Synchronization Risk and the NASDAQ Technology Bubble. Douglas W. Blackburn Kelley School of Business Indiana University

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1 Synchronizaion Risk and he NASDAQ Technology Bubble Douglas W. Blackburn Kelley School of Business Indiana Universiy Ruslan Y. Goyenko McGill Universiy Andrey D. Ukhov Kelley School of Business Indiana Universiy November 4, 006 Absrac We sudy he role of he synchronizaion risk in allowing sock prices o rise during he recen echnology bubble. In a recen heory by Abreu and Brunnermeier (Journal of Financial Economics 00; Economerica 00) synchronizaion risk leads o marke iming by arbirageurs and delays arbirage. Therefore, in he presence of synchronizaion risk and he need for coordinaion in aacking a bubble, asse prices may inflae o an exreme exen. We obain several resuls. We show how a measure of preferences oward risk of invesors in echnology socks can be used o sudy he presence of synchronizaion risk. We show ha changes in measured invesor risk preferences are closely relaed o changes in he demand for socks and affec rading aciviy. We also show ha changes in invesor preferences and aiudes were differen across differen echnology socks. Srucural changes in risk preferences ook place a differen poins in ime for differen socks in he sample. We infer from his evidence ha coordinaion risk may indeed have been presen, making he job of arbirageurs difficul or impossible. This suppors synchronizaion risk heory. We also observe a dramaic change in aggregae risk preferences across NASDAQ echnology socks during he bubble collapse. Ruslan Y. Goyenko, McGill Universiy, 00 Sherbrooke S. Wes, Monreal, Quebec HA G5. ruslan.goyenko@mcgill.ca Douglas Blackburn and Andrey D. Ukhov are a Kelley School of Business, Indiana Universiy, 09 E. Tenh Sree, Bloomingon, IN The addresses are: dwblackb@indiana.edu and aukhov@indiana.edu

2 Synchronizaion Risk and he NASDAQ Technology Bubble Absrac We sudy he role of he synchronizaion risk in allowing sock prices o rise during he recen echnology bubble. In a recen heory by Abreu and Brunnermeier (Journal of Financial Economics 00; Economerica 00) synchronizaion risk leads o marke iming by arbirageurs and delays arbirage. Therefore, in he presence of synchronizaion risk and he need for coordinaion in aacking a bubble, asse prices may inflae o an exreme exen. We obain several resuls. We show how a measure of preferences oward risk of invesors in echnology socks can be used o sudy he presence of synchronizaion risk. We show ha changes in measured invesor risk preferences are closely relaed o changes in he demand for socks and affec rading aciviy. We also show ha changes in invesor preferences and aiudes were differen across differen echnology socks. Srucural changes in risk preferences ook place a differen poins in ime for differen socks in he sample. We infer from his evidence ha coordinaion risk may indeed have been presen, making he job of arbirageurs difficul or impossible. This suppors synchronizaion risk heory. We also observe a dramaic change in aggregae risk preferences across NASDAQ echnology socks during he bubble collapse.

3 Inroducion Periods of fas rise in prices, followed by rapid declines ermed bubbles and crashes simulae economic debae on he reasons behind wide swings in asse values. Recen heoreical and empirical work suggess ha bubbles can inflae even if here are large numbers of highly capialized, raional arbirageurs. Abreu and Brunnermeier (00, 00) argue ha bubbles can persis in he presence of raional arbirageurs who experience a synchronizaion problem or inabiliy o coordinae heir rading sraegies. This occurs when arbirageurs lack he power o offse irraional exuberance unless hey can coordinae heir aacks on he bubble. Synchronizaion risk arises from arbirageur s uncerainy abou when oher arbirageurs will sar exploiing a common arbirage opporuniy (Abreu and Brunnermeier, 00 and 00). The arbirage opporuniy appears when prices move away from fundamenal values. In a marke populaed by raional invesors his arbirage opporuniy will be immediaely explored. However, he recen lieraure provides evidence ha small noise raders can drive prices significanly furher from fundamenals (Barber, Odean and Zhu 006; Hvidkjaer 006). The effec of noise raders is driven by marke preferences or senimen (Shleifer and Summers, 990). If he small invesors are opimisic abou he sock hey will exer buying pressure and move he prices furher up from fundamenal value. In his siuaion arbirage is no longer risk-less. Arbiragers acquire anoher facor o accoun for invesor preferences owards a paricular sock or a paricular ype of socks. If, for example, arbirager observes ha he sock is overpriced and wans o ener a shor posiion he migh face he risk ha he sock will be even more overpriced in he fuure. If arbirager canno predic invesors preferences owards he sock, or for how long he marke is going o be opimisic abou he sock, he arbirage becomes impossible. Synchronizaion risk, herefore, leads o marke iming by arbirageurs and delays arbirage. Undersanding he naure of synchronizaion risk is imporan for he inerpreaion of he recen rise and fall in echnology sock prices. Empirical evidence on he naure of synchronizaion risk, however, is difficul o obain. This is parly because he behavior of invesors and heir impac on prices is hard o observe simulaneously. Temin and Voh (004) use rading behavior of an informed invesor during he Souh Sea bubble in 70 s and find suppor for he synchronizaion Brav and Heaon (00) explore oher fundamenal reasons for he difficuly of separaing compeing heories of financial anomalies. They find ha behavioral heories buil on invesor irraionaliy, and radiional srucural uncerainy heories buil on incomplee informaion abou he srucure of he economy, have many mahemaical and predicive similariies. The heories are difficul o disinguish, in spie of he fac ha hey relax opposie assumpions of he raional expecaions paradigm.

