An Investigation into the Interdependency of the Volatility of Technology Stocks

Transcription

1 An Invesigaion ino he Inerdependency of he Volailiy of Technology Socks Zoravar Lamba Adviser: Prof. George Tauchen Spring 009, Duke Universiy The Duke Communiy Sandard was upheld in he compleion of his repor. This repor is submied in parial compleion of he Duke Universiy Deparmen of Economics requiremens for graduaion wih disincion.

2 ABSTRACT This paper examines he conemporaneous and dynamic relaionships beween he volailiies of he echnology socks in he S&P 100 index. Facor analysis and heerogeneous auoregressive regressions are used o examine conemporaneous and dynamic, iner-emporal relaionships, respecively. Boh echniques uilize high frequency daa by measuring sock prices every 5 minues from We find ha a srong indusry effec explains he bulk of he volailiy of he echnology socks and ha he marke s volailiy has very low correlaion wih he socks volailiy. Furher, we find he marke s volailiy has insignifican predicive conen for he socks volailiy. The socks hemselves conain large quaniies of unique predicive conen for each oher s volailiies.

3 ACKNOWLEDGEMENTS Principal adviser: Prof. George Tauchen Research guidance also provided by: o Prof. Tim Bollerslev o Prof. Bjorn Eraker 3

4 1. INTRODUCTION Undersanding he naure of equiy volailiy is of paramoun imporance o he financial services indusry. Many derivaive securiies and sock opions in paricular are priced based upon expecaions of fuure volailiy. Furhermore, in ligh of he recen chaos in he markes, effecive risk managemen has become more criical han ever before, which can only be achieved wih reliable esimaes of volailiy. Financial insiuions are required o use a sandard measure called Value a Risk (VaR), he esimaed possible loss o he insiuion over he upcoming en days ha is so severe ha i is expeced o occur only 1% of he ime (Hull 19). This measure is updaed daily and is used o decide he amoun of capial ha should be se aside o absorb any shocks or losses. The calculaion of VaR requires accurae and reliable informaion on he volailiy of various underlying asses and securiies. Moreover, he developmen of financial heory also exensively uilizes asse volailiy forecass. Thus, a clearer picure of equiy volailiy can be very beneficial and useful. In his paper, he volailiy of socks in he echnology secor will be examined. Convenional wisdom on he componens of sock reurns (from which volailiy is measured) suggess ha here is a sysemaic componen o reurns and an idiosyncraic, sock-specific componen. The sysemaic componen indicaes how he reurn on a sock changes due o changes in he overall marke and his saisic is known as he sock s bea (Sock 1). Table 1 shows he bea for every sock analyzed in his paper he range of he beas is around 1.00 o This means hey should all exhibi higher reurns and volailiy when he marke s reurn and volailiy increase, and 4

5 vice versa. We es his convenional wisdom by examining he conemporaneous relaionship beween he socks volailiy and he marke s volailiy using facor analysis. This analysis also enables us o explore how well he volailiies of differen series correlae wih each oher. Anoher benefi of facor analysis is ha i deermines how many common facors migh explain he socks volailiies. This would be useful in narrowing down he sources of volailiy in he daase being examined. Furher, we examine he dynamic, causal relaionships among he socks volailiies and he marke s volailiy by esing how well hey forecas each oher. I has been well esablished over he las several decades ha sock reurns follow a random walk and are very difficul o predic (Sock 665); however, forecasing volailiy is a differen sory alogeher. Bollerslev (006) explains ha volailiy appears in clusers over ime and ha asses do no have consan volailiy (variance) over ime, as was previously believed. Volailiy clusers over ime are summarized succincly in Bollerslev s lecure by he following quoaion from Mandelbro (1963): large changes end o be followed by large changes, of eiher sign, and small changes end o be followed by small changes Thus, by examining he rends in an asse s volailiy, one can expec o make reasonable and educaed projecions regarding he asse s volailiy in he fuure (Sock 665). We examine how well he socks volailiies and he marke s volailiy forecas each oher by conducing heerogeneous auoregressive (HAR) regressions (Corsi 003) and draw conclusions abou each sock s predicive power by examining he resuls of he appropriae Granger Causaliy Tes (Granger 1969). As will be seen, Granger Causaliy 5

6 is differen from, bu relaed o, he normal inerpreaion of causaliy and he oucome of a Granger Causaliy Tes shows us how much predicive power a sock s volailiy has for anoher sock s volailiy, or for he marke s volailiy, and vice versa. Neiher of hese wo echniques has been employed using high frequency daa before. As described in Andersen, Bollerslev, Diebold, and Labys (003), forecasing volailiy wih high-frequency daa provides beer resuls han does forecasing wih lower frequency daa. They also find Realized Variance, defined in Secion, o be he bes measure of volailiy for making forecass. The res of he paper coninues as follows. Secion explains he model of volailiy (realized variance) uilized here. Secion 3 conains imporan noes on he daa used in he paper boh he source of he daa, as well as daa preparaion are described. Secions 4 and 5 discuss he facor analysis and HAR-RV regressions, respecively. Secions 6 and 7 conain deailed discussions and inerpreaions of he resuls of facor analysis and HAR regressions, respecively. Secion 8 summarizes he paper and highlighs he key resuls.. A ROBUST MODEL OF VOLATILITY We model volailiy wih an approach ha uilizes he benefis of high frequency daa and hereby conains more informaion han measuremens aken a a large inerval, such as only once a day or once a week. Inra-day geomeric reurns hemselves are given by: 6

