Do not Fear the Fear Index: Evidence from US, UK and European Markets

Transcription

1 Do not Fear the Fear Index: Evdence from US, UK and European Markets Pankaj Chandorkar 1,# and Janusz Brzeszczyńsk 2 1 Lecturer n Fnance Northumbra Unversty, Newcastle Busness School Department of Accountng and Fnancal Management Cty Campus East, Newcastle upon Tyne, NE1 8ST Emal: pankaj.chandorkar@northumbra.ac.uk 2 Professor of Fnance Department of Accountng and Fnancal Management Newcastle Busness School Northumbra Unversty Cty Campus East Newcastle upon Tyne NE1 8ST Emal: janusz.brzeszczyńsk@northumbra.ac.uk # Correspondng author 1

2 Do not Fear the Fear Index: Evdence from US, UK and European Markets Abstract The VIX ndex s popularly known as the fear ndex both n the busness meda and n academc lterature. Followng the popularty of the VIX, smlar ndces were ntroduced n the UK and European stock markets as an ndcaton of nvestor uncertanty. In ths artcle, we nvestgate ths popular dea by examnng whether these ndces ndeed reflect nvestor fear. The results of long horzon predctve regressons show that these fear ndces as well as extreme jumps n them fal to predct statstcally sgnfcant negatve market returns up to next fve years. Moreover, response of valuaton ratos and leadng busness cycle ndcators to shocks n the fear ndces are statstcally nsgnfcant. However, monetary polcy n US, UK and Europe appear to respond sgnfcantly to fear ndces. Collectvely, the results mply that long-term nvestors do not need to fear these fear ndces. Keywords: VIX ndex, VSTOXX ndex, returns, nvestor fear, monetary polcy. JEL Classfcaton: C22, G17, E44, E47 EFM Classfcaton: 310, 330, 560, 570 2

3 1. Introducton The Chcago Board of Exchange s VIX ndex s ubqutously consdered as the Investor Fear Gauge for asset markets (Whaley, 2000). Whaley (2009) argue that the VIX ndex serves two purposes. Frst, VIX ndex provdes ex-ante or the expected measure of stock market volatlty for the next 30 calendar days. Thus, t s a forward-lookng measure of nvestor s anxety or fear for a short-term perod. Second, futures and optons contracts are desgned wth VIX ndex as the underlyng nstrument, thus helpng to mtgate the expected nvestor fear. In addton to ths, fnancal meda, often, consder VIX ndex as expected nvestor fear gauge and use t report calm or fear n the market. For example, on 8 th September 2015, Bloomberg publshed an artcle, whch ponts to a renewed nterest n market s most popular measure of volatlty, the Chcago Board s opton mpled volatlty ndex (VIX), whch s a measure of fear n the market 1 followng the devaluaton of Yuan n August Besdes the nterest shown by fnancal meda and practtoners, academc research has also reled on VIX as a measure of expected volatlty or the fear. For example, Bloom, (2009) shows that uncertanty shocks, measured usng the VIX ndex, have sgnfcant negatve mpact on busness cycle ndcators. Drechsler and Yaron (2011) show that the varance rsk premum, the dfference between squared VIX ndex and condtonally expected realsed varance s lnked to underlyng economc volatlty. Sarwar, (2012) studes the ntertemporal relatonshp between the VIX ndex and equty markets n Brazl, Russa, Inda and Chna (BRIC) to nvestgate whether VIX serves as nvestor fear gauge n these countres. Hs results suggest that VIX ndeed, serves as an nvestor s fear gauge n these markets as well as n the US. Bekaert, Hoerova and Lo Duca (2013), decompose VIX ndex n two components ndcatng rsk averson n fnancal markets and stock market uncertanty. They show that the proxy for rsk averson, derved from VIX ndex, co-moves wth monetary polcy. Fnally, Lubnau and Todorova (2015), assess the predctve ablty of nvestor sentment, measured usng mpled volatlty ndces such as VIX, n predctng future returns of fve stock market ndces. The VIX ndex s also consdered as an ndcaton of market partcpant s rsk-neutral expectaton of future market volatlty [Bollerslev, Tauchen and Zhou, (2009), Drechsler and Yaron, (2011)]. Followng the popularty of the VIX ndex, smlar ndces have been developed across the world such as the VFTSE ndex n the UK, VSTOXX ndex n Europe, whch ndcate the nvestor fear, and anxety n the respectve markets

4 Gven the nterest shown by both fnancal meda and the academc research, we nevertheless, queston to what extent nvestors should be fearful of the fear ndex. Alternatvely, do these volatlty ndces exaggerate fear n the market? The am of ths artcle s to answer these questons and nvestgate these, rather controversal, ssues. The nspraton for askng ths queston comes from Schwert, (2011) who show that the rse n the VIX ndex durng the 2008 Fnancal Crss dd not lead to persstent ncrease n the expected volatlty and the VIX ndex quckly returned to normal levels. He argues that comparsons made (based on rsng VIX ndex) wth the Great Depresson of 1929 durng the Fnancal Crss of 2008 were exaggerated and msguded. Furthermore, Chow, Jang and L, (2014) show that the VIX s not a true measure of expected volatlty and consst of nformaton regardng the skewness of returns. Ths ndcates that VIX may not capture the true expected volatlty of market returns and consderably understates the true market volatlty when the market partcpants expect the market returns to be negatvely skewed. If the VIX ndex ndcate the rsk-neutral expected fear n the short term, then rsng fear should lead to sgnfcant negatve future realsed market returns. In addton to ths, rsng expected fear should lead to a sgnfcant negatve mpact on leadng economc condtons and consumer confdence. Ths s because stock market returns are usually consdered as a forward-lookng measure of economc outlook. We examne these hypotheses n three dfferent markets the US, UK and European Monetary Unon (EMU) from the perspectve of tradtonal buy and hold nvestor and monetary polcy makers. From the perspectve of buy and hold nvestor (long-term nvestor), we assess whether the fear ndces n these three markets predct sgnfcant negatve holdng perod returns startng from next one month up to next fve years. We also nvestgate whether volatlty spkes (above average ncreases n fear) predct sgnfcant negatve market returns n these three markets. Furthermore, we also examne the response of four popular valuaton metrcs to shocks n the fear ndces. In ths respect, the novelty of our paper s two-fold. Frst, snce we examne the predctve ablty of the fear ndces and the jumps n the fear ndces n forecastng longhorzon market returns, we wll be able to uncover whether a long-term nvestor need to be fearful about the spkes n the fear ndces. Second, snce we regress the mpled volatlty ndces on future realsed market returns and snce future market returns represents the future nvestment opportunty set, we wll be able to examne whether nnovatons to the mpled volatlty ndces can predct the frst moment of future nvestment opportunty set. Ths s partcularly useful wthn the mult-factor cross-sectonal asset-prcng framework, whch uses Merton's (1973) Inter-Temporal Captal Asset Prcng Model (ICAPM) as theoretcal 4

