Department of Econometrics and Business Statistics

Transcription

1 ISSN 44-77X Australa Departent o Econoetrcs and Busness Statstcs Is systeatc downsde beta rsk really prced? Evdence n eergng arket data Don U.A. Galagedera and Robert D. Brooks May 5 Workng Paper /5

2 Is downsde beta rsk really prced? Is systeatc downsde beta rsk really prced? Evdence n eergng arket data Don U.A. Galagedera * and Robert D. Brooks Departent o Econoetrcs and Busness Statstcs Monash Unversty Abstract Several studes advocatng saety rst as a ajor concern to nvestors propose downsde beta rsk as an alternatve to the tradtonal systeatc rsk- beta. Downsde easures are concerned wth a subset o the data and thereore the results n the studes that consder the downsde beta only ay be based. Ths study addresses ths ssue by ncludng downsde co-skewness rsk n addton to the downsde beta rsk n the prcng odel. In a saple o 7 eergng arkets two-stage rollng regresson analyss al to support prcng odels wth downsde rsk easures. In a crosssectonal analyss ncluson o downsde co-skewness proves odel t. When consdered together, downsde beta s potental and downsde co-skewness s a rsk to the ratonal nvestor. Even though our results are nconclusve the evdence strongly suggests a need or urther nvestgaton o co-skewness rsk n prcng odels that adopt a downsde rsk raework. JEL Codes: G, G5 Keywords: Beta, Downsde rsk, Eergng arkets * Correspondng author: Don Galagedera, Departent o Econoetrcs and Busness Statstcs, Monash Unversty, PO Box 97, Cauleld East, Vc 345, Australa. E-al: Tssa.Galagedera@buseco.onash.edu.au

3 Is downsde beta rsk really prced?. Introducton The captal asset prcng odel (CAPM) due to Sharpe (964) conveys the noton that securtes are prced so that ther expected return wll copensate nvestors or ther expected rsk. Though the CAPM beta s stll one o the ost coonly used easures o securty prce oveent researchers have strongly questoned the eprcal valdty o the assuptons underlyng ts dervaton. In the ean-varance raework whch the CAPM s bult on, varance dentes extree gans as well as extree losses as undesrable. Advocatng saety rst as the ajor concern o ratonal nvestors soe argue that only downsde rsk ay be relevant to an nvestor. A nuber o studes nvestgated downsde rsk as a easure o securty rsk. Frst the concept o se-varance that akes reerence to a benchark return eerged and later several downsde rsk easures based on the se-varance raework eerged. When coputng downsde rsk only a subset o the return dstrbuton s used and nzaton o the se-varance concentrates only on the reducton o losses. Further, the se-varance s applcable only when portolo return dstrbuton s non-syetrcal. When the portolo return s norally dstrbuted sevarance below the expected return s hal the portolo s varance and hence varance ay stll be used to quanty rsk. Nantell and Prce (979) show analytcally that under the assupton o bvarate noral dstrbuton o returns or an asset and the arket, equlbru rates o return are equal whether we use a varance or se-varance noton o portolo rsk. Downsde beta s both ntutvely and theoretcally appealng, and eprcally can provde a better rsk easure than the regular beta (Post and van Vlet, 4). Hogan and Warren (974) n a theoretcal raework and Jahankhan (976) n an eprcal study copared ean-varance and ean-sevarance prcng odels and observed no derence n the two odels n ters o lnear assocaton between expected return and beta. Estrada () reveals that downsde rsk easures excel over the standard rsk easures n explanng varablty n the cross-secton o returns n eergng arkets. Pederson and Hwang (3) n an nvestgaton o UK equty data

4 Is downsde beta rsk really prced? show that even though the downsde beta explans a proporton o equtes n addton to CAPM beta the proporton o equtes benetng ro usng the downsde beta s not large enough to prove asset prcng odels sgncantly. Ang, Chen, and Xng () nd a slar result n the US arket. Ang, Chen and Xng () easured downsde rsk by correlatons condtonal on downsde oves o the arket. They observed that the portolo o stocks wth the greatest downsde correlatons outperors the portolo o stocks wth the lowest downsde correlatons and that ths eect cannot be explaned by the Faa and French (993) odel. Downsde rsk s approprate when the securty returns dstrbuton s skewed. Ths rases another queston. When the skewness o an asset return dstrbuton s negatve the downsde returns wll have a larger agntude o returns than the upsde returns. In other words, losses when they occur wll tend to be large. Thereore ratonal nvestors dslke securtes wth negatve co-skewness wth the arket portolo returns so that securtes wth low co-skewness tend to have hgh average returns. When the skewness o the securty returns dstrbuton s postve, the upsde returns wll have a larger agntude o returns than the downsde returns. Thereore when losses (gans) occur they wll be saller (greater). Hence nvestors preer postvely skewed arkets and wll be wllng to pay a preu or postve co-skewness. Thereore the questons that arse s whether co-skewness need be consdered as a easure o rsk n a ean sevarance raework and how t should be easured and nterpreted. Downsde beta s explctly condtonal on arket downsde oveents. On the other hand the tradtonal co-skewness easure does not explctly accentuate asyetres across up and down arkets. Ths akes nterpretaton o co-skewness easures dened n a downsde raework dcult. Ths study addresses ths ssue usng eergng arket data. We consder three downsde beta rsk easures: Estrada beta (E-beta), Hogan and Warren beta (HW-beta) and Bawa and Lndenberg beta (BL-beta). We dene the co-skewness counterparts o these downsde beta rsk easures and nvestgate whether downsde beta and downsde co-skewness are useul n explanng the cross-secton o expected returns. Our results reveal that when the CAPM beta 3

