EQUITY MARKET RETURN VOertertrettLATILITY: DYNAMICS AND TdsfsdfAertertNSMISSION AMONG THE G-7 COUNTRIES Lori L. Leachman Bill Francis I. INTRODUCTION The nearly contemporaneous collapse of the world stock markets in October 1987 and to a lesser degree in 1989 has led to a substantial increase in the num- ber of studies investigating the international transmission of changes in asset returns and volatility. Goodhart (1988), King and Wadhwani (1990), and Hamao, Masulis, and Ng (1990) have studied the transmission of volatility in interna- tional stock prices, while Eun and Shim (1988), Von Furstenburg and Jeon (1989), and Jeon and Von Furstenburg (1990) have investigated the international trans- mission of stock market movements.’ The consensus emerging from the broad class of investigations of international asset market comovements is that asset markets are linked internationally and volatility is transmitted from one market to another. The evidence is particularly striking for the post-1980 period. This paper builds on the studies noted above by examining the importance of volatil- ity in national equity markets as contributors to the variability of volatility in other national equity markets. In addition, the persistence of these spillover effects is examined. II. ECONOMIC BACKGROUND The capital asset pricing model (CAPM) predicts that each risky asset will be priced to earn a premium that is given by E(ri) = &ov(rir,) (1) Lori L. Leachman, Associate Professor of Economics, Northern Arizona University, PO Box 15066, Flagstaff, AZ 86011.5066; Bill Francis, Department Professor of Finance, University of North Carolina at Charlotte, Charlotte, NC 28223. Global Finance Journal, 7(l): 27-52 Copyright 0 1996 by JAI Press Inc. ISSN: 1044-0283 All rights of reproduction in any form reserved.
Transcript
EQUITY MARKET RETURN VOertertrettLATILITY: DYNAMICS AND TdsfsdfAertertNSMISSION AMONG THE G-7 COUNTRIES
Lori L. Leachman Bill Francis
I. INTRODUCTION
The nearly contemporaneous collapse of the world stock markets in October 1987 and to a lesser degree in 1989 has led to a substantial increase in the num- ber of studies investigating the international transmission of changes in asset returns and volatility. Goodhart (1988), King and Wadhwani (1990), and Hamao, Masulis, and Ng (1990) have studied the transmission of volatility in interna- tional stock prices, while Eun and Shim (1988), Von Furstenburg and Jeon (1989), and Jeon and Von Furstenburg (1990) have investigated the international trans- mission of stock market movements.’ The consensus emerging from the broad class of investigations of international asset market comovements is that asset markets are linked internationally and volatility is transmitted from one market to another. The evidence is particularly striking for the post-1980 period. This paper builds on the studies noted above by examining the importance of volatil- ity in national equity markets as contributors to the variability of volatility in other national equity markets. In addition, the persistence of these spillover effects is examined.
II. ECONOMIC BACKGROUND
The capital asset pricing model (CAPM) predicts that each risky asset will be priced to earn a premium that is given by
E(ri) = &ov(rir,) (1)
Lori L. Leachman, Associate Professor of Economics, Northern Arizona University, PO Box 15066, Flagstaff, AZ 86011.5066; Bill Francis, Department Professor of Finance, University of North Carolina at Charlotte, Charlotte, NC 28223.
Global Finance Journal, 7(l): 27-52 Copyright 0 1996 by JAI Press Inc. ISSN: 1044-0283 All rights of reproduction in any form reserved.
2.8 GLOBAL FINANCE JOURNAL 7(l), 1996
where E(rJ measures the expected excess returns for asset i, Y, is the excess return for the market portfolio, d is a measure of risk aversion, and COZI (0) is a covariance operator. The above relationship implies that the risk premium for the market portfolio is measured by the variance of its returns. Thus, the market risk premium is an increasing function of the variance of the returns of the mar- ket portfolio. It is important to note that the latter relationship is still valid even if the CAPM does not hold.
Several authors, using various proxies for the market portfolio, have investi- gated the relationship between the market risk premium and the variance of market portfolio returns. For example, Merton (1980) provides evidence that the risk premium is positively related to the contemporaneous variance of the mar- ket returns. French, Schwert, and Stambaugh (1987) and Chou, Engle, and Kane (1992), using generalized autoregressive conditional heteroskedasticity (GARCH) models, document a positive relationship between conditional expected excess returns of the market portfolio and the conditional variance of its returns. Poon and Taylor (1992), using UK data, also provide evidence of a positive relation- ship. Although these studies use data from differing countries, in general they assume that a country’s risk premium is determined by the variance of the domestic market portfolio. Thus, they have neglected the impact of foreign asset returns on the domestic risk premium.
