S&P 500 VIX Futures Long/Short Switch Index Methodology

Transcription

1 S&P 500 VIX Fuures Long/Shor Swich Index Mehodology S&P Dow Jones Indices: Index Mehodology May 07

2 Table of Conens Inroducion Highlighs Index Consrucion 4 Approaches 4 Excess Reurn Index Calculaions 4 Toal Reurn Index Calculaions 4 Curvaure and Weighs 5 Base Dae and Base Value 6 Index Governance 7 Index Commiee 7 Index Policy 8 Announcemens 8 Holiday Schedule 8 Unscheduled Marke Closures and New Holidays 8 Delising of Fuures Conracs 8 Index Disseminaion 9 Tickers 9 FTP 9 Web sie 9 Appendix: The S&P 500 VIX Shor-Term Fuures Spread Adjused Index Family 0 Excess Reurn Index Calculaions 0 Day Coun and Weighs 0 Bid, Ask and Mid Prices Real Time Excess Reurn End of Day Excess Reurn S&P Dow Jones Indices Conac Informaion 4 Index Managemen 4 Produc Managemen 4 Media Relaions 4 Clien Services 4 Disclaimer 5 S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology

3 Inroducion The S&P 500 VIX Fuures Long/Shor Swich Index seeks o simulae a dynamic porfolio ha allocaes beween cash and one-monh VIX fuures wih he aim of capuring VIX fuures roll yield and volailiy drops ( shor ) when volailiy declines and VIX fuures upside when volailiy spikes ( long ). The VIX fuures componen swiches beween a long and shor S&P 500 VIX fuures posiion wih a consan one-monh mauriy. The long or shor posiion is deermined by he curvaure of he VIX fuures erm srucure. Highlighs The S&P 500 VIX Fuures Long/Shor Swich Index moniors he curvaure of he VIX fuures erm srucure and allocaes o cash and VIX fuures, which could be eiher a long or a shor posiion in he one-monh S&P 500 VIX fuures conracs. The curvaure of he VIX fuures erm srucure is calculaed by comparing he price difference beween he firs monh and second monh fuures, and he price difference beween he fourh and he sevenh monh fuures. When he fuures erm srucure is convex, he index akes a long posiion in VIX onemonh fuures; when he fuures erm srucure is concave, he index akes a shor posiion in VIX onemonh fuures. Hisorically, he index has mosly had a shor posiion in VIX fuures since he S&P 500 VIX fuures curve is usually concave. The curvaure of he VIX fuures erm srucure is calculaed based on he mid prices (i.e. he average of he bid and ask prices) of he VIX fuures conracs. The bid and ask prices of he VIX fuures conracs used in his calculaion are capured a 04:5 PM ET. If he price of any conrac is no observed a 04:5 PM, he laes available price is used. The long and shor VIX one-monh fuures posiions are modeled in he following wo indices: The S&P 500 VIX Shor-Term Fuures Spread Adjused Index The S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index The S&P 500 VIX Shor-Term Fuures Spread Adjused Index and he S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index adjus he reurns of he S&P 500 VIX Shor Term Fuures Index, which calculaes index values using he las price of he wo fuures conracs. Insead, hese wo indices calculae index values using he mid price hroughou he day, and adjus end-of-day reurns using he bid/ask spread. The S&P 500 VIX Shor-Term Fuures Spread Adjused Index rolls coninuously from he firs monh o he second monh and mainains a consan one-monh mauriy. The index sells he firs monh fuures a bid and buys he second monh fuures a ask. The S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index assumes an inverse posiion of he S&P 500 VIX Shor-Term Fuures Spread Adjused Index. The index buys he firs monh fuures a ask and sells he second monh fuures a bid. The bid and ask prices of he VIX fuures conracs used in he S&P 500 VIX Shor-Term Fuures Spread Adjused Index and he S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index are capured a 04:00 PM ET. If he price of any conrac is no observed a 04:00 PM, he laes available price is used. S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology

4 For more deails abou hese wo indices, please refer o he Appendix of his documen. This mehodology was creaed by S&P Dow Jones Indices o achieve he aforemenioned objecive of measuring he underlying ineres of each index governed by his mehodology documen. Any changes o or deviaions from his mehodology are made in he sole judgmen and discreion of S&P Dow Jones Indices so ha he index coninues o achieve is objecive. S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology 3

