Investable Volatility Index

Transcription

1 Invesable Volailiy Inex Inroucion Inex Overview The Invesable Volailiy Inex ( he Inex ) is esigne o measure he reurn of an invesmen in he forwar implie volailiy of he S&P 500 Inex. The reurn of he Inex reflecs changes in he level of forwar implie volailiy of he S&P 500 Inex by using marke prices of lise S&P 500 Inex opions plus a reurn on he previous Inex level a he prevailing one-monh U.S. Treasury bill yiel. The Inex measures he forwar implie volailiy of he S&P 500 Inex for a hree-monh winow cenere approximaely five monhs in he fuure. The Inex level is publishe on Bloomberg uner he symbol VOL Inex an on Reuers uner he symbol.vol. Volailiy Backgroun The volailiy of an asse is a saisical measure of he variabiliy in he price of he asse over a perio of ime. The implie volailiy of an opion is he marke s measure of he price of volailiy of he unerlying asse from oay o he opion s expiraion. One well-known measure of implie volailiy of he S&P 500 Inex is he VIX inex (he VIX ) compue by he Chicago Boar Opions Exchange, Incorporae (he CBOE ). Forwar implie volailiy is he opion marke s measure of he price of volailiy beween wo aes in he fuure. Forwar implie volailiy beween wo aes in he fuure can be calculae by using he curren implie volailiy of opions expiring on each of he wo aes. The Inex Componens The CBOE publishes implie volailiy levels for opion expiraions (ogeher, he Lise Expiraion Daes ), which generally occur on he hir Friay of each monh, subjec o he CBOE s holiay scheule, in March, June, Sepember, an December. An implie volailiy level is compue separaely for each Lise Expiraion Dae using he opion prices for each respecive Lise Expiraion Dae an applying he same formula use in calculaing he VIX. The implie volailiy levels are publishe on Bloomberg uner he symbols VXMAR, VXJUN, VXSEP, an VXDEC (ogeher, he Inex Componens ) for he implie volailiy calculaions in March, June, Sepember, an December, respecively. The VIX formula is escribe in he CBOE whie paper on he VIX, available on he VIX websie a Calculaing Forwar Implie Volailiy from Inex Componens For he purpose of calculaing he Inex, forwar implie volailiies (ogeher, Forwar Implie Volailiies ) are compue from he Inex Componens. The hree poenial Forwar Implie Volailiies are calculae beween ajacen quarerly expiraions (i.e. March o June, June o Page of 8

2 Invesable Volailiy Inex Sepember, Sepember o December, an December o March). A Forwar Implie Volailiy can be hough of as he combinaion of a long posiion in (or a purchase of) he Inex Componen wih he longer mauriy an a shor posiion in (or a sale of) he corresponing Inex Componen wih he shorer mauriy. Calculaing Weighs an Conracs For he purpose of calculaing he Inex, he Forwar Implie Volailiies are reae like asses ha can be bough, hel, an sol. The level of he Inex is he resul of holing a heoreical porfolio of hese asses. This porfolio is rebalance on a aily basis o approximae he forwar implie volailiy of he S&P 500 Inex for a hree-monh winow cenere approximaely five monhs in he fuure. The Inex calculaion process uses weighs o calibrae he amoun of heoreical invesmen in each Forwar Implie Volailiy an conracs o represen he amoun of heoreical invesmen in each Forwar Implie Volailiy. The exac calculaion mehoology is escribe in he secion Inex Calculaion below. Inex Calculaion Calculaing he Inex For each scheule raing ay on he CBOE, each an Inex Calculaion Day, he Inex is calculae as follows: Sep : Calculae he Forwar Implie Volailiy levels from he Inex Componens On each raing ay, hree forwar implie volailiy levels can be compue from he Inex Componens. The Inex Componens on any given ay can be ienifie in chronological orer as IC, IC, IC, an IC4, wih IC represening he Inex Componen closes o he Inex Calculaion Day. For example, on June 5, 00, which is prior o he expiraion ae in June 00, IC woul represen VXJUN (wih an expiraion ae in June 00), IC woul represen VXSEP, IC woul represen VXDEC, an IC4 woul represen VXMAR. To provie furher illusraion, on June 4, 00, which is afer he expiraion ae in June 00, IC woul represen VXSEP, IC woul represen VXDEC, IC woul represen VXMAR, an IC4 woul represen VXJUN (wih an expiraion ae in June 0). The hree forwar implie volailiy levels, ienifie as FIVA, FIVB, an FIVC, are compue accoring o he following formulas: FIVA IC IC ( ) Page of 8