5 underpnnng. As shown by Mao and Santa-Clara (2012) one of the condtons that a partcular state-varable needs to fulfl n order for t to be consdered as asset-prcng factor and n order to prevent ICAPM from beng labelled as fshng lcence (Fama, 1991) s that state-varable should predct frst or second moment of future nvestment opportunty set. From the perspectve of polcy makers, we examne the mpulse response of leadng economc ndcator and the consumer confdence to nnovaton n the three fear ndces n these markets. Such an nvestgaton seems useful, as t wll help to examne whether postve nnovatons to fear ndces lead to declne n economc and consumer sentments. Furthermore, we study the response of monetary polcy and other fnancal market-related varables to postve nnovatons n the fear ndex. Bekaert et al., (2013) show that hgher rsk averson and uncertanty, measured by decomposng the VIX ndex, leads to looser monetary polcy, albet nsgnfcantly. Overall, ther result clearly reveals a dynamc relaton between VIX and monetary polcy stance. More recently, Mallck et al., (2017) show that nnovatons to VIX ndex are more promnent than nnovatons to Bond market volatlty. In partcular, they show that nnovatons to VIX ndex have asymmetrc mpact on term premum and economc actvty, before and after Fnancal Crss of Besdes the nsghts offered by academc research, Central Banks also regularly montor fear ndces n ther offcal publcatons. For example, Bank of England montors the VFTSE n ther quarterly Inflaton Reports as an ndcator of future market uncertanty 2. The result of our analyss usng monthly data from January 1990 untl June shows followng nterestng fndngs. Frst, usng long horzon predctve regressons we fnd the fear ndces n the three markets do not predct statstcally sgnfcant negatve future realsed market returns. On the contrary, the results for UK and EMU suggests that the VFTSE and VSTOXX ndces can predct statstcally sgnfcant postve returns on the FTSE 100 and EURO Stoxx 50 ndces respectvely. Furthermore, jumps n the fear ndces also fal to predct sgnfcant negatve future realsed market return n these three markets. On the contrary, extreme jumps n the VIX ndex (measured as two and three standard devaton spkes above mean) can sgnfcantly predct postve long horzon returns (9 to 24 months buy-and hold returns) n the US. Smlar moves n the VFTSE and VSTOXX ndces predct sgnfcantly postve future market returns (one to next fve years holdng perod returns) n the UK and n The sample for UK and Euro zone markets starts from January 2000 and January 1999 respectvely. 5

6 the EMU. Ths s presumably because, as we show later, monetary polcy makers are more nervous about postve shocks n these mpled volatlty ndces. That s, a postve shock n these volatlty ndces leads to decrease n the man polcy rates n these three markets, whch then further leads to postve realsed returns n the future. Second, the response of valuaton metrcs n the three markets to one standard devaton shocks n the correspondng fear ndces s heterogeneous. The results for the US market suggest a postve standard devaton shock n the VIX ndex sgnfcantly affects the valuaton metrcs, especally the PE rato over perod of four to 12 months after the ntal shock. However, we do not fnd such a sgnfcant response n the valuaton metrcs n the UK and EMU. Thrd, the leadng economc ndcators and the consumer confdence n these three markets do not seem to respond negatvely and sgnfcantly to one standard devaton shocks n the correspondng fear ndces. We also nvestgate whether shocks n the fear ndces from one market are transmtted sgnfcantly to these ndcators n the other market. To ths end, we fnd nterestng evdence. We fnd that the shocks n the fear ndces n one market are not sgnfcantly transmtted to the leadng economc ndcators. Whereas, the shocks n the fear ndces have sgnfcant negatve mpact on the consumer confdence n other markets, contemporaneously. However, the sgnfcance of ths response des down from second month after the ntal mpulse to the fear ndces. Fnally, and nterestngly, we fnd that the man monetary polcy rates n the three economes react negatvely and sgnfcantly to one standard devaton shocks n the respectve fear ndces. Ths response s sgnfcant at least untl four months from the ntal orgn of the shock. We fnd smlar evdence n the behavour of the nterbank markets n these three markets. However, changes n the yelds of generc 10-year government bonds and changes n the exchange rates do not seem to respond sgnfcantly to shocks n the correspondng fear ndces. Collectvely, these results mply that long-term nvestors need not fear not only the fear ndces and but also extreme jumps n the fear ndces. However, monetary polcy makers n these three economes seem to be nervous about the fear ndces. In fact, the negatve response of the monetary polcy makers to shocks n the fear ndces could be the reason why the long-term nvestors need not fear the fear ndces. We vew are results as supportng the argument n (Dhaene et al., 2012) and Da, Engelberg and Gao (2015) that a better ndcator s needed to measure nvestor fear. 6

