CBOE VIX PREMIUM STRATEGY INDEX (VPD SM ) CAPPED VIX PREMIUM STRATEGY INDEX (VPN SM )

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1 CBOE VIX PREIU STRATEGY INDEX (VPD S ) CAPPED VIX PREIU STRATEGY INDEX (VPN S ) The seady growh of CBOE s volailiy complex provides a unique opporuniy for invesors inen on capuring he volailiy premium. The volailiy premium is he risk premium ha he marke seems willing o pay o own realized or implied volailiy. The prevalen conjecure among financial economiss is ha he volailiy premium is explained by he negaive correlaion beween S&P 500 volailiy and S&P 500 reurns. The volailiy premium has always been refleced in he difference beween implied and realized volailiy, and i now has become apparen in he hisorical reurns of shor posiions in CBOE Volailiy Index (VIX ) and variance fuures. To benchmark he reurns of shor volailiy sraegies, CBOE has developed wo differen ypes of indexes. The CBOE S&P 500 VARB-X T Sraegy Benchmark (VTY) is based on selling realized variance while he VIX Premium Sraegy Index (VPD) and Capped VIX Premium Sraegy Index (VPN) are based on selling implied volailiy proxied by he VIX. The capped version of he VIX Premium Sraegy Index limis he risk of a shor VIX exposure wih long ou-of-he-money VIX calls. To clarify he difference beween he VPD and VPN and he VARB-X Benchmark, noe ha he VPD and VPN sraegies involve selling a succession of one-monh VIX fuures while he VARB-X sraegy involves selling a series of hree-monh realized variance fuures. The VPD and VPN creae a sequence of shor exposures o forward one-monh S&P 500 implied volailiy while he VARB-X creaes a sequence of shor exposures o spo S&P monh realized variance. This implies ha he VPD and VPN are inherenly more volaile han he VARB-X because implied volailiy risk says consan as VIX fuures move owards expiry while realized variance risk gradually decreases as each day reveals a new erm of he final variance. This aricle focuses on he VPD and VPN. The VPD racks he value of a porfolio ha overlays a sequence of shor one-monh VIX fuures on a money marke accoun. The VIX fuures are held unil expiraion and new VIX fuures are hen sold. The money marke accoun decreases leverage relaive o a sand-alone shor posiion in VIX fuures. To furher decrease he risk of being shor implied volailiy, he number of VIX fuures sold a each roll is se o preserve 75% of he iniial value of he porfolio in he even ha VIX fuures increase by 25 poins 1. 1 The decision o arge he maximum loss resuling from a 25 poin increase in VIX fuures is based on he hisorical frequency disribuion of one-monh changes in implied volailiy, as proxied by VXO, he old VIX. Over any one-monh period beween January 1986 and July 2007, VXO has increased by more han 25 poins 0.34% of he ime, and 0.037% if we omi he fall of CBOE Proprieary Informaion Copyrigh (c) 2007, Chicago Board Opions Exchange, Incorporaed. All righs reserved.

