Detecting Informed Trading Activities in the Options Markets

Transcription

1 Deecing Informed Trading Aciviies in he Opions Markes Marc Chesney Universiy of Zurich and Swiss Finance Insiue Remo Crameri Universiy of Zurich and Swiss Finance Insiue Loriano Mancini EPFL and Swiss Finance Insiue July 3, 2012 For helpful commens we hank Peer Carr, Fulvio Corsi, Rüdiger Fahlenbrach, Ramo Gençay, Rajna Gibson, Michel Habib, Michael Magill, Richard Meier, Claudia Ravanelli, Ganna Reshear, and Alex Wagner. Financial suppor by he Swiss Naional Science Foundaion NCCR-FINRISK and he Research Prioriy Program Finance and Financial Markes (Universiy of Zurich) is graefully acknowledged. Corresponding auhor: Marc Chesney, Deparmen of Banking and Finance, Universiy of Zurich, Plaensrasse 32, CH-8032 Zurich, Swizerland. Tel: +41 (0) Fax: +41 (0) Deparmen of Banking and Finance, Universiy of Zurich, Plaensrasse 32, CH-8032 Zurich, Swizerland. Swiss Finance Insiue a EPFL, Quarier UNIL-Dorigny, CH-1015 Lausanne. [email protected] Elecronic copy available a: hp://ssrn.com/absrac=

2 Deecing Informed Trading Aciviies in he Opions Markes Absrac We develop a saisical approach o deec informed rading in opions markes. The mehod is applied o approximaely 9.6 million of daily opion prices from a seleced se of 31 companies. Empirical resuls sugges ha deeced opion informed rades end o cluser prior o cerain evens, ake place more in pu han call opions, generae easily large gains exceeding millions, are no conemporaneously refleced in he underlying sock price, and involve liquid opions during calm imes and cheap opions during urbulen imes. These findings are no driven by false discoveries in informed rades which are conrolled using a muliple hypohesis esing echnique. Pricing, policy, and marke efficiency implicaions of hese findings are discussed. For example, opion pricing models should accoun for all relevan curren informaion. However nearly all opion prices involved in informed rades do no show any specific reacion o large incremens in open ineres and volume. The srong movemens in deeced opions are simply due o subsequen large movemens in sock prices originaed by specific firm news. As anoher example, if some of he deeced informed rades are indeed illegal, for example originaed by insiders, i can be opimal for regulaors o expend relaively more monioring effors on he opions markes. Keywords: Massive daase, False Discovery Rae, Opions Trades, Open Ineres, Informed Trading JEL Classificaion: G12, G13, G14, G17, G34, C61, C65 1 Elecronic copy available a: hp://ssrn.com/absrac=

3 1 Inroducion Informed rading aciviies play a key role in financial markes. Asse prices will evenually reflec relevan informaion because of rading aciviies of informed invesors. This is imporan because virually any financial aciviy, such as invesmen decisions, capial allocaions or risk measuremens, is affeced by curren asse prices, which should reflec he fundamenal values of he asses. While he exisence of informed rading is well documened in he empirical lieraure, very lile is known abou he characerisics of informed rades. The goal of his paper is o provide a deail analysis in order o undersand when opion informed rading happens, under wha circumsances, and which opions are involved. Shedding ligh on hese aspecs would ulimaely enhance our undersanding of he funcioning of financial markes. Informed rading aciviies occur boh in sock and opion markes; see, e.g., Hasbrouck (1991), Easley and O Hara (1992), Easley, O Hara, and Srinivas (1998), Poeshman (2006), and Boulaov, Hendersho, and Livdan (2011). However, as discussed in Grossman (1977), Diamond and Verrechia (1987), and ohers, opion markes offer significan advanages o informed raders as opposed o sock markes. Opions offer poenial downside proecion, an alernaive way of shor selling when shoring socks is expensive or forbidden, addiional leverage which migh no be possible in sock or bond markes, and possibly more discreeness for rading on privae signals. Indeed, Pan and Poeshman (2006) repor clear evidence ha opion rading volumes predic fuure price changes. Bali and Hovakimian (2009) show ha he difference beween realized and implied volailiies of individual socks predics he crosssecional variaion of expeced reurns. Cremers and Weibaum (2010) find ha deviaions 2 Elecronic copy available a: hp://ssrn.com/absrac=

4 from pu-call pariy conain informaion abou fuure sock reurns. Yan(2011) documens a negaive relaion beween he slope of implied volailiy smile and sock reurn. While hese (and oher) sudies provide srong evidence for he exisence of opion informed rades, he analysis is sysemaically conduced a an aggregae level (e.g., exracing informaion from all curren opion prices) and canno clarify he characerisics of he individual informed rades. We develop wo saisical mehods o deec opion informed rades. The firs mehod uses only ex-ane informaion and aims o deec opion informed rades as soon as hey ake place. We look for opion rades characerized by unusually large incremens in open ineres (i.e., number of ousanding conracs) which are close o daily rading volumes. In hose cases he originaor of such ransacions is no ineresed in inraday speculaions bu has reasons for keeping her posiion for a longer period. Applying his simple rule o our daase, a sriking paern emerges. The higher he incremen in open ineres and volume he higher he fuure reurn of he corresponding opion. The relaion is nearly monoonic. This finding is consisen wih informed raders being he originaors of he large incremens in open ineres and volume. A naural quesion is wheher ruly informed invesors or simply lucky raders were behind hose large gains. To answer his quesion we develop a formal es based on muliple hypohesis esing echniques o conrol for false discoveries. The firs mehod is furher refined by considering opion hedging. We develop a nonparameric saisical es o check wheher hose opion rades are hedged wih he underlying asse or used for hedging purposes. Our second mehod o deec opion informed rading uses also ex-pos informaion and encompasses he firs mehod by adding an addiional crierion. An opion rade is idenified as informed when he incremen in open ineres and volume is 3

5 unusual, no hedged (as in he firs mehod), and generaes large opion gains. Our approach o deec opion informed rading is differen from previous mehods in a leas wo dimensions, namely conrols for false discoveries in informed rades and accouns for opion hedging. Previous sudies do no conrol for false discoveries in informed rades. In any saisical mehod, he probabiliy ha an uninformed opion rade will appear o be informed simply by chance is no zero. This misclassificaion is induced by he Type I error in hypohesis esing, as he es of opion informed rade is repeaed each day. However, his misclassificaion error can be formally quanified using muliple hypohesis esing echniques. Inuiively, uninformed opion raders should achieve zero reurn on average, while informed raders should enjoy saisically large reurns. Under he null hypohesis ha all raders are uninformed, he proporion of lucky raders depends on he size of he es and can be calculaed using opion reurns. When he difference beween he acual fracion of large reurns (due o all raders) and he expeced fracion of large reurns due o lucky raders is saisically large, he es rejecs he null hypohesis ha all raders are uninformed. We also esimae he fracion of ruly informed opions raders. Previous sudies on opion informed rading do no check wheher informed rades are acually hedged or used for hedging purposes. We develop a nonparameric es o assess wheher such hedging akes place or no. For example, when sudying long posiions in pu opions, he idea is o decompose he underlying sock buyer-iniiaed rading volume in he hedging and non-hedging componens. This decomposiion is achieved using he heoreical amoun of sock rading which would have been generaed if no opion informed rading would have occurred. Then he es rejecs he null hypohesis of absence of hedging when he hedging componen is saisically large. 4

