Journal of Fnance and Accounng 2014; 2(1): 1-10 Publshed onlne January 30, 2014 (hp://www.scencepublshnggroup.com/j/jfa) do: 10.11648/j.jfa.20140201.11 A sudy of volaly rsk Kala Lama *, Jlan Faouz Graduae Insue of Busness and Accounng of Bzera, Unversy of Carhage, Unversy of Tuns El Manar, Faculy of economc Scences and Managemen of Tunsa Emal address: lamakala@yahoo.fr (K. Lama), faouz.jlan@fseg.rnu.n (J. Faouz) To ce hs arcle: Kala Lama, Jlan Faouz. A Sudy of Volaly Rsk. Journal of Fnance and Accounng. Vol. 2, No. 1, 2014, pp. 1-10. do: 10.11648/j.jfa.20140201.11 Absrac: Tme varaons of marke volaly consderably affec nvesmens rsk evaluaon and predcon of fuure reurns. They are presened as a source of sysemc rsk o whch s added a rsk relaed o socks sensvy o volaly shocks. Analyss of he relaonshp beween socks volaly and marke volaly allows for deermnng wheher socks sensves o volaly shocks may esmae marke s fuure rsk prce. Volaly shocks are defned n erms of volaly rsk hedgng facors, when marke volaly rsk prce s hgh and for socks ha are posvely correlaed o hese hedgng facors, he value of reurns s expeced o be low. Idosyncrac volaly s on he oher hand a varable omed from volaly oal rsk. If marke volaly rsk s a mssng componen of sysemac rsk, sandard models should ms-prce porfolos sored by dosyncrac volaly because hese models do no nclude facor loadngs measurng exposure o marke volaly rsk. Keywords: Volaly Shocks, Rsk Facors, Hedgng Facors, Sysemc Volaly, Idosyncrac Volaly 1. Inroducon Socks volaly vares n me. A number of sudes examned he relaonshp beween marke volaly and socks reurns. However, he queson on how volaly affecs socks receved less aenon by he leraure [1], [2]. Tme varaons of marke volaly affec consderably nvesmen rsk evaluaon and predcon of fuure reurns. They are presened as a source of sysemc rsk o whch s added a rsk relaed o socks sensvy o volaly shocks. Our sudy consss frs n analysng he relaonshp beween socks volaly and marke volaly n order o deermne wheher exposure o volaly rsk allows for esmang marke volaly s fuure rsk prce. Buldng up nvesmen porfolos wh dfferen sensvy degrees o marke nnovaons should show wheher volaly rsk prce s negave and wheher socks wh posve and hgh sensvy o volaly rsk should yeld low fuure reurns. Several fnancal heores explan why volaly rsk prce should be negave. Campbell and Henschell (1992), ndcae ha nvesors look for coverng hemselves agans rsk n perods of volaly varaons, whch generally concde wh a marke s downward movemen and deeroraon of nvesmen opporunes. They buy socks wh he lowes sensvy o volaly rsk whose evaluaon may be done hrough dfferen rsk facors. The poneerng work [1],[2],[3] ndcae ha socks wh he hghes sensvy o volaly are socks ha cover agans a downward marke rsk. Increasng demand of hese socks for he hghes sysemc volaly ncreases her prces and decreases her average reurns. The evdence n [4] relaes hs rend o coskewness. The auhors show ha when volaly ncreases, socks wh decreasng raes are he socks whose reurns are negavely skewed n conras o socks whose raes ncrease and accumulae posvely skewed reurns. Wh reference o hese sudes, our sudy examnes he relaonshp beween rsk flucuaons and socks dfferen degrees of exposure o volaly shocks. The am of hs paper s o esmae socks sensvy o volaly shocks n erms of he componen dosyncrac volaly expressed hrough resduals of Fama and French model [5]. We proceed as follows: f dosyncrac volaly s a rsk facor orhogonal o oher rsk facors, socks sensvy o dosyncrac volaly should be aken no accoun and he frms ha are he mos sensve o marke volaly should dsplay hgher dosyncrac volaly. Earler researchers fnd a sgnfcanly posve relaon beween dosyncrac volaly and average reurns, For example, [6] shows ha dosyncrac volaly carres a posve coeffcen n cross-seconal regressons.[7] fnd ha porfolos wh hgher dosyncrac volaly have
2 Kala Lama and Jlan Faouz: A Sudy of Volaly Rsk hgher average reurns, bu hey do no repor any sgnfcance levels for her dosyncrac volaly premums. On he oher hand, [8] fnds ha a cross-seconal regresson coeffcen on oal varance for sze-sored porfolos carres an nsgnfcan negave sgn. The goal of hs paper s o deermne wheher he volaly of he marke s a prced rsk facor, o esmae he prce of aggregae volaly rsk and o examne he relaonshp beween dosyncrac volaly and expeced reurns, where dosyncrac volaly s defned relave o he sandard Fama and French (1993) model Our paper s hen srucured as follows: he second secon sudes volaly rsk and evaluaes socks dfferen sensvy degrees o hs rsk usng nnovaon parameers as well as volaly hedgng facors. The hrd secon presens dosyncrac volaly and defnes as a deermnng facor of he global rsk of marke volaly. 