5 Is downsde beta rsk really prced? or any o the three downsde betas only s ncluded n the prcng odel the rsk preu assocated wth t s postve and only the E-beta s statstcally sgncant. However, E-beta and CAPM beta together al to explan the cross-secton o expected returns. When downsde coskewness s ncluded n addton to the correspondng downsde beta rsk the rsk preu assocated wth the beta (co-skewness) rsk s negatve (postve). Ths s observed only wth the Hogan-Warren and Bawa-Lndenberg easures. When the CAPM beta s ncluded n the prcng odel the evdence s even stronger. Hogan-Warren easures outperor the Bawa-Lndenberg easures n explanng cross-secton o expected returns. The paper s organzed as ollows. The downsde rsk easures are dened n the next secton ollowed by hypotheses o nterest. Thereater the ethodology and the data are descrbed n that order. The results and ther dscusson ollow next. The paper s concluded wth soe rearks.. Downsde rsk easures Estrada () dened an asset s covarance wth arket portolo n a downsde raework as = E[ n{ ( R µ ),} n{ ( R ), }] S µ leadng to a easure o systeatc downsde rsk, the E-beta, gven by β [ n{ ( R µ ),} n{ ( R µ ),}] E [ n( R µ ),] E =. () { } Followng the ratonale o ncludng only the returns below the respectve eans n the easureent o rsk, the downsde co-skewness (E-gaa) rsk ay be dened as γ [ n{ ( R µ ),}[ n{ ( R µ ),}] ] E [ n{ ( R µ ),}] 3 E =. () { } Hogan and Warren (974) n the developent o ther expected value-se-varance odel ( HW ) dened the co-se-varance as S E{ ( R R ) n( R R,)} =. The downsde beta 4

6 Is downsde beta rsk really prced? (HW-beta) and the downsde gaa (HW-gaa) correspondng to the Hogan and Warren (974) denton o co-se-varance can be gven as ( HW ) {( R R ) n( R R,)} E [ n( R R,) E β = (3) { ] } and ( HW ) {( R R )[ n( R R,)] } E [ n( R R,) 3 E γ =. (4) { ]} Bawa and Lndenberg (977) suggested the use o the ean return nstead o the rsk-ree rate n (3). In ths case the expresson or the downsde beta (BL-beta) becoes β ( BL) Cov = Var ( r, r r < µ ) ( r r < µ ) (5) where r ( r ) s securty s (the arket s) excess return and µ s the average excess arket return. The correspondng downsde gaa rsk (BL-gaa) ay be expressed as γ ( BL) {( R µ )[ n( R µ,) ] } E [ n( R µ,) 3 E =. (6) { ] } 3. Hypotheses o nterest It s clear n () that a securty contrbutes to the downsde beta rsk, β only when R < µ and R µ < or whch a preu s sought by a ratonal nvestor. Further, when R µ < and R < µ, a securty also contrbutes to the downsde gaa. Further, downsde rsk γ easures are approprate when returns dstrbuton s skewed and thereore only downsde beta s consdered n asset prcng odels we could get based results. In the conventonal sense coskewness s preerred by a ratonal nvestor n a negatvely skewed arket and hence they would 5

7 Is downsde beta rsk really prced? be wllng to orego expected return. Hence n a downsde raework the beta and gaa are lkely to have derng nluence on the expected return. Estrada () reported eprcal results to support the downsde CAPM gven as E ( R ) R + MRP β = b b, where MRP s the downsde arket beta-rsk preu. Now to ncorporate downsde gaa rsk n an asset prcng raework we extend the downsde CAPM odel as E ( R ) = R + MRP β + MRP γ b g (7) where MRP g s the arket rsk preu assocated wth the downsde gaa-rsk. In ths case we expect MRP b and MRP g to have opposte sgns. In the Hogan-Warren denton a securty adds to the beta rsk, β and gaa rsk, γ only when R < R. In ths case gans n the arket are not ncluded n the easureent o rsk and thereore account or only the returns on a allng arket. Accordng to (3), n a allng arket a securty adds to the downsde beta rsk when R < R and reduces the downsde beta rsk when R > R. Thereore the nterpretaton o beta rsk s not clear and hence the contrbuton o the assocated arket rsk preu on the expected asset return s not clear ether. The downsde gaa rsk poses a slar proble. That s when R < ( > ) R R a securty R enhances (reduces) γ rsk n a allng arket. The sae arguent holds n the case wth the Bawa-Lndenberg rsk easures the derence beng the rsk-ree rate s now replaced by the approprate ean. Even though t s not clear what sgns should be expected n the HW-beta (BLbeta) and HW-gaa (BL-gaa) rsk preus the act that both beta and gaa rsk The ult-oent odels are not sucently lexble to odel downsde rsk and t s generally dcult to restrct these odels to obey the standard regularty condtons o nonsataton (noarbtrage) and rsk averson (Post and van Vlet, 4). 6