2 Similar o he VPD, he VPN sells monhly VIX fuures over a money marke accoun. In addiion, i limis he risk of he shor VIX exposure wih long VIX calls sruck 25 poins higher han he VIX fuures price, or a he closes srike below when his srike is no lised. Since he muliplier of VIX opions is 100, each VIX fuures is covered by 10 VIX calls. Consrucion of CBOE VIX Premium Sraegy Index The VPD represens he value of an iniial invesmen of $100 in a porfolio ha passively follows he VIX Premium Index Sraegy. The porfolio is managed and calculaed as follows: A he close of June 15, 2004, he incepion dae, $100 is invesed a he hree-monh Treasury bill rae 2. On June 16, 2004, he firs roll dae, VIX fuures are sold a he opening bid price of VIX fuures. From hereon, he fuures are marked-o-marke daily a he close and he resuling cash flow is credied o or debied from he opening money marke balance. A he nex expiraion, July 14, 2004, he fuures posiion is seled a he open o he final selemen price, new VIX fuures are sold a he opening bid price. The cash flows from he final mark of expiring conracs and from he daily closing marks of he new conracs are financed from he money marke balance. This process is repeaed from expiraion o expiraion 3. Final Selemen Price of Expiring VIX Fuures and Opions A expiraion, VIX fuures and opions are seled o a Special Opening Quoaion (SOQ) of VIX. The SOQ is a special calculaion of VIX compiled from he opening prices of S&P 500 Index (SPX S ) opions. Calculaion of VPD CBOE currenly calculaes he VPD once per day a he close of rading. On any given dae, he index represens he mark-o-marke value of he iniial $100 invesed in he VIX Premium Index Sraegy. A he close of every business dae, he value of he VIX Premium Index is equal o he value of he Treasury bill accoun, obained by compounding he Treasury Bill balance a 2 The inra-day cash from seling fuures a he open is deemed o be invesed a he close of he roll dae. Similarly, selemen losses are deemed o be financed a he close. 3 During he firs wo years of VIX fuures, new conracs expiring in he nex monh were no lised on several occasions. The index was hen calculaed using a posiion in he second monh. CBOE Proprieary Informaion Copyrigh (c) 2007, Chicago Board Opions Exchange, Incorporaed. All righs reserved.

3 he previous close by he Treasury rae and neing he cash flow from marking VIX fuures o marke: VPD = = ( 1+ r VPD N las ( F F 1 ) where is he Treasury bill balance a he close of dae, r -1 is he effecive Treasury bill rae from dae -1 o dae, N las is he number of fuures sold a he las roll dae, F is he daily selemen price of VIX fuures, and 1000 is he muliplier of VIX fuures. On a roll dae, he cash flow from final selemen of he expiring fuures and heir daily mark a he close are boh need from he money marke balance: VPD = ( 1+ r VPD ( N las ( SOQ F N new ( F Fbid )) where SOQ is he final selemen price of he expiring VIX fuures, N new is he number of new VIX fuures sold, and F bid is he opening bid price of VIX fuures. This balance is reinvesed a he daily Treasury rae unil he nex dae. The number of new VIX fuures sold a he open on a roll dae is se such ha a 25 poin increase of VIX fuures a he nex roll sill preserves 75% of capial available afer he final selemen of VIX fuures: N new o = ( 1+ R.75) /(1000 * 25) where o is he amoun in he money marke accoun a he open afer he final selemen of VIX fuures, and R is he effecive hree-monh Treasury bill rae o he nex roll dae. o 1000N las ( SOQ F = 1 Consrucion of CBOE Capped VIX Premium Sraegy Index The VPN represens he value of an iniial invesmen of $100 in a porfolio ha passively follows he Capped VIX Premium Index Sraegy. The porfolio is managed similarly o he uncapped porfolio. The difference is ha one-monh ou-of-he-money VIX calls are bough a he same ime ha VIX fuures are sold: CBOE Proprieary Informaion Copyrigh (c) 2007, Chicago Board Opions Exchange, Incorporaed. All righs reserved.