2. Volaly Rsk 2.1. Socks Sensvy o Volaly Innovaons In hs paper, we examne he relaonshp beween socks fuure reurns and socks sensvy o volaly nnovaons n he Tuns Sock Marke, over a perod srechng from 1/1/1999 o 15/06/2011. The examned perod feaures a reform plan ha dsplays dfferen epsodes of socks flucuaons (growh, crss, recovery...) and neresng crcumsances o analyse n deph volaly characerscs. Daa used are daly frequences. The seleced sample ncludes 30 lsed frms, seleced from a common and balanced daa base of he se of socks. The used Tunndex s a synhec ndex of he Tuns sock marke. The ndex s value s gven by he socks arhmec mean, comparng he weghed ndex o her marke capalsaon. The rae ha s used o deermne hs ndex s eher he closng rae or he exceeded reserve hreshold. Our sudy suggess ha dosyncrac volaly should be posvely lnked o forward reurns where rsk-averse nvesors ask for a premum o compensae socks deenon rsk of whch volaly rsk s consderable We examne volaly rsk usng average reurns varaons of socks wh dfferen sensvy o volaly nnovaons. Volaly nnovaon parameer s defned by VIX whch represens Tunndex s varaons a daes and 1 (υ υ 1.). Our model akes hen he followng form: r ξ = 0 (1) Wh : marke rsk represened by a reurn surplus : volaly nnovaon ; and : respecvely sensvy of socks o marke rsk and volaly rsk To sudy evoluon of socks volaly rsk, we specfy observable marke and volaly rsk varables. Our esmaon covers regular and enough sreched me nervals. Then, our daly daa s esmaed over a monh. Ths choce s explaned by he fac ha under low-frequency effec of volaly nnovaons s more mporan and allows for esmang unpredcable marke varaons. Our esmaon procedure follows he followng seps. We deermne he values of esmaed a he begnnng of each monh and for each porfolo. The choce of nvesmen porfolos s based on frms whose sensvy o marke volaly s enough hgh. In parcular, we focus on he varaons of consruced by means of he daly daa of socks durng a monh. A he end of each monh, he socks are classfed no porfolos usng he coeffcen of sensvy o volaly rsk. Thus, frms belongng o he 1s porfolo are frms wh he lowes coeffcen whle frma belongng o he 5h porfolo are frms wh he hghes coeffcen. Descrpve sascs of he dfferen nvesmen porfolos are presened n Table (1). The frs wo columns represen respecvely he mean and sandard devaon of porfolos reurns. We noce ha because porfolos are classfed accordng o her sensvy o volaly rsk, he value s ncreasng and monoone. I s -7.26for he frs porfolo and 5.4 for he ffh. We noce ha he mean reurn value of hese porfolos decreases when ncreases, wh a sgnfcan monhly dfference of 0.16 beween porfolos wh he hghes and hose wh he lowes. 2.2. Hedgng Facors of Volaly Rsk Volaly rsk s defned n erms of hedgng facors of volaly rsk FVX esmaed hrough an nvesmen porfolo conssng of socks hghly correlaed wh volaly nnovaons. The regresson s defned by: VIX = c b µ (2) X Where X represens surplus of socks reurns; b X s facor whch represens marke volaly rsk ; coeffcen b represens wegh of a porfolo wh zero cos. Esmaon of b by regresson (2) ams a consung he hedgng facors of monhly volaly rsk. Once s obaned, our esmaon model s represened by he regresson: r = α ξ (3) Wh : marke rsk : hedgng facors of volaly; and : are respecvely socks sensvy o marke rsk and o volaly rsk. Then, he am of our sudy s o show he presence of a lnear relaonshp beween hedgng facors of volaly rsk and socks mean reurns. Thus, when marke volaly rsk s
Journal of Fnance and Accounng 2014; 2(1): 1-10 3 hgh and for he socks ha are posvely correlaed o, he value of r s expeced o be low. Column 2 of Table (1) repors he esmaed values of for he porfolos classfed n erms of pas. We noce ha for porfolo 1 he value of s -7.9 whle s 5.4 for porfolo 3. Sensvy beween volaly rsk and socks mean reurns s hen valdaed. However, we pon ou ha hese resuls are smlar o hose obaned for volaly nnovaon where s -6.9 for porfolo 1 and 4.9 for porfolo 5. 2.3. Inegraon of Rsk Facors Our sudy consss n esmang he ex-pos value of socks sensvy o volaly nnovaons afer a monh of nvesmens porfolo creaon. Table (1) repors he obaned resuls. We noce ha he ex-pos s monoone and ncreasng. I s -6.11 for porfolo 1 and 6.5 for porfolo 5. We noce as well ha he devaon beween he wo porfolos remans low enough. To esmae porfolos reurns, we evaluae ex-pos volaly rsk facors of and we negrae hese values n addon o he hree FF facors. Our regresson s hen wren as follows: Table (1). Porfolos classfed n erms of her exposure degree o volaly shocks P Mean (*100) Sandard Dévaon BM CAPM Alpha FF-3 Alpha Pre-creaon Pos-creaon 1 0,0319 0,003 0.734 0.0231 b 0.0463 b -7,269-6.987-6,119-7.908 2 0,0417 0,005 0.655 0.0520 b 0.0765 b -0,969-4.546-0,326-3.985 3 0,0958 0,004 0.343 0.072 b 0.0574 b 2,2875 1.2435-1,904-2.607 4 0,0241 0,003 0.244 0.0871 b 0.0987 b 3,2565 3.8796 2,015 3.002 5 0,0174 0,003 0.421 0.1867 b 0.0976 