Peculiari)esofVola)li)es

ErnestChan,Ph.D.QTSCapitalManagement,LLC.

•  Ph.D.intheore)calphysics.•  Previously,researcheratIBMT.J.WatsonLabinmachine

learning,researcher/traderforMorganStanley,CreditSuisse,andvarioushedgefunds.

•  ManagingMemberofQTSCapitalManagement,acommoditypooloperatorandtradingadvisor.

•  Author:–  Quan%ta%veTrading:HowtoBuildYourOwnAlgorithmicTradingBusiness(Wiley2009).

–  AlgorithmicTrading:WinningStrategiesandTheirRa%onale(Wiley2013).

•  Blogger:epchan.blogspot.com

AboutMe

2

Vola)lityPredic)on

•  Predic)ngvola)lity:That’sEasy!•  Successinpredic)ngrealizedvola)litydoesnotimplysuccessinpredic)ngimpliedvola)lity.

•  Canarbitragebetweenpredictedrealizedvola)lityandimpliedvola)lity.

Vola)lityPredic)on

•  “Therearemanythousandsofpapersonforecas)ngvola)lityusingahostofincreasinglysophis)cated,evenNobel-Prize-winning,sta)s)caltechniques.”–Ahmad&Wilmo\,2005.

•  Oneofthelatest,incrediblycomplicatedbutbrilliantpaper*:Gatheral,etal,2014,basedon“frac)onalBrownianMo)on”.

GARCH•  Mercifully,goodoldGARCHcanworkpre\ywellforus

prac)caltraders.•  GARCH(p,q):ifr(t)islogreturnfromt-1tot,𝑟↓𝑡 = 𝑚↓𝑡 + 𝜎↓𝑡 𝜖↓𝑡, 𝜎↓𝑡↑2 =𝜔+∑𝑖=1↑𝑝▒𝛼↓𝑖 𝜎↓𝑡−𝑖↑2  +∑𝑖=1↑𝑞▒𝛽↓𝑖 𝑟↓𝑡−𝑖↑2  where𝑚↓𝑡  is expected return, and 𝜖↓𝑡 isaGaussianrandomvariablewithzeromeanandunitvariance.•  𝜎↓𝑡↑2 isthecondi)onalvarianceof𝑟↓𝑡 .•  Simplyput:“predictedvarianceisalinearfunc)onofpast

predictedvariancesandpastrealizedsquaredreturns.”

GARCH

•  Weneedtoes)mate𝑝,𝑞,𝜔, 𝛼↓𝑖 , 𝛽↓𝑖 usingmaximumlikelihoodes)ma)on(withpenaltyonmodelcomplexity)onsometrainingdata.

•  Nottoworry:MATLAB,R,Pythonallhaveready-madetoolboxes/packagesgaloreforthis.

•  TrythisonSPY(stockindex),USO(oilfutures),GLD(gold),AAPL(singlestock),andEURUSD(currency).

GARCH:predic)veaccuracy

•  Out-of-sample(2010/11/30-2016/03/11)accuracyinpredic)ngsignof1-dayvola)litychange:– SPY:66%– USO:67%– GLD:59%– AAPL:60%– EURUSD:62%–  Ifwehavethataccuracyinpredic)ngsignof1-daypricechange,wewouldberich!

Tradingvola)lity?

•  Butwait…couldn’twetradevola)lityviaVXX,VXV,VXZ,XIV,XVZ,VXfuture,...?– NotemyomissionofVIXinabovelist.

•  Intui)vestrategy:GARCHpredictsincreaseinrealizedvola)lity→BuyVXX.Viceversa.

•  Result?

Implied≠RealizedVola)lity

•  VIXindexandrealizedvola)litymoveinsamedirec)ononly51%ofdays.– Almostzerocorrela)onbetweensignsofimpliedandrealizedvola)litychange!

•  Infact,on56%ofdayswithposi)vereturns,VIXandrealizedvola)litymoveinoppositedirec)on.– Lessdemandtobuyporoolioinsurancewhenmarketgoesup?

TradingVola)lity

•  Predictedchangeinrealizedvola)litywon’thelpuspredictchangeinimpliedvola)lity.

•  ButRV(t+1)-IV(t)(asopposedtoRV(t+1)-RV(t))can!–  RV(t+1)istheGARCH-predictedrealizedvola)lityfornextperiod.

–  IV(t)≡VIX(t)isthecurrentimpliedvola)lity•  Strategy:RV(t+1)-VIX(t)>0→BuyVXX.Viceversa.–  i.e.ExpectRV(t+1)tobebe\erpredictorofVIX(t+1)thanVIX(t)!

TradingVola)lity

•  Result:CAGR=26%,butSharpera)o=0.7only.–  (2010/11/30-2016/03/11).

•  Similarly,Ahmad&Wilmo\,2005suggested– RV(t+1)-IV(t)>0→Buyop)onanddelta-hedge)llexpiry→Profit!(Noviceversahere.)

– Supposedtoworkforanyop)ons,notjustindexop)ons,thatcanbemodeledbyBlack-Scholesequa)on.

VIXvsVXX(orVX)

•  WesuggestedtradingtheETNVXX(whichreflectsreturnsofVXfutures).

•  Wecannottradetheunderlyingvola)lityindexVIXitself.

•  TradingSPY≈tradingstockindexSPX but

TradingVXX ≉tradingvola)lityindexVIX!

VIXvsVXX(orVX)

•  VIXistheweightedaveragepriceofaporoolioofOTMSPXop)onswithtenorof23-37days.

•  Buttheporooliocomposi)oncanchangeminute-to-minute!– Seewww.cboe.com/micro/vix/vixwhite.pdf

•  E.g.ifVIX(t)=$20,andVIX(t+1)=$21,⇏poroolioweheldatthasappreciated$1byt+1.

Timedecayofop)onspremium

•  Evenifimpliedvola)lityremainsconstantin)me,marketvalueofVIXporooliowills)lldecline.– Timedecayofop)onspremium.– Nega)ve“theta”.

•  Nega)vethetaofSPXop)ons⇒nega4ve“rollreturn”ofVXXorVXfutures(whenmarketcondi)onremainsconstant).

RollreturnsofVX

•  Sign(RollreturnofVX)=Sign(VXfuture–VIXindex)isatradingsignal.

•  RollreturnofVX>0→BuyVX.Viceversa.•  Result:CAGR=60%,Sharpera)o=1.–  (2004/03/26-2015/08/28).

VXrollreturnstrategy

•  Notewherethereturnsstartedtofalter:2013.–  Justaxerthepaper(Simon&Campasano,2012)describingthisstrategywaspublished!

•  TradingofVXhavechangedpricesofSPXop)onsthemselves?

•  IsVIXs)llagoodpredictoroffuturerealizedvola)lityduetothisarbitrageac)vity?–  Ifnot,whatisitusefulfor?

Thankyouforyour)me!

www.epchan.comTwi\er:@chanep

Blog:epchan.blogspot.com