4 A he close of June 15, 2004, he incepion dae, $100 is invesed a he hree-monh Treasury bill rae 4. On June 16, 2004, he firs roll dae, VIX fuures are sold a he opening bid price of VIX fuures and 10 imes as many VIX calls are bough a a srike price 25 poins greaer han he opening bid price of VIX fuures. If his srike price is no lised, he calls are bough a he closes srike below. From hereon, as for he VPD, he fuures are marked-o-marke daily a he close and he resuling s cash flow is credied o or debied from he money marke balance. A he nex expiraion, July 14, 2004, he fuures and opion posiions are seled a he open o he final selemen price, new VIX fuures are sold a he opening bid price and new VIX calls are bough a he opening ask price. The cash flows from he final mark of expiring conracs and from he daily closing marks of he new fuures are financed from he money marke balance. This process is repeaed from expiraion o expiraion 5. Calculaion of VPN CBOE currenly calculaes he VPN once per day a he close of rading. On any given dae, he index represens he mark-o-marke value of he iniial $100 invesed in he Capped VIX Premium Index sraegy. A he close of every business dae, he value of he VPN is equal o he closing value of he Treasury bill accoun plus he mark-o-marke value of he VIX calls: VPN = +100 * 10N las C where is he Treasury bill balance a he close of dae, N las is he number of fuures sold and 10 N las is he number of VIX opions bough a he las roll dae, F is he daily selemen price of VIX fuures, and C is he average of he bid and ask quoes of he VIX calls a he close. The Treasury bill balance is obained by compounding he previous closing Treasury balance a he hree-monh Treasury bill rae and neing he cash flow from he mark of VIX fuures: = las ( 1+ r N ( F F = VPN 1 N lasc The inra-day cash from seling fuures a he open is deemed o be invesed a he close of he roll dae. Similarly, selemen losses are deemed o be financed a he close. 5 During he firs wo years of VIX fuures, new conracs expiring in he nex monh were no lised on several occasions. The index was hen calculaed using a posiion in he second monh. CBOE Proprieary Informaion Copyrigh (c) 2007, Chicago Board Opions Exchange, Incorporaed. All righs reserved.

5 where r -1 is he effecive Treasury bill rae from dae -1 o dae. A he close of a roll dae, as on regular days, he index is equal o he closing Treasury balance plus he mark of he new opions. The closing Treasury balance is now equal o he Treasury balance a he previous close compounded by he daily Treasury rae ne of he cash flows from ( final selemens of VIX fuures and opions, (2) he daily mark of new VIX fuures and (3) he purchase of new VIX calls. VPN = ( 1+ r N las (max[0, SOQ K ] ( SOQ F ) N new ( C Ca ( F Fbid )) where SOQ is he final selemen price of he expiring VIX fuures, K is he srike of he expiring VIX calls, N new is he number of new VIX fuures sold, C a is he ask price of he VIX calls bough a he open, F bid is he opening bid price of VIX fuures. As on nonroll daes, he Treasury balance is reinvesed a he Treasury rae. The number of new VIX fuures sold on a roll dae is se such ha a 25 poin increase of VIX fuures a he nex roll sill preserves 75% of capial available afer he final selemen of he VIX fuures and opions: o N new = ( 1+ R.75) /(1000 *(25+ (1+ R ) Cask ) o ( 1+ r N (max[0, SOQ K] ( SOQ F 1 )) = las where R is he effecive hree-monh Treasury bill rae o he nex roll dae. Hisorical Performance VIX Premium Uncapped VIX Premium Capped VARB-X S&P 500 Toal Reurn VIX Premium Char 1 Indexes June 04 - Ocober 07 VPD From June 2004 o Ocober 2007, he VPD increased by approximaely 61%, earning an annual geomeric reurn of 15.17%. Over he same period, he S&P 500 Toal Reurn Index (SPTR) increased by approximaely 43% and earned an annual geomeric reurn of 6/30/2004 8/30/ /30/ /30/2004 2/28/2005 4/30/2005 6/30/2005 8/30/ /30/ /30/2005 CBOE Proprieary Informaion Copyrigh (c) 2007, Chicago Board Opions Exchange, Incorporaed. All righs reserved. 2/28/2006 4/30/2006 6/30/2006 8/30/ /30/ /30/2006 2/28/2007 4/30/2007 6/30/2007 8/30/2007