b 5,4006 4.9877 6,531 2.897 (5-1) -0,0142 0,1636 0,0513 10,806 r = α ξ (4) Where he frs hree facors,, are he facors of marke, sze and book o marke rao. Values of are deermned hrough porfolos of frms classfed n erms of. The resuls are repored n Table (1). We noce ha durng he pos-creaon perod, s sgnfcan and ncreasng. I s -7.9 for porfolo 1 and 2.8 for porfolo 2. The obaned resuls draw us o conclude ha condoned by socks sensvy o volaly nnovaon, here s a sgnfcan dfference beween socks reurns ha are esmaed by consderng rsk facors of marke, sze and book o marke rao. 2.3.1. Porfolo Creaon Perod We showed prevously ha for a monh-long sudy perod, he obaned resuls reman nconclusve. We herefore mend for hs lmaon by exendng he porfolos pre-creaon perod from 1 o 3 and 12 monhs. In able (2), we noce ha exendng porfolos pre-creaon perod consderably mproves he resuls. For a 3-monh pre-creaon perod, he α of he FF model s 0.007 for he ffh porfolo wh a -sasc of 5.7 for a 3-monh sudy perod and 0,005 wh a -sasc of 4.9 for a 1-monh sudy perod. When pre-creaon perod reaches 12 monhs, he ffh porfolo scores an α of he FF model equal o 0.01 and a -sasc of 1.78. Table 2. Characerscs of porfolos creaed n erms of Panel A. Sudy of he dfferen porfolos pre-creaon perods VIX pre-creaon perods 1 2 3 4 5 5-1 1 monh 3 monh 12 monh 0.0065 (2.887) 0.0013 (2,430) -0.004 (-3,76) 0.006 (3.007) 0.0021 (2,703) -0.002 (-1.44) 0.008 (3.224) 0.003 (2,665) -0.0052 (-1.983) 0.0088 (2.466) 0.0076 (0,576) 0.0001 (1.5703) 0.0076 (5.785) 0.0055 (4,923) 0.0018 (1.785) 0,0011 0,4002 0,0062
4 Kala Lama and Jlan Faouz: A Sudy of Volaly Rsk Panel B. Sudy of sze and BM effec All frms Excludng he smalles and wh he mos mporan BM frms Porfolos Mean (*100) Sandard Devaon Mean (*100) Sandard Devaon 1 0,0544 0,00303 0.00241 0.00443 2 0.02802 0.06393 0.00463 0.00677 3 0.0199 0.00460 0.00201 0.00571 4 0.0238 0.00373 0.00259 0.00488 5 0.017 0.00331 0.00139 0.00455 5-1 -0.022-0.00102 Panel C. Sudy of he Momenum effec Porfolos Mean (*100) Sandard Devaon CAPM Alpha FF-3 Alpha Pre-creaon Pos-creaon 1-0.0262 0.005323-0,00285 (-1,384) -0.0027 (-1.4156) -3,1196-7.876 2 0.0462 0.00381 0.00331 (2.7079) 0.00311 (2,7063) -2,3269-3.332 3 0.0131 0.00421 0.00098 (0.0644) 0.0001 (0.0071) -1,67504-2.5649 Wh hese resuls, we may conclude ha he effec of ncreases when porfolos pre-creaon perod ncreases. Ths may be explaned by me varaons of marke sensvy o volaly nnovaons. The more resraned and lmed he pre-creaon perod and he condonal esmaon of, he lower he dfference beween porfolos reurns (3-1). One-monh span resuls repor more sgnfcan esmaons. 2.3.2. Sze and Book-o- Marke Rao (BM) I s ofen admed ha small-szed growng frms are he mos compeve frms when marke volaly ncreases. Then, we propose o sudy he effec of volaly varaons on hs ype of frms and he marke n order o check for he effec of sze and BM on porfolos mean reurns, classfed n erms of. To hs end, we exclude from he suded porfolos he smalles and wh he mos mporan BM frms and we reclassfy he frms n new porfolos. Examnng he mean and sandard devaon of he porfolos surplus reurns, we noce ha he dfference beween average monhly reurns beween porfolos 5 and 1 s - 0,002. A resul whch ndcaes ha socks sensvy o volaly bears on wo rsk facors: sze and BM. 2.3.3. The Momenum Effec To sudy momenum effec, we creae wo sock porfolos classfed n erms of mean reurns of he pas 12 monhs and value. Compung he dfference of mean reurns beween low-sensvy porfolos and porfolos wh hgh values s 0,003 per monh. Values of α for CAPM and he FF model n order o ake no accoun he momenum effec ndcae ha he dfferences beween porfolos (3-1) are sgnfcan. The value of s ncreasng and monoone. I ncreases from porfolo 1 o porfolo 3. These resuls allow us o conclude ha he momenum effec allows for akng no accoun socks sensvy o volaly rsk. 2.4. Volaly Rsk Prce We have shown prevously ha low reurns of hghly-sensve socks o volaly rsk canno be explaned unquely by facors lke sze, BM or momenum effecs, alhough hey dsplay an mporan dfference n hedgng facor of volaly rsk. Our nex procedure hen consss n esmang volaly rsk prce by ncludng he varables lkely o explan reurns varaons, n addon o whch represens marke rsk and hedgng facors of volaly rsk. In order o esmae hedgng facors premums noed by λ, we run a seres of ess where socks are classfed n erms of and. Classfyng hose socks n erms of s made possble hanks o regressng for each monh socks reurns surplus n erms of marke reurns surplus. Socks are frs classfed no porfolos n erms of, hen each porfolo s dvded n self no sub-porfolos n erms of. A hs level of esmaon, volaly rsk prce s negraed along wh rsk facors lkely o affec forward socks reurns. Our specfcaon ncludes hen he hree facors of he FF model as well as he momenum effec.