7 The remander of the paper s organsed as follows; secton 2 presents the methodology and s dvded nto four subsectons. Secton 3 dscuss the data used. In secton 4 we report the results, whch s agan dvded n for subsectons, and fnally, secton 5 concludes. 2. Methodology In ths secton, we dscuss the emprcal framework to test how fearful one should be about the fear ndces. We dvde ths secton n four sub-sectons. In sub- secton 2.1 we dscuss the methodology to assess the mpact of fear ndces and the spkes n the fear ndces on the future realsed returns on the correspondng market ndces. In sub-secton 2.2 we present the methodology to nvestgate the response of valuaton metrcs to nnovatons n the fear ndces. In subsecton 2.3 we outlne the methodology to examne the response varous monetary polcy ndcators to nnovatons n the fear ndces. Fnally, n subsecton 2.4 we outlay the methodology to examne the response of leadng economc ndcator and changes n the consumer confdence to nnovatons n the fear ndces. 2.1 Market returns and fear ndces To test how fearful nvestors should be of the fear ndex, we estmate long-horzon predctve regressons of buy-and-hold market returns on the correspondng fear ndex. We examne the sgn and the sgnfcance of the regresson coeffcents on the correspondng fear ndex to deduce how fearful one should be of these fear ndces. We estmate the followng long-horzon predctve regresson, whch s commonly used n the future market return-predctablty lterature (Kem and Stambaugh 1986; Campbell 1987; Fama and French 1989; Mao and Santa-Clara 2012). r t,t+h = α h + β h. V t + ε t,t+h (1) where, r t,t+h r t r t+h s the contnuously compounded return on th market ndex over h-perods (from t+1 to t+h ), V t s the th mpled volatlty ndex (fear ndex) n month t and ε t,t+h denotes the forecastng error wth an assumpton that ts expected condtonal mean s zero [E t (ε t,t+h ) = 0]. It s clear from (1) that the condtonally expected return on the th market ndex s E t (r t,t+h ) = α h + β h. V t at month t. The sgn and the sgnfcance of the slope coeffcent β h wll ndcate whether a partcular fear ndex predcts future realsed market returns thus ndcatng whether one should be fearful of the fear ndex. That s f β h < 0 and sgnfcant, then an nvestor wth nvestment horzon of h should be fearful about the 7

8 correspondng th fear ndex. We use buy-and hold forecastng horzons of h = 1,3, 6, 9, 12, 24, 36, 48 and 60 months ahead.e. from next one month tll next fve-year buy and hold returns. Furthermore, to nvestgate whether spkes or above-average rse n the fear ndces can/should nduce fear, we run the followng three separate long-horzon predctve regressons, smlar to (1): = α h + θ 1,h. D 1 V t + ε t,t+h (2) r t,t+h = α h + θ 2,h. D 2 V t + ε t,t+h (3) r t,t+h = α h + θ 3,h. D 3 V t + ε t,t+h (4) r t,t+h where, D 1 s a bnary dummy varable that takes value of 1 f the respectve fear ndex s between one and two standard devatons above ts respectve mean and 0 otherwse. D 2 s a bnary dummy varable that takes value 1 f the respectve fear ndex s between two and three standard devatons above ts respectve mean and 0 otherwse. Fnally, D 3 s a bnary dummy varable that takes value 1 f the respectve fear ndex rses three standard devatons above mean and 0 otherwse. θ 1,h, θ 2,h and θ 3,h captures the effect of one, two and three standard devaton volatlty jumps above the mean respectvely on the h-perod holdng returns. The sgn and the sgnfcance of the respectve nteracton slope coeffcents θ 1,h, θ 2,h and θ 3,h wll then ndcate whether an nvestor of horzon h, should be fearful about a move of one, two and three standard devatons above mean n the th fear ndex respectvely. Ths s n sprt of Bloom, (2009) who also analyse the mpact of volatlty shocks. He defnes volatlty shocks around 17 unforeseeable events. The measure of uncertanty takes the value of 1, around the 17 events, when stock market volatlty s more than 1.65 standard devaton above the Hodrck-Prescott detrended mean of the volatlty seres and 0 otherwse. We refran from measurng spkes n the fear ndces around any partcular events because ex-ante such events are unforeseeable and such a measure of spke n the fear seems to be based around these events. In addton to estmatng and analysng the results of forecastng regressons, we also examne the response of transmsson of fear orgnatng n one market to the returns n the other market. That s, we nvestgate whether postve one standard devaton shock n the VIX ndex has sgnfcant mpact on the market returns n the UK and EU. Smlarly, we nvestgate whether a postve one standard devaton shock n the VFTSE ndex s transmtted sgnfcantly to the market returns n the US and the EU. Ths s partcularly helpful snce our sample sze contans sgnfcant dosyncratc events related to UK such as the result of UK s referendum to ext the 8

9 European Unon on the 23 rd June For ths, we estmate the followng smple Vector Autoregresson model (VAR): p Z t = A + B. Z t p + ε t (5) =1 where the vector Z t [r US, VIX, r uk, VFTSE, r EU, VSTOX]. r US s contnuously compounded return on the S&P 500 ndex. VIX s the CBOE s VIX ndex, r uk s the contnuously compounded return on the FTSE 100 ndex, VFTSE, smlar to VIX, s the volatlty ndex derved usng optons on FTSE 100 and s consdered to be fear ndcators n the UK market, r EU s the contnuously compounded return on the EURO STOXX 50 ndex and VSTOX, smlar to VIX, s the s the volatlty ndex derved usng optons on EURO STOXX 50 ndex and s consdered to be fear ndcators n the EU market. p s the optmal lag order, decded usng the AIC crteron and ε t s the vector of nnovatons whch we maybe contemporaneously correlated to each other but uncorrelated wth ther own lagged values and ndependent of the elements n the vector Z t. The standard practce n VAR-based methodology s to orthogonalse the mpulse response of the varables ether by mposng recursve structure.e. decomposng the varance-covarance matrx of nnovatons usng standard Cholesky decomposton or by mposng theoretcally motvated structural restrctons on the contemporaneous coeffcent matrx. However, snce, the orthogonalsed mpulse response, generated by standard Cholesky decomposton of resdual covarance matrx, s not nvarant to orderng of the varables and requre rgorous theoretcal foundaton for orderng the varables n the above VAR, we follow Koop et al., (1996) and Pesaran and Shn, (1998) and construct generalsed mpulse responses. In partcular, we examne the generalsed mpulse response of market returns n the US, UK and EU to one standard devaton shock to all the three fear ndces, over the perod of next 12 months. If the market partcpants are truly fearful of the fear ndces and f the fear from one market s transmtted to other, then we should expect a statstcally sgnfcant negatve response to postve one standard devaton mpulse n the fear ndces. 2.2 Valuaton metrcs and Fear Indces In ths subsecton, we present the VAR framework to analyse the response of the valuaton metrcs to shocks n the fear ndces n the three markets. In addton to analysng the response 9