6 We underake an exensive empirical analysis of opion informed rading. We apply he wo saisical mehods o approximaely 9.6 million of daily opions prices of 31 seleced companies mainly from airline, banking and insurance secors. Several millions of inraday sock price and volume daa are also analyzed o assess wheher an opion rade is hedged or no. The sample period spans 14 years, from January 1996 o Sepember 2009 (he firs par of our sample ends in April 2006), and our analysis is a he level of individual opion, raher han on he cross-secion of sock reurns. 1 Our main empirical findings are summarized as follows. Firs, deeced opion informed rades end o cluser prior o cerain evens such as merger or acquisiion announcemens (M&A), quarerly financial or earning relaed saemens, he erroris aacks of Sepember 11h, and firs announcemens of financial disrupions of banking and insurance companies during he Subprime financial crisis We noe ha only underaking an exensive empirical analysis his finding could emerge. Second, prior o a paricular even which will impac a paricular company, informed rading can involve more han one opion bu rarely he cheapes opion, i.e., deep ou-of-he-money and wih shores mauriy. This finding is consisen wih informed invesors rading fairly liquid opions and aemping no o immediaely reveal heir privae signals. We deec informed rades in cheap opions mainly during he Subprime crisis prior o financial disrupion announcemens. Third, he majoriy of deeced informed rades ake place in pu raher han call opions. As sock prices end o fall sharply and rise slowly when reacing o negaive and posiive news, aking 1 As we rely on saisical mehods o deec opion informed rades, hose rades will be informed only wih a cerain probabiliy. For breviy, we refer o hose rades simply as opion informed rades. Moreover, deeced informed rades migh or migh no be legal. From a legal viewpoin his sudy does no consiue proof per se of illegal aciviies. Legal proof of he laer would require rader ideniies and heir moivaions, informaion which is no conained in our daase. 5

7 long posiions in pu raher han call opions can be more profiable for informed raders. Fourh, esimaed opion gains of informed raders easily exceed several millions for a single even. Those gains are likely o be realized as hey correspond o acual rades. Finally, he underlying sock price does no display any paricular behavior on he day of he deeced opion informed rade. Only some days laer, for example when a negaive company news is released, he sock price drops generaing large gains in long pu posiions. Alhough we use publicly available daa o deec opion informed rading, i appears ha he informaion conen of such rading is no conemporaneously impounded ino he underlying sock price. As an example, our saisical mehod deecs four informed pu opion rades on EUREX beween April and June 2006 wih he underlying being EADS, he paren of plane maker Airbus. These rades precede he June 14h, 2006 announcemen ha deliveries of he superjumbo je A380 would be delayed by a furher six monhs period, causing a 26% fall in he underlying sock, and a oal gain of approximaely 8.7 million in hese opion rades. 2 Some economiss even view insider rading as informed rading and argue ha laws making insider rading illegal should be revoked. Milon Friedman, laureae of he Nobel Memorial Prize in Economics, said: You wan more insider rading, no less. You wan o give he people mos likely o have knowledge abou deficiencies of he company an incenive o make he public aware of ha. Friedman believed ha any consrain o informed raders should be removed and ha buying or selling pressure is sufficien o impound new informaion ino asse prices. While his phenomenon may occur in sock markes, our findings sugges ha i does no ake place in he opions markes. The paper is organized as follows. Secion 2 inroduces our mehod o deec opion 2 A he ime of his wriing, execuives of EADS are under invesigaion for illegal insider rading. 6

8 informed rades. Secion 3 describes he daase. Secion 4 presens he empirical resuls. Secion 5 quanifies false discoveries in opion informed rades. Secion 6 discusses various robusness checks. Secion 7 concludes. 2 Deecing Opion Informed Trades We propose wo mehods o deec opion informed rades. The firs mehod relies on a broad bu empirically successful definiion of informed rade, based on open ineres and volume, and makes use only of ex-ane informaion. The second mehod is based on a more sringen definiion of opion informed rade and uses ex-pos informaion as well. We now describe he second mehod wih he firs mehod being a special case. We define an opion informed rade as follows: C 1 ) an unusual rade in an opion conrac, C 2 ) which is made a few days before he occurrence of a specific even and generaes large gains in he following days, and C 3 ) he posiion is no hedged in he sock marke and no used for hedging purposes. These hree characerisics, C i,i = 1,2,3, lead o he following mehod o deec informed rading aciviies in opions markes: firs on each day he opion conrac wih larges incremen in open ineres (i.e., number of ousanding conracs) and volume is idenified, hen he rae of reurn and dollar gain generaed by his ransacion are calculaed, and finally i is sudied wheher hedging occurs. Opions rades which are dela hedged or used for hedging purposes are no regarded as informed rades. The firs mehod relies only on characerisics C 1 and C 3, and heir pracical implemenaion. Imporanly, boh mehods require only commonly available daases and hus can be easily applied o deec opion informed rades in various seings. 7

9 Oher definiions of informed rading are probably conceivable, as informed raders can underake various rading aciviies wih differen degrees of complexiy, spliing heir orders or jamming heir privae signals. In his paper we resric our aenion o he economically sensibleinformedradecharacerizedbyc i,i = 1,2,3,above. Besideheclearinerpreaion, his definiion of informed rade is amenable o an empirical analysis wih publicly available daa. We now explain how o deec informed rades in pu opions. The applicaion o call opions can easily be deduced. In he empirical secion, we apply boh mehods o a large daase of pu and call opions. 2.1 Firs Crierion: Incremen in Open Ineres Relaive o Volume For every pu opion k available a day we compue he difference OI k := OI k OIk 1, where OI k is is open ineres a day and := means defined as. When he opion does no exis a ime 1, is open ineres is se o zero. Since we are ineresed in unusual ransacions, only he opion wih he larges incremen in open ineres is considered X := max k K OI k (1) where K is he se of all pu opions available a day. The moivaion for using open ineres is he following. Large rading volumes can emerge under various scenarios for example when he same pu opion is raded several imes during he day or large sell orders are execued. In conras large incremens in open ineres are usually originaed by large buy orders. These incremens also imply ha oher long invesors are unwilling o close heir 8