Journal of Fnance and Accounng 2014; 2(1): 1-10 5 r α λ λ λ λ λ ξ = UMD (5) UMD Where λ represens premum of he dfferen rsk facors; In hs sudy, we selec a sample of 30 socks and frs we esmae for he enre sample. Esmang rsk facors premums λ s hen done for he dfferen porfolos usng Fama, Mac Beh model [7]. Panel A of Table (6) repors he obaned resuls. Wh equaon I, we esmae marke rsk premum n addon o facor. Equaon II ncludes he hree facors of he FF model. Equaon III ncludes n addon o marke facors, sze, BM and he momenum effec (UMD). In Panel B, we sudy ex-pos facors of volaly rsk and rsk premums obaned from equaon I. The resuls of Panel A draw our aenon o he fac ha rsk facors premums are no all sgnfcan. Moreover, premums score negave values a regresson II, whch reflecs ha he BM effec poorly explan volaly rsk durng he sudy perod. For volaly rsk prce, hs facor s -2.19/monh. Ths resul s sascally sgnfcan a he 5% level. By negrang he hree facors n regresson III, volaly rsk prce exceeds -2.09. Ths negave value allows us o valdae he hypohess ha socks mean reurns generally reflec her exposure o volaly rsk represened by a decreasng relaonshp beween marke prce of volaly rsk and forward socks reurns. Equaon (I): Equaon(II): Equaon(III): r r r Cse Table (6). Esmaon of volaly rsk prce Panel A. Esmaon of rsk facors (I) (II) (III) -0,008 (-0.4016) 0.707 13.401-2.432 (-17.101) - - -0,001 (-0,0768) 0,6874 (11,665) -2,195 (-1,1437) 0.6471 (0.655) -0.1712 (-6,008) UMD - - = α λ λ ξ = α λ λ λ λ ξ = α λ λ λ λ λ ξ UMD Panel B. Esmaon of ex-pos hedgng facors of volaly UMD -0,0043 (-0,0772) 0,9784 (0,605) -2,0988 (-3,1437) 0.5077 (8.655) -0.5612 (-0,008) 0.1014 (2,7185) 1 low 2 3 1 low -3.876-5.8766-5.9968 2 1.5433-3.9954-1.9874 3 hgh 2.7677 5.009 3.2213 Panel B represens values of hedgng facors obaned from regresson I. In regresson III, we noce negraon of he momenum facor has no effec on he resuls and he esmaon of remans essenally unchanged. Includng he UMD facor, s rsk premum remans non-sgnfcan and he value of exceeds -2.19 o reach -2.09. The low momenum effec on coeffcen may be explaned by he low correlaon beween he wo varables. The resuls on hese varables show also ha pas reurns could no mprove low mean reurns of socks wh hgh sensvy o volaly rsk. For all regressons, he coeffcen decreases o reach -2.09 ye remans sgnfcan a he 5% level. We conclude here ha hs he only facor of all proposed ndependen facors ha remans sascally sgnfcan n he enre sudy. Panel B of Table (6) repors values of he ex-pos facors of nvesmen porfolos creaon. We noce ha he values confrm he hypohess ha mean reurns of porfolos
6 Kala Lama and Jlan Faouz: A Sudy of Volaly Rsk consruced n erms of her sensvy o rsk reflec n ex-pos her exposure degree o volaly rsk. The ex-pos value of of porfolos creaon ncreases n a monoone fashon from porfolo 1 (wh lowes porfolo 3 (wh he hghes classfed n erms of pas and ) o ). For porfolos, he values of are mxed. Comparng our resuls wh hose repored n Table (1) whch presens resuls on esmang volaly rsk exposure and explanng he mporan dfference n mean reurns beween he frs and he ffh porfolo, we noe ha he ex-pos dfference of s 10.8 compared o an ex-pos dfference of of 9.11 repored n Table (1). Then, does no allow akng no accoun he dfference of mean reurns beween porfolos. 