7 r, j j j 1 = p( 1 + ) p( 1 + ) (1), M M where p is he log price, represens he day, j = 1,,,M, and M = 78 is he sampling frequency. A sampling frequency of 78 corresponds o five-minue reurns. The nex secion explains in more deail ha five-minue reurns are being uilized in order o minimize marke microsrucure noise while reaining he benefis of high frequency daa. Daily realized variance is given by he formula: M RV = r j= 1, j (), where j, M, and r,j are all he same as for Equaion (1) above. Thus, a day s realized variance is he sum of he squared log reurns for ha day. Andersen and Bollerslev (1998) illusrae ha realized variance converges o he inegraed variance plus he jump componen as he ime beween observaions approaches zero: lim M RV = 1 σ ( s) ds + κ ( s) (3). 1 < s The firs erm in Equaion (3) represens he inegraed variance of he coninuous process and he second represens squared discree jumps. This limi is also he definiion of quadraic variaion. Therefore, realized variance consisenly esimaes quadraic variaion, as i accouns for boh he coninuous par of variaion and he discree jump componens in variaion. The nex par of his secion explains how marke microsrucure noise can cause significan disorion in esimaing saisics, such as a sock s volailiy. 7

8 Sock prices are frequenly modeled as he discouned presen value of heir fuure earnings, wih he assumpion ha he sock s expeced Earnings Per Share and expeced Dividend Per Share boh grow a a consan rae (Levy 498). These also resul in he share price growing a he same consan rae g. If he discoun rae, i.e., he required reurn according o he Capial Asse Pricing Model, is represened by k, hen he curren price P 0 of a share is given by: P 0 = = i 0 E( Di) D0(1 + g) = i k ( k g) (4). Since obaining his price requires calculaing he sum of an infinie series, even a small change in he marke s assessmen of he discoun rae can resul in a significan effec on he esimaed price and cause i o be subsanially differen from he sock s fundamenal price (Levy 501). The discoun rae can change over ime as i is highly firm-specific and depends upon he firm s asses and liabiliies, which are no consan over ime. Furhermore, he growh rae g can also cause major changes in a firm s worh, as he above equaion suggess. While he assumpion is ha he growh rae remains consan, as wih he discoun rae, his is frequenly no borne ou in realiy. In general, firms will exhibi impressive growh in heir infancy, bu as heir size increases, i becomes increasingly difficul o susain previous levels of growh. This illusraes how he heoreical price of a sock can differ from is observed price. Moreover, marke fricions such as bid-ask bounce and order imbalance can also cause a sock s observed price o deviae from is inrinsic value. This deviaion is called marke microsrucure noise and is represened as he error erm ε in he following: 8

9 * p = p( ) + ε (5), where p() is he logarihm of he sock s fundamenal price and p * is he observed price a ime. We shall see presenly how he derimenal effecs of his noise can be minimized. 3. DATA As saed in he inroducion, he objecive is o analyze he volailiy of he socks in he echnology secor. The echnology socks wih he larges marke capializaions represen a good sample o examine. They have high rade volumes and so are relaively more liquid and high-frequency daa for hem are readily available. All daa were purchased from hp://price-daa.com. The daa used were available a one-minue inervals; however, sampling a ha inerval did no appear o be very useful, as he microsrucure noise clouded he rue picure. Sampling a inervals larger han five-minues would cerainly reduce he noise even furher; however, i also resuled in he loss of enough of he informaion conained in he daase, hereby nullifying he benefis of uilizing high frequency daa. Thus, sampling reurns a a frequency of five-minue inervals provides a good balance beween he wo conrasing forces of looking for higher frequency daa o maximize he informaion conained in he daa and looking for lower frequency daa o minimize he microsrucure noise. 9

10 The socks seleced o represen he echnology secor, broadly defined, are as follows. Cisco (CSCO) is primarily engaged in producion and disribuion of neworking and communicaion devices. Dell (DELL) focuses mosly on providing deskops and lapops o privae consumers and businesses. EMC Corporaion (EMC) provides servers and oher soluions o he problem of soring enormous quaniies of daa. Google (GOOG) is he world s preeminen provider of inerne search services and has also expanded ino oher consumer-oriened applicaions such as web-based . Hewle- Packard (HPQ) provides producs and services similar o Dell, in addiion o echnology inegraion consuling and ousourcing services. IBM (IBM) used o be in he personal compuing business unil 004, when i sold is PC business and brand o Lenovo. Now IBM focuses on all aspecs of business compuing, from servers and neworking hardware and sofware o business process consuling and ousourcing services. Inel (INTC) is he world s larges microprocessor manufacurer. Microsof (MSFT) is he world s larges sofware corporaion, providing an exensive suie of producs for boh corporae users and he general consumer. Oracle (ORCL) is he world s second larges sofware corporaion and is bes known for is daabase managemen and enerprise resource planning producs. Texas Insrumens (TXN) manufacures educaional echnology producs and microprocessors. Xerox (XRX) provides all hardware and sofware needed for documen reproducion and ransmission. These represen all he echnology socks in he S&P 100, wih he excepion of Apple (AAPL), as reliable daa for i could no be obained. Daa for Google are only available from he ime of is Iniial Public Offering in 004, bu for all he oher socks, 10