10 of market returns to shocks n the fear ndces, we also nvestgate whether shocks to varous fear ndces nduces sgnfcant response n the varous valuaton metrcs n the three markets respectvely. In partcular, we examne the generalsed mpulse response of four popular valuaton metrcs, namely prce to earnngs rato (PE), net dvdend yeld (DY), Enterprse value to tralng 12-month sales rato (EVS) and enterprse value to tralng 12 months EBIT (EVEBIT) n the three markets to one standard devaton postve shocks to VIX, VFTSE and VSTOXX ndces. Ths wll enable us to dentfy whether rse n the fear n the market has sgnfcant negatve effects on market valuaton measures. For ths we estmate followng three separate VARs for the three ndvdual markets Z US t = A US + B US US. Z t p =1 Z UK t = A UK + B UK UK. Z t p =1 Z EU t = A EU + B EU EU. Z t p =1 + ε t US (6) + ε t UK (7) + ε t EU (8) Where for th country/economc zone, the elements of vector Z t are Z t [r, V, PE, DY, EVS, EVEBIT ]. r s the contnuously compounded market return, V s the correspondng volatlty ndex (fear ndex), PE s the prce-to-earnngs rato of companes n the correspondng market ndex, DY s the correspondng net dvdend yeld of the market ndex, EVS s the Enterprse value to tralng 12-month sales rato for the correspondng market ndex and fnally, EVEBIT s the enterprse value to tralng 12-months earnngs before nterest and tax of the companes n the correspondng ndex. 2.3 Monetary polcy ndcators and Fear ndces We now present the VAR framework to examne the response of the monetary polcy stance to shocks n the fear ndces n the respectve countres/economc zone. We estmate three separate VAR models for each country/economc zone, smlar to (6), (7) and (8) wth followng elements n the Z t vector Z t [r, V, br, r3m, r10y, x ], where r and V are same as n VAR (3). br are the changes n the base nterest rates or the 10

11 man polcy rate. In case of the US br s changes n FED Fund target rate (upper bound), n case of UK, t s changes n the Bank of England s Base Rate and n case of EU, t s the change n the man refnancng rate of the European Central Bank. r3m are the changes n the 3- month LIBOR rates n the respectve currences. r10y denotes changes n the 10-year government bond yelds n the respectve currences and fnally, x denotes the changes n the respectve effectve exchange rate ndces. We then study the generalsed mpulse response of these varables to one standard devaton postve nnovaton n the respectve fear ndces over the perod of next 12 months. If Central Banks n these three countres/economc zones are fearful of expected market volatlty, they should respond negatvely and sgnfcantly.e. the base rates should fall, to postve nnovaton n the fear ndces Leadng economc ndcators and fear ndces Fnally, n ths secton we present the VAR framework to examne the response of future economc actvty represented by leadng economc ndcator and changes n consumer confdence to nnovatons n the fear ndces. Smlar to subsecton 2.3, we estmate three separate VAR models for th country/economc zone wth followng elements n the Z t vector Z t [r, V, LI, CCI ]. In the vector, LI denotes the respectve leadng economc ndcator and CCI denotes the changes n the respectve consumer confdence. To account for the possblty of spllover of fear from one market to other, we also examne the cross-country mpulse response of leadng economc and consumer confdence to nnovatons n the fear ndces. That s, we examne the generalsed mpulse response of leadng economc ndcator and consumer confdence ndcators n the UK to one standard devaton postve nnovaton n VIX, VFTSE and VSTOXX ndces. For ths, we estmate the followng VAR model, p Z t = A + B. Z t p + ε t (9) =1 where the vector Z t conssts of followng elements Z t [r US, VIX, r EU, VSTOXX, r UK, VFTSE, LI US, LI UK, LI EU, CCI US, CCI UK, CCI EU ]. 3. Data We use monthly data from Bloomberg for US, UK and the EU. For the US, we use the VIX ndex as the proxy market s fear Index. The contnuously compounded return on S&P

