Changes in investors risk appetite an assessment of financial integration and interdependence 1

Transcription

1 Changes in invesors risk appeie an assessmen of financial inegraion and inerdependence 1 Laurence Kang-por Fung, Chi-sang Tam 3 and Ip-wing Yu 4 1. Inroducion Invesors aiude owards risk has increasingly been cied as a key facor driving he movemen in asse prices. A sysemaic shif in invesors aiude owards risk, or a decline in invesors risk appeie, may cause correlaion among prices of differen financial asses, hus undermining financial sabiliy and heighening he risk of financial conagion. Therefore, i is imporan o cenral banks o have he necessary ools ha allow he policy makers o rack he dynamics of invesors risk appeie and undersand he possible linkages beween risk appeies across differen markes. However, in recen sudies, he focus is mainly on developing indicaors o measure he risk appeie and showing he coincidence beween episodes of financial urmoil in individual counries and abrup declines in marke senimen from risk seeking o risk avoidance. 5 This paper conribues o he lieraure by applying he risk appeie measure o cenral banks monioring work in wo aspecs. Firs, i invesigaes wheher changes in he risk appeie are correlaed among differen economies (he Unied Saes (), he Unied Kingdom (),, and Hong Kong SAR () in his paper) and provides a measure of financial inegraion beween hem. Second, by examining he degree of comovemen beween he risk appeie measures and he sock and bond marke performance, i sheds he ligh on he inerdependence beween he sock and bond markes in hese economies, which may give rise o possible conagion risk during financial marke urmoil. The remainder of his paper is organised as follows. In Secion II, we provide a brief discussion on how we derive he risk appeie measures for he five economies. In his sudy, he derivaion of he risk appeie measures is based on he mehodology recenly proposed by Gai and Vause (006). Secion III reviews he issues relaed o financial inegraion and provides he various inegraion indicaors used in his sudy. The esimaion resuls of he inegraion indicaors and he empirical evidence of financial marke inerdependence based on dynamic condiional correlaions are presened in Secion IV. Secion V is a summary and conclusion The views and analysis expressed in his paper are hose of he auhors, and do no necessarily represen he views of he Hong Kong Moneary Auhoriy (HKMA). The auhors are graeful o Hans Genberg and Chohoi Hui for heir useful commens. We are also hankful o Ronald Ka-wai Leung, who worked as a summer inern a he HKMA in 007, for his ousanding research assisance. The assisance of he Chicago Board Opions Exchange (CBOE) in providing hisorical S&P 500 Index Opions daa is graefully acknowledged. All remaining errors are ours. Hong Kong Moneary Auhoriy; Laurence_KP_Fung@hkma.gov.hk. Hong Kong Moneary Auhoriy; Chi-sang_Tam@hkma.gov.hk. Hong Kong Moneary Auhoriy; Ip-wing_Yu@hkma.gov.hk. A survey of risk appeie indicaors can be found in Illing and Aaron (005). 94 IFC Bullein No 31

2 . Measure of invesors risk appeie The degree of invesors risk appeie can no be observed direcly in he marke. In he lieraure, here are differen marke-based and heory-based risk appeie measures proposed by financial insiuions, cenral banks as well as inernaional organisaions for monioring purposes. 6 In his sudy, we uilise he mehodology recenly developed by Gai and Vause (006) o derive he risk appeie measure which has is origin from he basic pricing equaion in he asse pricing heory. 7 While he analysis of asse pricing shows ha risky asses can be priced by evaluaing he expecaion of discouned payoffs in erms of invesors subjecive probabiliies abou various saes of he world, risk-free asse can be equivalenly deermined by discouning payoffs using he risk-free rae and evaluaing expecaions based on a se of risk-neural probabiliies. In heir paper, Gai and Vause show ha he measure of risk appeie can be deermined once he subjecive and he risk-neural probabiliy densiy funcions over fuure asse reurns are esimaed. This sudy follows Gai and Vause s mehod and esimaes he invesor s subjecive and he risk-neural probabiliy densiy (RND) funcions over fuure asse reurns, in his case he sock marke reurns. The underlying sock marke indices of he five economies where invesors risk appeie measures are derived are: Economy The Unied Saes The Unied Kingdom Hong Kong SAR Benchmark sock marke index S&P 500 Index FTSE 100 Index DAX 30 Index Nikkei 5 Sock Average Hang Seng Index The benchmark sock marke indices are aken from CEIC. Hisorical S&P 500 Index Opion daa are provided by he Chicago Board Opions Exchange (CBOE), while he index opion daa of oher sock marke indices are aken from Bloomberg. For each underlying sock marke index, seven spo monh conracs are considered for he RND esimaion. These seven conracs have srike prices a he curren index level and a hree srike inervals above and below he curren index level. 8 The risk-free ineres rae used in he RND Examples of risk appeie measures include he JPMorgan Liquidiy, Credi and Volailiy Index (LCVI), he Merrill Lynch Financial Sress Index, he Sae Sree s Invesor Confidence Index, he Credi Suisse Firs Boson Risk Appeie Index, he Goldman Sachs Risk Aversion Index, he Chicago Board Opions Exchange Volailiy Index (VIX), he Kumar and Persaud (00) Global Risk Appeie Index (GRAI) used by he IMF, he Tarashev e al. (003) Risk Appeie Index used by he BIS, and he Gai and Vause (006) Risk Appeie Index used by he Bank of England and he HKMA. Illing and Aaron (005) provide a brief survey of hese risk appeie measures. The approach by Gai and Vause (006) has some advanages over oher alernaive measures. For insance, he index developed by Gai and Vause is easier o inerpre han he JPMorgan LCVI because of he laer s ad hoc mehodology o aggregae differen financial risks. The srike inerval is differen for differen sock marke index opions. I is 5 index poins for he S&P 500 Index Opion, 5 index poins for he FT100 Index Opion, 50 index poins for he DAX 30 Index Opion, 500 index poins for he Nikkei 5 Sock Average index Opion, and 00 index poins for he Hang Seng Index Opion. IFC Bullein No 31 95