3. Idosyncrac Volaly In he prevous sub-secon, we suded he mpac of volaly rsk on mean reurns of socks classfed n erms of her sensvy o varaons n sysemc volaly rsk. In hs secon, we manly examne dosyncrac componen of volaly usng socks classfed n erms of her sensvy o hs ype of volaly. Then, f dosyncrac volaly rsk s an omed varable from oal volaly rsk, sandards esmaon models based essenally on sysemc volaly should under-evaluae porfolos classfed n erms of dosyncrac volaly as hese models do no nclude her exposure o hs ype of volaly rsk. 3.1. Invesmen Sraegy Idosyncrac volaly rsk s esmaed by Fama and French model. I s deermned hrough he square roo of resdual rsk varaon: followng regresson: var ξ obaned from he r = α λ λ λ ξ (6) Some economc heores sugges ha dosyncrac volaly should be posvely relaed o expeced reurns. If nvesors demand compensaon for no beng able o dversfy rsk, hen agens wll demand a premum for holdng socks wh hgh dosyncrac volaly. [8] In order o sudy he mpac of hs componen on socks reurns, we creae nvesmen porfolos based on a sudy perod of L monhs, a porfolos creaon perod on M monhs and a deenon perod of N monhs. We descrbe hs L/M/N sraegy as follows: durng each monh, we esmae dosyncrac volaly usng daly daa ha separae he -L-M perod from -L perod usng regresson (6). In erms of, we classfy socks accordng o her exposure o dosyncrac volaly rsk and hen we consruc nvesmen porfolos. Deenon perod of hese porfolos s evaluaed n N monhs n order o analyse volaly rsk. Our sudy refers o 1/0/1 sraegy for whch we smply classfy socks no porfolos accordng o her dosyncrac volaly rsk levels of daly reurns acheved durng he pas monh and we rean hs porfolo for a monh. 3.2. Toal and Idosyncrac Volaly Our sudy consss n analyzng mean reurns of socks porfolos classfed accordng o her sensvy o he dfferen volaly varaons. Panel A of Table (7) repors varaons of oal volaly rsk regardless of sysemc rsk. Our sraegy s he 1/0/1. Followng [3], we noce ha resuls of mean reurns of porfolo 1 (conssng of socks wh he lowes oal volaly) ncreases o reach 0.003 per monh. For Porfolo (2) ncrease of reurns s more sgnfcan and reaches 0.008. Mean reurns of porfolo 3 (conssng of socks wh he hghes volaly) s 0.006 per monh. Value of α of he FF model presened n he las column of Table (7) of porfolo 3 s 0.006 and s hghly sgnfcan. The dfference n α beween porfolos 3 and 1 s 0.003 per monh. Agans all hs, we conclude ha he more socks are sensve o oal rsk, he much lower her mean reurns are. Panel B of Table (7) repors varaons of mean reurns of sock porfolos classfed accordng o her sensvy volaly dosyncrac rsk and no accordng o oal rsk. We noce ha he obaned resuls are smlar o hose of panel A. The dfference of mean gross reurns beween porfolos 3 and 1 s 0.003. The α of he FF model s also unable o adequaely ake no accoun varaons of he dosyncrac componen of rsk as he dfference n α beween porfolos 3 and 1 s 0.002% per monh. The BM and sze componen score moreover neresng resuls. We noe ha socks wh he lowes sensvy o dosyncrac rsk are generally socks whose marke capalsaon s hgh and he BM s low whle socks wh he hghes sensvy o dosyncrac rsk are socks whose marke capalsaon s low and he BM s hgh. Weghed rsk of he FF model assumes ha socks of porfolo 3 reached mporan mean reurns whle obaned mean reurns are only 0.006. These resuls are confusng, n parcular he low mean reurn of porfolo 3. Ths may be explaned he fac ha hs porfolo represens only 30% of socks classfed accordng o dosyncrac volaly, whch a low marke poron and canno represen he effec of dosyncrac volaly on socks reurns. The queson o be asked, hen, s: wll hs resul be he same f we consder he uncondonal rsk facors suded prevously? To answer hs queson, n he followng secon we wll examne he mpac of dosyncrac volaly of facors whch he leraure denfed as poenal rsk facors.