10 posiions forcing he dealer or marke maker o issue new pu opions. Consequenly, we use large incremen in open ineres as a proxy for large buy orders. We focus on ransacions for which he corresponding volume almos coincides wih he incremen in open ineres. Le V denoe he daily rading volume corresponding o he pu opion seleced in (1). The posiive difference Z := (V X ) provides a measure of how ofen he newly issued opions are exchanged: he smaller he Z, he less he new opions are raded during he day on which hey are creaed. In ha case he originaor of such ransacions is no ineresed in inraday speculaions bu has reasons for keeping her posiion for a longer period possibly waiing for he realizaion of fuure evens. This firs crierion already allows us o idenify single ransacions as poenial candidaes forinformedrades. Leq denoeheex-anejoinhisoricalprobabiliyofobserving unusual large incremen in open ineres close o he rading volume q := P[X X,Z Z ] = 1 N N 1 {Xi X,Z i Z } (2) i=1 where P denoes he empirical probabiliy, N he lengh of he esimaion window, e.g., N = 500 rading days, and 1 {A} he indicaor funcion of even A. By consrucion, low values of q sugges ha hese ransacions were unusual. For example when q = 1/N, i means ha wha occurred on day has no precedens in he previous wo years. 2.2 Second Crierion: Relaive Reurn and Realized Gain The second crierion akes ino consideraion he ex-pos reurns and realized gains from ransacions wih a low ex-ane probabiliy q. For each day he rade wih he larges 9

11 incremen in open ineres is considered. Le r max denoe he maximum opion reurn generaed in he following wo rading weeks r max P +j P := max (3) j=1,...,10 P where P denoes he mid-quoe price of he seleced pu opion a day. When r max is unusually high, an unusual even occurs during he wo rading weeks. For he compuaion of realized gains, we consider decremens in open ineres, OI k, which occur when exercising or selling o he marke maker he pu opion. 3 Then we approximae he American pu opion value by is exercise or inrinsic value. Given our definiion of informed rade, i is likely ha on he even day he drop in he sock price is large enough o reach he exercise region making he previous approximaion exac. If opions are sold raher han exercised, our calculaion of realized gains underesimae he acual gains. Hence repored gains should be inerpreed in a conservaive manner. For breviy, we refer o decremen in open ineres as opion exercise. Also, we omi he superscrip k and whenever we refer o a specific opion we mean he one which was seleced because of is larges incremen in open ineres close o rading volume, i.e., lowes ex-ane probabiliy q. LeG denoehecorrespondingcumulaivegainsachievedhroughheexerciseofopions G := τ =+1 ((K S ) + P )( OI )1 { OI <0} (4) 3 On agivenday, opening newposiions (which increasesopen ineres) andclosingexising opions(which decreases open ineres) can off-se each oher. Hence he observed decremen in open ineres is a lower bound for acual exercised or sold opions. 10

12 where τ is such ha < τ T, wih T being he mauriy of he seleced opion. If he pu opions were opimally exercised (i.e., as soon as he underlying asse S ouches he exercise region), he payoff (K S ) + corresponds o he price of he opion a ime. Thecumulaive gainsg couldbeeasilycalculaedforevery τ T. This hashowever he disadvanage ha G could include gains which are realized hrough he exercise of opions which were issued before ime. 4 To avoid his inconsisency, he ime τ is defined as follows τ := arg max l {+1,...,T} τ := min(τ,30) l ( OI )1 { OI <0} X =+1 giving he informed rader no more han 30 days o collec her gains. In general in he square brackes he sum of negaive decremens ill ime τ will be smaller han he observed incremen in open ineres X. In ha case, we will add o G he gains realized hrough he fracion of he nex decremen in open ineres. Hence he sum of all negaive decremens in open ineres will be equal o he incremen X. Calculaing G for each day and each opion in our daabase provides informaion on wheher or no opion rades wih a low ex-ane probabiliy q generae large gains hrough exercise. Using he maximal reurn r max in (3), we can calculae he ime- ex-pos join 4 Consider for example an opion which exhibis an unusually high incremen in open ineres a ime, say OI 1 = 1000 and OI = 3000, resuling in X := OI OI 1 = Suppose ha in he days following his ransacion he level of open ineres decreases and afer h days reaches he level OI +h = 500. One should only consider he gains realized hrough exercise ill ime τ +h, where τ is such ha he sum of negaive decremens in open ineres during [+1,τ ] equals X =

13 hisorical probabiliy p of he even {X,Z,r max } p := P[X X,Z Z,r max r max ] = 1 N N i=1 1 {Xi X,Z i Z,ri max r max }. (5) The probabiliy (1 p ) can be inerpreed as a proxy for he probabiliy of informed rading in he opion marke. The higher (1 p ) he larger he opion reurn and he more unusual he incremen in open ineres close o rading volume. 2.3 Third Crierion: Hedging Opion Posiion Opion rades for which he firs wo crieria show abnormal behavior canno be immediaely classified as informed rading. I could be he case ha such ransacions were hedged by raders using he underlying asse. Wihou knowing he exac composiion of each rader s porfolio, i is no possible o assess direcly wheher each opion rade was hedged or no. We aemp o assess indirecly wheher unusual rades in pu opions are acually dela hedged using he underlying asse. The idea is o compare he heoreical oal amoun of shares bough for non-hedging purposes and he acual oal volume of buyer-iniiaed ransacions in he underlying sock. If he laer is significanly larger han he former, hen i is likely ha some of he buyer-iniiaed rades occur for hedging purposes. In he opposie case we conclude ha he new opion posiions are no hedged. One difficuly is ha he volume due o hedging is ypically a small componen of he oal buyer-iniiaed volume. Usually, when hedging occurs, newly issued opions are hedged on he same day which is our working assumpion. Hedging analyses a he level of single opion are no possible using our OpionMerics daabase. We herefore check wheher all 12

