Why Has Swedish Stock Market Volatility Increased?

Transcription

1 Why Has Seish Stock Market Volatility Increase? by John Hassler Institute for International Economic Stuies This revision: May 29, 1995 Preliminary Abstract Is the increase volatility on the Seish stock market ue to increase sensitivity to foreign markets or to inherently Seish factors? The finings in this paper is that the foreign influence on the Seish stock market shos a clear positive tren hile purely omestic factors have not become more volatile. Worl influence on omestic stock markets is also substantially larger uring international high volatility perios than uring calmer perios on the orl market. Furthermore, hen the volatility of the orl stock market shifts to its higher level, both the orl an the omestic markets simultaneously fall quite ramatically. I thank Magnus Dahlquist, Lars E.O. Svensson an Aners Warne for valuable comments. I am grateful to Karin Russel an the Morgan Stanley Capital International for proviing ata. Institute for International Economic Stuies, Stockholm University, S Stockholm, Seen. Telephone: , Fax: , John.Hassler@iies.su.se, WWW:

2 1. Introuction Events on financial markets have come to play an increasingly important role in meia an public iscussion. All big nes meia toay have aily coverage of the latest evelopments at the stock markets. Suen shifts in the value of the stock market an perios of higher than usual financial volatility get a lot of attention. The tight meia coverage is an inication that it is perceive, at least by journalists, that a lot of valuable information can be erive from the evelopments at the stock market. The stock market has the convenient feature that it is easily observable an reacts vigorously an ith short lags to nes. Although little formal ork has been one in this area, it is often suggeste that shifts in financial volatility can be of importance for macroeconomic performance. Christina Romer (1990), for example, argues that increase uncertainty associate ith financial istress as one of the riving forces behin the great epression. Also the very sharp recessions in Seen an Finlan in the beginning of the 90 s, in many respects comparable in size to the epression in the 30 s, is often attribute to increase savings cause by a shift in uncertainty even though the connection to the stock market may be less clear here. It is no a ell-establishe fact that financial volatility is a non-constant stochastic process ith a non-negligible egree of persistence if stock market volatility is high toay it tens to be high also uring the nearest future. This observation has receive much attention from the finance profession ue to its implications for asset pricing an portfolio management. The changing volatility an in particular its persistence, hoever, also has potential macroeconomic implications. To unerstan the implications of time varying financial volatility, more knolege of the processes that rive volatility is require. In particular, I am in this paper intereste in intra-market epenence of national stock markets. If a high or increasing volatility on the Seish stock markets can be attribute to a purely omestic nes source, this may have ifferent implications, both for policy an consumption/investment ecisions than if the volatility comes from a strong sensitivity to orl market evelopments. Here only a fe stuies have been conucte. Engle an Susmel (1993) an King et al (1994) estimate 2

3 multivariate moels ith common factors. An often note observation is that there appear to be regime shifts in the covariance matrix of ifferent national stock markets (see Bollerslev, 1992, p. 30). During perios of high volatility there appears to be a tenency of higher international epenence. 12 Figure 1 Moving Stanar Deviations of Nominal Returns on the Seish Stock Market % per Month Source: Upate ata from Frennberg an Hansson (1992). In Figure 1 I sho a graph over the stanar eviation of the return on the Seish stock market. The gray line represents the stanar eviation uring the perio starting 6 months before an ening 6 months after the observation ate, i.e., it covers one centere year aroun the observation ate. The soli black line represents the stanar eviation for the centere 3 year perio an the ashe the 5 year perio. In the graph e may observe that also the Seish market has perios of higher volatility. More striking is the strong tren in volatility. From hovering beteen 2 an 3 % a month the volatility starte increasing sometime uring the 60s to reach levels more than tice as high in the 90s. 1 Such a tren cannot be foun on the aggregate orl stock market or in US, for example. The purpose of this paper is to examine to hat extent this tren is ue to purely omestic factors or to an increase sensitivity to the orl market. Furthermore, I ant to 1 In the formal analysis belo I ill control for variations in inflation by stuying stock market return in excess of a safe interest rate. 3