Recent empirical analyses that address the issue of the integration of interna- tional capital markets now recognize that stock markets are reasonably well integrated. Studies by Cho, Eun, and Senbet (1986), Gultekin, Gultekin, and Penati (1989), Korajczyk and Viallet (1990), Harvey (1991), Bekaert and Hodrick (1992), and Campbell and Hamao (1992) all provide various levels of support for the hypothesis that capital markets are integrated with the degree of integration increasing over time. This suggests that an individual country’s equity market may no longer be an appropriate proxy for the market portfolio.
An important implication of the increase in the level of capital market integra- tion is that the conditional variance of each country’s market portfolio return may be significantly affected by the conditional variance of other capital markets’ returns. This suggests that neglecting the impact of foreign market volatility on domestic market volatility in studies of the relationship between the domestic market risk premium and its conditional variance may lead to faulty inferences. Of course, the severity of neglecting this relationship depends on the relation- ship between the conditional variances of the various capital markets. Therefore, this paper investigates the impact of the conditional variance of foreign stock returns on the conditional variance of domestic stock returns.
Recent studies which have found that both domestic volatility and innova- tions are transmitted across international capital markets use high-frequency data, both intra-day and daily. These papers find that transmission tends to con- tinue after the market from which the volatility or innovation originated closes. This leads to volatility and asset market movements in markets opening several hours later, irrespective of geographic location. Engle, Ito, and Lin (2990) label this phenomenon a “meteor shower” due to its similarity to how the world turns.
Equity Market Return Volatility 29
They conclude that meteor showers are consistent with the inability of asset mar- kets to fully incorporate information, thus possibly reflecting market inefficiency.
Explanations such as fads or bubbles have also been offered for volatility transmission. Diba and Grossman (1988) argue against their presence. Dwyer and Hafer (1990) find little evidence of the existence of rational bubbles. How- ever, more recent studies have found that rational bubbles are possible and can be caused by fundamentals (see Froot & Obstfeld, 1991).
Alternatively, at least three classes of theoretical models are consistent with meteor showers in the presence of market efficiency. The first examines stochas- tic variation in the conditional variances of traditional market fundamentals as sources of variability in expected returns and asset prices. These models are due to Lucas (1978), Abel (1988), Giovannini and Jorion (1989) and Hodrick (1989). In these models, the assumption of risk neutrality is relaxed, implying that risk pre- mia are time varying. This is one of the fundamentals that is theorized to be related to the conditional variances of the exogenous processes. In other words, market movements reflect in part changing risk premia induced by volatility exhibited in the exogenous processes. If markets are relatively integrated, then changes in risk premia may lead to the transmission of volatility across stock markets. Poterba and Summers (1986) point out that if time varying risk premia are to be responsible for variation in share prices, then shocks to volatility must be persistent. Evidence as to the degree of persistence is inconclusive.
The second class of models is based on the dissemination of information. Kyle (1985) and Admati and Pfleiderer (1988) present models in which private infor- mation is only gradually incorporated into prices, with all relevant information being fully reflected in prices by the end of the trading period. In a related con- text, Ross (1989) shows that the variance of price changes is related directly to the rate of flow of information. Thus, if an increase in the rate of flow of informa- tion in, say, the US increases the rate of flow of information to, say, Germany, transmission of volatility would occur.
Finally, transmission of volatility can result from stochastic policy coordination between countries (see Hamada, 1985). Consider the case where there is an announcement of a change in monetary policy in the United States (US). A reac- tion by the central bank of Japan to this announcement may lead to transmission of volatility. Notice that the formation of the Group of Five (G-5: US, United Kingdom [UK], France, Germany, and Japan) which was expanded to the Group of Seven (G-7: Canada and Italy along with the G-5) may be an example of such an attempt at policy coordination.
This paper differs from previous studies which address the transmission of volatility in several ways.
1. Both GARCH and vector autoregressive (VAR) models are used in the analysis. GARCH models are employed to obtain estimates of the condi- tional variance of the returns of each stock index. These estimates are then used to construct a VAR system. The VAR methodology is advantageous in that it allows the investigator to determine precisely how a shock to one market influences the dynamic adjustment of volatility in the remain-
30 GLOBAL FINANCE JOURNAL 7(l), 1996
ing markets and the persistence of these spillover effects.2 This is accom- plished via the impulse response function. Further, through variance decompositions (VARDs) the relative significance of each market in gener- ating fluctuations in the others is quantified.