14 he newly issued opions are hedged on a specific day. Given our definiion of informed opion rades, such rades cerainly accoun for a large fracion of he newly issued opions. For each day, he oal rading volume of he underlying sock is divided ino sellerand buyer-iniiaed using inraday volumes and ransacion prices according o he Lee and Ready (1991) algorihm. 5 Then he buyer-iniiaed volume of underlying sock, V buy, is divided ino rading volume due o hedging and o non-hedging purposes, V buy,hedge and V buy,non-hedge, respecively. Le P,k be he dela of pu opion k and K P be he se of pu opion (newly issued or already exising) on day. Similarly for C,k and K C. Le α := OI P,k OI P,k 1 P,k, γ := OI C,k OI C,k 1 C,k, k K P k K C β := P,k P,k 1 OIP,k 1, δ := C,k C,k 1 OIC,k 1. k K P k K C The α and γ represen he heoreical number of shares o buy for hedging he new opions issued a day, whereas β and δ are he heoreical number of shares o buy o rebalance he porfolio of exising opions a day. Absolue changes in open ineress and delas accoun for he fac ha each opion conrac has a long and shor side ha follow opposie rading sraegies if hedging occurs. The heoreical buyer-iniiaed volume of sock a day for hedging purposes is V buy,hedge-heory := α +β +γ +δ. When he firs wo crieria of our mehod do no signal any informed rade, we ap- 5 The algorihm saes ha a rade wih a ransacion price above (below) he prevailing quoe midpoin is classified as a buyer- (seller-) iniiaed rade. A rade a he quoe midpoin is classified as seller-iniiaed if he midpoin moved down from he previous rade (down-ick), and buyer-iniiaed if he midpoin moved up (up-ick). If here was no movemen from he previous price, he previous rule is successively applied o several lags o deermine wheher a rade was buyer- or seller-iniiaed. 13

15 proximae V buy,hedge by V buy,hedge-heory. Then he amoun of sock bough for non-hedging purposes is calculaed as V buy,non-hedge = V buy V buy,hedge-heory. When informed opion rades ake place on day i, V buy,non-hedge i helasequaionbecausev buy,hedge-heory i canno be compued as in would be disored by he unhedged opion informed rades. We circumven his issue by forecasing he volume V buy,non-hedge i on day i using hisorical daa on V buy,non-hedge. The condiional disribuion of V buy,non-hedge i is esimaed using he adjused Nadaraya Wason esimaor and he boosrap mehod proposed by Hall, Wolff, and Yao (1999) F(y x) = T 1 {Y y}w (x)k H (X x) =1 T w (x)k H (X x) =1 (6) wih Y := V buy,non-hedge, X := ( r,v buy,non-hedge 1 ), K H (.) being a mulivariae kernel wih bandwidh marix H, w (x) he weighing funcion, and r he sock reurn a day ; we refer he reader o Fan and Yao (2003) for he implemenaion of (6). We can now formally es he hypohesis, H 0, ha hedging does no ake place a day i. Whenever he observed V buy i is large enough, say above he 95% quanile of he prediced disribuion of V buy,non-hedge i, i is likely ha a fracion of V buy i is due o hedging purposes. Hence we rejec H 0 a day i when V buy i > q V buy,non-hedge i 0.95, where q V buy,non-hedge i α = F 1 (α X i ) is he α-quanile of he prediced disribuion of V buy,non-hedge i esimaed using (6). The separae appendix shows ha he power of he es depends on he condiioning variables X i bu can be as high as 20% when V buy i is 20% larger han V buy,non-hedge i. We noeha henull hypohesis H 0 ofno hedging (when informedrades occur) concerns 14

16 only long posiions in newly issued pu opions. Shor posiions in he same pu opions are irrelevan for our hedging deecion mehod. I is so because he oal volume of he underlying sock is divided ino buyer- and seller-iniiaed and only he former maers when hedging long pu opions. 2.4 Deecing Opion Informed Trades Combining he Three Crieria Le k denoe he seleced informed rade a day in pu opion k. The wo mehods o deec opion informed rades can be described using he following four ses of evens: Ω 1 := {k such ha q 5%}; Ω 2 := {k such ha H 0 : non-hedging, no rejeced a day }; Ω 3 := {k such ha r max q rmax 0.90 }; Ω 4 := {k such ha G q0.98}. G The firs mehod deecs an informed opion rade when i belongs o he firs wo ses, i.e., k Ω 1 Ω 2. According o he second mehod an opion rade is informed when i belongs o all four ses, i.e., k Ω 1 Ω 2 Ω 3 Ω 4. 3 Daa We organize our daase in wo pars. The firs par includes only pu opions, he second par pu and call opions. The firs par of our daase includes 14 companies from airline, banking and various oher secors. The lis of companies includes: American Airlines (AMR), Unied Airlines (UAL), Dela Air Lines (DAL), Boeing (BA) and KLM for he airline secor; Bank of America (BAC), Ciigroup (C), J.P. Morgan (JPM), Merrill Lynch (MER) and Morgan Sanley (MWD) for he banking secor; and AT&T (ATT), Coca-Cola (KO), Hewle Packard (HP), 15

17 and Philip Morris (MO) for he remaining secors. Opions daa are from he Chicago Board Opions Exchange (CBOE) as provided by OpionMerics. The daase includes he daily cross-secion of available pu opions for each company from January 1996 o April 2006 and amouns o abou 2.1 million of opions. Opions daa for DAL and KLM were available for somewha shorer periods. Sock prices are downloaded from OpionMerics as well o avoid non-synchroniciy issues and are adjused for sock splis and spin-offs using informaion from he CRSP daabase. Inraday ransacion prices and volumes for each underlying sock price are from NYSE s Trade and Quoe (TAQ) daabase. This daabase consiss of several millions of records for each sock and is necessary o classify rading volumes in buyer- and seller-iniiaed in order o complee he analysis relaed o he hedging crierion. Discrepancies among daases have been carefully aken ino accoun when merging daabases. 6 Addiionally, we analyze pu opions on 3 European companies, Swiss Re, Munich RE and EADS, using daily daa from he EUREX provided by Deusche Bank. The second par of our daase includes 19 companies from he banking and insurance secors. Pu and call opions daa are from January 1996 o Sepember 2009, covering he recen financial crisis, and amouns o abou 7.5 million opions. The lis of American companies includes: American Inernaional Group (AIG), Bank of America Corporaion (BAC), Bear Searns Corporaion (BSC), Ciigroup (C), Fannie Mae (FNM), Freddie Mac (FRE), Goldman Sachs (GS), J.P. Morgan (JPM), Lehman Brohers (LEH), Merrill Lynch (MER), Morgan Sanley (MS), Wachovia Bank (WB) and Wells Fargo Company (WFC). 6 For example daa for J.P. Morgan from OpionMerics and TAQ do no mach. Whereas he sock volume repored in OpionMerics for he years is given by he sum of he volume of Chase Manhaan Corporaion and J.P. Morgan & Co. (Chase Manhaan Corporaion acquired J.P. Morgan & Co. in 2000), TAQ only repors he volume of J.P. Morgan & Co. Same issue was found for BankAmerica Corporaion and NaionsBank Corporaion, whose merger ook place in 1998 under he new name of Bank of America Corporaion. 16