11 daa were available from April 1997 o January 008. Thus, we firs consider he daa for all he socks oher han Google, hen laer incorporae Google daa from he poin possible and see wheher including Google changes any resuls or conclusions. The S&P 500 fuures daa, which is used o represen he marke, conained some shorened rading days (i.e., days wih fewer han he required 78 five-minue reurns). A olerance limi of 70 was se for he required number of reurns. Days wih fewer han 70 five-minue reurns were removed from he enire daase, including from he hisory of each sock, prior o any calculaions. In addiion, for he facor analysis secion, insead of he daily realized variaions, heir logs have been used. This scales he resuls as shown in Equaion (3), reurns are squared o measure realized variaion, which can really exaggerae ouliers and skew he daa. 4. METHOD ONE: FACTOR ANALYSIS This secion is divided ino hree subsecions Secion 4.1 provides some hisorical conex and describes he siuaions in which one migh chose conduc facor analysis; Secion 4. explains how facor analysis acually works and how is resuls are inerpreed; finally, Secion 4.3 describes some mehods o rearrange he resuls of a regular facor analysis, which can make inerpreing he resuls of a facor analysis easier. 11

12 4.1 The purpose of Facor Analysis The echnique of facor analysis, while iniially pioneered for he domain of psychology in 1905 by Spearman, has a wide range of applicaions in economics and finance. Gorsuch (1976) saes ha here are hree major purposes of employing facor analysis: firs, ha he number of variables for furher research can be minimized while also maximizing he amoun of informaion in he analysis ; second, ha i enables us deermine manageable hypoheses when faced wih a huge amoun of raw daa; and hird, ha i enables us o es preexising hypoheses abou some daa, i.e., wheher or no i possesses cerain qualiies or disincions. Thus, i would be a good fi for examining he parallel variables being sudied here, paricularly since we do no know wha causal relaionships are a play here. 4. Theory, Technique, and Inerpreaions Nex is an examinaion of exacly wha facor analysis is, precisely wha resuls i provides, and how hey are o be inerpreed. Kim and Mueller (1978a) explain ha facor analysis involves recreaing he variables o be analyzed by aking linear combinaions of he fewes possible common facors, while minimizing he informaion los wih his daa reducion. The following equaion is insrucive: Y β Z β Z + i = 1i n ni 1 (6). Here, Y i represens a variable being examined by he facor analysis, Z ni represens a facor generaed by he analysis, β i represens he loading on he facor (i.e., he correlaion beween he dependen variable Y i and he facor Z ni ), and ε is he error erm. ε 1

13 In a regression, he loadings would be inerpreed as he regression coefficiens on each of he explanaory variables; however, in a facor analysis, he explanaory variables are rescaled as necessary o enable he inerpreaion of loadings as correlaion coefficiens. A facor loading of 0.7 or greaer is considered o be a benchmark figure for judging wheher a variable and a facor are srongly correlaed (SaaCorp 005). Equaion (6) appears o be similar o a regression; however, he key difference is ha he facors, unlike he explanaory variables in a regression, are no direcly observed. This is why i is ofen a challenge o produce appropriae and meaningful inerpreaions from a facor analysis. In addiion, resuls can be furher confounded, as facors could have significan correlaion, which is no consisen wih he base model assumpion ha here is no iner-facor correlaion. Garson explains ha such an analysis can help in deciphering he laen srucure of he variables being analyzed. In oher words, i provides informaion abou he srucure and make-up of a se of variables ha would no oherwise be apparen when analyzing a large quaniy of daa, i is useful o see how many differen facors explain mos of he variance wihin he daase. Each facor is associaed wih an eigenvalue ha indicaes how much of he oal overall variance ha paricular facor explains. Facors wih negaive eigenvalues can be compleely disregarded and in general, he greaer is eigenvalue, he greaer he variance explained by a paricular facor (Garson). Furhermore, facors wih eigenvalues very close o zero may also be ignored. In addiion, i is criical o undersand he conceps of Communaliy and Uniqueness. They are relaed as indicaed below: Uniqueness = ( 1 Communaliy) (7). 13

14 Uniqueness indicaes he amoun of a variable s variaion ha is no well explained by he common facors generaed by he facor analysis. Communaliy, as Equaion (5) suggess, is he measure of he percen of a variable s variance ha is well explained by he common facors. Naurally, high communaliy corresponds o low uniqueness, and vice versa. If a variable s uniqueness is below 0.6 (making he communaliy greaer han 0.4), hen we may say ha is variance is well explained by he common facors (SaaCorp 005). 4.3 Facor Roaions Facor Roaions can make inerpreing facor analysis resuls easier. There are wo primary echniques for roaing facors orhogonal and oblique. An orhogonal roaion enails roaing all he facors by a fixed angle, hereby keeping hem uncorrelaed, as before (Abdi 003). The goal is o obain facors wih eiher really high or really low loadings. This would heoreically make i easy o idenify which facors associae mos closely wih which variables. For an oblique roaion, he facors may be roaed by differen angles wihin he facor space, which usually leads o correlaed facors. An oblique roaion is open o meaningful inerpreaion only if he common facors ha i produces have low o medium correlaion (Garson). If he correlaion beween wo facors were oo high, hen hey would be beer inerpreed as only one facor (Abdi 003). In many cases, an oblique roaion provides new insigh ino he daa because allowing differen facors o be roaed by differen angles permis combinaions ha would no be possible under he rigidiy of an orhogonal roaion. 14