2. The volatility of the G-7 countries over the entire post-Bretton-Woods era, 1973:4 to 1993:5, is examined. The use of the G-7 countries should provide evidence as to the generality of the transmission of volatility throughout the industrialized world. In addition, the sample is parti- tioned at the month of the Plaza Accord (September, 1985), and the GARCH models and VAR systems are re-estimated for both subperiods. The Plaza Agreement opened an era of policy coordination. Specifically, the central banks of the G-5 embarked on a concerted effort to conduct simultaneous sales of dollars to lower the value of the dollar. Although the Plaza Accord did not specifically target equity markets, changes in exchange rates contribute to the variance of equity market returns through both their own variance and their covariance with equity market returns. Evidence provided by Eun and Resnick (1988) over the 1980 to 1985 period indicates that among the G-5 countries, changes in exchange rates contribute a low of 38 percent for France to a high of 58.49 percent for Germany to the variance of the dollar rate of return of equity invest- ments. Thus, the Plaza Accord provides us with a unique opportunity to verify the impact of stochastic policy coordination aimed at exchange rate management on the volatility of national equity markets.
3. Real monthly returns are used in the analysis. This is advantageous on a number of accounts.
a. The choice of monthly returns avoids the potential biases created by non-synchronous trading, the bid- ask effect, etc., which characterize high-frequency data.
b. Glosten, Jagannathan, and Runkle (1993) point out that there is no reason to expect the time series properties of monthly returns to be the same as daily returns. Thus, it is of interest to examine and com- pare transmission and persistence of monthly volatility shocks to those which characterize higher frequency data.
c. To the extent that changes in real returns represent changes in under- lying fundamentals, results of this study provide indirect evidence as to the transmission of real shocks internationally.
Evidence indicates that domestic return volatility is highly interlinked with volatility in the other markets. In fact, results show that while domestic market shocks are the largest single source of domestic volatility variation for all markets except possibly those of the UK and the US, shocks to foreign markets account for a significant portion of domestic market conditional variance. Further, results suggest that volatility transmission is asymmetric as is the persistence of volatil- ity shocks. The impulse response functions indicate that the spillover effects persist for approximately six months to a year. This degree of persistence is
Equity Market Return Volatility 31
much longer than that documented by Susmel and Engle (1992). Finally, the results intimate that the Plaza Accord affected the interdependence and trans- mission of volatility among national equity markets.
The rest of this paper is organized as follows. Section III describes the data. Section IV discusses the GARCH modeling. Section V contains the VAR results. Section VI concludes.
III. DATA
The data are equity price indices for the G-7 countries in terms of real US dollars. The data were obtained from Data Resources Incorporated and cover the period April 1973 to May 1993. The Canadian stock index is composed of common divi- dend-bearing shares of 65 Canadian companies whose shares are traded on at least one exchange. The French index includes a sample of approximately 180 shares which is updated each year. Selection is based on the market value of share capital and the volume of transactions. The Italian market index covers 60 percent of the total value of shares admitted to the Milan Exchange and is com- prised of approximately 40 major Italian companies, the majority of which are manufacturing based. The Japanese stock index measures the selling price of 690 shares listed on the Tokyo Exchange. The index of the United Kingdom is formed from a portfolio of 500 ordinary shares traded on the London Exchange and issued by industrial companies operating in the UK. The West German mar- ket index is composed of 192 companies and represents 90 percent of total authorized capital. It is a component of the General Index and relates to the com- mon shares of companies with headquarters in West Germany. Finally, the stock index for the seventh country, the United States, is the Standard and Poor’s (S&P) 500. Each index utilized is designed to approximate as closely as possible the average movement of all stocks on each individual country’s exchange.
The stock market returns, R,, used in the analysis are defined as
where Pt is the real value of the respective stock indices at time period t, con- verted to a common currency (i.e., the US dollar). Expressing all returns in terms of US dollars implies that the investigation is conducted from the perspective of a US, rather than an arbitrary, investor. This approach is standard practice in the literature and is consistent with that utilized by Bekaert and Hodrick and Kasa (1992) among others. Roll (1992) provides evidence that exchange rate effects are still present even when using a common currency. Thus, while conversion to a common currency will not eliminate exchange rate effects on volatility, the use of real series should reduce the noise in the data. The partitioning of the sample corresponding to the signing of the Plaza Accord should allow us to gain further insight on the issue of exchange rate effects on equity markets.