Table (7). A sudy of volaly effec Panel A. Porfolos classfed n erms of oal volaly porfolos Mean (*100) Sandard Devaon Sze BM Alpha CAPM Alpha F-F 1 0.0325 0.00881 258972,9 0,389923 2 0.0862 0.00443 248483 0,310475 3 0,0677 0.00377 264190,9 0,272901 0.00565 (2.664) 0.00218 (0.0443) 0,00873 (3.781) 0.00346 (2,785) 0.00131 (0.0098) 0,00344 (1.886) 3-1 0.0352 - - - 0.00308 0.00002 Panel B. Porfolos classfed n erms of dosyncrac volaly Porfolos Mean (*100) Sandard Devaon Sze BM Alpha CAPM Alpha F-F 1 0.0663 0.00051 290000 0,370151 0.00223 (4.211) 2 0.0688 0.00884 53315,67 0,230477 0.0121 (1.897) 3 0,0244 0.00066 182026 0,384347 0,01631 (3.002) 3-1 -0.0419 0.4104 0.00865 (1.057) 0.00131 (2.865) 0,00774 (0.544) 3.2.1. Sze Effec In order o sudy neracon beween sze effec and socks sensvy o dosyncrac volaly, we nroduce sze effec by consrucng sock porfolos accordng o her marke capalzaon sze. Nex, we classfy sze of socks of each porfolo accordng o dosyncrac volaly. Fnally, for each sze level we end up wh 3 porfolos; he frs s he one wh he lowes dosyncrac volaly and he hrd s he one wh he hghes dosyncrac volaly. Table (8). Values of α of porfolos consruced accordng o dosyncrac volaly Idosyncrac volaly 1 2 3 Sze 1 low 2 3 hgh Sze effec BM effec Coskewness effec -0.00447 (-2.6643) 0.00324 (2,5663) 0.00102 (1.042) -0.00527 (-1.9873) -0.00376 (-2,6652) -0.00776 (-3.224) 0.0009 (1.443) 0.00761 (2,7063) 0.00543 (0.0241) 0.00139 (0.5703) -0.00761 (-0,556) -0.0043 (-1.466) -0.00127 (-4.415) 0.02341 (2,7063) 0.00224 (4.0071) -0.00982 (-2.785) -0.00556 (-1,7223) -0.00358 (-4.785) Table (8) presens he resuls of he nvesmen sraeges 1/0/1. We noe ha for porfolo sze level, he porfolo wh he hghes dosyncrac volaly s ha wh he lowes α value of he FF model. Ths resul does no necessarly concern socks wh he lowes marke capalsaon. The value of α of he FF model for porfolo 2 s 0.02 and represens he hghes value compared o ha of porfolo 3. Ths resul s hghly sgnfcan wh a -sasc of 2.7. By conras, he dfference n α of he FF model for he porfolos wh lowes and hghes marke capalsaon s low and non-sgnfcan. We may conclude ha s no he socks wh he lowes marke capalsaon ha affec marke volaly. Then, marke capalsaon could no explan low reurns of socks wh hgh dosyncrac volaly. 3.2.2. Book o Marke Effec I s generally admed ha growh-orened frms wh he hghes BM acheve he hghes mean reurns by conras o value-orened frms wh he lowes BM whose mean reurns are he lowes. More precsely, BM effec seems o explan dosyncrac volaly. Hgh-dosyncrac volaly porfolos should essenally conss of growh-orened socks wh he hghes BM. Table (8) repors he resuls of nvesmen sraeges 1/0/1 whch conss n creang sock porfolos classfed accordng o he mporance of her BM and n classfyng socks of each porfolo accordng o dosyncrac volaly value. Lne 3 of able (8) ndcaes, conrary o prevous resuls, ha socks of porfolos wh he lowes BM, for each dosyncrac level, he hghes FF α reachng -0.003 for porfolo 1 and -0.005 for porfolo 3. The dfference n FF α for porfolos wh lowes and hghes BM s 0.002. Ths resul s sascally non-sgnfcan. Agans hese resuls, we may conclude ha BM has no effec on socks dosyncrac volaly nor on her mean reurns. 3.2.3. Coskewness Effec We have shown prevously referrng he works of [4] ha socks wh coskewness coeffcen acheve he hghes forward reurns. socks ha do badly when volaly ncreases end o have negavely skewed reurns over nermedae horzons, whle socks ha do well when
8 Kala Lama and Jlan Faouz: A Sudy of Volaly Rsk volaly rses end o have posvely skewed reurns[9]we propose here ha he socks wh hgh dosyncrac volaly should score a posve coskewness coeffcen as mean reurns acheved by hese socks are low. Our sudy consss n esmang coskewness coeffcen usng he followng equaon: SKD E 2 [ ε, 1ε M, 1] 2 2 [ ε ] E[ ε ] = (7) E, M, Where ε,1 = r,1 -a - r m,1 s a resdual of he regresson of socks reurns surplus on marke reurns. The resuls n Table (9) lead us o conclude ha exposure o coskewness effec does no parcularly explan he relaonshp beween socks sensvy o dosyncrac volaly and her acheved mean reurns. We noce ha he dfference of FF α for porfolos wh he lowes and hghes coskewness coeffcen s almos zero. 3.2.4. Sudy of he Momenum Effec Several sudes[6],[8] showed ha he momenum effec descrbed by [3] s asymmerc as he negave effec scored for decreasng socks s hgher han he posve effec scored for ncreasng