18 Mos of hese companies belong o he lis of banks which were bailed ou and, in which, he American Treasury Deparmen invesed approximaely $200 billion hrough is Capial Purchase Program in an effor o bolser capial and suppor new lending. Opions and sock daa are from he same daabases as before, namely CBOE, TAQ, and CRSP. Furhermore we analyze 6 European banks: UBS, Credi Suisse Group (CS) and Deusche Bank (DBK) whose opions are raded on EUREX, and Socieé Générale (GL), HSBC (HSB) and BNP Paribas (BN) wih opions lised on Euronex. Opions daa as well as inraday ransacion prices and volumes for he underlying sock are obained from EUREX provided by Deusche Bank, and from EURONEXT provided by NYSE Euronex daabase. All analyzed opions are American syle. 4 Empirical Resuls The wo proposed mehods o deec opion informed rades are applied o he companies lised in he previous secion. The firs mehod, which relies only on ex-ane informaion, aims a deecing informed rades as soon as hey ake place. On average, less han 0.1% of he oal analyzed rades belongs o he se Ω 1 Ω 2 defined in Secion 2.4. As an example for AMR our firs mehod deecs 141 opion informed rades, he oal number of analyzed opions being more han 137,000. This suggess ha already he ex-ane mehod can be quie effecive in signaling informed rades. The second mehod, which relies also on ex-pos informaion, selecs a significanly smaller number of opion informed rades. For example, only 5 informed rades are deeced for AMR. Imporanly, he empirical paerns of opion informed rades based on 17

19 he wo mehods are roughly he same. For example, boh mehods sugges ha mos informed rades for AMR occur before an acquisiion announcemen in May 2000 and he 9/11 erroris aacks. Due o space consrains we can only repor he deails of ransacions seleced by he ex-pos mehod. Moreover, he separae appendix repors a deailed analysis of various deeced opion informed rades. Analyzing he firs par of our daase, 37 ransacions on he CBOE have been idenified as belonging o he se Ω 1 Ω 2 Ω 3 Ω 4 defined in Secion 2.4. Nearly all he deeced evens can be assigned o one of he following hree even caegories: merger and acquisiion (M&A) announcemens, 6 ransacions; quarerly financial/earnings relaed saemens, 14 ransacions; and he erroris aacks of Sepember 11h, 13 ransacions. 4 ransacions could no be idenified. 4 informed rades around M&A announcemens are deeced in he airline secor. These opion rades have underlying sock American Airlines and Unied Airlines. 3 informed rades ook place on May 10h and 11h, 2000, wo weeks before UAL s acquisiion of US Airways was announced. 7 Anoher informed rade ook place on January 9h, 2003 wih underlying Dela Air Lines, a few weeks before a public announcemen on January 21s, 2003 relaed o he planned alliance among Dela, Norhwes and Coninenal. In boh cases, he underlying asses crashed a he public announcemens, generaing large gains ($3 7 As repored in he New York Times ediion of May 25h, 2000, AMR was considered he company mos hreaened by he merger, explaining herefore he 17% drop in is sock in he days afer he public announcemen. According o James Goodwin, chairman and chief execuive of UAL, wo major hurdles would challenge UAL: he firs is o ge US Airways shareholders o approve his ransacion. [The second] is he regulaory work, which revolves around he Deparmen of Transporaion, he Deparmen of Jusice and he European Union. The skepicism on Wall Sree was immediaely refleced on UAL shares which declined $7.19 o $53.19 on he announcemen day. 18

20 and $1 million, respecively) hrough he exercise of hese pu opions. In he airline secor 8 ou of 15 of he seleced ransacions can be raced back o he erroris aacks of 9/11. Companies like American Airlines, Unied Airlines, Boeing and o a lesser exen Dela Air Lines and KLM seem o have been arges for informed rading aciviies in he period leading up o he aacks. The number of new pu opions issued during ha period is saisically high and he oal gains G realized by exercising hese opions amoun o more han $16 million. These findings suppor he evidence in Poeshman (2006) who also documens unusual aciviies in he opion marke before he erroris aacks. The separae appendix discusses in deails our deeced opion informed rades before 9/11. In he banking secor 14 informed rading aciviies are deeced, 6 relaed o quarerly financial/earnings announcemens, 5 o he erroris aacks of Sepember 11h, and 3 no idenified. For example he number of pu opions wih underlying sock Bank of America, Ciigroup, J.P. Morgan and Merrill Lynch issued in he days before he erroris aacks was also a an unusually high level. The realized gains from such rading sraegies are around $11 million. The las se of companies we analyze includes AT&T, Coca Cola, Hewle Packard and Philip Morris. 2 informed rades occurred before he announcemen of he M&A deal beween Coca Cola and Procer&Gamble announced on February 21s, 2001 (leading o gains of more han $2 million), and 5 ransacions preceding he publicaion of quarerly financial/earnings saemens. News relaed o earnings shorfalls, unexpeced drops in sales and producion scale backs are he mos common in his las caegory. For example 3 informed rades in pu opions wih underlying Philip Morris sock are deeced. These rades ook place a few days before hree separae legal cases agains he company seeking a oal amoun of more 19

21 han $50 million in damages for smokers deahs and inoperable lung cancer. The realized gains amouned o more han $10 million. Perhaps as expeced, no informed opion rade is deeced wih underlying he previous companies in he days leading up o he erroris aacks of Sepember 11h. Tables 1 and 2 provide furher deails on opion informed rades for he airline secor. To save space, corresponding ables for he banking secor and he las group of companies are colleced in he separae appendix. The second par of our daase focuses on he banking and insurance secors. To save space he empirical resuls are colleced in he separae appendix. Alhough he sample period spans almos 15 years, from January 1996 o Sepember 2009, he vas majoriy of deeced informed rades occur during he Subprime crisis Large movemens in underlying socks lead relaively quickly o ne profis of more han $1 million hrough opion rading. Those profis are generally larger han he ones calculaed in he firs par of our daase. Due o he rapid collapse of he financial sysem, he number of corporae and governmenal decisions made has sharply increased, giving rise o numerous poenial informaion leakages and informed rading aciviies. To provide furher insighs on opion informed rading, below we discuss in deail he case of an acquisiion announcemen in he U.S. airline secor in May Addiional cases are discussed in he separae appendix. The ex-pos mehod deecs wo pu opion informed rades on May 10h and 11h, They involved AMR and UAL. On May 10h and 11h, he number of opions issued wih srike $35andmauriyJune2000wihunderlyingAMRisverylarge: 3,374onMay10hand 5,720 he day afer (a 99.7% and 99.9% quanile of heir wo-year empirical disribuions, respecively). These ransacions correspond o hose which exhibi he sronges incremens 20