3 esimaion is he one-monh inerbank rae of he respecive economy. 9 According o Gai and Vause (006), he uni price of risk ( λ ) a ime can be derived as: λ = 1 f R + 1 f var( f * ( s) ) ( s) where R is he gross risk-free rae of reurn a ime, f * ( s ) is he RND of he asse price s f a ime, f (s) is he subjecive hisory implied densiy funcion of he asse price s a ime, and var( ) is he variance operaor. The uni price of risk λ is he expeced excess reurn ha invesors require o hold each uni of risk of an asse in equilibrium. Risk appeie, which is he willingness of invesors o bear risk, can herefore be defined as he naural logarihm of he inverse of λ. In his sudy, similar o Gai and Vause, he subjecive probabiliy disribuion of fuure asse reurns is derived from he GARCH (1,1) model, while he risk-neural densiy funcion is esimaed by opion prices using he wo-lognormal mixure models. Full deails of he esimaion mehodology are given in Appendix I. Figure 1 shows he movemens of he derived risk appeie measures for invesors in he sock markes of he, he, (Figure 1a), and (Figure 1b) from heir earlies daa available up o December Higher values of his measure are inerpreed as an indicaion of higher risk appeie (higher invesor olerance of risk) for invesors. Figure 1 Risk appeie measures of differen sock markes (a) The, he and (b) and Risk appeie measure 8.0 Increase in risk appeie Concern over he sub-prime probelm Risk appeie measure Burs of he echnology bubble Increase in risk appeie -8.0 Jan-99 Jan-01 Jan-03 Jan-05 Jan Jan-96 Jan-98 Jan-00 Jan-0 Jan-04 Jan Source: HKMA saff esimaes For he, i is he dollar London Inerbank Offered Rae (LIBOR). The Briish Pound LIBOR for he, he Frankfur Inerbank Offered Rae for, he Tokyo Inerbank Offered Rae for and he Hong Kong Inerbank Offered Rae for. Daa are aken from Bloomberg. The saring daes of he risk appeie measures vary due o he availabiliy of index opion daa. The risk appeie measure for he sars from December 001. I is February 1999 for he, January 000 for, December 1999 for and January 1996 for. 96 IFC Bullein No 31

4 Similar o he observaion by Illing and Aaron (005), he risk appeie measures in he wo graphs in Figure 1 are quie volaile. Despie his, hey generally conform o he asse price swings in recen episodes of exreme marke senimen. For example, in he case of he in Figure 1a, he risk appeie measure declined when he sub-prime problem and he subsequen credi crunch emerged in July-Augus 007. In he case of in Figure 1b, he risk appeie measure dropped abruply o a low level during he period beween Ocober 1997 and January 1998 amid he speculaive aack agains he dollar resuling in grea financial marke disress. The burs of he echnology bubble in mid-000 and he subsequen bear marke unil he end of 00 coincided wih he gradual decline of he risk appeie measure. The bull run in he sock marke saring from he second half of 006 was also refleced in he sharp rise of he measure. In he analyses ha follow, we invesigae he financial marke inegraion and conagion issues hrough he examinaion of he risk appeie measures and heir ineracions wih he sock and bond markes Financial inegraion and inegraion indicaors There is, in general, no universal definiion of financial inegraion. Financial openness, free movemen of capial and inegraion of financial services are par of a broad range of definiion frequenly cied in he lieraure. 1 One commonly used definiion of financial inegraion is ha financial markes are said o be inegraed when he law of one price holds. Korajczyk (1995) noes ha if markes are financially inegraed, he price of risk should be he same across markes. Since he Gai and Vause s measure of risk appeie is defined as he inverse of he price of risk, we make use of heir measure and sudy he issue of financial inegraion by invesigaing wheher invesors willingness o bear risk is he same across differen markes. For monioring purposes, i is desirable for policy makers o have indicaors ha are frequenly available. In his sudy, we use monhly daa o consruc several indicaors o measure differen dimensions of marke inegraion in he five sock markes (namely he, he,, and ), including 1. cross-marke dispersion and correlaion;. he componen facors based on he principal componen analysis; 3. ime-varying β esimaed via Haldane and Hall (1991) Kalman filer mehod; and 4. dynamic condiional correlaion. 13 These indicaors are mainly model-based and provide high frequency measures for regular monioring purposes (see Table 1 below for a summary of he inegraion indicaors in his sudy). Deailed discussions on he mehodologies of consrucing hese indicaors and heir inerpreaion are presened in Appendix II. Given ha he consrucion of hese indicaors is The examinaion is based on boh he changes of hese measures and also he levels when i is appropriae. In some sudies, regulaory and insiuional facors such as he relaxaion of capial conrols, financial liberalisaion, prudenial regulaions, efficiency of he legal sysems and he sandardisaion of marke framework are also cied as measures of financial inegraion. These measures, however, are less popular han price-based measures in a regular monioring framework as hey are no imely available. Changes in risk appeie are used for he derivaion of he cross-marke dispersion and correlaion, he Haldane and Hall (1991) Kalman filer indicaor and he dynamic condiional correlaion, while boh levels and changes are used respecively in he principal componen analysis. IFC Bullein No 31 97