4 evaluate the effects on the Seish stock market hen the orl market goes into a spell of higher than typical volatility. Here I am intereste both in level shifts an changes in the egree of comovements. Lastly, I ant to compare the results ith a fe other relatively small European stock markets. We ill se that there is strong evience suggesting an increase international sensitivity as the main reason for the increase volatility on the Seish stock market. Domestic factors seem to play only a minor role for the increase. We ill also see that there is istinct states that etermine the volatility on the orl stock market. When a volatility perio is entere, both the orl an the Seish market take large falls in the orer of 5 to 9%. After that, the orl influence on the omestic markets are substantially larger than uring international calm perios. We ill also see that purely omestic nes sho systematic variations in volatility. The moel istinguishes high volatility perios of approximately tice the volatility of the lo volatility perios. Lo volatility perios are on average longer than high volatility risk. In Seen, a shift to the omestic high risk state is often folloe by an shift back the folloing month. Given that this shift back o not occur the omestic high risk state is fairly persistent ith an expecte length of over 7 months. For the other omestic markets e fin similar results. In section 2 I present the econometric moel. Diagnostic testing of moels ith sitching volatility is somehat intricate an a stanar proceure has yet to evelop. I thus evote Section 3 to a iscussion of iagnostic tests, test results an implications for re-specification. Such test are require since they are the only ay of evaluating ho ell the moel escribes ata. The estimation results are then presente in section 4 an section 5 conclues. 4

5 2. Moel 2.1 The Worl Market Suppose that there exists a stochastic nes process enote ε that rives the orl stock market. Suppose further that there exists a stochastic state variable, enote s t that etermine the volatility of this nes process. Assume that this risk state only can take to values, 0 an 1, although extension to any finite number of states is straight forar in principle. When the orl risk state is 0, the stanar eviation of the nes process is ω 1 an hen it is 1 the stanar eviation is ω 1 +ω 2. We can think of the risk state as inicating stable or unstable eather. Furthermore, assume that the orl risk state follos a first orer stationary Markov chain ith the probability of staying in each state given by q ( s t ). The expecte return on the orl stock market is likely to be ifferent in the to risk states. Furthermore, if a shift in the risk state occurs beteen time t an t-1, it is likely that the realize return is affecte. If, for example, the orl market may fall if it goes into the high risk but then have higher expecte returns as long as the high risk state prevails. We may then moel the excess return, i.e, realize return minus a safe interest rate as follos; 2 r r = µ + µ s + µ s + ( ω + ω s ) ε. (2.1) t+ 1 t t 3 t t+ 1 t+ 1 here r t +1 is the realize return on the orl stock market, r t+1 is the safe interest rate, µ 1 is the expecte return in risk state 0 if no state shifts occur, µ 2 is aitional expecte return in state 1. The shift in the level of the stock market at state shifts is given by µ 3. The nes, ε, is an i.i.. stanar normal so the stanar eviation of the last term is ω 1, an ω 1 +ω 2 in the to states respectively. No turn to the omestic stock market. The return on the omestic market is assume to be riven by both the orl nes to iviens an by an iiosyncratic omestic nes process enote ε. The influence of the foreign nes process is alloe to shift ith the international risk state. Also the intensity of the omestic nes process is alloe to shift as a omestic risk state, enote s t shifts. The omestic risk state can also take the values 0 an 1 an follos a 2 A formal erivation of base on a stanar asset pricing moel is presente in the appenix. 5

6 Markov chain ith continuation probabilities q ( st ), so it is assume to be inepenent of, in particular, the orl risk state. Expecte returns on the omestic market epens on both the omestic an the orl state. Realize return ill also be affecte by omestic an orl risk state shifts. As note in the introuction, there is evience of a tren increase in the volatility on at least the Seish stock market. To moel such a tren in the simplest possible ay, I allo a eterministic time tren in the volatility of the innovations to the omestic ivien process as ell as to the rift terms an their sensitivity to the risk states. 3 The final bivariate moel is then given by rt + 1 rt+ 1 = µ 1+ µ 2st + µ 3 st + 1+ ( ω1+ ω2st + 1) εt + 1, rt + 1 rt + 1 = µ 4 + µ 5st + µ 6 st + 1+ µ 7t/ T+ µ 8st t/ T + µ 9st + µ 10 st + 1+ µ 11st t/ T + ( ω3+ ω4st + 1+ ω5t/ T) εt + 1+ ( ω6 + ω7st + 1+ ω8t/ T) εt + 1 (2.2) here T is the total number of observations. If the market structure changes so that, for example, capital controls are lifte e expect to fin non-zero estimates of µ 7, µ 8 an/or µ 11. This since these changes affect ho the ifferent sources of risk are price. The sensitivity to the omestic state, for example, shoul plausibly fall as omestic volatility is iiosyncratic from the point of vie of an investor ith access to the orl market. This ill change the covariance beteen omestic an foreign returns also if the nes processes are invariant over time. If, on the other han, the omestic influence of foreign nes increases or if the strength of the omestic nes flo changes, ω 6 an/or ω 9 shoul be positive. 2.2 Data an estimation Stock market yiels are calculate from the Morgan Stanley Capital International (MSCI) inices, hich inclue re-investe iviens. The sample perio is 1970:1-1995:8. The returns are calculate as the log-ifference of month-en stock market inex calculate in US ollar terms. Yiels thus inclue an exchange rate term. Ieally e may ant to moel 3 Certainly, such trens cannot be infinitely live. There is no presumption, hoever, that the estimate moel is going to escribe ata ell that long. What e can hope for is a moel that oes a goo job as a local approximation to the true ata generating process. 6