15 This concludes he discussion of he echnique o be uilized for examining conemporaneous relaionships beween he socks realized variances. The nex secion explains he echnique for sudying he dynamic relaionships beween he socks realized variances. 5. METHOD TWO: HAR-RV REGRESSIONS This secion is divided ino 3 subsecions Secion 5.1 gives a brief inroducion o ime series analysis; Secion 5. explains heerogeneous auoregressive realized variance regressions, and finally, Secion 5.3 provides he raionale behind significance ess o be conduced on hese regressions, along wih a deailed explanaion of how hese ess are acually conduced and heir resuls inerpreed. 5.1 An Inroducion o Time Series and Lags A ime series measures he values of a paricular eniy a differen poins in ime. Time series regressions are paricularly helpful in examining he causal impac of one eniy on anoher. Prior o deails of hese regressions, however, i is criical o explain he concep of a lag, represened as follows: Y -j. If Y is he value of he series Y in he presen ime period, hen is j h lag Y -j is he value of Y j periods ago. Working wih a series lags enables he esing of is uiliy in forecasing ha series iself (auoregression), or anoher series, as desired. 15

16 5. The HAR-RV Model Andersen, Bollerslev, Diebold and Labys (003) show ha auoregression models exhibi beer resuls han oher models when i comes o forecasing variance. We use heerogeneous auoregressive realized variance (HAR-RV) ype models o forecas variance and hen perform Granger Causaliy Tess in order o es he regressors predicive power. Corsi (003) and Müller e. al (1997) developed he HAR-RV models. They are known o be simple o work wih, while also capuring and relaying informaion abou variance hrough lagged pas values effecively. These models seek o uilize lagged averages of realized variaion o forecas fuure realized variaion. We use lags averaged over 1, 5, and days in order o capure daa from he preceding day, week, and monh, respecively. 5 and were chosen for lagging by a week and a monh since hose are he number of rading days in a week and a monh, respecively. Specifically, he average lags are calculaed as follows: RV k = RV 1 + RV + k... + RV k (8) where RV -k is he k h average lag of he series realized variaion. The HAR-RV model may hen be expressed as: RV = β + βdrv 1 + βw RV 5 + β M RV + 0 (9) ε where indicaes he day and he beas are he coefficiens in he regression. The four beas correspond o he consan erm, he 1-day daily lag, he 5-day average weekly lag, and he -day average monhly lag respecively, and ε is he error erm. 16

17 5.3 Granger Causaliy We now discuss Granger Causaliy (Granger 1969), a very imporan resul in ime-series regression. Granger Causaliy is differen from he sandard idea of causaliy. If a series X has a causal impac on he series Y, hen we would expec Y o be a direc consequence of X; however, if he series X Granger-causes he series Y, hen he inerpreaion is ha X conains unique informaion useful for predicing Y above and beyond every oher series in he regression. From his poin onward, all references o causaliy should be aken o mean Granger-causaliy. The Granger Causaliy Tes is conduced by employing an F-Tes ha ess he join significance of muliple regressors in a regression. This F-Tes is based upon sandard errors, and i is criical o use Newey-Wes covariance marix esimaors o ge accurae sandard errors in a ime-lagged regression, wih a lag of 60 days o ensure heeroskedasiciy robusness. This is criical, as sock volailiy varies over ime. Specifically, Newey-Wes covariance marix esimaors accoun for correlaion amongs differen lags of a imes series and place more emphasis on correlaed observaions ha appear closer ogeher. In order o conduc a Granger Causaliy Tes, all he lags of a paricular series in he regression mus be joinly subjec o an F-Tes. The null hypohesis is ha he coefficiens on each of he lags of a paricular series are zero. If he null hypohesis is rejeced, hen a leas one of he coefficiens being esed is significan and he series being esed has unique predicive conen in is pas values for he dependen variable. Each Granger Causaliy Tes in his paper will examine he daily, average weekly, and 17

18 average monhly lags, as described in Equaion (6), of each ime series ha is used as an explanaory variable. The process of esing for Granger Causaliy can be furher illusraed as follows. Assume here are hree ime-series being examined: X, Y, and Z. Furher assume ha wo lag levels 1 and for each series are being employed, yielding he following independen variables: X -1, X -, Y -1, Y -, Z -1, and Z -. The following regressions would hen be run: X Y Z = β X1X 1 + βxxx + βy 1Y 1 + βy Y + βz1z 1 + βzz + εx, = β X1X 1 + βxx + βy 1Y 1 + βy Y + βz1z 1 + βzz + εy, = β X1X 1 + βxx + βy 1Y 1 + βy Y + βz1z 1 + βzz + εz,. Nex, suppose we wan o es wheher or no he series Y Granger-causes he series X. We would proceed by conducing an F-Tes on β Y1 and β Y in he firs regression o see wheher hey are joinly significan. If hey are, hen we conclude ha he pas values of he series Y conain unique predicive conen for he series X, above and beyond he predicive conen for X in X iself and Z. In oher words, Y Granger-causes X. Now suppose we waned o see if he series Z Granger-causes he series Y. If an F-Tes on β Z1 and β Z in he second regression indicaes hey are no joinly significan, hen we conclude ha he pas values of he series Z do no conain useful predicive conen for Y and ha Z does no Granger-cause Y. Thus, we can es ime series for predicive conen by joinly esing heir coefficiens in regressions of he ype described above. 18