32 GLOBAL FINANCE JOURNAL 7(l), 1996
IV. GARCH MODELS
The first ste f:
in the investigation is the assessment of the general characteristics of the data. For the full sample, as well as for both subperiods, the sample moments indicate that the evidence concerning skewness is mixed. More pro- nounced, however, is the presence of excess kurtosis in the data in all sample periods. For the full sample, only the Italian series does not exhibit significant excess kurtosis. Excess kurtosis is somewhat diminished in the Canadian, Ger- man, Italian, and US return series in the pre-Plaza period. In the post-Plaza era, all market returns, except for the Japanese market, display significant excess kur- tosis. The presence of fat tails frequently indicates that GARCH effects are present in the data series.
Inspection of the time series properties of the data (as represented by the autocorrelations of the returns [R,], the returns squared [R!], and the absolute value of the returns [ ) R, ) 1, for all three periods generally indicate that the series exhibit significant first-lag autocorrelation Consequently, the return series lagged one period is included as an explanatory variable in the conditional mean equation. The autocorrelations of the squared and absolute values of returns are generally higher than those of the simple return series for the full sample. In the 1973:4 to 1985:9 period, the same is true for Canadian, Japanese, UK, and US markets. In the 1985:9 to 1993:5 subperiod, the autocorrelations of Rf and IR, 1 appear to be higher for the market returns of France, Italy, Japan, the UK, and the US. The higher autocorrelation values of Rf and 1 R, I are an indication that large (small) changes are followed by the same, and hence (G)ARCH effects may be present.
ARCH effects can be modeled in a variety of ways. The simplest model, ARCH(q), specifies the conditional variance as a function of past errors. The GARCH(p,q) model developed by Bollerslev (1986) extends the simple ARCH model by incorporating past conditional variances into the conditional variance function. It therefore captures the autoregressive nature of the conditional vari- ance and reflects “some sort of adaptive learning mechanism,” (p. 309). It is specified as
R, = 6, + ~,X,E,
Ct n(o, h,)
9 P
h, = ao+ C c$-‘+ C Bih,_i
i= 1 i= 1
(3)
(4)
Bollerslev, Chou, and Kroner (1992) point out that ARCH effects have generally been significant in equity markets and that typically GARCH (p,q) models where p, q < 2 are appropriate. They conclude, from the evidence cited in their paper, that a small number of parameters seem to be sufficient to characterize the vari- ance dynamics of equity markets over long periods of time. Based on this
Equity Market Return Volatility 33
evidence as well as work by Nelson (1990), an AR(l)-GARCH(l,l) specification is employed to model national equity market volatility.
Using likelihood ratio statistics and testing the models against the null hypothesis of no ARCH effects necessitates rejection of the null. Therefore, mar- ket return volatility of each of the seven stock indices can be represented by an AR(l)-GARCH(l,l) process.5
V. VAR RESULTS
System Results and Impulse Response Functions
Now that it has been determined that each series displays GARCH effects, the focus shifts to discerning the impact of volatility in one market on another. To this end, a system of vector autoregressions comprised of the conditional vari- ance of market returns (h,) of each country’s stock index is formulated.
The first step in defining the VAR system is determining the appropriate number of lags for the system of variables. This is accomplished by over and underfitting equation (5) expressed below:
M
X, = C+ C A(S)Xt_s+ tst (5) s= 1
where X, is a 7 x 1 column vector of monthly stock market volatilities, C is a 7 x 1 vector of constants, A(s) is a 7 x 7 matrix of coefficients, &t is a 7 x 1 vector of errors, and m is the optimal lag length. On the basis of the likelihood ratio statis- tic suggested by Sims (1980), m is chosen to be three.
Results of the full sample VAR system are reported in Table 1. Inspection of the R2 indicates that the VAR equations corresponding to return volatility in Canada, France, Japan, the UK, and the US are quite successful in explaining vol- atility in those markets. However, for Germany and Italy, domestic stock return volatility is not as well explained by the system. Block F statistics indicate that with the exception of Canada, volatility in each market is a significant explana- tory factor in at least one other market. Furthermore, where the lags of a particular country are significant, in general their sum is positive, indicating that volatility in one market tends to heighten it in another.