4 risk hypohesis. They show ha he need for coordinaion in aacking he Souh Sea bubble was he key o allowing i o inflae. In his paper we focus on he behavior of he echnology socks during he period from 996 o 00. We develop a measure ha reflecs imporan characerisic of invesors in echnology socks an esimae of invesor risk aversion. Bakshi and Wu (006) show ha informaion in opions on he NASDAQ 00 Index can be used o measure he degree of invesor irraionaliy during NASDAQ bubble. Closely relaed are he mehods developed in Bliss and Panigirzoglou, (004) and Jackwerh (000) ha show how equiy opions on an asse and he reurns on his asse can be used joinly o exrac preferences oward risk of invesors in he asse. We measure preferences oward risk of invesors in echnology socks by esimaing he value of risk aversion for he socks in XCI Index for he period from 996 hrough 00. This is a major index of echnology socks. Our esimaes capure variaion in aiudes of invesors in individual socks. As suggesed by Shleifer and Summers (990), change in invesors beliefs, invesor senimen, or aiude oward risk affec he demand for risky asses. Therefore, changes in demand associaed wih change in risk preferences should be refleced in rading aciviy. We explicily es his hypohesis. We find ha changes in invesor risk preferences are an imporan deerminan of he demand for company shares and of he sock rading aciviy. Changes in risk preferences are closely relaed o rading aciviy. In paricular, changes in company specific risk preferences are posiively and significanly relaed o urnover. Our resuls are esablished a he level of individual echnology socks. This resul survives when, in addiion o change in risk preferences a he company level, we conrol for changes in he aggregae, marke-level, preferences oward risk. Our firs conclusion is ha changes in risk preferences of invesors in a sock are closely relaed o he demand for shares. When his is he case, socks ha experience similar changes in invesor risk preferences may be expeced o experience similar shifs in demand and herefore exhibi similariies in heir paerns of sock reurns and oher economic variables ha capure sock rading aciviy. We es his and we find ha socks wih similar behavior of invesor risk aversion also display similariy in oher economic characerisics: There is anoher very imporan difference. Noe ha he in case of he Souh Sea bubble whole bubble was concenraed in he one asse (The Souh Sea Company s sock), whereas he NASDAQ echnology bubble rading behavior was spread over many asses. This adds an new and imporan dimension o he noion of synchronizaion risk. Our sudy explores his dimension. This mehod has been used recenly by Blackburn, Goezmann and Ukhov (006) o sudy preferences of value and growh invesors. 4

5 Socks, for which risk aversion changes in a similar way also end o have similar reurns. Socks ha have similar changes in invesor preferences are also caegorized by similar rading behavior (share urnover). Socks wih similar changes in risk aversion have similar changes in liquidiy. The resuls sugges ha preferences oward risk on individual sock level are a significan deerminan of demand for he sock and of he sock price behavior. This, conclusion is consisen wih he lieraure which argues ha individual invesors can drive sock prices (Barber, Odean and Zhu (006), Hvidkjaer (006)). Nex, we urn o he recen rise and fall of prices of echnology socks. If he echnology price bubble was driven by similar changes in invesor aiudes (or senimen) across he echnology socks han we would expec similariies in he behavior of he esimaed risk preferences for invesors in hese socks. Specifically, he major even of his period--collapse of prices in March 000--should be observed in all he measures for all socks approximaely a he same poin in ime. To es for coordinaion risk we run a es of srucural break for each ime series of risk aversion. The srucural break in risk aversion can be associaed wih a significan change in marke senimen abou he sock. For example he change from opimism o pessimism would resul in change in rading behavior, a change from buying o selling. This would lead o significan price decline and evenually be refleced as a srucural break in ime series of esimaed risk preferences. This change in rading sraegies was observed during he bubble: hedge funds were riding he bubble ill March 000 and hey pooled ou before he bubble burs (Brunnermeier and Nagel, 004). Therefore, he change in marke opinion abou he sock or he signal of wheher o coninue or wihdraw from invesing ino he sock should be refleced as a srucural break (breaks) in esimaed risk aversion. We firs es for one srucural break a unknown dae using mehodology of Bai, Lumsdaine, and Sock (998). The advanage of his es is ha i does no ake an a priori sand on he dae of a srucural change. We, herefore, adop a flexible approach and le he daa deermine he dae of a srucural change for each sock in he sample. We find ha differen socks have srucural breaks a differen imes. I means ha invesors behavior in each individual sock was independen from oher socks in he same indusry (all socks in he sample are NASDAQ echnology socks and are members of a major echnology index). I furher suggess ha similar socks had differen levels of eiher opimism or pessimism during he bubble. The arbirage becomes very difficul in he siuaion like his. Arbiragers could no predic on average for how 5

6 long he marke opimism abou he bubble is going o persis. Shleifer and Summers (990) argue ha his makes arbirage a risky sraegy, and Abreu and Brunnermeier (00, 00) sugges ha i leads o a synchronizaion risk. We furher allow for hree srucural breaks a unknown daes. Three srucural breaks in esimaed risk preferences are consisen wih he inerpreaion where firs, marke shifs from a normal sae ino a bubble period, second, he bubble burss and a decline begins (a crash akes place), and finally he prices ener he sable period again. Our sand here is ha if coordinaion among arbiragers was possible han he second period for each individual sock should come on March or April of 000. March of 000 is he las monh when prices peaked up and we would expec he srucural shif in risk preferences eiher a his ime or in April of 000 if arbiragers can forecas marke opimism and pool ou before he prices collapsed. 4 Only one sock ou of weny one we analyze and he XCI index has srucural breaks associaed wih our null hypohesis. This provides furher suppor of coordinaion failure and synchronizaion risk advocaed by Abreu and Brunnermeier (00, 00). Brunnermeier and Nagel (004), however, repor ha hedge funds pooled ou from he bubble before prices collapsed. I suggess ha some coordinaion was, indeed, possible before he bubble burs. Since individual socks or he XCI index iself provide no evidence of a coordinaing signal, we analyze aggregae risk preferences. The aggregae risk preference is obained as equallyweighed average preferences in individual socks. This measure can sugges he general marke opinion abou he echnology socks. This informaion is no available a individual sock level, when socks are considered separaely from one anoher. Also, on he individual sock level we do no know which sock (or a group of socks) is more influenial in driving he echnology prices and susaining he same level of opimism. Thus, he aggregae daa can be informaive. As before, we run a es of srucural break (breaks) for aggregae ime series of risk preferences. The resul is remarkable. One-srucural break es a an unknown dae indicaes a break on April 000. I means ha he general marke aiude owards echnology socks changes a his ime. This is exacly wha we observe in he price daa. The las monh of marke opimism is March of 000, when he prices picked up he las ime. The hree-srucural break es a unknown daes indicaes ha, on average, marke enered he bubble in Augus 998, he bubble burss in April 000, and sabilizaion period began in July 00. This paern very closely corresponds o he 4 Brunnermeier and Nagel (004) show ha hedge-funds pooled ou from he marke before he prices drop indicaing ha o some exen hey were able o predic he marke opimism abou echnology socks. 6