6 11.08%. The pronounced skew of he VPD indicaes ha he Sharpe raio, based on he sandard deviaion of he reurn, is a misleading measure of risk-adjused reurn. The semi-sharpe raio based on he semi-deviaion is preferable. The semi-sandard deviaion of he VIX Premium Index was 5.31%, equal o he semi-deviaion of he S&P 500 Toal Reurn Index. Adjusing is monhly rae of reurn by is semi-deviaion, he VPD performed beer han he S&P 500 bu no as well as VARB-X. Char 2 VIX Premium Index Frequency Disribuion of onhly Reurns 35% 30% 25% 20% 15% 10% 5% 0% -5.00% -4.00% -3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% onhly Reurns 6/04-10/07 S&P 500 VARB-X VIX Premium 25% loss a 25 p vol increase VIX Premium Capped inimum Reurn -4.24% -1.77% -5.82% -6.29% Arihmeic ean onhly 0.91% 0.69% 1.21% 1.14% Annualized Geomeric ean 11.08% 8.50% 15.17% 14.22% Annualized Sd. Deviaion 8.47% 2.89% 8.04% 8.11% onhly Sharpe Raio Annualized Semi-Deviaion 5.31% 1.74% 5.31% 5.29% onhly Semi-Sharpe Raio Skew VPN Excess Kurosis In Char 1, he reason he VPN coincides wih he VPD unil arch 2006 is ha s when VIX opions were inroduced. From arch 2006 o Ocober 2007, he VPN earned an CBOE Proprieary Informaion Copyrigh (c) 2007, Chicago Board Opions Exchange, Incorporaed. All righs reserved.

7 annual geomeric reurn of 14.22%, compared o 15.17% for VPD and 11.08% for he S&P500 Toal Reurn Index. This smaller reurn will ypically be he case because he probabiliy of exercising calls purchased 25 poins ou-of-he-money is very small. Is semi sandard deviaion was comparable o ha of he VPD as was i semi-sharpe raio. onhly Reurns 3/06-10/07 S&P 500 VARB-X VIX Premium 25% loss a 25 p vol increase VIX Premium Capped inimum Reurn -3.10% -1.77% -5.82% -6.29% Arihmeic ean onhly 1.11% 0.61% 0.89% 0.75% Annualized Geomeric ean 13.82% 7.55% 10.70% 8.84% Annualized Sd. Deviaion 8.47% 2.89% 8.04% 8.11% onhly Sharpe Raio Annualized Semi-Deviaion 5.31% 1.74% 5.31% 5.29% onhly Semi-Sharpe Raio Skew Excess Kurosis Conclusion The marke demand for volailiy hedges has made i profiable o sell volailiy. While selling realized volailiy is a well-esablished sraegy, he aracive if riskier alernaive of selling pure implied volailiy is relaively recen as i could no be easily implemened before VIX fuures and opions were inroduced. The VIX Premium Sraegy Index and Capped VIX Premium Sraegy Index codify shor implied volailiy sraegies and give invesors useful benchmarks o gauge heir performance. CBOE, Chicago Board Opions Exchange, CFE, CBOE Volailiy Index and VIX are regisered rademarks, and SPX S, BX S, VPD S, VPN S, VXV S and VARB-X S are servicemarks of Chicago Board Opions Exchange, Incorporaed (CBOE). The mehodologies of he CBOE volailiy indexes and variance derivaives are owned by CBOE and may be covered by one or more paens or pending paen applicaions. Sandard & Poor's, S&P, and S&P 500 are regisered rademarks of The cgraw-hill Companies, Inc. and are licensed for use by CBOE. All oher rademarks and servicemarks are he propery of heir respecive owners. Opions involve risk and are no suiable for all invesors. Prior o buying or selling an opion, a person mus receive a copy of Characerisics and Risks of Sandardized Opions (ODD). Copies of he ODD are available from your broker, by calling OPTIONS, or from The Opions Clearing Corporaion, One CBOE Proprieary Informaion Copyrigh (c) 2007, Chicago Board Opions Exchange, Incorporaed. All righs reserved.

8 Norh Wacker Drive, Suie 500, Chicago, Illinois Pas performance does no guaranee fuure resuls. The informaion in his documen is provided solely for educaional and informaional purposes. CBOE Proprieary Informaion Copyrigh (c) 2007, Chicago Board Opions Exchange, Incorporaed. All righs reserved.

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