8 Is downsde beta rsk really prced? ncreases or decreases dependng on whether the securty return exceeds the ean (rsk-ree rate) or not suggests that ther rsk preus are lkely to have opposte sgns. 4. Methodology 4. Cross-sectonal analyss Frst, or each arket we estate the systeatc rsks and average return usng the ull set o saple data. The average return s then regressed on the estated systeatc rsk/s to nvestgate whether or not the correspondng rsk-return lnear relatonshps are sgncant. 4. Two-stage rollng regresson analyss We nvestgate the rsk-return relatonshps allowng or systeatc rsks to vary over te. The analyss here s based on a two-stage procedure. In the rst stage we estate systeatc rsks usng the ethod o ordnary least squares and wth te seres data. We start the procedure by estatng or each arket the systeatc rsks usng the data correspondng to the rst 6-onth perod. In the second stage adoptng the ethod o cross-sectonal regresson we test whether the systeatc rsks are prced or not. In each o the onths that ollows the 6-onth perod used n the rst stage, the onthly arket returns are regressed on the systeatc rsks estated n the precedng 6-onth perod. Here, t s assued that the systeatc rsks estated n the rst stage proxy systeatc rsks o the second stage. 3 The two-stage procedure s then repeated usng a rollng wndow technque, rollng orward onths at a te. The saple data or all arkets do not have the sae start date. Thereore, we repeat the analyss wth a shorter te perod so that or each arket the average return and the systeatc rsk/s s estated wth data n the sae perod. 3 Co-varances are easured wth error and easureent error reduces the statstcal power o any regresson. One way o crcuventng the easureent proble s to ocus on a settng where the true varaton n the data s large relatve to any nose (Char and Henry, 4). Incluson o downsde gaa rsk n the prcng odel s expected, at least partally, to allevate ths concern. 7

9 Is downsde beta rsk really prced? There are three derent start dates n the saple data. Thereore to accoodate all the 7 arkets n the two-stage rollng regresson analyss we use a truncated data set. Ths allows ve repettons o the two-stage procedure enablng estaton o systeatc rsk preus n 6 consecutve onths. 5. Data The data used here s ro the MSCI database on eergng arket onthly ndces. We consder 7 arkets- Asan, 7 Latn Aercan and Arcan, Mddle-Eastern and European. The saple perod vares where or arkets the start date s January 987, or arkets t s January 99 and or the rest the start date s January 994. For all arkets the data s collected up to Deceber 4. The returns are coputed as the derence n two consecutve onthly log prces. 4 The proxy used or the arket ndex s the world ndex avalable n the MSCI database and the proxy or the rsk-ree rate s the -year US Treasury bond rate. 5 The coplete lst o the arkets, the data start dates and soe suary statstcs s gven n Table. Entres n Table reveal that or arkets, the nu return ranges ro.8 percent to 5. percent whle the axu vares between 78. percent and 5.6 percent. 4 A study (Estrada, ) usng a data set coparable to ours exaned asset prcng odels wth downsde beta wth return coputed as the arthetc return. Thereore to copare our results to the results n that study we repeat the analyss wth arthetc returns. 5 I a arket s not lberalzed the relevant source o systeatc rsk or prcng stocks s the local stock arket ndex. When a country s stock arket s lberalzed the source o systeatc rsk o an asset becoes the world arket portolo. The saple data or all countres s n the post lberalzaton era and hence the reason or usng world ndex. We exane the robustness o our results wth equal-weghted average return o all the 7 arkets as a proxy or the world arket portolo return and the US 3-onth Treasury bll rate as the rsk-ree rate. 8

10 Is downsde beta rsk really prced? Excess kurtoss can be as hgh as 9.3 wth the nu beng.4. Excess kurtoss s postve n eleven arkets. The skewness ranges ro.4 to.9 wth eght arkets wth postve skew. The world arket return dstrbuton s negatvely skewed and has.7 excess kurtoss and.5 percent ean return. 6. Results and dscusson 6. Cross-sectonal odels Frst, we estate the ollowng cross-sectonal regresson odels. Model A: (ncludes the CAPM beta) Model B (ncludes E-beta) Model C (ncludes E-beta and E-gaa) Model D (ncludes HW-beta) Model E (ncludes HW-beta and HW-gaa) and Model F (ncludes E-beta and HW-beta) E E E E ( R ) R + MRPb β =, (8) E ( R ) R + MRP β =, (9) E E ( R ) R + MRP β + MRP γ E b b =, () HW ( R ) R + MRP β b g = () HW ( HW ) HW ( HW ) ( R ) = R + MRP β + MRP γ b g. () E E HW ( HW ) ( R ) = R + MRP β + MRP β b b (3) 9