7 observed price daa. Boh ess poin owards he fac ha he average marke opinion or marke opimism changed in April 000. Combined wih he evidence ha hedge-funds qui he bubble earlier (Brunnermeier and Nagel, 004), his resul suggess ha arbiragers were able o predic he aggregae srucural change in marke opimism and pooled ou before i changed. In aggregae, markes had a predicable change in preference which, as we find, coincides wih he ime of bubble burs. Overall, we infer from his evidence ha coordinaion risk may indeed have been presen, making he job of arbirageurs difficul or impossible. This suppors synchronizaion risk heory. We also observe a dramaic change in aggregae risk preferences across NASDAQ echnology socks during he bubble collapse. The res of he paper is organized as follows. Secion II describes mehodology and daa. Secion III characerizes he relaionship beween risk aversion, rading aciviy and oher marke variables. Secions IV and V describe he srucural break ess and he resuls. Secion VI concludes. II. Mehodology and Daa To assess presence of synchronizaion risk we build a measure of sock-specific characerisics of he represenaive invesor in his sock invesor risk preferences. In his secion we discuss how he marginal invesor s risk aversion for a paricular sock can be esimaed from he daa on sock reurns and opions wrien on he sock. Recovering Risk Aversion An esimae of risk aversion can be obained from asse prices. There is a relaionship beween he risk-neural probabiliy disribuion of reurns on a sock i, ( S i T ) probabiliy disribuion Q (, ), and invesor risk aversion. The relaion is, 5 S i T P,, subjecive (rue) U ( Si, T ) Q ( Si, T ) P ( Si, T ) Risk Aversion = =, U ( Si, T ) Q( Si, T ) P( Si, T ) where U () is he invesor s ime separable uiliy of wealh. Therefore, knowing he subjecive disribuion and he risk neural disribuion is sufficien o find risk aversion. To deermine he wo disribuions, we combine he mehodologies of Bliss and Panigirzoglou (00, 004) and Jackwerh (000). Using opion prices for a paricular underlying 5 See, for example, discussion in Jackwerh (000). 7

8 sock, we esimae he risk-neural probabiliy densiy funcion (PDF) according o Bliss and Panigirzoglou (00, 004). We hen use five years of pas monhly sock reurns o deermine a risk-adjused (or, subjecive) PDF using a nonparameric kernel densiy esimaor similar o he one used in Jackwerh (000). Risk aversion is he adjusmen required o ransform he risk-neural PDF ino he risk-adjused PDF. Using his mehod, he risk aversion coefficien can be esimaed for every rading day for any asse for which opion prices are available. Risk-neural probabiliy disribuion To find risk-neural disribuion we use he following approach. I is known from opion pricing heory ha he risk-neural PDF is embedded in opion prices. Le T be he expiraion dae of an opion. The PDF, f(s i,t ), for he underlying asse i a ime T has been shown o be relaed o he price of he European call opion, C(S i,, K, ), by Breeden and Lizenberger (978). Here, K is he opion srike price and S i, is he price of underlying i a ime where <T. This relaionship is f ( S i, T ) C( S r( T ) i, T = e. K, K, ) For each underlying asse, i, and for each expiraion dae, however, he funcion C( S, K ) K = S i, T i,, is unknown and only a limied se of call opions wih differen srike prices exis. Therefore, in order o calculae he second derivaive we esimae a smoohing funcion using opion prices wih differen srike prices bu wih he same expiraion daes. Insead of esimaing such a smoohing funcion in opion price/srike price space, we follow Bliss and Panigirzoglou (00, 004) by firs mapping each opion price/srike price pair o he corresponding implied volailiy/dela. We fi a curve connecing he implied volailiy/dela pairs using a weighed cubic spline where he opion s vega is used as he weigh. We ake 00 poins along he curve and ransform hem back o he opion price/srike price space. We hus obain a smoohed price funcion, which we numerically differeniae o produce he esimaed PDF. Bliss and Panigirzoglou (00) find ha his mehod of esimaing he implied volailiy smile and he implied PDF is remarkably free of compuaional problems. A weighed naural spline is used o fi a smoohing funcion o he ransformed raw daa. The naural spline minimizes he following funcion: min θ N j = w j ( IV j IV ( Δ j, θ ) + λ g'' ( x; θ ) dx, 8