22 in open ineres during a span of five years; see upper lef graph in Figure 1 and Figure 2. On May 10h, he underlying sock had a value of $35.50 and he seleced pu was raded a $2.25. For UAL 2,505 pu opions(a 98.7% quanile of is wo-year empirical disribuion) wih srike $65 and he same mauriy as hose of AMR were issued on May 11h a he price of $5.25 when he underlying had a value of $ The marke condiions under which such ransacions ook place are sable. For example he average reurn of he sock he week before is, in boh cases, posiive and less han 0.5%. The days of he drop in he underlying sock are May 24h and May 25h, 2000, wih he firs day corresponding o he public announcemen of Unied Airline s regarding a $4.3 billion acquisiion ofus Airways. Asreporedin hemay 25h, 2000ediion ofhe New York Times, shares of UAL and hose of is main rivals crashed (for deails see Foonoe7). The sock price of AMR dropped o $27.13 ( 23.59% of value losses when compared o he sock price on May 11h) increasing he value of he pu opions o $7.88 (resuling in a reurn of 250% in wo rading weeks). The same impac can be found for UAL: he sock price afer he public announcemen dropped o $52.50 ( 14.63% when compared o he value on May 11h) raising he pu s value o $12.63 (corresponding o a reurn of 140% in wo rading weeks). In he case of AMR, he decline in he underlying sock can be seen in Figure 2, where he opion reurn largely increased. On he day of he public announcemen 4,735 pu opions of AMR were exercised; see Figure 2. Afer his large decremen in open ineres, 1,494 and 1,376 addiional pu opions were exercised in he following wo days respecively (refleced in addiional drops in open ineress in Figure 2). The unusual incremens in open ineres observed on May 10h and May 11h are herefore off se by he exercise of opions when he underlying crashed. The 21

23 corresponding gains G from his sraegy are more han $1.6 million wihin wo rading weeks. These are graphically shown in he lower graph in Figure 1, from which we can see how fas hese gains were realized. In he case of UAL similar conclusions can be reached; see Tables 1 and 2. Based on hese rades, a oal gain of almos $3 million was realized wihin a few rading weeks using opions wih underlying AMR and UAL. The non-hedging hypohesis canno be rejeced suggesing ha such rades are unhedged opion posiions. 5 Conrolling False Discoveries in Opion Informed Trades Any saisical mehod can generae false discoveries in informed rades. In oher words, he probabiliy ha an opion rade can saisfy various crieria simply by chance is no zero. Conrolling for false discovery is hen an imporan ask which allows o separae ruly informed raders wih high gains from uninformed raders which luckily achieved also high gains. To separae he wo groups of raders we use a muliple hypohesis esing echnique. Recenly, Barras, Scaille, and Wermers (2010) adoped a similar approach o discriminae beween skilled and lucky muual fund managers based on fund performance. Suppose we observe opion reurns generaed by M raders characerized by differen degrees of informaion, ranging from highly accurae privae informaion o no informaion (or possibly even misleading informaion). Le π 0 denoe he fracion of uninformed raders andδ m,m = 1,...,M, heexpeced reurngeneraedbyraderm. Under henull hypohesis all opion raders are uninformed. Formally, his muliple hypohesis reads H 0,m : δ m = 0,m = 1,...,M. Each hypohesis is esed a significance level γ (e.g., 10%) using a woside -saisic, i.e., H 0,m is rejeced when he corresponding -saisic is eiher below he 22

24 5h or above he 95h perceniles of is disribuion under H 0,m. When he null hypohesis is rue, all p-values based on -saisics are uniformly disribued beween 0 and 1. When he null hypohesis is no rue, large opion reurns and corresponding low p-values are generaed by boh informed and lucky raders. Under such alernaive hypohesis, denoe E[S γ + ] he expeced fracion of p-values below γ/2 corresponding o posiive and significan -saisics. The key sep is o adjus E[S γ + ] for he presence of lucky raders. The expeced fracion of ruly informed raders is E[T γ + ] = E[S+ γ ] π 0γ/2. Noe ha under he null hypohesis all raders are uninformed, i.e., π 0 = 1, and half he size of he es γ/2 = E[S γ + ], hence E[T γ + ] = 0. The las sep is he esimaion of π 0. Inuiively, large p-values correspond o esimaed δ m no saisically away from zero and hence generaed by uninformed raders. The fracion of p-values above a cerain hreshold λ is exrapolaed over he inerval [0, 1]. Muliplying his fracion of p-values by 1/(1 λ) provides an esimae of π 0. This esimaion approach has been developed by Sorey (2002); see, e.g., Romano, Shaikh, and Wolf (2008) for a review. We choose λ using he daa-driven approach in Barras, Scaille, and Wermers (2010). The observed fracion of posiive and significan -saisics provides an unbiased esimae of E[S γ + ]. Obviously, we do no observe direcly opion reurns achieved by raders wih various degrees of privae informaion. Consisenly wih our deecion mehod, we use he ex-ane hisorical probabiliy q of observing unusual incremens in open ineres and volume as a proxy for privae informaion. The working assumpion is ha he smaller such probabiliy, he higher he degree of privae informaion of he opion rader. Indeed, as shown below, q urns ou o be an accurae proxy for privae informaion as refleced in opion reurns. For every underlying asse, for every day, and for every opion rade k = 1,...,K 23

25 in our sample, we compue he corresponding ex-ane hisorical probabiliy q k as in (2) of observing an incremen OI k in open ineres and disance Z k := (V k OI k ) beween rading volume and incremen in open ineres. The fuure reurn r k of opion s rade k is compued by considering gains hrough subsequen exercise, afer day, according o (4). By definiion, he probabiliy q k lies in he inerval [0,1]. We sor in ascending order all q k and divide such uni inerval ino M = 1,000 subinervals I 1,...,I M such ha in every subinerval he same number of q k is available. Then we group all opion rades q k and corresponding reurns r k according o which subinerval I m hey belong. This procedure allows us o consruc M hypoheical opion raders, each one of hem characerized by a differen degree of privae informaion and opion reurns. In subinervals I m,m = 1,...,M, he lower m, he more informed he rader is, and herefore, he more likely i is ha she will generae large posiive reurn r k. Wihin each subinerval I m, we regress unadjused annualized opion reurns r k on a subinerval-specific consan δ m, esimaing he expeced reurn of rader m. 8 As an example Figure 3 shows esimaed δ m for American Airlines. Esimaes for he remaining companies are similar. A sriking paern emerges. The smaller he m, he higher he esimaed δ m. The relaion is nearly monoonic. Moreover, for small m, he esimaed δ m are posiive and significan, whereas for increasing m, δ m becomes saisically indisinguishable from zero. This finding suggess ha q k is indeed an accurae proxy for privae informaion as refleced in opion reurns. 8 In he regression, we do no adjus opion reurns for marke reurn or any oher variable because he focus is on he abiliy of he opion rader o generae large reurns, including hose reurns based on predicing fuure marke or oher variable movemens. In order o make leas square esimaion somehow more robus we winsorize negaive reurns a 5%. The impac of winsorizing on he false discovery rae is virually negligible. 24