11 Is downsde beta rsk really prced? The results reported n Table gve the paraeters estated n the above odels where or each arket the ean return and the rsk easures are estated usng the ull set o sapled data. 6 The data does not support the tradtonal CAPM odel. The estates shown n panel reveals weak support (sgncant at the percent level) or the Estrada downsde CAPM odel wth a postve preu however when the downsde gaa rsk s ncluded n the odel (Model C) both E-beta and E-gaa are not sgncantly derent ro zero. The results n Model D reveal that the preus assocated wth the HW-beta and BL-beta rsk easures are not sgncant. However, when the gaa rsk s ncluded (Model E) the preus correspondng to downsde beta and downsde gaa are sgncant at the ve percent level when Hogan-Warren easures are used and at the ve and ten percent levels respectvely when Bawa-Lndenberg easures are used. Further, the two preus have opposte sgns wth a negatve preu or downsde beta rsk. We also estate a odel (Model F) where both the E-beta and the HW-beta s ncluded n the prcng odel. In ths case both rsks tend to be prced wth a postve preu or E-beta rsk and a negatve preu or HW-beta rsk. When the rsk-ree rate n the HW-beta easure s replaced wth the approprate ean only the Estrada beta rsk preu s prced wth a postve sgn and at the ten percent level. In general, as ar as the sgn o the rsk preu s concerned, whenever the CAPM beta or any o the three downsde betas s ncluded n the prcng odel separately the rsk preu assocated wth t s always postve. 7 On the other hand, when the gaa s ncluded n addton to the correspondng beta rsk the rsk preu assocated wth the beta (gaa) rsk s negatve (postve). 8 The R-square/adjusted R-square values ndcate that the t n these odels s very 6 ( HW ) ( HW ) The correlaton between the estated β, β, γ, β andγ s very hgh. Ths s addressed under urther testng when robustness o the results s dscussed. The varaton n arket returns s rather sall and thereore heteroscedastcty s not a concern here. 7 In soe nstances the rsk preu s not sgncantly derent ro zero. 8 In soe nstances the rsk preu s not sgncantly derent ro zero.

12 Is downsde beta rsk really prced? poor. The best t s revealed n Model F wth an adjusted R-square value o less than nneteen percent. Now we dscuss the results when the CAPM beta s ncluded n odels A F. These results are gven n Table 3. The results n the rst panel o Table 3 reveals that when the prcng odel (Model AA) ncludes the CAPM beta rsk together wth E-beta none o the s prced and the odel has a very poor t. A slar result s obtaned n Model BB where the CAPM beta, E-beta and E-gaa are present. When the HW-beta together wth the CAPM beta s n the odel (Model CC) both rsks are prced wth nvestors deandng a preu or the beta rsk and wllng to orego expected return or the downsde beta rsk. 9 When the CAPM beta and the BLbeta are consdered none o the correspondng rsk prea are sgncant. On the other hand, when Model CC s enhanced wth the gaa rsk (Model DD) all three rsks are prced wth nvestors requrng a preu or the CAPM beta rsk as well as the gaa rsk and wllng to pay a preu or the downsde beta rsk. Ths s observed whether or not the excess return n the downsde raework s based on the rsk-ree rate or the ean return. Ths together wth the result n Model E gven n Table suggests that when downsde beta and downsde gaa are present together n the prcng odel nvestors dsplay a preerence or downsde co-skewness and dslke downsde beta rsk. The presence o the CAPM beta n the prcng odel akes these observatons even stronger (adjusted R-square ncreases ro 7 percent to 4 percent). Earler we observed n Model F, Table that when the E-beta and HW-beta are n the odel ther assocated rsk preus are prced wth nvestors dsplayng a preerence or the Hogan- Warren downsde rsk and dslke or E-beta rsk. Model EE where Model F s extended to 9 Pederson and Hwang (3) usng UK equty data show that even though the downsde beta explans a proporton o equtes n addton to CAPM beta the proporton o equtes benetng ro usng the downsde beta s not large enough to prove asset prcng odels sgncantly. Ther results show that downsde betas are o lted use n asset prcng copared to CAPM beta.