socks. Remarkably, he lowes pas reurns socks are socks whch represen hgher sensvy o dosyncrac volaly. I s clear ha socks of pas wnnng socks presen also hgher dosyncrac volaly, ye s he pas losng socks ha are overesmaed durng evaluaon of reurns acheved by socks wh he hghes dosyncrac volaly. In hs secon, we sudy he relaonshp beween dosyncrac volaly and he momenum effec. To hs end, a seres of esed s conduced. The resuls are presened n Table (9). Panel A presens he values of FF α for he dfferen porfolos classfed accordng o dosyncrac volaly and her pas reurns. Our analyss consss of sudyng characerscs of momenum porfolos n dfferen sudy perods of pas reurns, n parcular our 1-monh, 6-monh and 12-monh span sudy. Table (9) repors he obaned resuls. We noe ha hese resuls are smlar o he prevous ones. The value of FF α n a 1-monh perod s monoone and ncreasng, n parcular α of he 3 rd porfolo, and s 0.006 and he dfference n α beween he 3rd porfolo and he 1s porfolo s 0.001. These resuls are sascally sgnfcan. Table(9). Sudy of momenum effec on α of porfolos classfed accordng o dosyncrac volaly. 1 monh 6 monh 12 monh Panel A. Sudy of Momenum effec 1 low 2 3 hgh 3-1 0.00494 (2.642) 0.00154 (2,4303) -0.00164 (-1,543) 0.00431 (2.224) 0.00291 (1,703) 0.00762 (1.897) 0.00664 (3.987) 0.00442 (2,665) 0.00752 (2.683) 0.0017 0.00288 0.00916 loser 1 2 wnner 3 Panel B. Sudy of he 12-monh perod. 1 low 2 3 hgh 3-1 -0.00224 (-2,776) -0.00143 (-1,523) 0.00254 (2,082) -0.00246 (1,442) 0.001 (1.247) 0.00142 (1.393) 0.00327 (1,876) 0.00262 (2.021) 0.00365 (2.677) 0,00551 0,00305 0,00111 For a 6-monh sudy, he dfference n α beween he 3 rd porfolo and he 1 s porfolo s 0.002. Ths dfference s even more mporan and reaches 0.009 for he 12-monh sudy. These sascally-sgnfcan resuls lead us o conclude ha he momenum effec could no explan dosyncrac volaly effec on socks mean reurns. Panel B represens values of FF α for porfolos classfed n erms of pas 12 monhs and socks sensvy o dosyncrac volaly. We noe ha FF α values for hese dfferen porfolos are smlar o hose obaned n Panel A of Table (9). Several mporan facs can be concluded from hese resuls. Frs, We noce ha low reurns of dosyncrac volaly are more observable for losng socks han for wnnng socks. The α dfference beween he 3 rd porfolo and he 1 s porfolo s 0.005 for he losng socks and 0.001 for he wnnng socks. Second, hs endency of momenum effec remarkable for losng socks canno represen low reurns n case of hgh dosyncrac volaly, as dosyncrac volaly value s sgnfcan for all ypes sock reurns porfolos, n parcular for low mean reurns porfolos. Ths s wheher socks are wnnng or losng. A remarkable effec s also presence of asymmery n he momenum effec. We noe for he frs dosyncrac volaly porfolo ha α values of exreme wnnng and losng porfolos are symmerc. For he frs level of porfolos wh he lowes dosyncrac volaly, α for he losng porfolo s -0.0022 where as ha of he wnnng porfolo s 0.0025. For he second level of porfolos, α for he losng porfolo s -0.002 where as ha of he wnnng porfolo s 0.001. The hgher dosyncrac volaly s, he more skewed he momenum effec becomes for exreme socks wh low mean reurns and hgh dosyncrac volaly. Ths resul leads us o conclude ha he mos profable momenum sraegy consss n sellng pas losng socks wh he hghes dosyncrac volaly and purchasng pas wnnng socks wh he hghes dosyncrac volaly. 3.3. Toal Volaly and Idosyncrac Volaly We es here he alernave ha hgh negave reurns of socks wh hgh dosyncrac volaly resul from her hgh exposure degree o volaly varaons. To hs end, we classfy socks frs accordng o he coeffcen of her sensvy o volaly rsk varaons and second accordng o her volaly esmaed by hedgng facors. Choce of as an esmaon parameer of volaly rsk s suppored by he prevously obaned resul