9 where we omi he company-idenifying index, i, for breviy; opion on sock i in he cross secion; (,θ ) j IV j is he implied volailiy of he IV Δ is he fied implied volailiy which is a funcion h j of he h j opion dela, Δ, and he parameers, θ, ha define he smoohing spline, g ( x;θ ) j ; and w j is he weigh applied o he h j opion s squared fied implied volailiy error. Following Bliss and Panigirzoglou (004), we use he opion vegas, v C / σ, o weigh he observaions. The parameer λ is a smoohing parameer ha conrols he radeoff beween goodness-of-fi of he fied spline and is smoohness measured by he inegraed squared second derivaive of he implied volailiy funcion. From he esimaed cubic spline curve, we ake 00 equally spaced delas and heir corresponding implied volailiies and ransform hem back o opion price/srike price space using he Black-Scholes opion pricing formula ha accouns for dividends paid on he sock. However, alhough he delas are equally spaced, he srike prices ha are obained afer he conversion are no. We use a cubic spline for a second ime o fi a curve connecing he 00 unequally spaced call price/srike price pairs. This allows us o choose 00 equally spaced srike prices wih heir corresponding call prices. Finally, we use finie differences o esimae he second derivaive of he call price wih respec o he srike price. This yields he risk-neural PDF. This procedure does no depend on a specific opion pricing model (Bliss and Panigirzoglou 004). Subjecive probabiliy disribuions We use a kernel densiy esimaor o esimae he subjecive (risk-adjused) probabiliy densiy funcions. Similar procedure is used in Jackwerh (000). 6 We use he mos recen 60 monhs of sock reurn daa o esimae he risk-adjused disribuion. To find esimaes for January 996, we use monhly reurn daa from January 99 o December 995. All informaion used in he calculaion is par of he invesors informaion se. Oher windows were considered bu resuls were highly correlaed. For example, we ried a window of pas reurns wih a lag of one year or six monh, and we ried using 7 monhs of reurns insead of 60. Varying our iniial choices does no change he resuls. 6 This is differen from Bliss and Panigirzoglou (004) who firs hypohesize a uiliy funcion (power and exponenial uiliy) for he invesor and hen use his funcion o conver he risk-neural PDF o he subjecive PDF. We do no follow his approach because we do no hypohesize a uiliy funcion. 9

10 We calculae monhly non-overlapping reurns from our 5-year sample and compue he kernel densiy wih a Gaussian kernel. The bandwidh [ 4 /( )] / 5 h = σˆ n, where h is he kernel bandwidh, σˆ is he sandard deviaion of he sample reurns, and n is he number of observaions, is seleced by recommendaion of Jones, Marron and Sheaher (996). Daa The daa for his sudy consiss of daily closing prices of call opions wrien on he socks ha are included in he XCI Index. This is he index of 0 major echnology socks. The sudy covers he eigh-year period from January, 996 hrough December, 00, since his is he period when prices of opions are available o us. In addiion o he daily closing opion prices, we use monhly sock reurns and daily sock closing prices from CRSP. Table liss he firms in he sample. We include all socks for which daa on exchange-raded opions is available. This gives a sample of echnology firms. Microsof is he larges firm in our sample, wih marke capializaion of $95 Billion a he end of he period. The smalles firm in he sample is Advanced Micro Devices (AMD) wih marke capializaion of $5 Billion. The sample includes noable and prominen firms ha were a he cener of aenion during he echnology bubble Apple, Cisco Sysems, Dell, IBM, Inel, Moorola, Sun, and ohers. To esimae risk aversion we need prices of opions wrien on he socks in he sample. All previous researchers have sudied risk aversion using he opions on he S&P 500 Index. For index opions, a relaively large cross secion of srikes exiss, all wih he same expiraion dae. Because of his large selecion of opions, Bliss and Panigirzoglou (004) require a leas 5 such opions in order o do heir esimaion. We are considering individual socks. Companies end o have a smaller cross secion of opions wih differen srike prices and heir opions are comparaively less liquid han index opions. Because of his, we require a firm o have opions wih a leas hree differen srike prices. Similar o Jackwerh (000), we esimae risk aversion wih a consrain on he moneyness. Jackwerh only considers opions such ha he raio of he srike price o he sock price is beween 0.84 and.. This procedure eliminaes far-away-from-he-money observaions. This may cause a problem of missing observaions, bu only when here are large movemens in he sock price. Since opions wih only a few differen srikes are raded for each firm (usually five or six srikes), a large enough movemen in he sock price causes he money-ness o fall in a window ha does no have hree opion conracs for us o use. We do no esimae risk aversion for such days. 0

11 No surprising, ossing ou opions ha are way in he money or way ou of he money affecs risk aversion esimaes in he ales of he disribuion. Our robusness checks indicae ha he esimaes in he middle of he disribuion are generally unaffeced by he money-ness consrains. We find our resuls o be robus o he selecion of opions. For our esimaion, we use opions ha expire beween one and four monhs from day. Opions on socks generally exis wih expiraion daes a hree-monh inervals. For example, opions on Microsof expire in January, April, July, and Ocober. Therefore, for all days in January, we use opions expiring in April. For all days in March, we use hose opions expiring in July. We use his approach o mainain a relaively consan horizon for our analysis, and a he same ime o have a sufficien number of opion conracs o obain reliable risk aversion esimaes. For each of he echnology socks in he sample, for each rading day beween January 4, 996 and December, 00 we calculae esimaes of Arrow-Pra risk aversion coefficien, a compuaionally inensive process. We use daily esimaes o compue a monhly esimae of risk aversion for he sock. Thus, for each sock we have a ime series of risk aversion esimaes a monhly frequency, from January 996 hrough December 00. III. Trading Aciviy and Risk Aversion As a firs sep owards undersanding he connecion beween changes in risk preferences and asse prices we sudy wheher changes in risk aversion are relaed o rading aciviy. Changes in demand for securiies can reflec changes in risk aversion (Shleifer and Summers, 990; Barberis and Shleifer 00). If his is he case, hen rading aciviy will be affeced by changes in risk preferences. When preferences oward risk change, invesors adjus heir porfolios accordingly. We conduc several ess o deermine wheher here is a connecion beween invesor risk aversion and rading aciviy. In he firs se of ess we perform individual regressions for all companies in he sample. For each firm we esimae a linear model, TRN RA TRN = α + Δ ε. We use urnover, TRN, as a measure of rading aciviy. Turnover is defined as rading volume divided by he number of shares ousanding, for a given firm in a monh. Change of he risk aversion of invesors in he sock over he monh, ΔRA = RA RA, is he variable whose affec R