A caveat of VAR systems is that coefficients of the various equations reflect complicated cross-equation feedback and are intuitively difficult to interpret. Thus, the preferred approach is to analyze the system’s response to a typical ran- dom shock. This is done with the moving average representation (MAR). The right-hand side of the autoregressive representation contains a disturbance term as well as explanatory variables. This disturbance term is the only new contribut- ing factor to the dependent variable in the current period; hence, it is known as the innovation in that variable. A time series of all innovations is calculated for each variable. Then, through the process of successive substitution, the current values of the dependent variable are expressed in terms of current and lagged
Tab
le 1
Full
Sam
ple
Vec
tor
Aut
oreg
ress
ion
Res
ults
; R
2s,
Coe
ffic
ient
Es
timat
es,
and
Bloc
k F
Test
s of
Var
Lag
s
lnd
Var
. R2
Can
ada
B,_I
=
B,_z
=
Bt_
3 =
FA
=
France
B,, =
B,.,
=
Bt.3
=
F=
Germany
B,I
=
B,_z
=
Bt_
3 =
F=
Can
ada
France
0.4492
0.6705
0.0332
0.1121
0.7798
0.7392
0.6003
0.4794
-0.7782
-0.3116
0.0905
-0.0668
0.0598
0.0133
(4.8869)
(-1.5126)
(-2.1535)
(0.5469)
(-0.8516)
(0.2337)
(0.5467)
0.2658
0.8826
0.0546
-0.2810
0.0511
-0.1642
0.0100
(2.4222)
(1.5334)
(0.3370)
(-1.5180)
(0.5819)
(-0.5733)
(0.3648)
0.0351
0.4415
0.3185
0.0911
-0.0125
-0.0007
0.0272
(0.3554)
(0.8523)
(2.1864)
(0.5470)
(-0.1586)
(-0.0027)
(1.1086)
29.1675*
1.8229
2.7756*
0.8165
0.2721
0.1573
1.7809
-0.0150
0.9809
-0.0030
0.0204
0.0222
0.6872
(-1.0197)
(12.6859)
(-0.1390)
(0.8206)
(1.8801)
(17.8620)
0.0147
-0.5023
-0.0377
0.0237
-0.0274
-0.8962
(0.6093)
(-3.9706)
(-1.0602)
(0.5837)
(-1.4222)
(-14.2362)
0.0044
0.1992
0.0233
-0.0099
0.0014
0.3202
(0.2154)
(1.8600)
(0.7751)
(-0.2885)
(0.0876)
(6.0089)
0.5593
61.2010*
0.5100
0.7727
1.7348
132.8802"
0.0403
0.3388
0.1408
0.3500
0.1230
0.5422
(0.7303)
(1.1706)
(1.7292)
(3.7611)
(2.7884)
(3.7649)
-0.0554
-0.6165
AI.0447
0.0340
-0.0370
-0.3139
(-0.9479)
(-2.0107)
(-0.5187)
(0.3449)
(-0.7913)
(-2.0576)
-0.0901
-0.2671
-0.0473
0.0042
0.0104
0.0033
(-1.6745)
(-0.9464)
(-0.5958)
(0.0462)
(0.2421)
(0.0237)
1.5188
2.1323'
1.2005
4.9028"
2.6761'
5.6810"
Germany
Dependent
Var
.
lfaly
Ja
pan
UK
US
0.0025
9
(0.6718)
s
-0.0081
F
(-1.3553)
0.0092
$
(1.8172)
%
1.4201
2
0.0561
2
(4.0919)
!z
-0.0058
F
(-0.3972)
-0.0135
v
(-1.0063)
g
6.0446*
s
z?