13 Is downsde beta rsk really prced? nclude the CAPM beta reveals a slar result wth a better odel t (adjusted R-square ncreases ro 8 percent to 38 percent) wth a postve and sgncant CAPM beta rsk preu. In general, ncluson o the CAPM beta n the prcng odel wth downsde rsk easures proves odel t and the sgns o the rsk preu observed n the prcng odel wthout the CAPM beta are preserved. Downsde rsk easures due to Hogan and Warren sees ore approprate than Bawa-Lndenberg easures when the CAPM beta s n the prcng odel. We also nvestgate the assocaton between the ean return and rsk when the 7 arkets are dvded nto three equally-weghted portolos ranked on CAPM beta, E-beta, HW-beta, E-beta and E-gaa and HW-beta and HW-gaa. I the systeatc coponent o a gven rsk s prced then stocks sorted by the relevant easure o rsk should exhbt cross-sectonal spreads n expected returns. The rst portolo (P) conssts o the arkets wth the lowest nne rsk estates and the thrd portolo (P3) consst o the arkets wth the hghest nne rsk estates. The results reported n Table 4 reveals that the average return n P les between that o P and P3 when the portolos are ored on the CAPM beta and the E-beta o the arket. Ths s an unexpected result especally when portolos are ored on the CAPM beta. On the other hand the average portolo return appears to ncrease wth ncreasng HW and BL portolo beta suggestng that the relatonshp between E-beta and return ay not be onotoncally ncreasng. Ths ay be one o the reasons why the saple data do not support the prcng odels that nclude E-beta and E-gaa. When portolos are ored on downsde beta and downsde gaa a onotoncally ncreasng average return-rsk relatonshp s observed only wth BL easures o rsk when excess return s coputed wth reerence to the ean return. 6. Rollng regresson Note that the two-stage rollng regresson analyss s carred out wth a reduced saple and the odel paraeters are estated n 6 cross-sectonal regressons. The odels estated here are A-E descrbed n Table. The results (not shown) reveal that none o the prcng odels are

14 Is downsde beta rsk really prced? supported. Ths result does not change when the prcng odels are tested n each o the ve rollng wndow perods separately. We repeated the portolo analyss wth the reduced saple as well. Here the average return n P s negatve whle the average return n P and P3 are postve wth P3 havng a hgher average rrespectve o the rsk easure used n orng the portolos. The results are reported n Table Robustness o the results 6.3. Market return We repeated the cross-sectonal and the rollng regresson analyss wth the equally-weghted return o the 7 sapled arkets as the arket return. The results are largely unchanged ro those obtaned wth world ndex return as a proxy or the arket portolo return. When the US -year Treasury bond rate s replaced wth the US 3-onth Treasury bll rate there s no notable change n the results Arthetc returns Estrada () n a study o the sae set o eergng arkets that we sapled ound strong eprcal evdence to support the E-beta aganst the CAPM beta when arthetc arket returns are used. In our data set the suary statstcs wth arthetc returns, whch we do not report or the sake o brevty, clearly ndcates an ncrease n average onthly return (ro.64 percent to.3 percent), average skew (ro -. percent to.53 percent) and average excess kurtoss In arthetc (dscrete) returns a percentage gan ollowed by the sae percentage loss n two consecutve perods does not revert back to the orgnal nvestent whereas n log (contnuously copounded) returns such a ove does. Even though returns are consdered to be generated contnuously through te soetes returns are treated as they are generated at dscrete ntervals due to tradng that occur at dscrete ntervals. See Bralsord, Fa and Olver (997) or a detaled dscusson on ths ssue. 3

15 Is downsde beta rsk really prced? (ro.68 percent to 3.3 percent) ro those calculated wth the log returns. In vew o ths varaton we nvestgate the senstvty o our results when the arket return s coputed as an arthetc return. The results n the cross sectonal regresson analyss reported n Table 6 reveals that when CAPM beta, E-beta, HW-beta and BL-beta are consdered separately n a prcng equaton the nvestors requre a preu that s sgncantly derent ro zero to accept the correspondng rsk. In log returns statstcal evdence s ound only wth E-beta. When E-gaa s ncluded wth E-beta n the sae odel none o the assocated rsks are prced. Ths was uncovered n the log returns as well. On the other hand, when HW-gaa s ncluded n the prcng odel together wth HW-beta the rsk preu assocated wth both rsks are prced where a preerence or the HW-beta (BL-beta) rsk and an averson or the HW-gaa (BL-gaa) rsk s noted. A slar observaton s ade n log returns. When E-beta and HW-beta both are n the prcng odel the odel t proves and they are both prced such that E-beta has a postve rsk preu and HW-beta (BL-beta) has a negatve rsk preu. When we construct portolos and exane the average portolo return aganst portolo rsk we nd that the CAPM beta and return and HW-beta and return have a postve relatonshp. The results n Table 7 also reveal a postve relatonshp between portolo rsk and return when portolos are ored by rankng the arkets on HW-beta and HW-gaa. Wth Estrada easures P (.947 percent) has a slghtly lower return than P (.95 percent) and P3 has a uch hgher return (.56 percent) than P. The coposton o portolos does not change when E-gaa s also used n the rankng. Consequently the returns n portolos ored on ranked ES-beta and ranked E-beta and E-gaa are the sae. A slar observaton s ade n Tables 4 and 6 when log return n the ull saple and a truncated saple s used. Ths ay be the reason why we aled to nd evdence n support o E-gaa n any o the odels consdered. Besdes the presence o E-gaa n the prcng odel akes the rsk preu assocated wth E-beta nsgncant. In arthetc returns the spread between P and P3 s larger than n log returns. 4