19 This concludes he discussion of he mehods o be applied in his paper. Now we proceed o examine he resuls of applying facor analysis and conducing HAR-RV regressions. 6. FACTOR ANALYSIS RESULTS The resuls of facor analysis enable he examinaion of conemporaneous relaionships beween he realized variances of he socks in he echnology secor. All he echniques described in Secion 4 are applied and analyzed in his secion, saring wih a hrough explanaion of he inuiion behind he expecaion ha he socks volailiy should be a funcion of an indusry/sock-specific (idiosyncraic) effec and a marke (sysemaic) effec. 6.1 Moivaion The expecaion is ha here will be wo dominaing common facors and ha he volailiy of he en larges echnology socks would be largely explained by (1) an indusry effec, and () a marke effec. The moivaion for his comes from he Marke Model, which Sharpe (181) describes as follows: r i, α i + βirm, + εi, = (10), where r i, is he reurn on sock i, α i is he inercep, β i is he sensiiviy of he sock s reurn o he reurn on an average marke porfolio, r m, is he reurn on he average marke porfolio, and ε i, is he error erm. The Marke Model indicaes ha he reurn 19

20 on a sock is made up of wo componens he reurn on he marke and sock-specific idiosyncraic reurn, represened by he error erm as he unexplained par of he oal reurn on he sock. Thus, he quesion arises wheher or no a sock s volailiy would also be dependen on boh he marke and sock-specific facors, such as he indusry o which he sock belongs, since we would expec reurns and volailiy in a paricular indusry o be correlaed. If Equaion (10) describes reurns accuraely, hen he variance of a sock i s reurn would be given by r i m, ε σ = β σ + σ (11); i, i, in addiion, he covariance of he variances of wo socks i and j would be given by r r i j Cov( σ, σ ) = β β Var( σ ) (1), m, i, j, assuming ha σ εi, is independen of σ εj,. Should hey no be independen, hen he above covariance would be as shown in Equaion (13) below: Cov( σ i r i,, σ + β Cov( σ r j, m, ), σ = ε j, β i ) + j β Var( σ Cov( σ ε m, i, ) +, σ ε j, β Cov( σ ) j m,, σ ε i, ) (13), As has been menioned before, Table 1 indicaes ha he bea of every sock being examined is non-zero. Thus, based upon Equaions (11), (1), and (13) he variance and covariance of he socks reurns should have srong influence from he general marke and wihin he indusry. 0

21 6. Correlaion among he socks Realized Variances In anicipaion of he facor analysis, we also examine how well he realized variances of he each of he socks, as well as he marke, correlae wih each oher. These resuls are summarized in Table. 1 I is eviden ha all he socks realized variaions have high correlaions wih each oher and are in he range The marke s realized variaion, on he oher hand, only has a medium correlaion wih all he socks, around 0.5 in each case. The resuls of adding Google s realized variaion ino he daase are in Table 3. I is clear ha all he correlaions reduce noiceably. The original socks Realized Volailiies sill have medium correlaion wih each oher; however, Google s realized variaion has excepionally low correlaion wih every oher sock and he marke. 6.3 Sandard Facor Analysis We now look a he firs facor analysis, shown in Table 4. The upper par of he able liss all he discovered common facors and heir eigenvalues. Facor 1 (eigenvalue = ) is very significan. Facor (eigenvalue = ) may be inerpreed as a weak, bu no enirely insignifican facor. The remaining facors do no have adequae eigenvalues and will be ignored hereafer. Conclusions from he facor analysis may now be drawn, keeping in mind he cavea ha inerpreing a facor analysis requires sifing hrough differen roaions for 1 As he variable names in Table 1 sugges, hese correlaions (as well as he subsequen facor analyses) are on he logs of he Daily realized variances. The raionale for aking logs prior o any analysis here has been explained in Secion 3. 1

22 inerpreable resuls, which is why is second purpose was saed o be o provide firm hypoheses o be esed using oher mehods. The lower par of Table 4 conains facor loadings and uniquenesses. All he socks variances correlae very srongly wih Facor 1 and also exhibi high communaliy. This appears o confirm par of our hypohesis ha a dominan indusry effec would explain a significan porion of he socks volailiy. Tha he marke s volailiy has relaively low correlaion wih his facor and high uniqueness provides furher credence o his inerpreaion. Facor has very low facor loadings hroughou, even wih he marke. This suggess ha a marke effec, if any, is no discernible here and as such, he marke does no appear o play a significan role in explaining echnology socks volailiy. Again, he marke s high uniqueness suggess ha is volailiy has lile in common wih ha of he socks. Figure 1 (a plo of he facor loadings of he wo mos significan facors) shows ha he marke appears o be quie disinc from he socks, all of which are clusered ogeher. Nex, he Saa oupu is forcibly resriced o only wo facors by giving he command ha only facors wih eigenvalue of 0.1 or greaer be reained. Table 5 indicaes ha he wo reained facors have idenical loadings as he wo facors in Table 4. However, i is imporan o noe ha he uniqueness for each of he variables has increased slighly, which indicaes ha removing he so-called insignifican facors does indeed reduce he measured communaliy.