5 Index Consrucion Approaches The S&P 500 VIX Fuures Long/Shor Swich Index seeks o simulae a dynamic porfolio ha allocaes beween cash and one-monh VIX fuures wih he aim of capuring VIX fuures roll yield and volailiy drops ( shor ) when volailiy declines and VIX fuures upside when volailiy spikes ( long ). When he fuures erm srucure is convex, he index akes a long posiion in VIX one-monh fuures; when he fuures erm srucure is concave, he index akes a shor posiion in VIX one-monh fuures. The index calculaes he curvaure of he VIX fuures erm srucure on daily basis. If he curvaure signal flips and remains consan for hree coninuous business days, he index swiches is posiion accordingly. The index has a consan scale facor of /3 on he VIX fuures posiion. Excess Reurn Index Calculaions On any business day when he index is calculaed, he excess reurn index value is calculaed as: IndexER IndexER *( + ER ) = () IndexER = Excess reurn index level on day. ER ER = Excess reurn on day, calculaed as: W * LER W * SER ) ( L, + S, * SF = () LER = Excess reurn of he S&P 500 VIX Shor-Term Fuures Spread Adjused Index on day. SER = Excess reurn of he S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index on day. W L.- = Weigh of he S&P 500 VIX Shor-Term Fuures Spread Adjused Index on day -. W S,- = Weigh of he S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index on day -. SF = Scale facor = /3. Toal Reurn Index Calculaions On any business day when he index is calculaed, he oal reurn index value is calculaed as: IndexTR IndexTR *( + ER + CashDR ) = (3) IndexER = Excess reurn index level on day. ER = Excess reurn on day, calculaed as in formula (). CashDR = Cash daily reurn on day, calculaed as: S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology 4

6 Dae Dae CashDR = * Rae (4) 360 Dae Curvaure and Weighs = The valuaion dae. Dae - = The previous valuaion dae. Rae - = The previous day value of overnigh LIBOR, expressed as a percenage. On any business day when he index is calculaed, he index calculaes he curvaure of he VIX fuures erm srucure as follows: VX( c ) VX( c) VX( c7 ) VX( c4 ) Curvaure = (5) VX( c ) 3* VX( c7 ) VX(c) = The mid price of he firs monh VIX fuures on day. VX(c) = The mid price of he second monh VIX fuures on day. VX(c4) = The mid price of he fourh monh VIX fuures on day. VX(c7) = The mid price of he sevenh monh VIX fuures on day. Define he direcion of curvaure as follows: C + if Curvaure = if Curvaure 0 < 0 (6) On he firs day of index calculaion, he index consiss of cash only and has no allocaion o eiher long or shor volailiy posiions. The index does no allocae o volailiy unil i observes hree consisen signals. W W 0 (7a) L, 0 = S,0 = On all oher business days when he index is calculaed, he index mainains is previous allocaion o he long and shor VIX fuures posiion unil he curvaure flips and remains consan for hree coninuous business days. The weighs of he long and shor VIX fuures a he end of day are deermined as follows: W W L, S, if C = C = C = 0 if C = C = C W L, oherwise 0 if C = C = C = if C = C = C W S, oherwise = * C = * C = * C = * C = = + = = + W L. = Weigh of he S&P 500 VIX Shor-Term Fuures Spread Adjused Index on day. (7b) S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology 5

7 W S, = Weigh of he S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index on day. The mid price is calculaed as he average of he bid and ask prices. bid + ask mid = (8) The bid and ask prices of he VIX fuures conracs used in his calculaion are capured a 04:5 PM ET. If he price of any conrac is no observed a 04:5 PM, he laes available price is used. The index processes he real-ime bid and ask prices as follows: If a quoe only has a bid price, defaul ask o he bid price. If a quoe only has an ask price, defaul bid o he ask price. In oher words, if he index receives a one-sided quoe, i assumes bid = ask = mid. Valid bid/ask quoes mus saisfy he following crieria: o The bid mus be greaer han 0. o The ask mus be greaer han or equal o he bid. o The bid/ask spread, calculaed as per below, mus be less han or equal o 5%. Base Dae and Base Value ask bid spread = (9) ask The base dae for he index is January 9, 006. The base value on ha dae is 00 for boh he excess reurn and oal reurn versions of he index. S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology 6