7 exchange rate fluctuations as a separate stochastic process. This is not one in this paper. The risk-free interest rate is the 30-ays Euroollar rate, provie by the Seish Central Bank. The orl market return is calculate from the MSCI value-eighte orl inex. The moel is estimate in the recursive ay evise by Hamilton (1989). Employing this recursive metho makes it very easy to change the specification of the moel. It is, in particular, easy to inclue time varying parameters. Stanar errors are calculate from the Hessian of the loglikelihoo function at the estimate parameters. Instea of estimating the transition probabilities irectly, I estimate them as argument in the cumulative normal istribution function. The stanar eviation of these parameters are calculate using the δ- metho. 3. Diagnostic Tests 3.1 Moel Diagnostics Before examining the results of the estimation of the moel, e ant to juge hether the moel can be thought of as a reasonable escription of the ata. For this purpose I ill, in some etail, first present the results from some iagnostic tests, base on ork by Hamilton (1996). One coul certainly test the statistical moel in many imensions an it is a priori clear that the probability of this moel being exactly right is zero. The tests shoul thus be thought of as quantitative evaluations of ho ell the moel, in some imensions, escribe ata. Base on the purpose of this paper an the suggestions by Hamilton (1996), I have chosen to evaluate the moel along the folloing imensions: 1) We ant to juge hether the volatilities of the information processes are reasonably ell escribe by the to-state moel. This ill be teste against the hypothesis that there remains some autocorrelation in the volatility, i.e., that some ARCH-effects remain. 7

8 2) We also ant to see if there is strong evience against states follo inepenent first orer Markov processes. Alternatively they may have higher orer, be interepenent an/or epen on the level of the realize return. 3) Lastly I ant to check hether the average return is constant in the to states, after potential linear time trens have been remove. Alternatively, there may remain some autocorrelation in the return. The test are base on an examination of the erivatives of the loglikelihoo function the scores. Define as the vector of scores at time t as h() t ln f 4r r r t t 1,, 1; Φ9 Φ (3.1) here f is the log-likelihoo function, r t is the vector of excess returns at time t an Φ is the vector of parameters to estimate. If the moel is correctly specifie, each element of h(t), is uncorrelate ith all information in t-1. In particular, it shoul be uncorrelate ith previous values of the itself an other scores. Intuitively, if this is violate e expect that our parameter estimates ill change in some knon irection hen a ata point is ae to our sample. This coul never be a feature of a reasonable estimator. By looking at linear relations beteen scores in t an t-1 e may etect eviations from the assumptions in the moel an may unerstan ho they are violate. To this en I ill stuy the folloing regressions hi() t = α0 + α jhj( t 1 ) + ε (3.2) t j J here h i (t) is the ith element of the score an J is a subset of the parameters I estimate. If the moel is a reasonable escription of ate, regression (3.2) shoul have insignificant explanatory poer. We shoul note that the resiual in (3.2) in general is heteroscheastic, implying potentially serious small sample problems. These ill be particularly severe for parameters that influence the likelihoo function only at state realizations that occur ith lo probability. As e ill soon see, the transition probabilities for both the omestic an the orl state are lo. This means that state sitches are rare events. The scores for parameters that only affect the likelihoo function at state sitches, i.e., µ 3, µ 6, an µ 10, ill thus follo very heteroscheastic 8