5 subjec o echnical limiaions and modelling assumpions, as well as he raher shor daa sample available, hese indicaors should be inerpreed wih cauion and aken as indicaive bu no conclusive evidences on he general rend of he inegraion process. Table 1 Summary of inegraion indicaors Mehod Indicaor Indicaion of marke inegraion Cross-marke dispersion and correlaion Principal componen analysis Haldane and Hall (1991) Kalman filer mehod Dynamic condiional correlaion (DCC) model Hodrick-Presco filered dispersion and correlaion The facors derived from he principal componen analysis Time-varying β esimaed via Kalman filer Time-varying correlaion esimaed from he DCC model Falling dispersion and high level of posiive correlaion imply higher convergence and larger comovemen The idenificaion of a small number of common facors which are able o explain a high proporion of oal variance among he risk appeie measures Average β moving owards zero indicaes an increasing sensiiviy o regional influence The higher he correlaion, he larger he co-movemen beween markes is 4. Esimaion resuls 4.1 Inegraion indicaors and financial inegraion The risk appeie measures of invesors in he sock markes of he, he,, and, as shown in Figure 1, are used o examine he financial inegraion beween hese sock markes. This is done by looking a wheher invesor senimen (as indicaed by hese risk appeie measures) spreads over naional boundaries. As a preview, Tables and 3 provide he simple cross-marke correlaion coefficiens beween hese risk appeie measures in heir levels and heir changes respecively. Table Cross-marke correlaion marix of risk appeie measures (a) Common sample (December 001 o December 007) * * * * IFC Bullein No 31

6 Table (con) Cross-marke correlaion marix of risk appeie measures (b) Pair-wise bilaeral sample * * * * indicaes significance a he 5% confidence level. Source: HKMA saff esimaes. Table shows ha in heir levels, he cross-marke correlaion coefficiens range from 8 o 0.4. Less han half of he cross-marke correlaion coefficiens are saisically differen from zero, suggesing a very limied co-movemen beween hese risk appeie measures. The pair of risk appeie measures ha has he highes (posiive) correlaion coefficien is and a 85 (common sample) and 0.41 (pair-wise bilaeral sample), while he correlaion coefficiens beween he and as well as he and are around and. Table 3 Cross-marke correlaion marix of risk appeie measures (a) Common sample (January 00 o December 007) (b) Pair-wise bilaeral sample Source: HKMA saff esimaes. IFC Bullein No 31 99

7 For he changes in heir risk appeies, he co-movemen is even smaller. The correlaion coefficiens range from o 3 and none of hem is saisically differen from zero, suggesing ha here is lile connecion beween he changes in risk appeie among hese economies Cross-marke dispersion and correlaion The cross-marke dispersion approach suggess a sense of convergence beween he changes in he risk appeie measures if heir discrepancy is falling and becoming small. The series of dispersion is filered using he Hodrick-Presco (HP) smoohing echnique o reveal he long-erm rend componen of he series. Figure Cross-marke dispersion indicaor Cross-marke dispersion HP-filered rend Source: HKMA saff esimaes. Figure shows ha he dispersion depics a gradual decline since mid-004, suggesing ha he variaion beween he changes in he risk appeie measures has narrowed and some kind of convergence process may have aken place bu hen salled since mid-006. As he dispersion indicaor does no provide any indicaion of co-movemen, Figure 3 illusraes he cross-marke covariance and correlaion. 300 IFC Bullein No 31

8 Figure 3 Cross-marke covariance and correlaion of he changes in he risk appeie measures (a) Covariance (b) Correlaion Cross-marke covariance HP-filered rend Cross-marke correlaion HP-filered rend Source: HKMA saff esimaes. The cross-marke correlaion is defined as he raio of cross-marke covariance o he square of cross-marke dispersion. An increase in he correlaion can sem eiher from an increase in he covariance or from a reducion in he dispersion. The cross-marke correlaion as shown in Figure 3b varies and ranges from 5 o From he HP filered rend line, i is shown ha he only significan posiive correlaion was around lae 004 o early 006 (which coincides wih he gradual decline in he dispersion and he increase in covariance). The cross-marke correlaion was slighly negaive by he end of 007. Judging from he crossmarke dispersion and he correlaion of he risk appeie measures, even hough he dispersion indicaor has narrowed, i has salled since mid-006. Wih he low level of crossmarke correlaion, he exen of marke inegraion beween hese five sock markes is no apparen Principal componen analysis The main objecive of principal componen analysis (PCA) is o find a small number of facors ha can explain mos of he variaion in he original daa series. In many sudies, he PCA has been used regularly as one of he ools for he idenificaion of a common facor among differen risk measures. For insance, wih a se of eigh risk premia on corporae bond spreads and swap spreads of he euro area, he and emerging markes, Couder and Gex (006) are able o derive he firs componen facor which explains 68% of he common variaion of hese risk premia. Wih he risk aversion indicaors of he, he and, Tarashev e al. (003) derive he firs principal componen which accouns for 80% of he overall variaion in is consiuen series. This is inerpreed as a common facor driving he dynamics of he hree risk aversion indicaors. In his secion, he risk appeie measures of he five sock markes in boh heir levels and changes are used in he PCA o exrac a lis of common facors. 14 Table 4 repors he PCA resul based on he level. 14 The PCA is conduced afer mean cenering he original risk appeie measures, eiher in heir levels or changes. For he definiion of mean cenering and oher deails, please refer o Appendix II. IFC Bullein No