26 We briefly discuss now he esimaes of false discovery raes for American Airlines and Ciigroup. For he remaining companies, similar resuls have been found. Because of space consrains, figures and ables are no repored bu available upon reques from he auhors. For AMR, he oal number of analyzed opion rades amouns a 137,000, implying ha each regression coefficien δ m has been compued by relaying on 137 opion reurns r k. The expeced fracion of ruly informed raders has been esimaed o be E[T + ] = 9.8% (wih sandard error 1.15%, opimal λ = 0.65, and γ = 0.11), corresponding o 98 raders. As he ex-ane procedure deecs 141 rades for AMR, he es resul suggess ha some of hese rades may be acually uninformed. In conras, he ex-pos procedure is more conservaive and deecs only 5 informed rades, which implies ha hese rades are mos likely informed. For he case of Ciigroup, opion rades amoun a 246,000 and he esimaed fracion of ruly informed raders E[T + ] = 10.6% (wih sandard error 1.09%, opimal λ = 0.612, and γ = 0.07), corresponding o 106 raders. The ex-pos mehod deecs only 2 informed opion rades. Thus even in his case he deecion procedure is conservaive and deeced rades are mos likely informed. For he remaining companies we found similar resuls. We noe ha he probabiliy q k can be used o implemen a simple rading sraegy as depends only on informaion available on day. Low values of q end o predic fuure drops of he underlying sock providing a signal when o ener long posiions in pu opions and generaing he reurn r k. As can be seen from Figure 3, enering long pu posiions when q k < 0.2% easily generaes annual reurns above 5% on average. 25

27 6 Robusness Checks The inpu parameers in our deecion procedure are: he lengh N of he esimaion window, chosen o be N = 500 rading days, used for he compuaion of he ex-ane probabiliy q, he condiional disribuion of V buy,non-hedge, and he quaniles q rmax α and q G α ; he ime period afer he ransacion day used for he compuaion of r max, chosen o be 10 rading days; he ime horizon τ used for he calculaion of he gains G, chosen o be 30 rading days; he quanile levels α and α in q rmax α and q G α used for he compuaion of he ses Ω 3 and Ω 4, chosen o be α = 90% and α = 98%; he probabiliy level used o selec rades belonging o he se Ω 1, chosen o be 5%. In wha follows we se he inpu parameers o differen values and we repea all previous analysis for all companies. To save space we repor only some of he resuls and for a few companies giving a sense of he robusness of our resuls. Addiional resuls are available from he auhors upon reques. When varying he lengh of he esimaion window N beween 200 and 1,000, (all oher parameers being unchanged) he number of seleced ransacions does no change significanly. For example in he case of AMR, we seleced 5 informed rades when considering he las wo rading years (N = 500 days); for N [200,1000] he number of deeced informed rades ranges beween 4 and 6; for UAL, we deeced 2 informed rades when considering he las wo rading years (N = 500 days); his number remains unchanged wih respec o he original choice for N > 450 and decreases by one when N [200,450]. In he case of BAC and AT&T, he deviaion from he original number of seleced rades is less han 2. Wih respec o he choice of he ime period used for he compuaion of r max and τ, our resuls are also robus. We le he lengh of he firs period vary in he range [1,30] days and he 26

28 second one in [1,40] days. In he case of AMR, he number of ransacions ranges from 2 o 8, being herefore cenered around he original number and wih a small deviaion from i. For UAL, he corresponding range is from 1 o 4, for BAC from 2 o 8 and for AT&T from 1 o 6. The number of deeced rades is obviously a decreasing funcion of α and α (all oher parameers being unchanged). In he case of AMR, when {α,α } [0.85,0.95] [0.96,1], he number of ransacions seleced does no exceed 15. For UAL, he number of seleced rades varies beween 1 and 10, for BAC beween 5 and 25, and for AT&T beween 1 and 18. Finally, wih respec o he probabiliy level used o deermine he se Ω 1, our findings are very robus aswell. When increasing he level from1%o 10%, he number ofrades seleced for AMR varies beween 1 and 6; for UAL i ranges beween 2 o 4, for BAC and AT&T from 1 o 7. We simulaneously changed several parameers and found ha he number of deeced ransacions does no change significanly and in almos all cases in seps of one. We recall ha approximaely 9.6 million of opions are analyzed. Based on hese resuls, we conclude ha our findings are robus. 7 Conclusion We develop wo saisical mehods o deec informed rading aciviies in he opions markes. We apply hese mehods o a large daase uncovering various feaures of opion informed rading. Deeced opion informed rades end o cluser prior o cerain evens (such as acquisiion or financial disrupion announcemens), involve ofen liquid opions (which is consisen wih informed raders aemping no o immediaely reveal heir privae signals), ake place more in pu han call opions (which is consisen wih he asymmeric 27

29 reacion of sock prices o negaive and posiive news), generae easily large gains exceeding millions (which is likely a conservaive esimae), and are no conemporaneously refleced in he underlying sock price (which has obvious implicaions for rading sraegies). These findings are no driven by false discoveries in informed rades which are conrolled using a muliple hypohesis esing echnique. Our findings have policy, pricing, and marke efficiency implicaions. If some of he deeced informed rades are indeed illegal, for example originaed by insiders, i can be opimal for regulaors o expend relaively more monioring effors on he opions markes. Pricing models should accoun for all relevan curren informaion. However nearly all opion prices (and underlying asses) involved in informed rades do no show any specific reacion o large incremens in open ineres and volume. The srong movemens in deeced opions are simply due o subsequen large movemens in sock prices originaed by specific firm news. Finally, our findings sugges ha cerain incremens in open ineres and volume may predic large price movemens and simple opion rading sraegies can generae large reurns. Furher research is necessary o assess wheher hose reurns are ruly abnormal, quesioning marke efficiency, or raher reflec compensaion for hidden risk facors. Analyzing oher aspecs of opion informed rading or using differen saisical ools o deec such rading aciviies appear o us as ineresing direcions for fuure research. 28