16 Is downsde beta rsk really prced? Further testng We observe hgh correlaton between CAPM beta, downsde beta and downsde gaa where the Pearson correlaton coecent exceeds.9. Hence we conduct urther tests to deterne whether or not downsde beta and downsde gaa s prced when the CAPM beta s n the prcng odel. Frst downsde beta s regressed on a constant and CAPM beta. The resduals ro ths regresson whch are orthogonal to CAPM beta are eectvely the orthogonalsed coponent o downsde beta. Thereater expected returns are regressed on CAPM beta and orthogonalsed downsde beta. The results o the analyss are shown n Table 8. The results n Table 8 ndcate that the orthogonalsed coponent o E-beta and BL-beta s not sgncant. Ths suggests that E-beta and BL-beta ay not be useul n explanng crosssecton o asset returns when the CAPM beta s n the prcng odel. On the other hand, the orthogonalsed coponent o HW-beta s sgncant at the percent level. Hence our results provde soe backng or ncluson o HW-beta n the prcng odel n addton to the CAPM beta. A slar observaton was ade n odel CC whose results are shown n Table 3. Further, odel DD whose results are shown n Table 3 reveals that HW-gaa together wth CAPM beta and HW-beta explans n excess o 4 percent o varaton n the cross secton o expected returns. We test ths result adoptng a two step procedure slar to the one used earler when testng the approprateness o downsde beta n explanng asset prces. Here HW-gaa s regressed on a constant, CAPM beta and HW-beta rst. In the second step the cross secton o expected returns s regressed on a constant, CAPM beta, HW-beta and the resduals obtaned n the rst step. The a s to see whether there reans any unexplaned varaton n expected returns whch HW-gaa ay account or n addton to those explaned by CAPM beta and HW-beta. The results shown n Table 8 provde evdence n support o the earler observaton that the varaton n cross-secton o expected return ay be explaned better by CAPM beta together wth HW-beta and HW-gaa. 5

17 Is downsde beta rsk really prced? 7. Concludng rearks In general, when the CAPM beta or any o the three downsde betas s ncluded n the prcng odel the rsk preu assocated wth t s always postve. On the other hand, when the downsde co-skewness s ncluded n addton to the correspondng downsde beta rsk the rsk preu assocated wth downsde beta (downsde co-skewness) rsk s negatve (postve). When the CAPM beta s ncluded n such a prcng odel the evdence s even stronger. In ths case downsde rsk easures due to Hogan and Warren are ore approprate than Bawa and Lndenberg easures. Our results however are nconclusve. Eergng arket rsk preu ay not be deterned solely by rsk actors coon to all countres. A cobnaton o global and local rsk actors ay nluence soe arkets. Our observatons suggest that nvestgaton o downsde co-skewness s crucal n understandng asset prcng n a downsde raework. 6

18 Is downsde beta rsk really prced? Reerences Ang, A., J. Chen, and Y. Xng,, Downsde correlaton and expected stock returns, Bawa, V, and E. Lndenberg, 977, Captal arket equlbru n a ean lower partal oent raework, Journal o Fnancal Econocs, 5, 89-. Bralsord, T.J., Fa, R.W. and B.R. Olver, 997, Research desgn ssues n the estaton o beta, McGraw-Hll, Australa. Char, A. and P.B. Henry, 4, Rsk sharng and asset prces: evdence ro a natural experent, The Journal o Fnance, Vol LIX, No 3, Estrada, J.,, Systeatc rsk n eergng arkets: the D-CAPM, Eergng Markets Revew, Faa, E. F., and K. R. French, 993, Coon rsk actors n the returns on stocks and bonds, Journal o Fnancal Econocs, 33, Hogan, W. and J. Warren, 974, Toward the developent o an equlbru captal-arket Model based on sevarance, Journal o Fnancal and Quanttatve Analyss, 9,, -. Jahankhan, A., 976, E-V and E-S captal asset prcng odels: soe eprcal tests, The Journal o Fnancal and Quanttatve Analyss,, 4,

19 Is downsde beta rsk really prced? Nentell T.J. and B. Prce, 979, An analytcal coparson o varance and sevarance captal arket theores, The Journal o Fnancal and Quanttatve Analyss, 4,, -4. Pedersen, C.S. and S. Hwang, 3, Does downsde beta atter n asset prcng? Workng Paper, Cass Busness School, London, UK. Post, T. and P. van Vlet, 4, Downsde rsk and asset prcng, http;//ssrn.co/abstract=534. Sharpe, W.F., 964, Captal asset prces: a theory o arket equlbru under condtons o rsk, Journal o Fnance, 9,