9 Eigenvalue Table 4 Principal componen analysis resul (based on he levels) Value Proporion of variance explained Each eigenvalue represens he proporion of variance accouned for by he corresponding principal componen (PC). Normally, he firs principal componen accouns for as much of he variabiliy in he daa as possible, and each succeeding componen accouns for as much of he remaining variabiliy as possible. Source: HKMA saff esimaes. Two crieria are used o choose he number of principal componens in his analysis. The Kaiser (1960) crierion keeps hose principal componens wih heir corresponding eigenvalues greaer han one. The Joliffe (197) crierion discards hose remaining principal componens once he percenage of explained variance reaches a cerain hreshold (for example 80%). The resul shown in Table 4 indicaes ha he firs wo principal componens, PC1 and PC, saisfy he Kaiser crierion as heir corresponding eigenvalues are greaer han one. However, hese wo PCs accoun for only 5.% of he variabiliy in he daa, wih he PC1 explaining a mere 8.5% of he common variaion. Based on he Joliffe crierion, i akes a oal of four PCs agains he five risk appeie measures in order o accoun for abou 87% of he oal variance of hese measures. 15 These findings seem o sugges ha here does no exis one common facor ha drives hese risk appeie measures. The sysemaic shif in invesors risk appeie across financial markes can also be assessed by how he changes in he risk appeie measures are correlaed. Table 5 repors he PCA resul based on he changes in he risk appeie measures in he five economies. 15 If he underlying series are highly correlaed, normally i akes only a few componen facors o explain a large bulk (for example 80%) of he oal variance, and he firs componen facor, which is generally inerpreed as he common facor of he underlying series, usually consiues he larges proporion (60% o 70%) of he common variaion. 30 IFC Bullein No 31

10 Table 5 Principal componen analysis resul (based on he changes in he risk appeie measures) Eigenvalue Value Proporion of variance explained Each eigenvalue represens he proporion of variance accouned for by he corresponding principal componen (PC). Normally, he firs principal componen accouns for as much of he variabiliy in he daa as possible, and each succeeding componen accouns for as much of he remaining variabiliy as possible. Source: HKMA saff esimaes. Based on he Kaiser crierion, he firs hree PCs are chosen as heir corresponding eigenvalues are greaer han one. Neverheless, hese hree PCs accoun for less han 70% of he oal variance, wih he firs PC explaining only 6.3% of he variabiliy of he original daa. In erms of he Joliffe crierion, a oal of four PCs is needed o reach he hreshold of 80% explained variabiliy. Therefore, similar o he resuls based on he level measure, here does no exis any significan facor driving he changes in he risk appeies in hese economies. From he above PCA, he dynamics of he risk appeie measures, eiher in levels or changes, are likely o be driven by more han one facor. As a resul, he five sock markes ogeher are hardly inegraed Haldane and Hall (1991) Kalman filer mehod For his indicaor, we ake he changes in he s risk appeie measure as he dominan source. Based on he signal equaion of Equaion (A10) in Appendix II, he esimaed β measures he sensiiviy of an individual economy s risk appeie changes o ha in he relaive o ha in anoher economy. An economy s risk appeie changes which are more sensiive o he changes in he risk appeie in he will show β s rending close o one, a sign inerpreed as a convergence (or inegraion) wih he marke. A endency for β o approach owards zero suggess a convergence wih anoher marke. Negaive values of β or β s greaer han one sugges ha he marke drifs away from he and he oher 16 I is noed ha Tarashev e al. (003) obain he firs principal componen which accouns for 80% of he overall variaion in is hree risk aversion indicaors of he, he and. To examine wheher his is sill rue in recen years, we also apply he PCA on he risk appeies of hese hree economies using our risk appeie measures. The new PCA resuls show ha he firs principal componen only accouns for 44% of he common variaion in he hree risk appeie measures in heir levels and 38% in heir changes respecively. The new resuls sugges ha here is only a weak common facor driving he dynamics of he risk appeie measures in hese hree economies. IFC Bullein No

11 markes. Figure 4 shows he paerns of he β esimaes for each of he marke oher han he. Figure 4 Haldane and Hall sensiiviy indicaor (β ) (based on he changes in he risk appeie measures) vs vs vs vs -1.0 vs vs vs vs vs vs vs vs A endency for β o approach owards one suggess a convergence wih he s risk appeie change. Source: HKMA saff esimaes. From Figure 4, in he case of, is β esimaes are found o be more sensiive o he changes in he risk appeie measures of he and, as he respecive β esimaes were closer o zero (around ) han one in he period beween January 00 and Sepember 003. They began o rend upward in 004, suggesing an increase in he sensiiviy of he changes in s risk appeie o he s changes. The β esimaes varied wih respec o and he. Bu since 007, he sensiiviy o he change in ese risk appeie had increased. Such resuls appear o sugges an increased influence from and a gradual decline in he sensiiviy wih he and. The siuaion is very much he same in, where he influence from he and had compleely been dominaed by ha from he, while he sensiiviy o ha of had also increased since 007. For he, he paern of is β esimaes indicaes ha i had been consisenly more sensiive o ha from han from he. While is sensiiviy o ha of had declined, influence from had picked up. Finally, for, is β esimaes for he pas wo years poined o an increased sensiiviy o ha of he, as he β esimaes rended owards one. The overall resuls from he Haldane and Hall 304 IFC Bullein No 31

12 approach sugges some sors of marke segmenaion beween he five sock markes. While he risk appeie measures of and in heir changes are very sensiive o each oher, he influence of he on hem has been increasing. The German s risk appeie changes are highly influenced by ha of he, while ha of he is closer o he German s. As he convergence processes from hese four markes (wih he as he major source of influence) did no poin o any paricular marke as a dominan facor, hese five markes are no highly inegraed Dynamic condiional correlaion (DCC) A GARCH(1,1)-DCC model using a wo-sep esimaion procedure as oulined in Appendix II is esimaed wih monhly changes in heir risk appeie measures. Basically, higher and posiive correlaion beween he changes in he risk appeie measures implies higher comovemen and greaer inegraion beween he markes. Table 6 highlighs he average pairwise dynamic condiional correlaion beween he changes in hese risk appeie measures. Table 6 Average pair-wise condiional correlaion (based on he changes in he risk appeie measures) Source: HKMA saff esimaes. The able shows ha, in general, he co-movemens beween he changes in he risk appeie measures are no high wih heir condiional correlaions ranging from -30 o 67 only. Of he en pair-wise risk appeie measures, only hree pairs are posiively correlaed. The resul is similar o ha repored in Table based on simple correlaion. The hree posiivelycorrelaed pairs are, and. Again, he resuls coincide wih he findings from he Haldane and Hall approach which show ha he changes in risk appeie is highly sensiive o ha of, he German marke is more influenced by he marke and he change in he risk appeie is closer o ha of. Figure 5 shows he ime-varying condiional correlaions beween he five risk appeie measures. IFC Bullein No