23 6.4 Facor Roaions We now examine he resuls of Facor Roaions in his case. Table 6 shows he correlaions among he facors produced by an oblique roaion on he facor analyses in Tables 4 and 5. Pracically every correlaion is really weak. The only medium correlaion is beween he original Facors 4 and 5, which are he wo mos insignifican facors. This can be aribued o sampling errors and indicaes ha his is no a robus measure a all. We conclude ha an oblique roaion will no be helpful in enhancing our previous analysis, since such a roaion admis meaningful inerpreaions only when he facors produced have medium o srong correlaion. An orhogonal roaion yields uncorrelaed facors by consrucion, wih hese facors eiher having a very srong or very weak correlaion wih all he variables by design. A firs glance, his would appear o be ideal for idenifying disinc indusry and marke effecs. The resuls of an orhogonal roaion on he original Facor Analysis of Table 4 are in Table 7. An orhogonal roaion would in all likelihood be helpful if here were muliple srong common facors; however, in his case his mehod does no provide meaningful resuls he correlaions (i.e., facor loadings) end o be in he range, i.e., mos of he socks have medium correlaion wih facors. This is probably because his echnique places a high premium on he original Facors and 3, which were previously deemed o be insignifican. However, upon examining closely he new facor loadings on he facors F1 (Table 5) and F (Table 5) in Table 7, which resul from an orhogonal roaion on he Facor Analysis of Table 5 (where Saa was forced o resric oupu o only wo facors), 3

24 we can perhaps see a really basic Diversified/Business Technology effec. The loadings on F1 for Cisco, Dell, IBM, Microsof, and Oracle are acually quie high and cerainly seem o be in a higher range han he loadings for he oher socks. These 5 socks are for companies ha are major players in boh Personal and Business Compuing ( Diversified ), or are really srong in Business and Server Compuing. Thus, we may conclude ha here appears o be some evidence of a Diversified/Business Technology effec here, alhough wih he cavea ha EMC appears o be a noable excepion. 6.5 The resuls of including Google ( ) Finally, we sudy he effecs of adding Google ino he daase (please see Tables 8 and 9). As has been emphasized previously, daa for Google are only available from 004 onwards, since ha is when he company wen public. The marke s communaliy is almos exacly he same as is previous communaliy (see Table 4). Some of he socks from before also have higher uniqueness and lower communaliy. However, he mos imporan resul o noe is ha Google has exremely high uniqueness (0.8878) and very low correlaions wih all of he common facors, ranging from The common facors explain pracically none of Google s realized volailiy and his suggess ha here is no much o pursue by way of rying o esablish communaliy beween Google s realized variaion and ha of oher echnology socks and he marke. This view is furher reinforced by he fac ha he facor loadings for all he socks oher han Google exhibi almos no change from Table 8 o Table 9. This suggess ha including Google in he analysis has no significan impac on he preexising correlaion srucure 4

25 wihin he echnology secor and ha Google s variance is fundamenally differen from ha of echnology companies. A possible explanaion for Google s separaion from boh he echnology indusry and he marke, presened visually in Figure, is ha Google s revenues derive largely from adverisemens placed on searches conduced hrough is search engine, unlike he oher echnology firms, all of which generae revenue primarily hrough providing hardware and sofware. 7. REALIZED VARIATION PREDICTIVE CONTENT REGRESSIONS This secion examines he resuls of applying he regressions described in Secion 5 o examine he dynamic relaionships beween he realized variances of he socks in he echnology secor. Since sock price daa for Google are available only from he ime of is Iniial Public Offering in 004, firs regressions are conduced on all he oher socks for he period Afer analyzing hese regressions, he resuls of including Google in regressions on all he socks over he period are examined. 7.1 Resuls from (excluding Google) We examine he resuls of regressing every sock s daily realized variaion, as well as ha of he marke, agains he lagged values of all en socks and he marke, 5

26 uilizing he HAR-RV model as described in Equaion (6). We hen conduc Granger Causaliy Tess using heeroskedasiciy-robus sandard errors as explained in Secion 5. Table 10 compares he explanaory power of only he socks found o be significan in each case hrough he Granger Causaliy Tess wih ha of all he socks and he marke. We see ha he overwhelming majoriy of he explanaory power (94.40% or more, in some cases nearly 100%) is conained in he series deemed significan by Granger Causaliy Tess. The resuls of all he Granger Causaliy Tess are summarized in Table 11. In his able, reading across a row shows all he socks he realized variaions of which Grangercause a paricular sock s realized variaion. Reading down a column provides a quick view of all he socks ha have realized variaions Granger-caused by a paricular sock s realized variaion. As can be seen by he significance all across he diagonal, he pas volailiy of every series is useful in predicing ha series own volailiy. There are several oher ineresing observaions o be made here. Hewle-Packard, which wen hrough a lo of urmoil in he shape of a chaoic merger wih Compaq ha wen o a shareholder voe, as well as exensive resrucuring, is he only sock for which he marke has significan predicive power. Microsof, which makes sofware o go wih Dell and Inel s producs, is very significanly explained by hem. EMC Corporaion and IBM are major rivals in he server business and all he socks ha are significan for he former are also significan for he laer. Mos echnology companies exensively use Inel-made processors and are also significanly explained by Inel. I should be noed ha for he 6