12 ndex s used as proxy of market return and s calculated as r t US = ln ( P t P t 1 ) 100 for the month t. We use month-on-month changes (n percentage) n Conference Board Leadng Economc Indcator of US as a proxy for leadng Economc ndcator. Changes n the consumer confdence s measured usng log-changes (n percentage) n seasonally adjusted Conference Board Consumer Confdence Index. Changes n monetary polcy stance n the US are measured usng changes n the upper bound of Federal Funds Target nterest rate. Changes n the money market nterest rate are measured usng changes n the 3-month US dollar LIBOR rates. We also use changes n the yelds on generc 10-year US government Bond, as a proxy of long term nterest rate and changes n US dollar trade-weghted ndex as a proxy of US dollar exchange rate. The sample sze s January 1990 to June *** Please nsert table 1 about here*** For the UK, we use the VFTSE ndex as a proxy of fear n the UK market. The contnuously compounded return on the FTSE 100 ndex s used as a proxy of market returns n the UK. The month-on-month change n the Conference Board Leadng Economc Indcator for the UK s used as proxy of leadng economc ndcator. Changes n the consumer confdence n the UK are measured as log changes n GFK consumer confdence ndcator. To measure the changes n the monetary polcy stance n the UK, we use changes n the Bank of England s Base Interest rate. Changes n the money market nterest rate are measured usng changes n the 3-month UK Sterlng LIBOR rates. Changes n the long-term nterest rate are measured usng changes n the yelds on generc 10-year UK government bond. Changes n the Sterlng s exchange rate s measured as log-changes n the trade-weghted Sterlng Effectve Exchange Rate Index. The sample sze s January 2000 to June For the EU, we use the VSTOXX ndex as a proxy of fear ndex n the European stock market and the contnuously compounded return on the correspondng Euro Stoxx 50 ndex as a proxy of returns on the market. The month-on month change n the Deutsche Bank Eurozone Leadng Economc ndcator s used as a proxy of changes n the leadng economc ndcator n the EU. To measure the changes n the consumer confdence, we use monthly percentage changes n the seasonally adjusted European Commsson s consumer confdence ndcator. The changes n the monetary polcy stance s measured usng changes n the European Central Bank s man refnancng operatons rate. The changes n the 3-month EURIBOR s used as proxy of changes n the money market nterest rates. Changes n the long-term nterest rates are measured usng the changes n the generc 10-year Euro denomnated Government Bond. Fnally, the log 12

13 changes n the trade-weghted EURO effectve exchange rate ndex s used a proxy of changes n the exchange rate of EURO aganst the basket of the EU s tradng partners. The sample sze s January 1999 to June The start of the sample sze s dfferent for each country/economc zone because the dfferent start dates of the fear ndces. Table 1 presents bref descrptve statstcs of the data. Panels A, B and C shows the summary for the US, UK and EU data respectvely. For the US, the average monthly return on the S&P 500 ndex s 0.61% wth a standard devaton of 4.15%. The average level of VIX s 19.56%.e. on average market partcpants n the US expected next 30-days annualsed volatlty of returns of S&P 500 ndex to be 19.56% wth standard devaton of 7.49%. The average monthly change n the Fed s target rate s ndcatng that, on an average, the Fed Fund target rate has reduced over the sample sze. Smlar argument can be made about the 3-month USD LIBOR, the yelds on 10-year US Government bonds and the trade-weghted effectve exchange rate of US dollar. Furthermore, a smlar nference can be drawn about the UK and EU from Panels B and C respectvely. Overall, there are four nterestng ponts to note, notwthstandng the unequal sample sze. Frst, the average monthly return on EURO Stoxx 50 s negatve and least compared to other two market ndces wth hgher standard devaton. Second, the level of fear ndex n the EU s hghest. Thrd, nterest rates and exchange rates, on average, have been fallng over the sample perod. Fnally, valuaton metrcs are relatvely hgher n the UK and the EU compared to ther US counterparts wth hgher volatlty. *** Please nsert fgure 1 about here*** Fgure 1 shows the three fear ndces. Panel A of fgure 1 shows the VIX ndex along wth three types of jumps vz, a jump of one, two and three standard devatons above mean. Panels B and C shows smlar data for VFTSE and VSTOXX ndces n the UK and the EMU. 4. Results 4.1 Market Returns and fear ndces *** please nsert table 2 about here*** We begn our analyss by examnng the results of long-horzon predctve regressons of fear ndces on market returns. As mentoned earler, f the market partcpants are reasonably fearful about the market s most popular measure of fear then a rse n expected fear ndces should lead to sgnfcantly decreased realsed future returns on market. That s, the sgn of 13

14 slope coeffcent β h n (1) should be negatve and statstcally non-zero. Furthermore, f the sgns of the coeffcents θ 1,h, θ 2,h and θ 3,h n (2), (3) and (4) are respectvely negatve and are sgnfcantly non-zero, then an nvestor of nvestment horzon h should be sgnfcantly fearful of one, two and three standard devaton jump above mean n the fear ndex n the three markets respectvely. In table 2, panels A, B, C and D present the results of models (1), (2), (3) and (4) respectvely for the US market. Smlarly, tables 2 and 3 presents the results for UK and EU markets respectvely. The t-statstcs assocated wth the slope coeffcents are computed usng Newey and West, (1987) heteroscedastcty and autocorrelaton corrected standard errors. From panel A of table 2, we can see that although there s negatve contemporaneous relaton between the VIX and the returns on the S&P 500 ndex (β h=1 =-0.001), a result whch s qualtatvely smlar to Got, (2005), yet the coeffcent s not sgnfcant. Furthermore, R-squared assocated wth the regresson s low. The three, four and fve year holdng perod returns on S&P 500 ndex are also negatvely related to VIX but not statstcally sgnfcant. Panel A, thus, suggests that market partcpants mght be exaggeratng the fear n the market s most popular measure of fear. In panel B, we study the mpact of one standard jump n the VIX ndex above ts mean on the varous holdng perod returns of S&P 500 ndex. A one standard devaton postve spke above mean does not seem to predct sgnfcant negatve realsed returns at any horzon. On the contrary, such as spke n the VIX ndex sgnfcantly predcts postve realsed returns over sx-month holdng perod return (β h=6 = 0.15) wth R-squared of 1.51%. A jump of two standard devaton above mean n the VIX ndex s able to predct statstcally sgnfcant postve realsed holdng perod returns of S&P500 ndex over a horzon of nne and 12 months (β h=9 = 0.25, and β h=12 results can be seen from panel D. = 0.28 ) wth an R-squared of 1.15% and 0.99% respectvely. Smlar *** Please nsert table 3 about here*** Panels A, B, C and D of table 3, present the results of the predctve regressons (1), (2), (3) and (4) n the UK market respectvely. Specfcally, they show whether VFTSE and the jumps n the VFTSE can predct sgnfcant returns of the FTSE 100 ndex over long horzons. Smlar to results n Table 2, we can see from Panel A that although VFTSE s contemporaneously negatvely correlated wth the FTSE 100 ndex over one-month perod, yet the slope coeffcent ( β h=1 = ) s nsgnfcant. However, unlke the results n Panel A of table 2, the VFTSE 14