13 Figure 5 DCCs of risk appeie measures (based on he changes in he risk appeie measures) Source: HKMA saff esimaes. From he graphs in Figure 5, he condiional correlaions are in general smooh wih only occasional spikes. For hose economies wih heir changes in he risk appeie posiively correlaed, heir condiional correlaions are low and less han. Given ha he condiional correlaions are a a low level wih only hree pairs of he risk appeie measures are posiively correlaed, and heir condiional correlaions are no even increasing, he five financial markes do no appear o be inegraed. Overall, our four inegraion indicaors sugges a limied degree of inegraion beween he sock markes in he, he,, and. The only encouraging sign is from he dispersion indicaor which shows a gradual declining rend in he discrepancy bu he process appears o be salled since mid-006. Even if he risk appeies in hese markes are no equal, i is sill possible ha a shif in invesors risk appeie in one paricular 306 IFC Bullein No 31

14 economy has an influence on oher economies financial markes because of he paricipaion of inernaional invesors in heir domesic markes. The nex secion invesigaes he inerdependence beween financial markes arising from changes in invesors risk appeie. 4. Financial marke inerdependence Apar from examining he issue of financial inegraion, he risk appeies in he five economies are also used o assess he inerdependence beween financial markes. This is done by examining he co-movemen beween hese risk appeie measures and he performance in he sock and bond markes using he dynamic condiional correlaion mehod (DCC). In he analysis ha follows, for he sock marke he DCC is conduced in erms of he changes in he risk appeie measures and he sock marke reurns. In general, one would expec a posiive relaionship (posiive DCC) beween he changes in he risk appeie measures and he sock marke reurns. Hence, an increase (decrease) in invesors risk appeie is associaed wih a rise (fall) in he sock marke. For he bond marke, he DCC is relaed o he risk appeie levels and he benchmark bond yields of differen mauriies. The fligh-o-qualiy phenomenon of he bond marke suggess a posiive relaionship (posiive DCC) beween he risk appeie levels and he bond yields. For insance, if invesors become more risk averse (heir risk appeies fall), hey seek a safe haven by invesing in he bond markes, hus bidding up bond prices and leading o a fall in bond yields. In addiion o he inra-economy co-movemen beween an individual economy s risk appeie measure and is sock and bond markes, we are also ineresed in he iner-economy spillover effec across anoher economy s sock and bond markes. Such an analysis should provide insigh on he possible conagion risk arising from a sysemic shif in invesors risk appeie. We mus emphasise ha he analyses are no examining he causal relaionship or he ransmission mechanism beween risk appeie changes (level) and sock (bond) marke performance, bu simply looking ino heir co-movemen and correlaion. Table 7 shows he average condiional correlaions beween he changes in he risk appeie measures and he monhly reurn of he sock marke benchmark indices. 17 Table 7 Average condiional correlaion beween he changes in he risk appeie and he sock marke reurn Sock marke Risk appeie Source: HKMA saff esimaes. 17 The monhly reurn of he sock marke is calculaed as he log difference of he sock marke benchmark index. IFC Bullein No

15 The diagonal elemens in he able show he inra-economy condiional correlaion beween he changes in he risk appeie measures and he sock marke reurn. I is shown ha for he, and, he inra-economy condiional correlaions are posiive, while for he and, hey are negaive. Thus, he convenional inuiion ha an increase (decrease) in invesors risk appeie is associaed wih a rise (fall) in he sock marke can be applied o he sock markes in he, and, bu no o hose in he and. The resuls from iner-economy condiional correlaions (he off-diagonal elemens) are more revealing. I is shown ha he changes in he risk appeie in and are posiively relaed o he sock marke reurns of oher economies (wih he excepion of s risk appeie changes and s sock marke reurn performance). Hence, a drop in invesors risk appeie in eiher or will be associaed wih falls in oher economies sock markes. Changes in he s risk appeie are also posiively relaed o he sock marke reurns in and, while hey are negaively relaed o ha in he and. Thus, here may be possible conagion effec beween he changes in he risk appeies in he, and and he sock marke reurns, given ha hey are posiively inerdependen. On he conrary, risk appeie changes in he and are negaively associaed wih oher economies sock marke reurn. Figure 6 shows he imevarying condiional correlaions beween individual economy s risk appeie and heir sock marke performance. Figure 6 DCCs of individual economy s changes in he risk appeie and he sock marke reurn IFC Bullein No 31