27 majoriy of he ime over which he daa was obained, IBM was in boh he personal compuer as well as office server business, and we see ha i is significanly explained by companies ha relae srongly o boh hese lines of business. Xerox provides relaively unique producs and his is borne ou by he fac ha is volailiy only has significan predicive conen for Texas Insrumens, anoher echnology company ha provides services differen from mos of he companies in he secor. In general, i appears ha he volailiy of a company in a paricular line of business wihin he echnology secor ends o have significan predicive conen for he volailiy of oher companies in ha specific focus wihin he overall echnology secor. Furhermore, he marke s realized variaion does no have significan predicive conen for any echnology sock s realized variaion, oher han Hewle-Packard, which is he one sock ha experienced grea umul over his period. This suggess ha he marke s realized variaion s apparen significance in explaining HP s realized variaion could be aribued o oo much noise crowding ou he real signal sen ou by HP s realized variaion. Overall, he resuls of he Granger Causaliy Tess make remendous inuiive sense. 7. Resuls from (including Google) The final sep in he regression analysis is o examine how much predicive conen Google s realized variaion conains for he oher socks and he marke, and vice versa. Table 1 indicaes ha only 36.6% of Google s realized variaion is explained by he regression, which goes along wih he previously esablished disconnec beween 7

28 Google and he res of he indusry and he marke. Google s realized variaion conains significan predicive conen only for Microsof and Dell. I mus be menioned ha his is no due o an overall decrease in explanaory power in he regression he adjused R in mos cases is comparable o he corresponding R in Table 10. Table 13 indicaes ha neiher he marke, nor any echnology sock (oher han Google iself) conains significan predicive conen for Google. Thus, we may conclude ha he resuls from he regression corroborae hose obained hrough facor analysis ha is unique revenue model and limied ime as a publicly held company make he naure of is volailiy very differen from ha of oher echnology companies and he marke. 8. CONCLUSION This paper employs wo major analysis echniques o see how he volailiies of he major echnology socks and ha of he marke relae o each oher boh in erms of measuring heir communaliy, as well as for seeing how much predicive conen hey have for each oher. The marke, which was found o have pracically no communaliy wih he echnology socks by conducing facor analysis, is significan only for explaining Hewle-Packard s volailiy, he one sock ha experienced grea umul over his period, which suggess ha here is oo much noise clouding he rue signal of HP s volailiy. Oherwise, i would no make much sense for he marke s volailiy o have predicive conen for only one echnology sock s volailiy. 8

29 Ulimaely, we see ha uilizing he informaion conained in high frequency daa provides useful insigh ino he naure of equiy volailiy wihin he echnology secor. Employing echniques ha ake advanage of his informaion, we deermine ha some long held beliefs on he naure of equiy volailiy are quie robus, while ohers require examinaion in greaer deph i was esablished ha, as suggesed by he Marke Model, a sock s volailiy has a major idiosyncraic componen. On he oher hand, i appears ha he Marke Model s implicaion of a sysemaic componen o equiy volailiy can be called ino quesion a bes, our resuls are indicaive of a raher weak and insignifican sysemaic componen. The indusry effec compleely overshadows any impac he marke migh have on echnology sock volailiy. To he auhor s knowledge, hese resuls are unprecedened. The significance of hese resuls is ha analyss focusing on he echnology secor can focus primarily on rends wihin he indusry and he specific sock hey are examining, wihou being oo concerned wih exernal evens in he marke ha have lile apparen influence on he echnology secor. I would no be pruden, however, o dismiss he marke s role in influencing equiy volailiy. As can be seen from he curren financial siuaion, he echnology secor is relaively insulaed from he general marke, compared o oher secors, such as he banking secor. Examining his in more deph by applying one or boh of he echniques uilized in his paper, as well as oher mehods, o deermine he exen of he inerdependency of he volailiy of socks wihin oher indusries, as well as he naure of heir associaion wih he marke s volailiy, would consiue ineresing and useful fuure research. 9

30 9. TABLES Table 1: Beas of socks analyzed (aken from Yahoo! Finance) Sock CSCO DELL EMC HPQ IBM INTC MSFT ORCL TXN XRX GOOG Bea Table : Correlaions beween he naural logs of each sock s realized variaion (excluding Google) ln CSCO DELL EMC HPQ IBM INTC MSFT ORCL TXN XRX SP CSCO DELL EMC HPQ IBM INTC MSFT ORCL TXN XRX SP Table 3: Correlaions beween he naural logs of each sock s realized variaion (including Google) ln CSCO DELL EMC HPQ IBM INTC MSFT ORCL TXN XRX GOOG SP CSCO DELL EMC HPQ IBM INTC MSFT ORCL TXN XRX GOOG SP

31 Table 4: Facor Analysis on RVs (excluding Google) Eigenvalue Difference Proporion Cumulaive Facor Facor Variable (ln) F1 F Uniqueness Communaliy CSCO DELL EMC HPQ IBM INTC MSFT ORCL TXN XRX SP Only Facors 1 and are shown as Facors 3-5 had rivial eigenvalues, indicaing ha hey are insignifican Table 5: Same as Table 4, wih new Uniqueness and Communaliy numbers, by employing mineigen(0.1), which forcibly resrics oupu o wo facors, by enforcing a minimum eigenvalue of 0.1, insead of he defaul 0 Variable (ln) F1 F Uniqueness Communaliy CSCO DELL EMC HPQ IBM INTC MSFT ORCL TXN XRX SP