9 processes an tests base (3.2) ill be quite unreliable 4. We can unerstan this in the folloing ay; espite the relatively large nominal number of egrees of freeom, e have relatively little information about of hat happens at state shifts since these events are rare. I ill thus exclue the scores for theses parameters from the tests. I am in effect thus testing the moel accoring ho it behaves ithin the states, not hat happens exactly at the state shifts. To test the Markov assumption that the probability of state shifts only epen on the current state, I have performe to tests. The first, Markov I, is to run one regression for each of the scores ith respect to the probabilities q (0), q (1), q (0) q (1). In this test, one perio lagge values of the four scores are use as regressors. This test is aime at etecting eviations from the inepenent first orer Markov assumption. If lagge values of scores preict scores for the same state variable, this is an inication of violation of the first orer assumption. Similarly, if lagge scores can preict the score of the other state variable, this inicates non-inepenence beteen the to state variables, e.g., that a state shift on the orl market tens to be associate ith state shifts in the purely omestic state variable. In the secon test, Markov II, the same epenent variables are use, but they are no regresse on the lagge scores for the rift parameters µ 1, µ 2, µ 4, µ 5, µ 7, µ 8, µ 9 an µ 11. This test can etect if the level of the stock return in the previous perio contains information about the likelihoo of staying in the state, hich oul violate the Markov assumption. The thir test, AR, is aime at etecting eviations from the assumption of a constant expecte return (except for the time tren) in each state. I run regressions for each of the scores for µ 1, µ 2, µ 4, µ 5, µ 7, µ 8, µ 9 an µ 11 against the lagge scores for the same parameters. If there is some autocorrelation in the return processes left unaccounte for by the moel, these regressions shoul contain some information. The last test is an ARCH test. I run regressions for each of the scores ith respect to the volatility parameters. ω 1,..., ω 8. Significance here inicates remaining ARCH effects. If, for example the lagge score ith respect to ω 1 helps preict the current value of the score, there seems to be ARCH effects in state 1. Hamilton s (1996) propose the same four tests. The 4 The scores for these parameters shoe long perios of values close to zero interrupte by a small number of very large values. 9

10 ifference is only that he tests hether all regressions ithin a test simultaneously have zero R 2. Stuying the regressions separately can, hoever, give an inication of hat causes a potential rejection an guie moel re-specification. I have chosen to use a critical level of 1% to reject the moel. Hamilton s (1996) notes that in Monte Carlo simulations there is a tenency to reject to often. This is probably ue to that many iniviual scores are far from being normal, ith large outliers occurring ith relatively long intervals as iscusse above. Consiering this an the large number of tests, 1% rejection level oes not seem overly in favor of the moel. Table 1 Score tests Markov Test I Markov Test II AR Test Country q (0) q (1) q (0) q (1) q (0) q (1) q (0) q (1) µ 1 µ 2 µ 4 µ 5 µ 7 µ 8 µ 9 µ 11 R Seen p-value R Belgium p-value R France Prob ARCH Test Country ω 1 ω 2 ω 3 ω 4 ω 5 ω 6 ω 7 ω 8 R Seen Prob R Belgium Prob R France Prob In Table 1 I present the results of the score test for the bivariate moel for excess returns on the Seish an the orl market. I report the centere R 2 together ith the asymptotic p- value for R 2 =0. The iagnostic test results are iscusse in the folloing sections. 10

11 3.1.1 Diagnostic results for Seen In Table 1 e fin evience of violations of the Markov assumption. These are relate to the scores ith respect to the transition probabilities. The assumption that the omestic state follo a first orer, inepenent Markov chain is significantly rejecte. In the regression of q (1) in Markov test 1 e fin a strong epenence on lagge scores ith respect to the other transition probabilities. A closer inspection of the regression results inicates that the t-values in the regression are 0.03, -0.27, 5.79 an 2.77 for the scores for q (0), q (1), q (0) q (1). 5 This inicates that it is the first orer assumption rather than the assumption of inepenence beteen the state variables, that is violate. I ill thus reestimate the moel alloing the probability of staying in omestic state 1 to epen on the current as ell as the lagge state. The probability of staying in omestic state 1 if the current an the previous state as 1 ill be enote by q (1,1) an the probability of staying in state 1 if the previous state as 0 by q (1,0). There is also an inication that previous returns may influence the probability of staying in orl state 1 the secon regression in Markov test II is significant. The significance is, hoever, ue to the score ith respect to µ 8. This oul mean that the realization of Seish returns affects the probability of the orl process to stay in its high risk state hich seems unreasonable. A closer inspection of the regression also shos that the significance is ue to only one single observation September If this is exclue the significance of the regressions is reuce to a marginal p-value of The Seish stock market ha its loest rate of return over the ho sample this month -25%. Apparently this occurre one perio before a realization on the orl market that tene to push the estimate of q (1) upars. This seems to be a coincience rather than a causal relationship. To hanle this I inclue a ummy for the Seish return in September I thus treat the return for this month as an outlier unexplaine ithin the moel. None of the regressions in the AR an the ARCH tests are significant at conventional levels. So there oes not seem to be any significant AR or ARCH effect left in the ata. 5 t-statistics for all regressions are presente in the Appenix. 11