12 on urnover we would like o assess. Pas urnover can affec curren urnover (Lee and Swaminahan 000) and we include lag of urnover, TRN, as well as lag of reurn on he sock, R, in he regression. Table II repors resuls of hese regressions. Change in risk aversion is a significan deerminan of he urnover in ou of firms in he sample. The demand for company shares may be driven by changes in risk preferences of invesors in his paricular sock as well as by marke-wide changes in risk aversion. These are wo separae effecs. Individual socks are a par of an indusry group and are also a par of he overall U.S. sock marke. The demand for socks here depends on changes in indusry-wide and marke-wide preferences. In view of his complicaion we es wheher changes in risk aversion a he company level remain significan conrolling for marke-wide changes in preferences. To es his, we include change of he risk aversion a he marke level, ΔRA M = RA RA, and esimae he model TRN RA TRN RA = α + Δ Δ M + ε. R We use risk aversion for he XCI Index for indusry-level preferences and risk aversion for he S&P 500 Index as he marke-wide measure. The resuls of individual company regressions are no changed. The coefficien of he change in company-specific risk aversion remains significan (Table III). GLS regressions In his secion we repor he resuls of pooled cross-secion ime-series regressions of he urnover on risk aversion and he conrol variables. By esimaing simulaneously he coefficien of he risk aversion and he coefficiens for conrol variables, we avoid he poenial errors-in-variables problems associaed wih he radiional Fama and MacBeh (97) procedure. 7 We conduc he analysis using he daa for echnology firms ha are members of he XCI Index for which esimaes of risk aversion are available. The esimaion proceeds as follows. Define TRN as he ( T ) vecor of individual company urnover (defined as rading volume over a monh divided by he number of shares ousanding), where T is he oal number of ime-series observaions. The vecor is ordered by monh so ha he firs observaions correspond o he urnover in monh. Define X as he pariioned marix 7 Brennan and Subrahmanyam (996) use his approach in heir sudy of reurns and liquidiy.

13 X = W Z, where Z is a ( T 4) marix of conrol variables. There are wo conrol variables: lagged rading volume and lagged reurn on he sock. The firs columns of Z consis of T sacked ( ) diagonal marices wih elemens TRN i, he lagged urnover for company i in monh ; he, second columns of Z consis similarly of he lagged reurn on he sock, R i. The marix W is a ( T ) marix, whose firs column is a vecor of ones and second column is he vecor of changes in risk aversion, Δ RA i,, whose influence on rading aciviy we wish o assess. We firs perform he OLS pooled cross-secion ime-series regression TRN = X + ε, () where is a 44 vecor of coefficiens, he firs elemen of which is he consan erm of he regression, he nex elemen of which is he coefficien of he change in risk aversion variable, and he las 4 elemens of which are he coefficiens of he wo conrol variables for he socks ordered by securiy. ε is a T vecor of errors. In our applicaion he sample consiss of monhly urnover and risk aversion changes from February 996 o December 00 so ha T = 95. To obain he GLS esimaor of, we esimae Ω, he variance-covariance marix of errors in () assuming ha he sock urnover errors are serially independen, bu allowing for cross-secional dependence. Then Ω is a ( T T ) block-diagonal marix, whose ypical elemen is he covariance marix of errors: i is esimaed using he residuals from (). The GLS esimae of is given by ( X ˆ X ) X ˆ Ω Ω Y ˆ =, where Ωˆ is he esimae of Ω from he firs-sage regressions. The resuls of he GLS regression (Table IV) confirm he resuls from individual company regressions. The consan erm is α = wih -saisics of 9.7. The regression coefficien for he change in risk aversion is = 0. 0 wih -saisics of.64. For breviy, we do no repor he remaining 4 company-specific coefficiens for he conrol variables. We repea GLS esimaion while conrolling for changes in he risk preferences a he marke level. To do his we modify he Z marix o become a ( T 6) marix of conrol variables. The firs 4 columns of Z remain unchanged. We add columns o he righ. The new columns consis,

14 of T sacked ( ) diagonal marices wih idenical elemens Δ RAM, he change in he risk aversion a he marke level in monh, =,..., T. We use wo differen indices as he marke. Firs, we use risk aversion compued from opions on he XCI Index o capure changes in risk preferences of invesors in he echnology secor. Second, we use risk aversion compued from opions on S&P 500 Index o reflec changes in marke-wide aiude oward risk. Conrolling for marke-wide changes in risk preferences does no aler our findings. The resuls are given in Table IV. The coefficien on he change in company-specific risk aversion remains unchanged and reains significance. We conclude ha changes in risk aversion significanly affec urnover a he level of individual firms. This resul esablishes a connecion beween risk aversion, rading aciviy, and demand for securiies. This is an imporan finding. I is a es of a widely discussed (refer o Shleifer and Summers 990) bu previously unesed hypoheses ha changes in preferences oward risk may affec he demand. We also esablish ha changes in company-specific risk preferences remain o be a significan deerminan of he urnover when we conrol for marke-wide changes in risk aversion. This finding highlighs he imporance of changes in risk aiude a a company level as a deerminan of demand. Addiional Evidence Changes in risk preferences of invesors in a sock are closely relaed o he demand for shares. When his is he case, socks ha experience similar changes in invesor risk preferences may be expeced o experience similar shifs in demand and herefore exhibi similariies in heir paerns of sock reurns and oher economic variables ha capure sock rading aciviy. We perform several ess o invesigae wheher socks wih similariies in he behavior of risk aversion also display similariies along oher dimensions. To measure he degree of similariy in risk aversion for wo socks i and j we compue correlaion beween ime series changes in risk aversion for wo securiies, [ ΔRA ΔRA ] CORRΔ RA =, i, j Corr i j. This variable measure wheher wo socks experienced similar changes in invesor risk preferences. In our firs es, we compue correlaion beween reurns on wo socks as a measure of similariy in reurns, CORRRET Corr[ r, r ] i, j = i j. We hen regress pair-wise correlaion coefficiens of reurns on pair-wise correlaion coefficiens of ime series of changes in risk aversion, 4