3 Invesable Volailiy Inex FIVB FIVC IC IC ( ) 4 IC4 IC ( ) 4 wih,, an 4 represening he year fracion, calculae using minues, from he curren ime oay o 9:0am (New York Time) on he Lise Expiraion Dae, for IC, IC, IC, an IC4, respecively. Sep : Deermine he appropriae Forwar Implie Volailiies o use for he Inex calculaion The Inex uses wo of he hree Forwar Implie Volailiies. The wo Forwar Implie Volailiies use for he Inex Calculaion are efine as FIV an FIV. On each Inex Calculaion Day, ienify FIV an FIV using he process below: Calculae he average ime o mauriy ( ) for each Forwar Implie Volailiy. The represens he average of he ime o mauriy for he wo Inex Componens use in calculaing a Forwar Implie Volailiy. A B C where,, an 4 represen year fracions, calculae using acual ays/65, from oay o he Lise Expiraion for IC, IC, IC, an IC4, respecively. Compare he values for FIVA, FIVB an FIVC an ienify he value ha is boh closes o an less han 5/. The Forwar Implie Volailiy o which his perains is efine as FIV for he purposes of he Inex calculaion. The of FIV is efine as. Compare he values for FIVA, FIVB an FIVC an ienify he value ha is boh closes o an greaer han or equal o 5/. The Forwar Implie Volailiy o Page of 8

4 Invesable Volailiy Inex which his perains is efine as FIV for he purposes of he Inex calculaion. The of. FIV is efine as Sep : Deermine he weighs for FIV an FIV Calculae he Forwar Implie Volailiy weighs w an w, for he forwar volailiies FIV an FIV, respecively, such ha (i) w w + w w + is approximaely 5/ an (ii). The weighs are esigne o keep he weighe values of he Forwar Implie Volailiies use for he Inex calculaion a approximaely 5/. As ime passes (over a w perio of roughly hree monhs), will ecrease o approach 0, an w will increase o approach. On he ay (efine as a New Conrac Day ) when crosses over from being greaer han 5/ o being less han 5/, he Forwar Implie Volailiies are rolle, such ha he Forwar Implie Volailiy efine as FIV becomes FIV an he nex Forwar Implie Volailiy becomes FIV. If he Inex Calculaion Day is a New Conrac Dae, hen w an w 0. Oherwise: w 5 an w w. Sep 4: Deermine he number of conracs for FIV an FIV The conracs n an FIV an FIV FIV an n represen he amoun of heoreical invesmen he Inex has in, respecively. The conracs are ajuse aily o keep he exposure o FIV consisen wih he weighings w an w, an o accoun for ransacion coss which woul be incurre in implemening a sraegy o replicae he Inex. Calculae For n : n an n for FIV an FIV : n w S n FIV n + when w S n FIV > 0 FIV* ExecuionFacor. Oherwise, incluing on he Base Dae: Page 4 of 8

5 Invesable Volailiy Inex n w S FIV For n : n w S n FIV n + when w S n FIV > 0 FIV * ExecuionFacor. Oherwise, incluing on he Base Dae: n ws FIV where: S n FIV + n FIV The Execuion Facor is equal o.05 an is esigne o reflec he ransacion coss ha woul be incurre in implemening a sraegy ha replicaes he Inex. The Execuion Facor is only applie o he equaion where n or n is o be increase from he level of n or n, respecively. Sep 5: Calculae he simple reurn of he Inex on he Inex Calculaion Dae The simple reurn of he Inex, r, is equal o: r S S S Sep 6: Calculae he Inex closing level The Inex closing level, I, is equal o: ( + InexMuliplier r IA ) I I + where: Inex Muliplier 0% Ineres accrual IA Rae 60 Page 5 of 8

6 Invesable Volailiy Inex where Rae - is he closing level of he 0-ay U.S. Treasury Yiel on Inex Calculaion Day -, an is he number of calenar ays from, bu excluing, Inex Calculaion Day -, o an incluing, Inex Calculaion Day. I is roune o ecimal places. Base Dae The Base Dae of he Inex is December, 004. I an S are boh efine as 50 on he Base Dae. Oher Imporan Informaion Hypoheical Hisorical Closing Levels of he Inex Levels of he Inex publishe for aes prior o March, 00 represen hypoheical resuls base on hisorical aa an are provie for purposes of illusraion only. Where he appropriae hisorical S&P 500 Inex lise opions aa is unavailable, prices for oher financial insrumens are use, incluing lise variance fuures. Merrill Lynch Inernaional ( MLI ) believes ha such aa is a reasonable proxy for unavailable hisorical S&P 500 Inex lise opions aa. The publishe hisory may be subjec o change by he CBOE or MLI if i is eermine ha more suiable aa is available. None of he CBOE, MLI, or MLI s affiliaes offers any assurance abou he accuracy of hisorical aa or wheher hisorical resuls are inicaive of fuure performance. Marke Disrupion If a marke isrupion (as eermine by MLI in is sole iscreion) occurs on a scheule Inex Calculaion Day here will be no inex closing level. Furhermore he reweighing as escribe in Seps an 4 above will be carrie o he nex scheule Inex Calculaion Day which is no a isrupe ay. On such Inex Calculaion Day immeiaely following a isrupion, for purposes of calculaing Seps o 6 above, - will refer o he prior Inex Calculaion Day for which here was no isrupion. The calculaion will hen resume as escribe above. MLI in is sole iscreion may ajus he mehoology of he Inex so ha he Inex may coninue o be calculae in a pracical manner. If a marke isrupion coninues o occur for more han 0 scheule Inex Calculaion Days (as eermine by MLI in is sole iscreion) MLI will eermine he level of he Inex using a commercially reasonable meho. Page 6 of 8