15 ndex seems to predct the four and the fve-year realsed holdng perod return sgnfcantly and postvely ( β h=48 = 1.10 and β h=60 = 1.46) wth relatvely hgher R-squared. Furthermore, smlar to the results for the US, t can be seen from Panel B that one standard devaton jump above mean n the VFTSE ndex seems to predct postve realsed returns over sx-month holdng perod (β h=6 = 0.17) wth R-squared of 1.02%. However, unlke the results for the US, a two standard devaton jump above t mean n the VFTSE ndex seems to predct, sgnfcantly and postvely, longer horzon returns of FTSE 100 ndex. For example, (β h=24 = 0.44, β h=36 = 0.59, β h=48 = 0.73 and β h=60 = 0.87) wth relatvely hgher R- Squared. Smlar nference can be drawn from Panel D regardng a three standard devaton jump n the VFTSE ndex above ts mean. *** Please nsert table 4 about here*** In table 4, we present the results for the EU market. Unlke the results for US and UK, t can be seen from Panel A that the returns on the EURO STOXX 50 ndex are not negatvely correlated, contemporaneously. However, smlar to the results n the UK, the VSTOXX seems to predct longer horzon holdng perod returns postvely and sgnfcantly ( β h=48 = 1.55 and β h=60 = 2.17) wth relatvely hgher R-Squared. Furthermore, unlke the results for UK and US, a one standard devaton jump above ts mean n the VSTOXX ndex seems to predct longer horzon returns n on the EURO Stoxx 50 ndex, postvely and sgnfcantly. For example, (β h=48 hgher R-Squared. = 0.65 and β h=60 = 0.84) wth relatvely We now turn out attenton and nvestgate whether shocks to the fear ndces from country are transmtted to market returns n other country/economc zone. We do ths by examnng the generalsed mpulse response of the market returns over the next twelve months to one standard devaton nnovaton n three fear ndces. The results are reported n table 5. The mpulse response functons are generated by estmatng the VAR model (5). We do not present these mpulse responses n the form of graphs, as s usually done n the VAR lterature, but n tabular format. Ths s because when the mpulse responses are presented as graphs, t s hard to judge the statstcal sgnfcance of response for each tme perod. Panel A of Table 5 reports the response of S&P 500 returns to a shock n the VIX, VFTSE and VSTOXX ndex over the next 12 months. Smlarly, panels B and C report the repose of returns of FTSE 100 and Euro Stoxx 50 ndces to shocks n VIX, VFTSE and VSTOXX ndces over the next 12 months respectvely. The standard errors that are requred to compute the t-statstcs are estmated usng 15

16 Monte-Carlo smulaton wth 5000 repettons. If the fear from one market s sgnfcantly transmtted to other, then we should see sgnfcantly negatve response to a shock n the fear ndces. However, observng the results n table 5, t can be seen that, the response of the three market returns s negatve to the shocks n three fear ndces, albet none of the response s statstcally sgnfcant. *** Please nsert table 5 about here*** Collectvely, the results from table 2, 3, 4 and 5 ndcate that, () the volatlty ndces do not predct statstcally sgnfcant negatve market returns, thereby ndcatng that nvestors need not be fearful about the market s most popular measure of fear. () In addton to the level of the volatlty ndces, large spkes n these fear ndces do not predct sgnfcant future negatve returns. On the contrary, larger spke n the volatlty ndces leads to statstcally sgnfcant postve returns over the longer horzon. () The fear of one standard devaton shock from one market does not seem to nduce statstcally sgnfcant negatve response of the three market returns. In secton 4.4, where we analysed the response of monetary polcy to one standard nnovatons n the fear ndces, we provde a possble explanaton of these results. 4.2 Response of valuaton metrcs to fear ndces In the prevous secton, we examned the mpact of the fear ndces on buy and hold returns of the correspondng stock market ndces for varous horzons. One of the nterestng concluson from the analyss was that jumps n the fear ndces seem to predct postve long horzon returns. Ths nvarably leads to the queston; how does dfferent valuaton metrcs respond to shocks n the fear ndces? Earler research suggests that there s a dynamc nteracton between realsed or condtonal volatlty stock returns and corporate proftablty 4. If hgher expected volatlty, reflected by the dfferent fear ndces, results n hgher realsed volatlty, then there should sgnfcant dynamc relaton between the dfferent fear ndces and the correspondng measures of valuaton. We analyse the response of four valuaton measures; dvdend yelds (DY), Prce-to-(tralng 12 months) earnngs rato (PE), Enterprse to tralng 12-month Sales rato (EVS) and Enterprse to tralng 12-months EBIT (EVEBIT). We use enterprse valuebased valuaton ratos because they ncorporate both forms of captal, debt and equty. Ths s n sprt of the fnancal leverage-volatlty relaton of Black, (1976) and Chrste, (1982). 4 (Fama and Fama, (1988); Fama and French, (1989); Kem and Stambaugh, (1986); Schwert, (1989a); Schwert, (1989b) 16