12 After re-estimating the moel alloing q (1,1) q (1,0) an using a ummy for the Seish return in September 1990 the moel survives the tests in the sense that no regressions are significant at conventional significance levels. The p-values of the regressions are given in Table 2. The ne parameter estimates are very close to the estimates for the rejecte moel Diagnostic results for Belgium From Table 1 e see that the moel survives the tests. The only case here the test us close to reject is the ARCH test for ω 7 ith a marginal level 1.7%. This turns out to be u to one single observation February 1986, hen the Belgium stock market realize its largest return in the sample, amounting to 23%. Since the tests are not rejecte I accept the base moel. I have, hoever, re-estimate the moel incluing a ummy for omestic return in February Then the marginal significance level of the see that this takes aay the rejection of the ARCH test for ω 7 increases to 45%. The parameter estimates are very close in the to estimations. Table 2 Score tests for Final Moels Markov Test I Markov Test II AR Test Country q (0) q (1) q (0) q (1) q (0) q (1) q (0) q (1) µ 1 µ 2 µ 4 µ 5 µ 7 µ 8 µ 9 µ 11 R Seen p-value R Belgium p-value France For Seen the test is for the parameter q (1,1) ARCH Test Country ω 1 ω 2 ω 3 ω 4 ω 5 ω 6 ω 7 ω 8 R Seen Prob R Belgium Prob R France Prob

13 3.1.3 Diagnostic results for France For France the AR-test rejects the last AR-test at the 1% level an the next to last is close to being rejecte. There thus seem to be some omestic autocorrelation left to explain. As in the previous cases, an extreme realization seems to be accountable for the rejection in January 1988 the realize return as -17%. After incluing a ummy for this observation, no test is rejecte at the 1% level, although next to last ARCH test is fairly close at a nominal p- value of 1.5%. The parameter estimates i not change very much after the re-estimation 4. Results The estimate parameters together ith asymptotic stanar errors, calculate from the Hessian of the loglikelihoo function, are presente in Table 3. The estimates for the orl process varies somehat beteen the ifferent estimations espite of the fact that the same values for orl returns are use in all estimations. These ifferences are ue to that also the omestic returns contain information about the orl state process an thus affect the estimation of its parameters. Common for all the estimations is that the lo risk state is more persistent than the high risk state, both for the orl an the omestic state processes. This also means that economies spens most of the time in the lo risk state. The unconitional probability of the lo risk state is aroun 0.8 for all state processes 6. The estimate probability of staying in the orl high risk state is, although loer than the probability of staying in the lo risk state, as high as beteen 0.72 an This means that a sitch to the high risk state is something more than just one extreme realization of returns. This is also true for the omestic processes. For Seen e fin evience that that it is more likely to stay in the high risk state given that it has continue at least to months. About half of the times a sitch to omestic high risk state, is 6 In the case ith a first orer Markov chain the unconitional probability of being in state 0 is ( 01- q(1) 5 02 q(1)- q(0) 5. In the case of secon orer Markov chain, as for Seen, one can iterate on the transition matrix for the state to calculate the unconitional probability of state 0. For Seen this is