32 Table 6: Correlaions among facors afer Oblique roaions on Tables 4 and 5 Facor F1(4) F(4) F3(4) F4(4) F5(4) F1(5) F(5) F1(4) 1 F1(5) 1 F(4) F(5) F3(4) F4(4) F5(4) F1(4)-F5(4) are he 5 facors and heir correlaions afer an oblique roaion on Table 4. F1(5) and F(5) are he facors and heir correlaions afer an oblique roaion on Table 5. Table 7: Facor Loadings afer Orhogonal roaion Variable (ln) F1 (Table 4) F (Table 4) F1 (Table 5) F (Table 5) CSCO DELL EMC HPQ IBM INTC MSFT ORCL TXN XRX SP The wo mos significan facors afer performing Orhogonal Roaions on he Facors in Tables 4 and 5 (Uniqueness and Communaliy are no shown as hey do no change) 3

33 Table 8: Facor Analysis on RVs, , excluding Google Eigenvalue Difference Proporion Cumulaive Facor Facor Facor Variable (ln) F1 F F3 Uniqueness Communaliy CSCO DELL EMC HPQ IBM INTC MSFT ORCL TXN XRX SP Table 9: Facor Analysis on RVs, , including Google Eigenvalue Difference Proporion Cumulaive Facor Facor Facor Variable (ln) F1 F F3 Uniqueness Communaliy CSCO DELL EMC HPQ IBM INTC MSFT ORCL TXN XRX GOOG SP

34 Table 10: Explanaory power of lagged values of socks, as deermined by Granger Causaliy Tess ALL EXPLANATORY SIGNIFICANT % R DEPENDENT VARIABLES AND STOCKS ONLY AND RETAINED VARIABLE ADJUSTED R ADJUSTED R CSCO 11 x x % DELL 11 x x % EMC 11 x x % HPQ 11 x x % IBM 11 x x % INTC 11 x x % MSFT 11 x x % ORCL 11 x x % TXN 11 x x % XRX 11 x x % SP 11 x x % A comparison of how well each sock s daily realized variance is prediced by all 3 lag levels of all 10 socks and he marke, and how well i is prediced by only he socks deemed significan by Granger causaliy ess (see Table 10 for which socks are significan in which case). The calculaion depiced in he second and fourh columns is designed o indicae he number of regressors in ha paricular regression. For example, he enry for Cisco is 4 x 3. This indicaes ha 4 of he 11 socks were found o be significan and since here are 3 lag levels for each sock, here are 4 x 3 = 1 regressors in ha paricular regression. SP = S&P 500 (all ohers are sandard icker symbols, in order from op o boom: Cisco, Dell, EMC Corporaion, Hewle Packard, IBM, Inel, Microsof, Oracle, Texas Insrumens, and Xerox). 34

35 Table 11: Resuls of Granger Causaliy Tess on HAR-RV regressions CSCO DELL EMC HPQ IBM INTC MSFT ORCL TXN XRX SP CSCO ** *** *** ** DELL ** *** *** *** EMC *** *** *** * HPQ *** * *** * * IBM ** * *** *** * ** ** INTC ** *** *** * MSFT ** *** *** *** ORCL ** *** *** *** TXN *** *** ** XRX * ** *** SP *** * *** * p < 0.05, ** p < 0.01, *** p < The resuls of regressing he Daily Realized Variance of each of he socks and he marke agains all 3 lag levels of all 10 socks and he marke, from The firs column indicaes he sock whose daily RV is he regressand for ha paricular regression. For example, he hird row indicaes ha when EMC s daily RV is he regressand, he RVs for Dell (DELL), EMC (EMC) iself, Oracle (ORCL), and Xerox (XRX) pass heir respecive Granger Causaliy Tess, while he oher socks and he marke (denoed by SP) all fail his es. The p-values shown are obained by conducing a Granger causaliy es on all 3 lag levels of he sock for ha paricular regression. Since 3 lag levels were esed for each sock, he degrees of freedom also equal 3 for each es.

36 Table 1: The predicive conen conained in pas lagged values of Google s RV for all Dependen Variable Adjused R (all 1 x Granger Tes on 3 = 36 regressors) Google CSCO DELL *** EMC HPQ IBM INTC MSFT * ORCL TXN XRX SP GOOG *** * p < 0.05, ** p < 0.01, *** p < echnology socks and he marke Table 13: The predicive conen for Google s RV conained in pas lagged values of all oher echnology socks and he marke Adjused R Explanaory Variable Resul of Granger Tes CSCO DELL EMC HPQ IBM INTC MSFT 0.4 ORCL TXN XRX SP GOOG 0*** * p < 0.05, ** p < 0.01, *** p <

37 10. FIGURES Figure 1: Facor Loadings 3 on he wo facors wih he highes eigenvalues in he Facor Analysis of he naural logs of Daily Realized Variaions (corresponds o Table 4) Figure : Facor Loadings corresponding o Table 9. Noe how disinc Google s volailiy is from he marke as well as all he oher echnology socks. 3 Recall ha a facor loading is he correlaion beween he facor and he variable in quesion. 37

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