17 *** Please nsert table 6 about here*** In table 6, we report the generalsed mpulse responses of the four valuaton measures to one standard devaton shocks n the fear ndces. Panel A shows the response of the valuaton ratos of the S&P500 ndex to shocks n the VIX ndex over the next 12 months. VAR model (6) s used to generate these mpulse responses. Panel B shows the responses of the valuaton metrcs of the FTSE 100 ndex to one standard devaton postve shocks to the VFTSE ndex n the UK over the perod of next 12 months. Model (7) s used to generate these responses. Fnally, panel C reports the generalsed mpulse response of the valuaton metrcs of the EURO STOXX 50 ndex to one standard devaton shocks to the VSTOXX ndex n the EU over the perod of next 12 months. Observng panel A, we can see that a one standard devaton shock n the VIX ndex nduces a statstcally sgnfcant negatve mpact on the EVS rato mmedately after one and two months from the orgnaton of shocks. A smlar result can be seen for EVEBIT rato. Ths s ntutve as rse n expected fear could push down the total market captalsaton of the ndex companes and thereby of the ndex. Ths could lead to ncrease n the fnancal leverage and hence reducng the enterprse value relatve to sales or EBIT. However, ths effect des down after three months. Dvdend yeld of the S&P 500 ndex shows a sgnfcant postve response to one standard devaton postve shock to the VIX ndex after two months from the orgnaton of the shock. However, dvdend yeld does not respond sgnfcantly from thrd month onwards. Observng the response of the PE rato of the S&P 500 ndex to one standard devaton shock n the VIX, we fnd that, unlke other valuaton ratos, PE reacts sgnfcantly to a shock n the VIX ndex. The ntal response of the PE rato s not statstcally sgnfcant, however, after four months from the orgnal shock n the VIX, the response of PE seems statstcally sgnfcant, especally after eght months tll 12 months. Ths suggests that the an ntal one standard devaton shock n the VIX makes S&P 500 sgnfcantly expensve after eght months onwards. However, unlke the response of the valuaton ratos n the US, the response of the valuaton metrcs n the UK and EU to one standard devaton shock n the respectve fear ndces does not seem to nduce statstcally sgnfcant mpact. Overall, we can see from table 6 that, except for the response of EVS and EVEBIT n the US, the fear ndces n the three markets does not seem have to statstcally sgnfcant negatve mpact on the correspondng valuaton ratos. 17

18 4.3 Response of Leadng Indcators to fear ndces In the prevous two sub-sectons, we examned the response of stock market-varables to nnovatons n correspondng the fear ndces n that market. We also examned whether fear from one market s transmtted sgnfcantly to stock market-related varables of other. We now broaden the scope of our nvestgaton by examnng the response of leadng economc and polcy-related varables to nnovatons n the fear ndces n the respectve countres/economc zone. In ths sub-secton, we study the response of leadng economc ndcators, such as conference board leadng economc ndcator and the consumer confdence ndcator to one standard nnovaton n the fear ndces. We also examne whether of shocks n the fear ndces from one market can sgnfcantly affect these leadng economc ndcators n dfferent countres/economc zone. *** Please nsert table 7 about here*** In panel A of table 7, we report the response of Conference Board leadng ndcator and changes n the consumer confdence n the US to one standard devaton postve nnovaton to VIX Index over a perod of next 12 months. Smlarly, n panels B and C we report the responses of the same ndcators to one standard devaton nnovaton n the VFTSE and the VSTOX ndex n the UK and the EMU respectvely. The VAR models used to generate these generalsed mpulse responses are smlar to models (6), (7) and (8) wth the vector Z t [r, V, LI, CCI ]. From the all the three panels we can see that none of the forwardlookng ndcators n the three countres/economc zone respond negatvely and sgnfcantly to one standard devaton shock n the fear ndces n the respectve markets. *** Please nsert table 8 about here*** We also test whether shocks to the fear ndex orgnated from one country has a sgnfcant mpact on the leadng economc ndcator and the changes n the consumer confdence n other country/economc zone. In table 8, we study the generalsed response of leadng economc ndcator to nnovatons n three fear ndces. Panel A reports the response of leadng economc ndcator n the US to one standard devaton shocks n the VIX, VFTSE and the VSTOXX ndex. Smlarly, panels B and C report the generalsed response of leadng economc ndcator n the UK and the EMU to the one standard devaton shocks n the three fear ndces respectvely. Model (9) s used to generate these responses. We can see that the conference board leadng economc ndcator n the all the three countres/economc zone does not respond negatvely and sgnfcantly to one standard devaton shocks n the fear ndces. Ths not only 18

19 renforces the results from table 7, but also goes a step ahead n showng that a shock n the fear ndex from one market s not sgnfcantly and negatvely transmtted to leadng economc ndcator n other country/economc zone. *** Please nsert table 9 about here*** Table 9 reports the generalsed mpulse response of the changes n the consumer confdence to transmsson of shocks n domestc and foregn fear ndces. Panel A of table 9 shows the response of the changes n the US consumer confdence ndcator to one standard devaton shocks n VIX, VSTOXX and VFTSE ndces. Smlarly, Panels B and C report the response of changes n the consumer confdence n the UK and the EMU to shocks n these three fear ndces respectvely. We can see that the consumer confdence n the US responds negatvely and sgnfcantly to shocks n the three fear ndces one month after the shock s orgnated. Nevertheless, ths response reduces and becomes nsgnfcant from second month onwards. On the contrary, observng Panel B we can see the consumer confdence n the UK responds postvely and sgnfcantly to shocks n the VFTSE and VSTOXX ndces respectvely. 4.4 Response of monetary polcy ndcators to fear ndces In ths subsecton, we study the response of monetary polcy ndcators to one standard devaton postve nnovaton n the fear ndces n the three economes. In partcular, we examne the response of changes n monetary polcy rates, changes n the 3-month nterbank rates, changes n the yelds of generc 10-year government bonds and changes n the tradeweghted exchange rates n the respectve countres/economc zones. Such an nvestgaton seems useful, as t wll uncover how polcy makers respond to the nnovatons n the correspondng fear ndces and whether there s heterogenety n the response of the three polcy makers n these three countres /economc zone. Moreover, the response of monetary polcy may also provde an explanaton as to why buy-and hold market returns, analysed n secton 4.1, do not respond negatvely to levels and extreme jumps n the fear ndces. *** Please nsert table 10 about here*** Table 10 reports the generalsed mpulse responses of the monetary polcy ndcators to one standard devaton postve shocks to the fear ndces. In partcular, Panel A reports the response of US monetary polcy ndcators to nnovaton n the VIX, panel B reports the response of UK monetary polcy ndcators to VFTSE and fnally, panel C reports the response of the EMU monetary polcy ndcators to VSYOXX. The t-statstcs are reported n 19