14 folloe by an immeiate shift back. If this oes not occur, the high risk state is expecte to continue for another 7 months. The rift parameters for the orl return are estimate ith rather goo precision an stability over the ifferent estimations. From the negative an large value of µ 3 e see that there is a large fall in the stock market hen the high risk state is entere. This as a negative (positive) component to expecte returns in the lo (high) risk state. On the other han, the rift term µ 2 is negative aing a negative component to expecte returns in the high risk state. This outeighs the effect ue to µ 3 so expecte returns are loer in the high risk state. The precision in the rift terms for omestic returns is loer. For Seen, only µ 6, (µ 8 ) an µ 10 are significant at conventional significance levels. We fin that the also the Seish market falls hen the orl risk state shifts to high risk. A shift to the omestic high risk state has a quantitatively similar effect, the point estimates are -7.0% an -8.3%. The negative value for µ 8 means that the effect of the orl high risk state on expecte Seish returns has become more negative over time. This coul be an effect of the extensive capital market liberalization that has taken place in Seen uring the sample perios. Also the rift terms for the return in Belgium an France are estimate ith lo precision. A notable result is, hoever, that µ 6 is significantly negative an large in absolute value for all three countries. The effect of a shift to high volatility on the orl stock market is thus a large fall on all omestic stock market. Except for µ 6, only µ 10 in Belgium is significant. It is positive an relatively large. The parameters capturing the volatility of the nes process are estimate ith better precision than the rift parameters. The stanar eviation of the nes process at the orl market is estimate to be beteen 1.8% an 2.6% higher in high risk state than in the lo. This amounts to somehat less than a oubling of the stanar eviation. The increase is significant, an strongly so hen e consier Belgium an France. Turning to the omestic markets an focusing on the influence of the orl nes process e fin both important ifferences an similarities beteen the markets. First, ω 5 is positive an significant in Seen. There is thus strong evience of an increasing Seish sensitivity to the orl stock market. If such a tren exists in the other to countries, it is of much less 14

15 importance. Secon, in all countries, ω 4 is positive an significant inicating that the foreign influence is substantially larger uring international high volatility perios. This tenency is largest for Belgium, folloe by Seen. We see that for all the estimations ω 4 is larger than ω 2. A high volatility perio on the orl market thus has larger effects on omestic volatility than on orl market volatility. Conversely, ω is smaller than ω 3 1 for all estimations inicating that the orl influence is relatively lo hen the orl market is in a state of calmness. The foreign influence on the Seish market uring international lo volatility perios as not even significant uring the beginning of the sample. Table 3 Estimate Parameters - Final Moels Seen Belgium France q (0) (31.06) (31.48) q (1) (13.28) (11.92) q (0) (21.45) (26.32) q (1,0) (1.85) q (1,1) ( 8.65) q (1) (14.10) (10.03) µ 1 x ( 3.89) (3.07) (3.12) µ 2 x (-3.40) (-1.98) (-1.95) µ 3 x (-6.41) (-7.26) (-6.87) µ 4 x ( 0.53) (1.42) (-0.37) µ 5 x ( 0.18) (-0.63) (-0.78) µ 6 x (-3.32) (-3.34) (-3.10) µ 7 x ( 1.01) (-0.14) (0.48) µ 8 x (-1.73) (0.44) (0.83) µ 9 x (-0.52) (-0.44) (1.00) µ 10 x (-3.16) (3.33) (1.17) µ 11 x ( 0.58) (0.39) (-0.52) ω 1 x (17.34) (14.33) (13.80) ω 2 x ( 2.24) (4.92) (5.09) ω 3 x ( 1.54) (2.14) (3.04) ω 4 x ( 2.92) (4.55) (3.19) ω 5 x ( 3.14) (1.74) (0.68) ω 6 x ( 7.99) (8.73) (7.66) ω 7 x ( 2.79) (3.58) (3.77) ω 8 x ( 0.88) (-0.73) (-2.13) Dummy (-1.98) (-4.85) Parameter estimates ivie by asymptotic stanar eviation in parenthesis. Stanar eviations calculate from Hessian of loglikelihoo function. 15

16 The omestic nes process is of strong importance for all the omestic markets. Both ω 6. an ω 7 are large an significant for all three countries. Also the omestic state process seems to have been of substantial importance throughout the sample. The stanar eviation of omestic nes oubles in the omestic high risk state in Seen an Belgium. The increase is slightly smaller in France, but still clearly significant. France also stans out from the other to by having a strong an significant negative tren in the volatility of omestic nes. No such tren can be foun on the Seish stock market. Figure 2 State Probabilities 1.0 Worl Market Seen Belgium France