8 Index Governance Index Commiee The Commodiies Index Commiee mainains he S&P 500 VIX Fuures Long/Shor Swich Index. All members of he Commiee are full-ime professionals a S&P Dow Jones Indices. The Commiee mees quarerly. A each meeing, he Commiee reviews any significan marke evens. In addiion, he Commiee may revise index policy for iming of rebalancing or oher maers. S&P Dow Jones Indices considers informaion abou changes o is indices and relaed maers o be poenially marke moving and maerial. Therefore, all Index Commiee discussions are confidenial. For informaion on Qualiy Assurance and Inernal Reviews of Mehodology, please refer o S&P Dow Jones Indices Commodiies Indices Policies & Pracices documen locaed on our Web sie, S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology 7

9 Index Policy Announcemens Announcemens of he daily index values are made afer he marke close each day. Holiday Schedule The index is calculaed daily from 3 AM EST o 4:5 PM EST, excluding holidays and weekends. A complee holiday schedule for he year is available a Unscheduled Exchange Closures and New Holidays For informaion on Unexpeced Exchange Closures, please refer o S&P Dow Jones Indices Commodiies Indices Policies & Pracices documen locaed on our Web sie, Delising of Fuures Conracs If one or more fuures conracs included in he index are no longer lised, S&P Dow Jones Indices may choose o cease publicaion of he index a ha ime. For informaion on Calculaions and Pricing Disrupions, Exper Judgmen, Daa Hierarchy and Error Correcions, please refer o S&P Dow Jones Indices Commodiies Indices Policies & Pracices documen locaed on our Web sie, S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology 8

10 Index Disseminaion Index levels are available hrough S&P Dow Jones Indices Web sie a major quoe vendors (see codes below), numerous invesmen-oriened Web sies, and various prin and elecronic media. Tickers Index Bloomberg Reuers S&P 500 VIX Fuures Long/Shor Swich Index ER SPVXLSP.SPVXLSP S&P 500 VIX Fuures Long/Shor Swich Index TR SPVXLST.SPVXLST S&P 500 VIX Shor-Term Fuures Spread Adjused Index ER SPVXFSAI.SPVXFSAI S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index ER SPVXSFID.SPVXSFID FTP Index reurns and daa are available via FTP subscripion. For produc informaion, please conac S&P Dow Jones Indices, Web sie For furher informaion, please refer o S&P Dow Jones Indices Web sie a S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology 9

11 Appendix: The S&P 500 VIX Shor-Term Fuures Spread Adjused Index Family The S&P 500 VIX Shor-Term Fuures Spread Adjused Index family seeks o simulae a long or shor S&P 500 VIX fuures posiion in he firs monh and second monh conracs. I consiss of wo indices: The S&P 500 VIX Shor-Term Fuures Spread Adjused Index The S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index The S&P 500 VIX Shor-Term Fuures Spread Adjused Index rolls coninuously from he firs monh o he second monh and mainains a consan one-monh mauriy. The index sells he firs monh fuures a bid and buys he second monh fuures a ask. The S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index assumes an inverse posiion of he S&P 500 VIX Shor-Term Fuures Spread Adjused Index. The index buys he firs monh fuures a ask and sells he second monh fuures a bid. For boh indices, index values are calculaed hroughou he day using he mid prices of he firs monh and second monh VIX fuures. A he index close (04:00 PM ET), he bid and ask prices of he VIX fuures conracs are capured. The indices use he mos recen valid bid and ask prices o adjus he index values. If he price of any conrac is no observed a he close, he laes available price is used. Excess Reurn Index Calculaions On any business day, he excess reurn index value is calculaed as: IndexER IndexER *( + ER ) = () IndexER = Excess reurn index level on day. ER = Excess reurn on day. Day Coun and Weighs On any business day when he index is calculaed, he index allocaes weighs o he firs monh and second monh fuures as follows: dr W, = 00* () d d dr, = 00* (3) d W d = The oal number of business days in he curren Roll Period beginning wih, and including, he saring CBOE VIX Fuures Selemen Dae and ending wih, bu excluding, he following CBOE VIX Fuures Selemen Dae. The number of business days says consan in cases where a new holiday is inroduced inra-monh or an unscheduled marke closure akes place. S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology 0