15 CORRRET i, j CORRΔRAi, j (0.000) (0.08) =, where p-values are repored in parenheses. The regression shows ha socks for which invesor risk aversion changes in a similar way also end o have similar reurns. Nex, we sudy he relaionship beween similariy in rading aciviy and similariy in invesor preferences. We regress pair-wise correlaion of urnover on pair-wise correlaion coefficiens of ime series of changes in risk aversion, CORRTURNOV ERi, j CORRΔRAi, j (0.000) (0.04) =, where p-values are repored in parenheses. Companies ha have similar changes in invesor preferences are also caegorized by similar rading behavior. Since rading behavior may be conneced o sock liquidiy, we also invesigae he relaionship beween changes in sock liquidiy, measured by effecive spread, and similariy in risk preferences. The effecive spreads are obained from TAQ daa. Specifically, he effecive spread of a paricular sock on he h k rade is defined as EFSPREAD k = ln ( P ) ln( M ) k k where P k is he price of he a he ime of he h k rade and M k is he midpoin of he consolidaed BBO prevailing h k rade. For a paricular sock aggregaed over a ime inerval i (eiher a monh or a year), he EFSPREAD is he dollar-volume-weighed average of EFSPRAED k compued over all rades in each monh. We regress pair-wise correlaion in changes in effecive spread on pair-wise correlaion coefficiens of ime series of changes in risk aversion, CORR EFSPREADi, j = CORRΔRAi, j (0.000) (0.00) Δ, where p-values are repored in parenheses. There is a srong relaionship. Companies wih similar changes in risk aversion also have similar changes in liquidiy. IV. Tesing for a Srucural Break March 000 is an imporan monh in he recen capial markes hisory. I is he monh when he recen echnology burs. All marke indices dropped significanly and all aggregae marke rading daa experienced a srucural shif a his dae. Of course, he imporance of his dae and he prevailing inerpreaion of i as he dae when he bubble burs surfaced afer he evens. 5

16 We use esimaes of risk aversion for invesors in differen echnology socks o assess hese evens. In he presence of synchronizaion (or coordinaion), he srucural change in measured invesor risk preferences would occur a he same (or very similar) poin in ime for all echnology socks. If, however, changes in risk preferences for invesors in differen socks occur a differen poins in ime, his evidence would sugges he presence of synchronizaion risk, or co-ordinaion risk. In he laer case, synchronizaion risk comes from inabiliy o predic shifs in invesor preferences oward differen socks and he resuling shifs in demand. For example, arbirageurs can observe ha on average noise raders are overly opimisic oday and hence on average may be expeced o be less opimisic in he fuure, bu he arbirageurs canno be cerain when his shif in preferences will happen. The coordinaion becomes even more complicaed if arbiragers observe differen level of opimism or pessimism across differen echnology socks. If he significan change across risk preferences occurs during differen imes for differen socks han his will provide evidence ha i was incredibly difficul o predic for how long he marke opimism abou echnology socks will persis. We do no ake an a priori sand on he dae of a srucural change. We adop a flexible approach and le he daa deermine he dae of a srucural change for each sock in he sample. We hen compare he daes of srucural change for differen echnology socks. We describe he saisical procedure and empirical resuls in his secion. Mehodology: Wald Tes for a Break a an Unknown Dae A es for a srucural break a an unknown dae has been developed in Bai, Lumsdaine, and Sock (998). The mehodology imposes minimal requiremens on he daa generaion process and allows saisical inference abou srucural breaks. Non-parameric echnique developed in Bai, Lumsdaine, and Sock (998) searches for a single break in univariae or mulivariae ime series models. To es for a srucural regime shif we specify he relaion RA i ( k) [ γ + γ RA + γ ] ε. = + RAi + + d i + In he above expression, RA i is an esimae of risk aversion for a securiy i a ime, k is a poenial break dae, and ( k) = and γ ( γ. γ γ ) =, d if k, and zero oherwise. Define vecors ( ). This is a model of full srucural change. =, 6

17 The ess for a break in he coefficiens are based on he sequence of F-saisics esing γ = 0, for k = k* +, K, T k*, where k * is some rimming value. Trimming is necessary for he model o be of full rank before and afer any poenial break dae k. The null hypohesis is ha no break exiss ( = 0) γ. For each k, he esimaor ( ) ( ˆ ˆ ) obained by OLS and he F-saisic esing γ = 0 are compued. F ˆ ( k) = T ˆ γ R T X X ( ˆ σ ) ˆ k =, γ of he regression parameer is ( ) R ˆ γ. The marix X conains independen variables, so ha he row is (, RA,, d ( k) (, RA ) ) ˆ σ is he esimaor of,, σ based on OLS residuals under he alernaive hypohesis given k, and = so ha R = γ, where I is a ideniy marix. The esimaed break dae he marix R ( 0, I ) is he one ha gives he highes F-saisics, kˆ = arg max Fˆ ( k) significan if F( k ˆ ). The break dae is saisically ˆ is greaer han a criical value a he chosen significance level. In our sudy we use criical values for he es developed in Bekaer, Harvey, and Lumsdaine (00). Empirical Evidence Table V presens he resuls of he es of a srucural break a an unknown dae for each individual sock risk aversion from he XCI index and for he index iself. If we assume ha he esimaes of ime varying invesor risk aversion should have one srucural break associaed wih bubble collapse, he able clearly demonsraes how coordinaion failure in arbirageurs rading sraegies can occur. Risk aversion esimaes for differen socks all have differen srucural break daes. For example, Microsof has srucural break in January, 999, when some hedge-funds wihdraw from he marke (Brunnermeier and Nagel, 004) in expecaion of prices o decline. Dell experiences srucural break in January, 00, almos a year afer he bubble collapsed. The risk aversion of he XCI index iself was giving a false signal suggesing a bubble burs in June of 999. Indeed, as repored by Brunnermeier and Nagel (004), several hedge-funds pull ou from he marke in he second half of 999, bu here were also many hedge-funds which increased heir holdings of echnology socks during his ime. Abreu and Brunnermeier (00), Abreu and Brunnermeier (00) and Brunnermeier and Nagel (004) argue ha synchronizaion risk derives from arbirageurs uncerainy abou when oher arbirageurs will sar exploiing a common arbirage opporuniy. This uncerainy is represened by he dispersion of opinion characerized by 7