Journal of Fnance and Accounng 2014; 2(1): 1-10 9 whch ndcaes ha socks wh he hghes pas are generally he socks ha are mos exposed o hedgng facors of volaly. Table (10) repors he resuls of mean values of FF α for each level of porfolo and for each level of. Table (10). Sudy of he effec of dosyncrac volaly on volaly rsk Panel A. Sudy of α of FF-3 Idosyncrac volaly 1 low 2 3 hgh 3-1 volaly rsk -0.004672 (-3.0023) 0.00243 (2.6403) Panel B. Sudy of facors 0.00564 (1.9776) 0.01031 Idosyncrac volaly 1 low 2 3 hgh 3-1 1 low 2 3 hgh -0.00658 (-2.8863) -0.00542 (-1,7852) -0.00442 (-1.224) -0.00539 (-1.903) 0.00261 (2,9556) 0.00247 (0.466) 0.00122 (-2.0285) 0.00664 (1,8823) -0.00358 (-2.675) 0.00780 0.01196-0.00104 Accordng o Panel A of able (10), sudyng exposure degree of socks o volaly, α value correspondng o he dfference beween porfolos (1-3) s 0.0103 compared o 0.086 n Table (6) when sysemc volaly s no aken no accoun. Ths resul leads us o conclude ha he coeffcen of sensvy o volaly rsk varaons akes only a par of low mean repors socks wh hgh dosyncrac volaly. Panel B presens values of α obaned for porfolos consruced accordng o hedgng facors and sensvy facors porfolos wh he lowes. We noce ha for he frs, value s monoone and ncreasng wh a negave value equal o (-0.006) for socks wh he lowes dosyncrac volaly and a posve value (0.001) for socks wh he hghes dosyncrac volaly. Moreover, we noe ha he hedgng facors canno explan he sock porfolo wh he hghes fac whch leads us o conclude ha low reurns of socks wh he hghes dosyncrac volaly can be explaned only for socks exposed o volaly negave shocks. 4. Concluson One he mos famous puzzles n he leraure s excessve marke volaly. Neverheless, n realy we noce ha volaly has more han a smple excessve componen o. I presens an mporan componen, whch s ha of asymmery. Ths s rue, knowng ha s reacon o a shock on reurns dffers accordng o shock sng. Deermnans of sock marke varaons help beer defne. A volaly characerscs. Effec of socks exposure degree o volaly s undersood as a deermnng facor of Tunsan sock marke volaly, defned n erms of hedgng facors of volaly rsk or n erms of dosyncrac volaly as suggesed by [5]. Our resuls ndcae ha socks sensvy o prce shocks resuls from an excessve componen of volaly. We noce n parcular ha rsk-averse nvesors ask for a premum o compensae for a deenon rsk of socks wh hgh sensvy o volaly rsk. [3][10]. we fnd ha socks wh hgh sensves o nnovaons n volaly have low average reurns. In addon, we fnd ha socks wh hgh dosyncrac volaly relave o he Fama and French (1993) model have low average reurns. These low average reurns o socks wh hgh dosyncrac volaly canno be explaned by exposures o sze, book-o-marke and momenum effecs. The effec also persss n volale and sable perods, and s robus o consderng dfferen formaon and holdng perods as long as one year. Alhough we argue ha volaly rsk s a new sysemac facor, exposure o volaly rsk accouns for very lle of he anomalous low reurns of socks wh hgh dosyncrac volaly. Hence, he expeced reurn paerns found by sorng on dosyncrac volaly presen somehng of a puzzle. References [1] J. Campbell and Henshel. L (1992), No news s Good news: An asymmerc model of changng volaly n sock reurn, Journal of fnancal economcs, vol 3, pp 281-318 [2] L. Glosen, R. Jagannahan and D. Runkle (1993), On he relaon beween he expeced value and he volaly of he nomnal excess reurn on sock, Journal of fanance 48,5, pp 1779-1801. [3] A. Ang, R. Hodrck, X. Yuhang and Z. Xaoyan (2004), The cross secon of volaly and expeced reurns, NBER workng paper seres. [4] C. Harvey and A. Sddque (2000), Condonal skewness n asse prcng Tess, Journal of fnance, vol 3, pp 1263-1295. [5] E. Fama and K. French (1996), Mulfacor explanaons of asse prcng anomales, Journal of Fnance, Vol 51, pp 55-84. [6] V. Huang, L. Qanqu, S. Rhee and L. Zhang (2011), Anoher Look a Idosyncrac Volaly and Expeced Reurns, Journal Of Invesmen Managemen (JOIM), Fourh Quarer 2011. [7] V. Acharya, H. Almeda and M. Campello (2012), Aggregae Rsk and he Choce beween Cash and Lnes of Cred, CEPR Dscusson Paper No. DP8913 [8] R F. Sambaugh, J. Yu and Y. Yuan (2012), Arbrage Asymmery and he Idosyncrac Volaly Puzzle NBER Workng Paper No. w18560. [9] S.A. Anhonsz (2012), Asse Prcng wh Paral-Momens,Journal of Bankng and Fnance, Vol. 36, No. 7, pp 214-221.
10 Kala Lama and Jlan Faouz: A Sudy of Volaly Rsk [10] D. Brown and M. Ferrera (2003), The nformaon n he dosyncrac volaly of small frms, Workng paper, Unversy of Wsconsn-Madson. [11] E. Fama and J. MacBeh (1973), Rsk reurn and equlbrum: Emprcal ess, Journal of polcal economy 71,607-636. [12] N. Jegadeesh and S. Tman (2001), Profably of momenum sraeges: An evaluaonof alernave explanaons, Journal of Fnance, Vol 56, pp 699-720 [13] M. Rocknger and E. Jondeau (2000), Condonal volaly, skewness and kuross: exsence and perssence, Workng paper [14] V. Torous, and Yan (2004), On Predcng Sock Reurn whh nearly negraed explanaory varables, Journal of Busness, Vol 77,pp 973-966.