30 29 Summary of Airline Secor Jan Apr 2006 Day Id S/K τ OI 1 OI q OI OI o Vol r max τ 2 G τ 3 %ex. American Airlines (AMR) Jan Apr 2006 q p-value 1 p 10 May % % 9 906, % May % % 10 1,647, % Aug % % 7 662, % Sep % % 2 1,179, % Aug % % 8 575, % Unied Airlines (UAL) Jan Jan May % % 10 1,156, % Sep % % 7 1,980, % Dela Air Lines (DAL) Jan May 2005 *1 Oc % % 6 537, % Aug % % 9 328, % Sep % % 7 331, % Jan % % 9 1,054, % Boeing (BA) Jan Apr Nov % % 7 883, % Aug % % 10 1,972, % Sep % % 8 1,805, % Sep % % 7 2,704, % *7 Sep % % 6 5,775, % *17 Sep % % 4 2,663, % KLM Jan Nov Sep % % % Table 1: This able shows day on which he ransacion ook place, Day; idenificaion number of he pu opion, Id; moneyness, i.e., sock price divided by srike price, S/K; ime-o-mauriy, τ; level of open ineres he day before he informed rade, OI 1 ; incremen in open ineres from day 1 o day, OI ; is quanile wih respec o is empirical disribuion compued over he las wo years, q OI ; oal incremen in open ineres, i.e., when considering all he available opions a day and no only he ones which had he highes incremen, OI o ; corresponding volume, Vol ; maximum reurn realized by he seleced opion during he wo-week period following he ransacion day, r max ; number of days beween ransacion day and when his maximum reurn occurs, τ 2 ; gains realized hrough he exercise of he opion issued a ime as in (4), G ; minimum beween he number of days (saring from he ransacion day) needed for he exercise of OI and 30 days, τ 3 ; percenage of OI exercised wihin he firs 30 days afer he ransacion, %ex.; ex-ane probabiliy in (2), q ; p-value of he hypohesis ha dela hedging does no ake place a ime, p-value; proxy for he probabiliy of informed rading in (5), 1 p.

31 30 Summary of Airline Secor Jan Apr 2006 Day of ransacion Marke condiion Reurn Crash in sock Even s descripion American Airlines (AMR) Jan Apr May % 17.6% 24/25 May 00 Announcemen 24 May 00: Airline Deal UAL s acquisiion of US Airways 11 May % 17.6% 24/25 May 00 Announcemen 24 May 00: Airline Deal UAL s acquisiion of US Airways 31 Aug % 39.4% 17 Sep 01 9/11 Terroris aacks in New York 10 Sep % 39.4% 17 Sep 01 9/11 Terroris aacks in New York 24 Aug % 5.3% 30 Aug 05 Augus 05: Hurricane Karina, inerruped producion on he gulf coas, je fuel prices Unied Airlines (UAL) Jan Jan May % 12% 24 May 00 Announcemen 24 May 00: Airline Deal UAL s acquisiion of US Airways 6 Sep % 43.2% 17 Sep 01 9/11 Terroris aacks in New York Dela Air Lines (DAL) Jan May 2005 *1 Oc % 11.4% 07/08 Oc 98 No idenified 29 Aug % 44.6% 17 Sep 01 9/11 Terroris aacks in New York 19 Sep % 24.4% 27 Sep 02 Announcemen 27 Sep 02: Expeced loss for 3rd quarer 9 Jan % 15.7% 21/22 Jan 03 Announcemen 21 Jan 03: Resricions on planned alliance of Dela, Norhwes and Coninenal Boeing (BA) Jan Apr Nov % 22.0% 02/03 Dec 98 Announcemen 02 Dec 98: producion scale back and cu in work forces 29 Aug % 25.0% 17/18 Sep 01 9/11 Terroris aacks in New York 5 Sep % 25.0% 17/18 Sep 01 9/11 Terroris aacks in New York 6 Sep % 25.0% 17/18 Sep 01 9/11 Terroris aacks in New York *7 Sep % 25.0% 17/18 Sep 01 9/11 Terroris aacks in New York *17 Sep % 25.0% 17/18 Sep 01 9/11 Terroris aacks in New York KLM Jan Nov Sep % 31.6% 17/18 Sep 01 9/11 Terroris aacks in New York Table 2: This able shows day on which he ransacion ook place, Day of ransacion; marke condiion a day measured by he average reurn of he underlying sock during he las wo rading weeks, Marke condiion; minimum reurn of he underlying sock during he wo-week period following he ransacion day, Reurn (comparable wih r max ); day when he underlying sock drops, Crash in sock; shor descripion of he even and why he sock drops, Even s descripion. * means ha he hypohesis of non-hedging can be rejeced a a 5% level.

32 6000 Analysis of Pus Jan 1997 Dec x 104 Analysis of Pus Jan 1997 Jan corresponding V May May 2000 corresponding V Sep Aug max OI max OI x 10 4 Gains G 2 x Cumulaive gains G May May Aug Sep Aug ime Figure 1: Upper graphs show on he x-axis maximal daily incremen in open ineres across all pu opions wih underlying American Airlines (AMR), and on he y-axis he corresponding rading volume. Upper-lef graph covers he period January 1997 December 2001, upperrigh graphs he period January 1997 January Lower graph shows cumulaive gains G in USD as in equaion (4) for deeced opion informed rade on AMR. Gains correspond o hose realized by daily exercising/selling he opions. 31

33 Open Ineres Volume 10 May May Open Ineres/Volume Reurn on he opion invesmen 10 May May Reurn on he opion invesmen Apr00 May00 Jun00 Jul00 0 Figure 2: Seleced pu opion for informed rading wih underlying sock American Airlines (AMR) before he Unied Airlines (UAL) announcemen of $4.3 billion acquisiion of US Airways in May The solid line shows he daily dynamic of open ineres, he bars show he corresponding rading volume (lef y-axis) and he dash-do line he opion reurn (righ y-axis). The empy circle is he day of he ransacion, he filled circle is he day of he announcemen (parially covered by he highes bar). This pu opion had a srike of $35 and maured a he end of June

34 q q sa p value Frequency q q p value Figure 3: False Discovery Rae for American Airlines. The upper-lef graph shows on he x-axis he ex-ane probabiliy q, he righ-end poin in each subinerval I m, and on he y-axis he corresponding average opion reurns δ m associaed o he mh opion rader. The upper-righ graph shows he same quaniies when 0 q Dashed-doed lines represen 95% confidence inervals for δ m. The lower graphs, from lef o righ, show -saisics of opion reurns associaed o he M opion raders for he null hypohesis H 0 : δ m = 0,m = 1,...,M, corresponding p-values, and hisogram of p-values, respecively.

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