20 Is downsde beta rsk really prced? Table. Suary statstcs o eergng arket onthly log return Country Mn Max Mean SD Skew Kurtoss Saple start date Argentna Dec, 87 Brazl Dec, 87 Chle Dec, 87 Chna Dec, 9 Coloba Dec, 9 Czech Republc Dec, 94 Egypt Dec, 94 Hungary Dec, 94 Inda Dec, 9 Indonesa Dec, 87 Israel Dec, 9 Jordan Dec, 87 Korea Dec, 87 Malaysa Dec, 87 Mexco Dec, 87 Morocco Dec, 94 Pakstan Dec, 9 Peru Dec, 9 Phlppnes Dec, 87 Poland Dec, 9 Russa Dec, 94 South Arca Dec, 9 Sr Lanka Dec, 9 Tawan Dec, 87 Thaland Dec, 87 Turkey Dec, 87 Venezuela Dec, 9 Notes: The returns are expressed as a percentage per onth. 9

21 Is downsde beta rsk really prced? Table. Cross-sectonal analyss o prcng odels usng log return Model Model A: Rt = + β + ε t R-square =.948 Mean Standard error t-value Model B: R = + β + ε R-square =.5 t t Mean Standard error t-value *** - Model C: R = + β + γ + ε Adjusted R-square =.98 t t Mean Standard error t-value ( HW ) Model D: R = + β + ε R-square =.394 (.647) t t Mean.43 (.3594).8 (.877) - Standard error.47 (.388).5 (.88) - t-value.748 *** (.55).3 (.345) - ( HW ) ( HW ) Model E: R = + β + γ + ε Adjusted R-square =.797 (.388) t t Mean.433 (.384) -.68 (-.83).336 (.7776) Standard error.9 (.49).9656 (.393).89 (.8636) t-value.973 ** (.6956 *** ) ** (-.748 *** ).539 ** (.584 ** ) ( HW ) Model F: R = + β + β + ε Adjusted R-square =.874 (.58) t t Mean -.86 (-.45).363 (.493) -.8 (-.8336) Standard error.94 (.339).553 (.639).559 (.6343) t-value (-.44).595 ** (.87 *** ) ** (-.343) Notes: The statstcs are based on 7 estates. The ean and standard error s expressed as a percentage. *** denotes sgncance at the percent level and ** denotes sgncance at the 5 percent level. The gures n parentheses are the estates when the rsk-ree rate n the Hogan and Warren downsde beta and downsde gaa (equatons (4) and (5)) s replaced wth the correspondng ean.

22 Is downsde beta rsk really prced? Table 3. Cross-sectonal analyss o prcng odels wth CAPM beta and usng log return Model 3 Model AA: R = + β + β + ε Adj R-sq =.54 Mean Standard error t-value Model BB: R = + β + β + γ + ε Adj R-sq =.79 3 Mean Standard error t-value Model CC: R = + β ( HW ) + β + ε Adj R-sq =.374 (.594) Mean.59 (.3989).6445 (.349) -.84 (-.997) - Standard error.3 (.366).894 (.9579).878 (.99) - t-value.36 ** (.6859 *** ).958 * (.36) * (-.4) - Model DD: R = + β ( HW ) ( HW ) + β + γ + ε Adj R-sq =.433 (.99) 3 Mean.5 (.479).595 (.4865) ( ).9854 (.935) Standard error.853 (.87).7776 (.8876).84 (.3583).677 (.836) t-value.764 * (.9565 *** ) * (.6748 *** ) * (-.463 ** ).9557 * (.763 ** ) Model EE: R = + β ( HW ) + β + β + ε Adj R-sq =.38 (.569) Mean.59 (-.3).3654 (.3357).8 (.647) (-.948) Standard error.59 (.375).835 (.97).463 (.5996).8587 (.57) t-value.78 (-.334).979 * (.476).553 ** (.945 *** ) * (-.989 ** ) Notes: The ean and standard error s expressed as a percentage. *** denotes sgncance at the percent level and ** denotes sgncance at the 5 percent level. The gures n parentheses are the estates when the rsk-ree rate n the Hogan and Warren downsde beta and downsde gaa (equatons (4) and (5)) s replaced wth the correspondng ean.

23 Is downsde beta rsk really prced? Table 4. Portolo (log) return and rsk Markets sorted by β Portolo β Return Markets sorted by β β Return P P P Spread (P3-P) Markets sorted by β β Return (.458) (.5857) (.9967) (.647) (.4835) (.6889) (.36) (.33) Portolo Markets sorted by β and by γ Markets sorted by β and by γ β γ Return β γ Return P (.458) (.59) (.57) P (.9967) (.675) (.68) P (.4835) (.75) (.75) Spread (P3-P) (.36) (.96) (.798) Notes: P consst o the arkets that has the lowest nne estates and P3 consst o the arkets that has the hghest nne estates. All entres are arthetc averages. The rsk easures are based on log returns, arket portolo return s the world ndex return and the rsk-ree rate s the US -year bond rate. The gures n parentheses are the estates when the rsk-ree rate n the Hogan and Warren downsde beta and downsde gaa (equatons (4) and (5)) s replaced wth the correspondng ean.