18 srucural changes in risk preferences in Tables V a differen imes across differen socks. Therefore, arbirage was highly risky (if no impossible), and as Brunnermeier and Nagel (004) repor, many hedge-funds chose o ride he echnology bubble insead of exering a price correcing force. V. Tesing for Muliple Srucural Breaks Our sudy of invesor risk preferences covers he period from he beginning of 996 hrough he end of 00. If his was he period when US marke shifed from a normal sae ino a bubble period, hen experienced he bubble bursing and a decline (or a crash ), and finally sabilized, hen here may be hree poins of srucural change in risk preference. The firs poin reflecs he shif from a normal marke ino he bubble. The second poin of srucural change corresponds o he bubble bursing, and o he beginning of he decline. The hird poin corresponds o he end of he period of decline and o he reurn o he normal sae. We address he hypohesis of muliple srucural breaks aking place a he same ime across differen securiies using he following es for muliple srucural breaks. Mehodology: Wald Tes for Muliple Breaks a Unknown Daes We generalize he es for a srucural break a an unknown dae of Bai, Lumsdaine, and Sock (998) o he case of muliple srucural breaks, all aking place a unknown daes. Le { k, l, m} κ be a riple conaining hree possible daes of srucural breaks, k, l, m. To es for several srucural regime shifs we specify he relaion RA i + d, + RAi + + d, ( k) [ γ + γ RAi + γ ] ()[ l δ + δ RA + δ ] + d ( m) [ λ + λ RA + λ ] + ε. = The variables are: an esimae of risk aversion for securiy i a ime, d if x {,,}, ( x) = i, i RA i ; he dummy variables are and zero oherwise for x { k, l, m}. Define (, ) γ ( γ, γ γ ), δ ( δ, δ δ ), and λ ( λ, λ λ ) =, =, =, =,,. The ess for srucural breaks in he coefficiens are based on he value of F-saisics compued for all possible riples κ { k, l, m} srucural break daes. The null hypohesis is ha no break exiss ( γ = δ = λ = 0 ). For each κ, he of 8

19 esimaor ˆ( ) ( ˆ ˆ ˆ ˆ ) are compued, κ =, γ, δ, λ of he regression parameer is obained by OLS and he F-saisics ( ) R ˆ. F ˆ The marix X conains independen variables, so ha he row is ( ) ˆ κ = T R T X X ( ˆ σ ) (, RA,, d ( k) (, RA, ), d ( l) (, RA, ), d (, RA ) ),,,,, ˆ σ is he esimaor of σ based on OLS residuals under he alernaive hypohesis given κ. The esimaed riple of break daes is he one ha gives he highes F-saisics. The break dae is saisically significan if F( k ˆ ) ˆ is greaer han a criical value a he chosen significance level. Empirical Evidence The resuls of he es are presened in Table VI. Technology socks experience differen srucural breaks corresponding o he hree periods in he life cycle of he firm during he bubble: enering he bubble, he bubble burs and subsequen sabilizaion. Similarly o evidence repored in Table V, we find ha differen socks experienced srucural changes a differen daes. We find no evidence ha he bubble burs a individual firm level occurs in March 000 for all socks. We do find a sock which fis he expeced paern. This is Sun Microsysems (SUNW). I eners he bubble in June 998. In April 000, righ afer he bubble burs, he risk preferences of invesors in his sock experience he second srucural break. Finally, he sock eners he normal pah in July 00. The oher socks eiher exi he bubble and sabilize before March 000 (for example IBM Corp (IBM), and Hewle Packard (HPQ)) or experience he srucural break associaed wih bubble collapse and sabilizaion afer March 000 (for example, Dell Compuer (DELL), Apple Compuer (AAPL)). These findings suppor he hypohesis of synchronizaion risk as a barrier o arbirage. By looking a individual socks i was impossible o predic for how long he same aiudes owards he echnology socks will persis, or for how long he marke opimism will las. The challenges in predicing invesor preferences resul in difficulies in forecasing demand for hese socks. Differen socks can be sending very differen signals o an arbirageur who is aemping o forecas appeie for risk and he demand for socks in he echnology secor. When invesor risk preferences in each of he echnology socks differ, an arbirageur may infer from one sock ha senimen oward hese securiies worsens, while a very similar can signal srong opimism. In he absence of a srong coordinaion signal, aacking he echnology bubble becomes a risky proposiion. This finding is in 9