16 Source: HKMA saff esimaes. The graphs in Figure 6 show ha he condiional correlaions vary a lo bu in general move in a igh range wih occasional spikes. For hose posiive condiional correlaions, hey are generally low and less han 0.4. There is no clear indicaion of paricular rend or paern in he condiional correlaions. To assess he inerdependence in he bond marke, we examine he ineracion beween he risk appeie measures and he yields of 3-monh as well as 10-year governmen bonds respecively. 18 The resuls may reveal wheher he fligh-o-qualiy phenomena from sock o bond markes are apparen in hese five economies. Table 8 provides he average condiional correlaions beween he risk appeie measures and he governmen bond yields. Table 8 Average condiional correlaion beween risk appeie measures and governmen bond yields (a) 3-monh governmen bond (b) 10-year governmen bond Risk appeie GER JAP HK SAR GER JAP HK SAR GER JAP HK SAR The abbreviaions in he able are as follows: GER for and JAP for. Source: HKMA saff esimaes. 18 All yield daa are he yields of he benchmark governmen bonds and are aken from CEIC. Noe ha for, he 3-monh governmen bill yields are hose of he 3-monh Exchange Fund Bills, while he 10-year governmen bond yields are hose of he 10-year Exchange Fund Noes. For, he 3-monh yield is he 3-monh EURIBOR. IFC Bullein No

17 The condiional correlaions as shown in Table 8 are mosly posiive regardless of he mauriy. The condiional correcions beween he risk appeie measures and he 3-monh yields (ranging from 5 o 0.78) are, in general, higher han hose beween he risk appeie measures and he 10-year yields (from -9 o 0.45). This suggess ha he relaionship beween he risk appeie measure and he bond yield is sronger for bonds wih a shorer mauriy han hose wih a longer mauriy. The diagonal elemens under he wo mauriies show he inra-economy condiional correlaion beween an economy s risk appeie and is corresponding governmen bond yields. I is shown ha he inra-economy condiional correlaions are all posiive. Such a posiive relaionship suggess ha, o a cerain exen, here exiss a fligh-o-qualiy phenomenon in he bond marke of hese five economies. As invesors become more risk averse (heir risk appeies fall), hey seek a safe haven by invesing in he bond markes, hus bidding up bond prices and leading o a fall in bond yields. The resuls from iner-economy condiional correlaions are also consisen wih he fligh-oqualiy phenomenon as all bu one off-diagonal condiional correlaion are posiive. The only excepion is he condiional correlaion beween s risk appeie and German s 10-year bond yield which is negaive bu a a low level. The degree of posiive associaion beween he risk appeie level and he bond yields in he economies are also differen o each ohers. For insance, he condiional correlaions beween he risk appeie measures in he, he and and he 3-monh bond yields (from 3 o 0.78) are much higher han he correlaions beween he risk appeie measures of heir Asia counerpars and he 3-monh bond yields. Meanwhile, beween he wo Asian economies, he condiional correlaions beween he risk appeie measure in and he 3-monh bond yields (from 5 o 0.58) are higher han he risk appeie measure in and he 3-monh yields (from 9 o 8). The resuls highligh he fligh-o-qualiy phenomenon in he bond marke of he five economies when invesors in a paricular economy are becoming risk averse. The imevarying condiional correlaions beween individual economy s risk appeie measures and he bond marke performance are given in Figures 7 and 8. Figure 7 DCCs of individual economy s risk appeie measures and 3-monh bond yields IFC Bullein No 31

18 Source: HKMA saff esimaes. The graphs in Figure 7 show ha he condiional correlaions beween he risk appeie measures and he 3-monh bond yields vary and in a few occasions hey urn ino a negaive relaionship. Such a negaive correlaion is he mos obvious beween he risk appeie measure in and he 3-monh bond yields during mid-00 o mid-003 and he whole year of 004. Noe ha during hese wo periods, he risk appeie measures in were a a low level (see Figure 1b), which was associaed wih higher 3-monh bond yields (lower bond prices) in he five economies, suggesing a possible conagion effec for bonds wih a shor mauriy when ese invesors became risk averse. Noneheless, he condiional correlaions are mosly posiive over he sudy period and many of hem were a a high level (above 0.5) a he end of 007. Figure 8 DCCs of individual economy s risk appeie measures and 10-year bond yields IFC Bullein No

19 Source: HKMA saff esimaes. The condiional correlaions beween he risk appeie measures and he 10-year bond yields in Figure 8 are very smooh. For he risk appeie measures in he and, heir correlaion wih oher economies 10-year bond yields were rending upwards, suggesing an increasing relaionship beween he wo. The correlaions beween s risk appeie measure and 10-year bond yields also increased bu have levelled off since early 006. For he and, he condiional correlaions beween heir risk appeie measures and he bond yields were also a a relaively high level, suggesing evidence of fligh-o-qualiy due o he sock marke urmoil near he end of Summary and Conclusion This sudy exends he use of invesors risk appeies in cenral banks monioring work in wo aspecs, namely financial inegraion and cross-border financial marke inerdependence. Various inegraion indicaors are consruced o gauge he relaionship beween he risk appeies derived for five economies: he, he,, and. Furhermore, we examine he degree of co-movemen beween he risk appeie measures and he sock and bond marke performances in hese economies. The evoluion of such comovemens provides some insighs o policy makers on he inerdependence beween sock and bond markes in hese economies, which may give rise o possible conagion risk during financial marke urmoil. Table 9 provides a summary on he financial marke inegraion aspec from he indicaors derived using he risk appeie measures. 31 IFC Bullein No 31