17 An output from the estimation of the regime sitching moel is probabilities of being in the high risk states, conitional on realize returns. The probabilities of being in the to high risk states for each perio t, conitional on realization up to t+1 are plotte in Figure 2. 7,8. One important observation stans out immeiately from the graphs. This is that the omestic state processes in Belgium an France seems to be almost ientical. The Seish states, on the other han, are not at all synchronize ith the other state processes. 5. Conclusion I have in this paper applie the Hamilton regime sitching moel to bivariate stock market ata. The results regaring volatility transmission are fairly clear-cut; 1. The increase volatility on the Seish stock market can be attribute to an increase sensitivity to the orl markets an not to increase omestic nes flos. Such a tren cannot be foun in France an Belgium. 2. During a high volatility perio on the orl market, hich has an expecte uration of aroun 5 months, the omestic sensitivity to the orl market increases in all three stuie countries. This means that the increase in volatility is larger on the omestic than on the orl market. 3. Domestic volatility sho clear evience of shifting levels of volatility in all three countries. The results regaring the rift terms, i.e., expecte return conitional on the realize state are estimate ith loer precision. One clear results stans out, hoever, i.e., hen the orl market goes into a perio of high volatility, both omestic an orl markets falls simultaneously. The fall is large in the orer of 5 to 8 %. What e thus see is that occasionally the orl market is hit by a large negative shock. This shock has a similar effect 7 The smoothe probabilities, base on the full sample, has for computational reasons not been calculate. 8 The Seish state probabilities are somehat sensitive to the choice of moel. The preliminary moel, ith first orer state Markov chains. prouce probabilities that generally here closer to zero. 17

18 on the level of the omestic markets. After the shock the orl market is more volatile over an extene perio of time an the omestic markets are substantially more sensitive to the orl markets than otherise. The fining of relatively large variations in the intensity of the nes flo from the stock market may have important macroeconomic implications. A shift to a high level of nes flo from the stock market may be important also for househols that o not on shares. Certainly, there are other ays a consumer can be affecte by changes in expecte future firm profits than from its associate capital gains. It seems more than likely the information flo from the stock market may contain information about future ages, prices or groth rates, for example. In Hassler (1995) I sho that there is evience of a link beteen financial volatility an urables eman. When financial volatility increases urables purchases fall substantially hile nonurables eman seems to be largely unaffecte. In Hassler (1996) this is given a structural interpretation: High stock market volatility implies a high current flo of information. Given that investments in urables involve some egree of irreversibility, the value of aiting to purchase a ne urable increases in the current flo of information. Increase volatility shoul then lea to a higher tenency to postpone purchases. What it is exactly, in the nes flo from the stock market that is important for, say, a representative househol is of course an open question. Another open question is the reason for hy the Seish stock market have become more sensitive to the orl market. As note above, results in this paper o not point in the irection of a change pricing behavior on the stock market but rather that the unerlying funamental, i.e., expecte future firm profits, have become more sensitive to the orl evelopments. Given that the moel in this paper has lo precision in the pricing parameter, i.e., the µ s, this conclusion is not strongly foune an nees more examination. Lastly, some ors about the moeling approach. The moel in this paper is highly stylize in the sense that e only allo for to states of volatility. In reality there may, of course, be many more states. The moel oes, hoever, seem to be ell suite to etect shifts in the nes processes that rive the stock market. It also survives the rather extensive testing I have performe. Alternative moels of ARCH type may instea ten to blur the istinction 18

19 beteen lo an high volatility perios. Which class of moel performs best in terms of escribing the ata is, hoever, certainly an open question. Although such comparisons is outsie the scope of this paper, one can be sure that they ill be one ith scrutiny in the near future. 19