20 parentheses and the standard errors requred to compute the t-statstcs are estmated usng Monte Carlo smulaton usng 5000 repettons. Observng panel A, we can see that the Federal Reserve reacts negatvely and sgnfcantly to a postve one standard devaton shock n the VIX ndex. That s, a shock n the VIX by one standard, makes the Federal Reserve nervous enough to relax the monetary polcy and reduce the Fed Funds target rate. The response s sgnfcantly negatve untl four months after the shock to the VIX ndex s observed ntally. Ths s qualtatvely consstent wth results of Bekaert et al., (2013). The nterbank market n the US seems to take about three to four months to respond sgnfcantly to a one standard devaton shock n the VIX. The 3-month US dollar LIBOR respond negatvely and sgnfcantly after three and four months. On the contrary, the yeld on the 10-year US government seems to react mmedately one month after the shock n the VIX s observed. The response of 10-year yeld s sgnfcantly negatve (-0.05). Unlke the response of these ndcators, the response of the trade-weghted US Dollar ndex does not seem to be sgnfcant to a one standard nnovaton n the VIX ndex. Observng Panel B, we can see a smlar reacton by the Monetary Polcy Commttee of the Bank of England. The offcal bank rate responds sgnfcantly and negatvely to a one standard devaton postve shock n the VFTSE ndex after two months and untl four months after the shock s ntally observed. A smlar response can be observed n the UK nterbank market. The 3-month Sterlng LIBOR rates responds negatvely and sgnfcantly to a one standard nnovaton n the VFTSE ndex after 2 months untl 4 months. Smlar to the response of the US dollar trade-weghted ndex, the Sterlng trade-weghted exchange rate ndex also does not respond sgnfcantly to the one standard devaton shock n the correspondng fear ndex. However, unlke the response of the US 10-year government bond yeld, the yeld on the UK 10-year government seems to be mmune from the shocks n the VFTSE ndex. The 10-year government bond yeld does not react sgnfcantly to the shocks n the VFTSE untl next 12- months. From panel C, we can see a smlar response of the European Central Bank (ECB) to a one standard devaton nnovaton to the VSTOXX ndex. ECB s man refnancng rate responds negatvely and sgnfcantly to one standard devaton shocks n the VSTOXX ndex. However, unlke the response of the polcy rates n the US and the UK, the response of the ECB s polcy rate s sgnfcant untl next seven months. Smlarly, the nterbank market n the EMU also respond sgnfcantly negatve to one standard devaton shock n the VSTOXX. The 3-month 20

21 EURIBOR responds negatvely and sgnfcantly to a shock n the VSTOXX after 3 months untl next 7 months. Unlke to the response of the trade-weghted exchange rates n the US and the UK, the trade-weghted exchange rate of EURO reacts sgnfcantly and negatvely to one standard nnovaton n the VSTOXX mmedately after one month. Overall, from table 10 t can be nferred that the monetary polcy makers are more fearful and nervous about the fear ndces n ther respectve stock market. The negatve response of the polcy rates to postve one standard devaton shock n the fear ndces found here are ndrectly consstent wth results Rgobon and Sack, (2003) who fnd that changes n the stock market returns nfluence short term nterest rates n the same drecton. Ths nervous reacton from the polcy makers could be a plausble explanaton for the results n secton 4.1. A postve one standard devaton shock n the fear ndces has a sgnfcant negatve mpact on man polcy rates and the nter-bank rates n these three economes. Ths s could lead push up the prces of rsky assets thereby leadng to hgher realsed returns n the future. 5. Concluson The VIX ndex s colloqually referred to as nvestor fear gauge n asset markets. Fnancal meda unanmously reles on t to report market fear or calm. Besdes ths, academc research has also reled on VIX ndex to develop measures for economc uncertanty and rsk averson n the stock market. Followng the popularty of VIX ndex, smlar ndces have been desgned across the world, for example the VFTSE and the VSTOXX ndces n the UK and EMU. In ths paper, we queston the noton of fear, as reflected and perceved n these ndces, and nvestgate to what extent tradtonal long-term nvestors need to fear these ndces. We test ths from the perspectve of buy-and hold nvestors, whch consttutes majorty of the nvestors n stock market. For ths, we employ long-horzon predctve regressons and test the predctve ablty of the fear ndces and extreme jumps n the fear ndces n predctng longhorzon market returns. Furthermore, we also examne the response of valuaton metrcs to shocks n the fear ndces and also consder the possblty of the transmsson of shocks n the fear ndces from one market to valuaton metrcs n the other. In addton to ths, we also test our central hypothess from the perspectve of monetary polcy makers. To ths end, we examne the response the leadng economc ndcator and consumer confdence ndcator to shocks n the fear ndces. We also examne how money polcy makers and the nterbank market respond to the shocks n the fear ndces. 21

22 The results from long-horzon predctve regressons of market returns on the correspondng fear ndces suggests that long-term nvestors not only need not fear the fear ndces but also the need not fear extreme jumps n these ndces. Ths s because the results show that fear ndces do not predct sgnfcant negatve realsed returns n the future. Furthermore, the valuaton ratos also seems to be sgnfcantly mmune from the shocks n the fear ndces. The examnaton of response of the leadng ndcators and the consumer confdence to the shocks n the fear ndces also seems to reveal that these ndcators are mmune from the shocks n the correspondng as well as the shocks to fear ndces from other markets. The response of monetary polcy makers n the US, the UK and the EMU to the shocks n the correspondng fear ndces, however, appear to be sgnfcantly negatve. That s, man monetary polcy rates respond negatvely (falls down) to shocks n the fear ndces. Smlar response s observed n the nterbank market n these economes. Ths suggest that monetary polcy makers are relatvely more nervous about the shocks n the fear ndces. Ths s could be a plausble explanaton why long-term nvestors do not need to fear these fear ndces. 22

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