. Xu (1997). Risk and reurn revisied. The Journal of Porfolio Managemen, 23(3): Meron, R. C. (1987). A simple model of capial marke equilibrium wih incomplee informaion. Journal of Finance, 42: Ooi, J. T. L., J. Wang, e al. (2009). Idiosyncraic risk and REIT reurns. The Journal of Real Esae Finance and Economics, 38(4): Rosenberg, Barr, K. Reid and R. Lansein, (1985). Persuasive evidence of marke inefficiency. Journal of Porfolio Managemen, 11(3): Sharpe, W. F. (1964). Capial asse prices: A heory of marke equilibrium under condiions of risk. The Journal of Finance, 19(3): Saman, D. (1980). Book values and sock reurns. The Chicago MBA: a journal of seleced papers, 4: Xu, Y., & Malkiel, B. G. (2003). Invesigaing he behaviour of idiosyncraic volailiy. Journal of Business, 76,
27 Table 1: Yearly Summary Saisics This able shows he average number of socks, average monhly reurn, average size (in millions) of he companies, average monhly BE/ME, and average monhly idiosyncraic volailiy over he sample period. Summary Saisics Year Number of Socks Reurn Size BE/ME Idiovol
28 Table 2: Descripive Saisics of he Relevan Variables Descripive Saisics Variables Mean Median Max Min Sd Dev Skewness Kurosis Marke Proxy Reurns Ln(SIZE) BE/ME Idiovol RMRF SMB HML HIMLI Table 3: Summary Saisics of en Idiosyncraic Volailiy Porfolios Porfolio Monhly Excess Reurn Sd Dev Size (millions) BE/ME 1(high) 4.16% 11.67% % 9.57% % 8.71% % 7.79% % 6.62% % 5.81% % 5.02% % 4.43% % 3.98% (low) 1.51% 5.55%
29 Table 4: Socks are sored on December each year from 1992 o 2010 ino 10 decile porfolios based on heir December idiosyncraic volailiy. Socks wih highes idiosyncraic volailiy comprise decile 1 and socks wih lowes idiosyncraic volailiy comprise decile 10. The dependen variable is he equalweighed excess reurn of he socks. RMRF is he excess reurn on he accumulaive ASX All Ordinary Index, SMB is Fama and French risk facor mimicking porfolios for size. HIMLI is a risk facor mimicking porfolio for idiosyncraic volailiy. Alpha is he inercep of he regression model. r rf ( rm rf ) i HIMLI 2Facor Model Porfolio Alpha RMRF HIMLI ADJ Rsq 1(high) *** *** *** *** *** *** *** 0.71 (0.01) *** *** 0.67 (0.91) *** *** 0.66 (0.60) *** *** 0.67 (1.12) *** *** 0.66 (0.07) *** *** *** *** *** (low) *** *** (0.01) 29
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