20 References Bollerslev, Tim, Ray Chou an Kenneth Kroner, (1992), ARCH moeling Finance: A Revie of the Theory an Empirical Evience, Journal of Econometrics 52. Engle, Robert. F. an Raul Susmel, (1993), Common Volatility in International Equity Markets, Journal of Business & Economic Statistics, Vol. 11, No.2. French, Kenneth R., G. William Schert an Robert F. Stambaugh, (1987), Expecte Stock Returns an Volatility, Journal of Financial Economics, 19. Frennberg, P. an B. Hansson, (1992), Computation of a Monthly Inex for Seish Stock Returns , Scaninavian Economic History Revie, Vol. XL, No. 1. Hamilton, James D., (1989), A Ne Approach to the Economic Analysis of Non-Stationary Time Series an the Business Cycle, Econometrica, Vol. 57:2. Hamilton, James D., (1996), Specification Testing in Markov-Sitching Time-Series Moels, Journal of Econometrics, forthcoming. Hassler, J., (1995), Fluctuating Risk in an Aggregate Ss Moel some empirical results, mimeo, Institute for International Economic Stuies, Stockholm University Hassler, J. (1996), Variations in Risk an Fluctuations in Deman a theoretical moel, Journal of Economic Dynamics & Control 20:6-7, p King, Mervin, Enrique Sentana, an Sushil Wahani, (1994) Volatility an Links Beteen National Stock Markets, Econometrica, Vol. 62, No.4. Romer, C.D., (1990), The Great Crash an the Onset of the Great Depression, Quarterly Journal of Economics, vol. 105, No. 422,

21 Appenix In this appenix I use a stanar asset pricing moel to erive the process for asset prices hen the volatilities of the unerlying stochastic nes or ivien processes follo to-state processes. Assume that the orl ivien process follos ln = ln + µ + µ s + ( ω + ω s ) ε E ε t t+ 1 t t t+ 1 t t+ 1 t t+ 1 = 0, E ( ε ) = 1 (A.1) here t is the aggregate ivien of the orl market at time t. Furthermore, assume that the orl risk state follos a first orer stationary Markov chain ith the probability of staying in each state given by q t ( s ). The representative orl agent maximizes a stanar CRRA objective function Et β ct+ s. s= 0 Assume that c= in each perio. Then the price process of the orl stock market inex must satisfy 4 9! 3 t t 8 t 3 t t 8 t ps ~, = E ~ ps, + t β + 1 t α " $ #. (A.2) Since time t expecte future iviens are linear in t an expecte MRS are inepenent of t it follos that stock market inex is linear in t. Diviing both sies of the pricing relation by t an using the linearity of the price inex e fin that price ivien ratio only epens on the current state an satisfies ~ ps 3, t t 8 ps 3 t 8= E 4ps β t t t t + 1 t Furthermore, the return, efine as r ln4p3s ln p3s 8, satisfies t rt+ 1 = ln4p3st ln p3st 8+ ln! 1 α " $ # t+ 1 t + 1 t + 1 t t + 1 t µ µ ω ω ε = ln ps + 1 ln ps + + s + ( + s ) t t t t t The real risk-free rate is also etermine by the current state; 3 8 ln β! r s = E t t + 1 t t + 1 t We can no rite the excess return in regression form 1 α " $ # (A.3) (A.4) (A.5) r r = µ + µ s + µ s + ( ω + ω s ) ε. (A.6) t+ 1 t t 3 t t+ 1 t+ 1 Here it shoul be note that the three µ i in (2.1) are not sufficient to ientify the to state prices an the rift parameters µ an µ. Knolege of, for example the risk aversion α, coul ientify all parameters an thus isentangle the risk premium component of expecte returns. This is not of prime interest in this context an (2.1) is in any case a vali regression to run an ω 1 an ω 2 are ientifie. No turn to a omestic stock market. The return on the omestic market is assume to be riven by both the orl nes to iviens an by an iiosyncratic omestic nes process.,, t t t t t t t t ln = ln + µ + µ s + ( ω + ω s ) ε + µ s + ( ω + ω s ) ε, 3 8 E ε = E ε ε = 0, E ( ε ) = 1 t t t t t t t (A.7) 21

22 The influence of the foreign nes process is alloe to shift ith the international risk state. Also the intensity of the omestic nes process is alloe to shift as a omestic risk state, enote s t shifts. The omestic risk state follos a Markov chain ith continuation probabilities q ( st ), so it is assume to be inepenent of, in particular, the orl risk state. The price of the omestic asset is linear in so if the asset is price by a orl investor consuming pst st Et pst st t 3, 8= 4 3, 8+ 19! + 1 t+ 1 β t t α " $ # (A.8) hile if the price setter is omestic an restricte to consume it is pst st Et pst st t 3, 8= 4 3, 8+ 19β! + 1 t 1 α " $ #. (A.9) To allo a tren in volatility in the simplest possible ay, I allo a eterministic time tren in the volatility of the innovations to the omestic ivien process as ell as to the rift terms an their sensitivity to the risk states. The final bivariate moel is then given by (2.2). 22