12 dr = The oal number of business days wihin a Roll Period beginning wih, and including, he following business day and ending wih, bu excluding, he following CBOE VIX Fuures Selemen Dae. In cases where a new holiday is inroduced inra-monh, he number of business days includes hose business days up o he business day preceding such a holiday. Afer he close on he Tuesday corresponding o he sar of he Roll Period, he oal weigh of he index is allocaed o he firs monh conrac. On each subsequen business day, a fracion of he firs monh VIX fuures holding is sold and an equal noional amoun of he second monh VIX fuures is bough. The fracion, or quaniy, is proporional o he number of firs monh VIX fuures conracs as of he previous index roll day, and inversely proporional o he lengh of he curren Roll Period. In his way, he iniial posiion in he firs monh conrac is progressively moved o he second monh conrac over he course of he monh. This coninues unil he following Roll Period sars, when he previous second monh VIX fuures conrac becomes he new firs monh VIX fuures conrac and hen is sold off incremenally following he same process. Bid, Ask and Mid Prices The index capures he real-ime bid/ask prices of boh VIX fuures conracs, and calculaes mid prices as follows: bid + ask mid = (4) The index processes he real-ime bid and ask prices as follows: If a quoe only has a bid price, defaul ask o he bid price. If a quoe only has an ask price, defaul bid o he ask price. In oher words, if he index receives a one-sided quoe, i assumes bid = ask = mid. Valid bid/ask quoes mus saisfy he following crieria: o The bid mus be greaer han 0. o The ask mus be greaer han or equal o he bid. o The bid/ask spread, calculaed as per below, mus be less han or equal o 5%. ask bid spread = (5) ask Real Time Excess Reurn The excess reurn is calculaed using mid prices hroughou he day. For he S&P 500 VIX Shor-Term Fuures Spread Adjused Index, he real ime excess reurn is calculaed as: W * mid i= ER = (6a) W * mid i= W - = Weigh of he i h monh fuures on day -. mid,-, mid, = Mid price of he firs monh fuures on day - and, respecively. mid,-, mid, = Mid price of he second monh fuures on day - and, respecively. S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology

13 For he S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index, he real ime excess reurn is calculaed as: i= i= ER = (6b) W - W W * mid * mid, = Weigh of he i h monh fuures on day -. mid,-, mid, = Mid price of he firs monh fuures on day - and, respecively. mid,-, mid, = Mid price of he second monh fuures on day - and, respecively. A any ime during he day when he index does no have valid bid or ask prices on eiher fuures conrac, he index value says unchanged. End of Day Excess Reurn Index calculaion sops a 04:00 PM ET on any day he index is calculaed. A his ime, he index akes he mos recen snapsho of he valid bid and ask prices, as described above, and calculaes he end-ofday excess reurn. For he S&P 500 VIX Shor-Term Fuures Spread Adjused Index, he end-of-day excess reurn is calculaed as: W * mid W * ( mid, bid, ) W *( ask, mid, ) i= ER = (7a) W * mid W - i= = Weigh of he i h monh fuures on day -. mid,-, mid, = Mid price of he firs monh fuures on day - and, respecively. mid,-, mid, = Mid price of he second monh fuures on day - and, respecively. bid, = Bid price of he firs monh fuures on day. ask, = Ask price of he second monh fuures on day. For he S&P 500 VIX Shor-Term Fuures Inverse Daily Spread Adjused Index, he end-of-day excess reurn is calculaed as: W * mid + W *( ask, mid, ) + W *( mid, bid, ) i= ER = (7b) W * mid W - i= = Weigh of he i h monh fuures on day -. mid,-, mid, = Mid price of he firs monh fuures on day - and, respecively. S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology

14 mid,-, mid, = Mid price of he second monh fuures on day - and, respecively. ask, = Ask price of he firs monh fuures on day. bid, = Bid price of he second monh fuures on day. W = Weigh ha is rolled on day, calculaed as: W (8) = W W,, For he avoidance of doub, on he business day subsequenly following he las rade dae of he firs monh fuures: subscrip and subscrip in all he formulas above are re-se, and W equals he weigh ha is rolled o he new second monh fuures. S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology 3

15 S&P Dow Jones Indices Conac Informaion Index Managemen David M. Blizer, Ph.D. Managing Direcor & Chairman of he Index Commiee Produc Managemen Vini Srivasava Managing Direcor Media Relaions Soogyung Jordan Communicaions Clien Services S&P Dow Jones Indices: S&P 500 VIX Fuures Long/Shor Swich Index Mehodology 4

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