20 line wih recen heoreical work by Abreu and Brunnermeier (00) and wih he empirical findings in Temin and Voh (004) who sudy he rading by Hoare s Bank during he 70 Souh Sea bubble and find evidence consisen wih synchronizaion risk. Evidence from Aggregae Behavior The evidence repored above indicaes ha i was difficul o predic he movemens of acive invesors on he individual sock level. The level of he XCI index iself does no provide any indicaion of when he bubble can burs. The presence of coordinaion risk is eviden from his daa. Brunnermeier and Nagel (004), however, repor ha hedge funds had some success in exiing he bubble before prices collapsed. This indicaes ha hedge-fund managers had some abiliy o miigae some of he coordinaion risk by predicing on average when changes in preference may occur or had he abiliy o forecas invesors senimen (Shleifer and Summers, 990). Can we observe a change in risk preference in our daa during he bubble collapse? Was here a signal, albei a weak one, for hedge funds o pool ou? To address hese quesions we analyze an aggregae risk aversion obained as equally-weighed average of risk aversion esimaes for individual socks. The moivaion for looking a aggregae daa is ha on individual sock level he marginal invesors in differen socks are differen and we do no know which one leads he marke. On he aggregae level, however, we can observe and measure a general rend in risk preferences of a marginal invesor in he whole marke. This represens a general opinion abou socks in he bubble marke. We analyze aggregae risk aversion. Table VII presens a es of one and hree srucural breaks for he aggregae ime series. One srucural break es indicaes ha he break occurred in April 000 (Panel A). The es for hree srucural breaks suggess ha on aggregae, he marke enered he bubble in Augus 998, he bubble burss in April 000, and sabilizaion period began in July 00. This finding is remarkable. March 000 is he las monh when he prices peaked during he bubble. Righ afer his, in April 000, we observe a significan change in risk preferences a he aggregae level. A srucural change in aggregae risk aversion in April 000 is informaive in ligh of he high persisence of aggregae risk aversion. Auocorrelaion coefficiens for one, wo, and hree lags are 0.9, 0.90, and 0.87, respecively (p-values in all cases are below 0.000). Because of he high persisence, he bes predicor for he fuure value is based on he recen pas. An abrup change in preferences, herefore, can serve as a signal. If, on average, hedge funds were able o predic he 0

21 srucural change in he markes in April 000, hen hey would be able o wihdraw from he marke before prices fell. Our finding of a major srucural change in April 000 is consisen wih he hypohesis where hedge funds were able o forecas he fuure change in marke-level opimism of marke senimen and qui he marke before he collapse. VI. Conclusion Asse price bubbles may inflae when raional arbirage forces do no preven prices from deviaing from fundamenal values. One of he reasons for arbirageurs no o aemp acions ha force prices o fundamenals may be synchronizaion risk. This risk arises when arbirageurs lack he power o offse irraional exuberance unless hey can coordinae, or synchronize, heir acions. If synchronizaion is difficul or risky, and when individual arbirageurs are no large enough o bring down he marke on heir own, prices may deviae from fundamenal values. This approach has been used recenly o inerpre he rise and fall in prices of echnology socks. We use a novel approach o sudy wheher synchronizaion risk was presen in he recen NASDAQ echnology bubble. Firs, we develop a measure ha reflecs an imporan characerisic of invesors in individual echnology socks--an esimae of invesor risk aversion. Change in demand associaed wih change in preferences should cause porfolio rebalancing and subsequenly affec rading aciviy. We hen show ha his predicion holds and ha changes in esimaed risk preferences of invesors in a sock are closely relaed o changes in demand for he sock, and o he rading aciviy in he sock. Afer demonsraing he robusness of his resul, we expec and find he following: Socks, for which risk aversion changes in a similar way also end o have similar reurns. Socks ha have similar changes in invesor preferences are also caegorized by similar rading behavior (share urnover). Socks wih similar changes in risk aversion have similar changes in liquidiy. We herefore esablish ha preferences oward risk on individual sock level are a significan deerminan of demand for he sock and of he sock price behavior. Nex, we urn o he recen rise and fall in prices of echnology socks. If he echnology price bubble was driven by similar changes in invesor aiudes (or senimen) across he echnology socks han we would expec similariies in he behavior of he esimaed risk preferences for invesors in hese socks. Specifically, he major even of his period--collapse of prices in March 000--should be observed in all he measures for all socks approximaely a he same poin in ime.

22 In he presence of synchronizaion risk, however, his will no be he case. Esimaed preferences for invesors in differen socks will experience changes in differen poins in ime. This will be source of synchronizaion risk. We sudy srucural changes in esimaes of invesor risk preferences. Srucural changes do ake place in our sample, bu hey occur a very differen poins in ime for differen socks. This means ha similar socks have differen levels of opimism or pessimism and may be exposed o differen rading sraegies a he same ime. This finding is consisen wih he presence of synchronizaion risk. We also find ha significan changes in individual risk preferences do no occur during he ime of bubble collapse, bu raher eiher before or afer he burs. This is no surprising, given he finding of Bakshi and Wu (006) who repor ha volailiy of he NASDAQ 00 index spiked afer he bubble burs, no before. Taking all he resuls ogeher, we conclude ha coordinaion uncerainy or synchronizaion risk was very high and he arbirage was highly risky, if no impossible. This evidence simulaes he discussion of wha has become a signal for marke paricipans o pool ou from he marke before he prices dropped (Brunnermeier and Nagel, 004). I means ha some coordinaion may have become possible righ before he markes collapsed. The analysis of individual socks and he XCI index does no provide a clear answer. We also find ha our measures conain imporan informaion abou he burs of he bubble in March 000. The aggregae marke preference is obained as equally-weighed average of he preferences for individual socks. The advanage of using an aggregae daa is ha on individual level we do no know which sock (or group of socks) is more influenial in driving he echnology prices and susaining he same level of opimism. The aggregae risk preference experiences a srucural shif in April 000, righ afer he March of 000 when he prices peaked for he las ime. This is a srong and asonishing resul. I suggess ha change in aggregae marke opinion, he change from marke opimism o pessimism, was expeced o occur in April. Hedge-funds sared wihdrawing from he bubble before his happened (Brunnermeier and Nagel, 004). We infer ha overall, changes in invesor preferences and senimen, and he presence of synchronizaion risk, made he job of raional arbirageurs very difficul, risky, or virually impossible.