20 Table 9 Summary of financial marke inegraion Mehod Indicaion of marke inegraion Resul Cross-marke dispersion and correlaion Principal componen analysis (PCA) Haldane and Hall (1991) Kalman filer mehod Dynamic condiional correlaion (DCC) model Falling dispersion and high level of posiive correlaion imply higher convergence and greaer comovemen The idenificaion of a small number of facors which are able o explain a high proporion of oal variance among he risk appeie measures Average β moving owards zero indicaes an increasing sensiiviy o regional influence The higher he (posiive) correlaion, he larger he comovemen beween markes is Even hough he dispersion indicaor has narrowed, i has salled since mid The degree of posiive crossmarke correlaion is also a a low level The PCA resuls (based on levels or heir changes) are less han saisfacory and we fail o obain a firs componen facor ha can accoun for a large proporion of he common variaion beween he risk appeie measures The overall resuls sugges some degrees of marke segmenaion beween he five sock markes, and no paricular marke acs as a dominan facor in influencing he risk appeie of anoher economy For hose posiive condiional correlaions, hey are generally low and less han 0.4. There is no clear indicaion of paricular rend or paern in he condiional correlaions From Table 9, despie he differen focus of each of hese indicaors, he picure ha emerges from he empirical resuls is quie uniform. In erms of co-movemen, boh he crossmarke correlaion and he DCC poin o a low level of correlaion beween he changes in he risk appeie measures. While he dispersion has narrowed, he process has haled since mid-006. Resuls from he Haldane and Hall approach sugges ha here is no indicaion of a paricular economy whose changes in risk appeie play a dominan role in influencing oher economies risk appeie changes. Finally, as he firs componen facor derived from he PCA is unable o accoun for a high proporion of he common variaion among he risk appeie measures (eiher in heir levels or changes), i is difficul o conclude ha a common facor is driving he dynamics of hese risk appeie measures. There may only be a weak inegraion beween he five financial markes and our inegraion indicaors sugges some degrees of marke segmenaion in he process. For insance, he risk appeie measures of and, eiher in heir levels or changes, are negaively correlaed wih he firs common facor from he PCA, when oher economies risk appeie measures are posiively relaed o ha common facor. Furhermore, resuls from he Haldane and Hall approach also indicae ha he changes in risk appeie measures of and are very sensiive o each oher. Meanwhile, he risk appeie in is highly influenced by ha of he, while ha of he is closer o he German risk appeie measure. While here is limied financial inegraion among he five sock markes, however, he risk appeie measures reveal he inerdependence beween shifs in he risk appeie measures and financial marke performance. For he sock marke, he resuls from he dynamic condiional correcion indicae ha here may be possible conagion risk beween changes in he risk appeies in he, and and he sock marke performance, given ha hey are posiively inerdependen. For he bond marke, wih mainly posiive correlaions beween he risk appeie measures and he 3-monh or 10-year governmen bond yields, he fligh-o-qualiy phenomenon is apparen in he bond marke of he five economies. IFC Bullein No

21 Given he informaion conained in invesors risk appeie measures and he evidence of inerdependence in he sock markes, policy makers should coninue monioring heir movemens for financial sabiliy reasons. However, as invesors risk appeie is no direcly observable in he marke and he developmen of he mehodology for he derivaion of invesors risk appeie is sill an on-going process, he applicaion of he risk appeie measure in cenral banks monioring framework should be used wih cauion. 314 IFC Bullein No 31

22 Appendix I: Mehodology for he derivaion of he risk appeie measures This Appendix provides a brief descripion of he Gai and Vause (006) mehodology for he derivaion of he risk appeie measures. As menioned in he main ex, he derivaion of he invesor s risk appeie requires he esimaion of he opion-implied risk-neural probabiliy densiy (RND) funcion and he subjecive hisory implied densiy funcion. The following secions describe he mehods for finding hese wo funcions. AI.1 Esimaing he RND by fiing he wo-lognormal mixure disribuion The prices of European call and pu opions a ime can be wrien as he discouned sums of expeced fuure payoffs: rτ X c ( X, τ) = e f * ( S )( S X ) ds T T T (A1) X rτ p ( X, τ) = e f *( S )( X S ) ds 0 T T T where c ( X, τ) and p ( X, τ) are he call and pu prices respecively. The opion prices are funcions of he srike price (X ), he ime o mauriy (τ), he asse price a he expiry ( S T ), he risk-free ineres rae (r) and he densiy funcion of he asse price as a expiry ( f * ( ST )). Assuming ha he densiy funcion is a wo-lognormal mixure, f * ( ST ) a ime can hen be expressed as: f ( ST ) = i L( ai, bi ; ST ) 1θ where: i= σi a i = ln S + ( μi ) τ (A4) b σ τ (A5) i = i L ( ai, bi ; ST ) is he i-h lognormal densiy funcion wih parameers a i and b i, θ i is he weigh of he i-h densiy in he mixure and he mixures are summed o uniy, μ i and σ i are he mean and volailiy (in sandard deviaion) of asse reurn respecively. A any ime, five parameers ( a 1, b1, a, b, θ1 ) in he wo-lognormal densiy funcions are esimaed by solving he following minimisaion problem: (A) (A3) Min ai, b1, a, b, θ1 { N n= 1 [ c( X, τ) c obs ] + N n= 1 [ p( X, τ) p obs ] } (A6) IFC Bullein No

23 where N is he number of possible expiry asse price, c obs and p obs are he observed call and pu prices a respecively. By subsiuing he esimaed parameers from (A6) ino (A3), he probabiliy densiy a differen prices can be calculaed accordingly. 19 AI. Esimaing he subjecive probabiliy by he hreshold GARCH model The subjecive hisory implied probabiliy is esimaed by he hreshold GARCH model of he underlying sock marke index reurn ( r ) 0 : r = β + ε (A7) σ = φ + φ ε + φ ε D + φ σ (A8) D = 1 if ε < 0 and 0 oherwise (A9) where r is he reurn of he sock marke index a, σ is he volailiy of he reurn which follows he hreshold GARCH (1,1) model. To derive he risk appeie measure a ime, we need o obain he forecas of he subjecive probabiliy as a + 1. For his purpose, we firs esimae he GARCH model by he daa up o ime. In order o have monhly esimaes of he mean reurn and he variance, and in view of he possible srucural change in he daa series, he GARCH esimaion is based on a 10-year rolling sample. The expeced reurn and variance of he reurn as a + 1 can hen be forecased by (A7) and (A8). Plugging hese forecass ino he lognormal densiy funcion of asse price gives he subjecive probabiliy of he sock marke index Noe ha L is he sandard lognormal densiy funcion: e Li = S b (ln ST ai ) bi Differen specificaions for GARCH model, such as AR(1) and AR() for he mean equaion, GARCH (1,) and GARCH(,) for he GARCH equaion have been ried and hey make no or insignifican difference on he resuling densiy. Therefore, he simples one (GARCH (1,1)) is chosen for he sake of convenience. As he underlying sock marke index is assumed o be lognormally disribued, is log-reurn should be normally disribued. Therefore he normally disribued GARCH-implied reurn and he corresponding variance can be direcly plugged ino he lognormal disribuion funcion. T i π 316 IFC Bullein No 31