7 Invesable Volailiy Inex Moificaions o he Inex The above informaion reflecs he policies of, an is subjec o change by MLI, as he Inex Sponsor, an he CBOE, as he Inex Calculaion Agen. The Inex Calculaion Agen calculaes an isseminaes he level of he Inex using he mehoology provie by he Inex Sponsor, an has no obligaion o coninue o compile or mainain he Inex an may isconinue publicaion of he Inex a any ime in is sole iscreion. MLI, as he Inex Sponsor, may moify he Inex wihou he consen of any person for purposes of curing any ambiguiy or correcing or supplemening any provision ha is efecive or inconsisen wih he oher provisions or replacing any informaion provier or informaion source or any previous replacemen informaion provier or source. MLI or he CBOE may revise isseminae Inex values ue o echnical errors, operaional evens, or marke isrupions ha prohibi he calculaion of he Inex or ha resul in values inconsisen wih he Inex mehoology or wih prevailing marke coniions. Any moificaions o Inex aa or mehoology may aversely affec he value of any securiies linke o he Inex, an MLI will have no obligaion o inform any person (incluing holers of securiies linke o he Inex) abou such moificaion, change or replacemen. MLI will make reasonable effors o assure ha such moificaions, changes an replacemens will resul in a mehoology ha is consisen wih he mehoology escribe above. For Aiional Informaion: Iniviuals: Please conac your financial avisor or fin one by calling: -800-MERRILL Insiuions: Please conac Equiy Derivaive Sales ( ) or InvesableVolInfo@baml.com Disclaimer S&P 500 is a raemark of Sanar an Poor's Financial Services, LLC ( S&P ) an has been license for use by Merrill Lynch, Pierce, Fenner an Smih Incorporae an is permie affiliaes ( Merrill Lynch ). Chicago Boar Opions Exchange, CBOE, CBOE Volailiy Inex an VIX are regisere raemarks of Chicago Boar Opions Exchange, Incorporae ( CBOE ). Merrill Lynch has conrace wih CBOE o calculae an isseminae he Invesable Volailiy Inex (he Inex ). The mehoology of he CBOE Volailiy Inex is use in he calculaion of values of he Inex. The mehoology of he CBOE Volailiy Inex is owne by CBOE. The Inex is no sponsore, enorse, sol or promoe by S&P or CBOE. Neiher S&P nor CBOE makes any represenaion regaring he avisabiliy of invesing in any invesmen prouc ha is base on he Inex. Values of he Inex an any oher informaion wih respec o he Inex are presene AS IS an wihou any warrany of merchanabiliy or finess for a paricular purpose or any oher represenaion or warrany of any kin. Page 7 of 8

8 Invesable Volailiy Inex Bank of America Merrill Lynch is he markeing name for he global banking an global markes businesses of Bank of America Corporaion. Lening, erivaives, an oher commercial banking aciviies are performe globally by banking affiliaes of Bank of America Corporaion, incluing Bank of America, N.A., a member of he Feeral Deposi Insurance Corporaion. Securiies, sraegic avisory, an oher invesmen banking aciviies are performe globally by invesmen banking affiliaes of Bank of America Corporaion ( Invesmen Banking Affiliaes ), incluing, in he Unie Saes, Banc of America Securiies LLC an Merrill Lynch, Pierce, Fenner & Smih Incorporae, which are boh regisere broker-ealers an members of he Financial Inusry Regulaory Auhoriy an he Securiies Invesor Proecion Corporaion, an, in oher jurisicions, locally regisere eniies. This ocumen is no a prouc of an has no been reviewe or approve by he Bank of America Merrill Lynch research eparmen. I is furnishe for informaional purposes only; may be change a any ime; is no a soliciaion or recommenaion o purchase any securiy or financial insrumen, or o inves in any ype of invesmen sraegy; an is no ax, legal, or accouning avice. Opions, fuures an oher volailiy proucs may involve significan risk an are no suiable for every invesor. Please consul your professional avisor before invesing. Bank of America Merrill Lynch an is affiliaes may offer avice on or ransac in sraegies or financial insrumens ha compee wih or aversely affec he price of he sraegies or financial insrumens escribe herein. The informaion is provie AS IS an Bank of America Merrill Lynch an is affiliaes expressly isclaim all represenaions or warranies, incluing merchanabiliy or finess for a paricular purpose or use. Bank of America Merrill Lynch shall no be liable for loss or amage, irec, inirec, or consequenial, arising from or relae o he informaion herein, or any acion aken in reliance, excep o he exen of is gross negligence or willful oruous misconuc. Invesable Volailiy Inex is a raemark of Bank of America Merrill Lynch. 0 Bank of America Corporaion. All righs reserve. Invesmen Proucs offere by Invesmen Banking Affiliaes are: * No FDIC Insure * May Lose Value * No Bank Guaranee. Page 8 of 8