24 Is downsde beta rsk really prced? Table 5. Portolo (log) return and rsk n saple perod Jan 995 Dec 4 Markets sorted by β Markets sorted by β Markets sorted by Portolo β Return β Return β β Return P P P Spread (P3-P) Portolo Markets sorted by β and by γ Markets sorted by β and by γ β γ Return β γ Return P P P Spread (P3-P) Notes: P s ade up o arkets that have the lowest nne rsk estates and P3 s the one wth the hghest nne estates. The rsk easures are based on log returns, arket portolo return s the world ndex return and the rsk-ree rate s the US -year bond rate. 3

25 Is downsde beta rsk really prced? Table 6. Cross-sectonal analyss o prcng odels usng arthetc return Model Model A: Rt = + β + ε t R-square =.393 Mean Standard error t-value.758 *** * - Model B: R = + β + ε R-square =.5435 t t Mean Standard error t-value * - Model C: R = + β + γ + ε Adjusted R-square =.555 t t Mean Standard error t-value Model D: R ( HW ) = + β + ε R-square =.768 (.8) t t Mean.658 (.4783).8 (.949) - Standard error.37 (.99).346 (.33) - t-value.75 ** (.599).368 ** (3.93 * ) - Model E: R ( HW ) ( HW ) = + β + γ + ε Adjusted R-square =.478 (.464) t t Mean.4468 (.374) (-.5775) 3.48 (3.43) Standard error.68 (.69).53 (.3).9743 (.456) t-value.6667 *** (.399) * ( ** ) * (.7435 * ) Model F: R ( HW ) = + β + β + ε Adjusted R-square =.66 (.658) t t Mean -.43 (-.635).78 (.65) (-.649) Standard error.654 (.85).3569 (.4848).475 (.568) t-value (-.5 ** ) 6.48 * (5.468 * ) * (-3.9 * ) Notes: The statstcs are based on 7 estates. The ean and standard error s expressed as a percentage. *** denotes sgncance at the percent level, ** denotes sgncance at the 5 percent level and * denotes sgncance at the percent level. The gures n parentheses are the estates when the rsk-ree rate n the Hogan and Warren downsde beta and downsde co-skew (equatons (4) and (5)) are replaced wth the approprate eans. 4

26 Is downsde beta rsk really prced? Table 7. Portolo (arthetc) return and rsk Markets sorted by β Markets sorted by Portolo β Return P P β β Return Markets sorted by β β Return (.3948) (.95) (.9436) (.36).6.54 (.333) (.799) (.9384) (.848) P Spread (P3-P) Portolo D Markets sorted by β and by γ Markets sorted by β and by γ D β γ Return β γ Return P (.3948) (.474) (.38) P (.9436) (.7) (.978) P (.333) (.4959) (.768) Spread (P3-P) (.9384) (.6) (.747) Notes: P s ade up o arkets that have the lowest nne estates and P3 s the one wth the hghest nne estates. All entres are averages based on nne values. The rsk easures are based on arthetc returns, arket portolo return s the world ndex return and the rsk-ree rate s the US -year bond rate. The gures n parentheses are the estates when the rsk-ree rate n the Hogan and Warren downsde beta and downsde gaa (equatons (4) and (5)) s replaced wth the correspondng ean. 5

27 Is downsde beta rsk really prced? Table 8. Cross-sectonal analyss wth orthogonalsed coponents Model 3 Rt = + β + Oβ + εt Adjusted R-square =.54 Mean Standard error t-value ( HW ) Rt = + β + Oβ + εt Adjusted R-square =.374 (.594) Mean (.36).363 (.363) (-.997) - Standard error.3 (.36).9 (.43).878 (.99) - t-value.595 (.4339).7976 *** (.69) * (-.) - ( HW ) ( HW ) Rt = + β + β + 3Oγ + εt Adjusted R-square =.433 (.99) Mean.59 (.3989).6445 (.349) -.84 (-.997).9854 (.935) Standard error.85 (.83).7774 (.884).7573 (.8483).677 (.836) t-value.749 * (.868 *** ) 3.46 * (.476) -3.6 * (-.96).9557 * (.76 ** ) Notes: Oβ, Oβ and O γ are the orthogonalsed coponent o the E-beta, the HWbeta and HW-gaa respectvely. The ean and standard error s expressed as a percentage. *** denotes sgncance at the percent level, ** denotes sgncance at the 5 percent level and * denotes sgncance at the percent level. The gures n parentheses are the estates when the rsk-ree rate n the Hogan and Warren downsde beta (equaton (4)) s replaced wth the correspondng ean. 6