24 Appendix II: Indicaors of financial marke inegraion: Mehodology and inerpreaion This Appendix provides in deails he mehodologies of consrucing he differen indicaors for assessing financial marke inegraion and heir inerpreaion. All inegraion indicaors are derived based on changes in he risk appeie measures, wih he principal componen analysis also considering he level of he risk appeie measures. The sample period for he esimaion of hese inegraion indicaors is from December 001 o December 007. i. Cross-marke dispersion and correlaion The idea behind he cross-marke dispersion approach inroduced by Solnik and Roule (000) is simple and inuiive. This can be used as an alernaive o he ime-series approach o esimaing he level of correlaion of financial markes. Following he law of one price, idenical or comparable asses across differen economies should generae he same reurn. If here is a large discrepancy in financial marke reurns across economies, as measured by he cross-marke dispersion indicaor, i will imply ha he financial markes are no fully inegraed. In his measure, a low level of dispersion implies a higher degree of marke inegraion and vice versa. The mehod has been applied by Adjaoue and Danhine (003) and Baele e al. (004) o assess he equiy marke inegraion in Europe. While he mehod is commonly used on financial asse reurns, we apply he mehod on he changes in he risk appeie measures. To consruc his measure, for N economies, he monhly change in he risk appeie measure of economy i a monh ( R ) is specified as: i i i R = RA RA 1 i i where RA is he risk appeie measure of economy i a monh. The cross-marke dispersion indicaor is defined as: Cross-marke dispersion a monh = 1 N N i= 1 ( i R ) In addiion o he cross-marke dispersion indicaor, he cross-marke correlaion is also derived. Firs, we obain he cross-marke covariance, which is defined as: Cross-marke covariance a monh = 1 N N i j R R N N i= 1 j= 1 j i The cross-marke correlaion is hen calculaed as he raio of he cross-marke covariance o he square of he cross-marke dispersion. While he cross-marke dispersion measures he degree of discrepancy across markes, he cross-marke covariances and correlaions provide an alernaive mean o rack he co-movemen a each poin in ime. The derivaion of he dispersion indicaor, as well as he cross-marke covariance and correlaion follows Adrian (007). IFC Bullein No

25 ii. Principal componen analysis If a se of series are correlaed, i may be he case ha heir co-movemens are driven by one or more common facors which are no direcly observable. To esimae hese facors, a facor analysis mehod such as he principal componen analysis (PCA) is needed. In his sudy, he PCA is applied on he levels as well as he changes of he risk appeie measures in order o idenify he respecive common facors in heir variaions. The firs componen facor is generally inerpreed as he common force driving he dynamics of hese risk appeie measures. PCA involves he calculaion of he eigenvalue decomposiion of he daa covariance marix. 3 From a se of n mean-cenered series which are supposed o be correlaed wih one anoher, PCA exracs a new lis of p variables called facors f1,..., f p ( p n) which are uncorrelaed among one anoher. The common facors are consruced as linear combinaions of he iniial n series. The proporion of oal variaion accouned for by he firs k facors ( k < p ) represens he overall qualiy of he PCA. 4 One usually hopes o accoun for mos of he original variabiliy using a relaively fewer number of componen facors. In his sudy, he degree of inegraion is measured by wo crieria: a) he number of he firs k facors required o explain over 80% of he common variaion he less he number he beer; and b) he percenage of he common variaion explained by he firs facor he higher he percenage he beer. iii. Haldane and Hall (1991) Kalman filer mehod The noion of convergence or inegraion is ha he difference beween wo (or more) series should become arbirarily small or hey converge o some consan c as ime elapses, such ha lim E( X Y ) = 0 or c, where X and Y are he wo series. The convergence may k + k + k be a gradual and on-going process over ime. If we expec he convergence process o ake place over ime from a lower o a higher level, we need a measure which would allow for such dynamic srucural change. This measure will be useful in describing he process of srucural change in erms of boh degree and iming. The Kalman filer approach suggesed by Haldane and Hall (1991) is a mehod ha can be used o measure he ime-varying convergence dynamic. 5 In his sudy, he Haldane and Hall mehod esimaes a simple equaion via Kalman filer esimaion wih he signal equaion as: B ( R R ) + i, ε ~ N(, ) (A10) B i R R = α i, + βi, ε, and he sae equaions as: i = α i + ξ, ~ N( 0, α,, 1 ξ U ) i, 0 V β = β + μ, ~ N(, ) (A11) i, i, 1 μ 0 W Before calculaing he eigenvalue of he daa marix, he original daa series are pre-reaed by subracing he mean from each of he original daa series of ineres. The mean subraced is he simple average of he respecive original daa series. This procedure is called mean cenering. For more deails see Johnson and Wichern (199). Serleis and King (1997) and Manning (00) use he Haldane and Hall approach o measure convergence of European Union and Souh Eas Asian equiy markes respecively. Yu e al. (007a, 007b) also apply he approach o assess he sock and bond marke inegraion in Asia. 318 IFC Bullein No 31