Ital
y B
,, =
81.2
=
h-3
=
&as
-t
B,,
=
B,,
=
Bt.3
=
F=
us
B,_
l =
B&
2 =
h-3
=
-0.0124
(~.308~
0.0729
(1.7575)
-0.0204
(-0.5209)
1.0348
-0.0650
(-0.7569)
0.0390
(0.3338)
0.0511
(0.5774)
0.4371
-0.0121
(-0.4428)
-0.0039
(-o.2106)
-0.0126
(-0.6953)
0.2681
0.6893
(1.9673)
-0.4499
(-1.1464)
-0.3699
(-1.1103)
0.1746
(0.8266)
0.0268
(0.1232)
-0.0263
(-0.1279)
0.2566
-0.0559
(--o.1240)
-0.1466
(-0.2392)
0.3909
(0.8419)
0.3768
0.1377
(0.9581)
0.0684
(0.6966)
-0.0546
(-0.5736)
0.5423
3.8277
(2.0827)
-2.8824
(-1.4004)
0.5198
(0.2975)
0.0696
(1.1723)
AL0426
(-0.6971)
-0.0189
(-0.3269)
0.5781
-0.1951
(-1.5399)
0.3400
(1.9714)
0.0470
(0.3598)
4.6562'
0.0335
(0.8293)
0.0174
(0.6305)
-0.0015
(-0.0545)
0.3634
0.5780
(1.1183)
-0.1816
(-0.3137)
0.8658
(-1.7619)
0.1919
(2.8250)
0.0479
(0.6853)
0.0743
(1.1229)
4.1752*
-0.0215
(-0.14~)
-0.1842
(-0.9345)
0.1978
(1.3246)
0.6783
-0.0279
(-0.6036)
-0.0332
(-1.0518)
-0.0389
(-1.2709)
1.0956
-0.5632
(-0.9531)
0.6842
(1.0339)
-0.0592
(-0.1054)
-0.0365
(-1.1342)
-o.oo43
(-0.1304)
0.0116
(0.3694)
0.4866
0.9133
(23.2947)
-0.2081
(-2.2259)
0.1896
(2.6786)
233.2596*
-0.0072
f-0.3279)
0.0128
(0.8532)
0.0056
(0.3948)
0.3205
0.0055
(0.0198)
-0.1337
(-0.4260)
-0.1142
(-0.4286)
0.3443
-0.1822
(-1.7337)
0.1338
(1.2362)
0.0423
(0.4129)
1.3698
-0.1526
(-0.6807)
-0.0702
(-0.2301)
0.2539
(1.0992)
0.5828
0.29
03
(4.0583)
0.1017
(2.0814)
-0.0376
(-0.7949)
6.9889*
1.6921
(lBSO5)
-0.5065
(-0.4945)
-0.0275
(-0.0316)
1.268
-2
0.0052
(0.5226)
0.0032
E
(0.3097)
ii
0.0020
k
(0.2078)
% f
0.1948
;
-0.0244
f:
L
(-1.1420)
zf
0.0291
(l.OooO)
0.0048
(0.2195)
0.8806
o.oo70
(1.0246)
-0.0047
(-1.0121)
-0.0051
(-1.1251)
1.0303
0.6204
(7.1244)
-0.0427
(-0.4375)
0.0101
(0.1220)
24.1062*
F=
1.9583
1.5549
1.6749
0.4797
Not
es:
L3,
t_, is
the
coe
ffic
ient
es
timat
e of
vol
atili
ty
in t
helth
m
arke
t at
lag
t -
i. T
stat
istic
s ar
e in
par
enth
esis
. T
he F
sta
tisitc
te
sts
the
null
hypo
thes
is,
H,,:
BI 1
.1 =
B, t
-2 =
B/ ,
_j =
0
%
’ in
dica
tes
sign
ific
ance
at
a =
0.1
0
36 GLOBAL FINANCE JOURNAL 7(l), 1996
values of innovations in all the variables in the system, thereby deriving the MAR. It is defined as
Wt = 5 W)&,_, (6) s=o
The i,jth component of p(s) indicates the response of the ith market to a shock in the ifh market after s periods.
The system of MARS traces out the time path of a given innovation on a spe- cific variable through what is termed the impulse response function (IRF). The set of impulse response functions are therefore useful for depicting the adjust- ment dynamics. Specifically, the impulse response functions indicate the volatility response in all markets due to a one standard error shock to volatility of a particular market. Figures l-3 depict the impulse response functions of shocks to market volatility in the US, UK and Japan, respectively.’ All other fig- ures are available from the authors on request.
The figures illustrate that all markets respond most dramatically to volatility shocks to themselves and the remaining markets within the first six months. More specifically, the figures indicate that shocks to the volatility of the Japanese (Figure 3) and Italian stock returns produce the least notable foreign reactions. In addition, neither country reacts strongly to shocks to other G-7 market return volatilities. In fact, Japan displays virtually no reaction or undershoots volatility shocks to all other markets except the UK. These findings are attributed to the closed nature of the Japanese market throughout much of the sample period and the relative insignificance of the Italian market in the global arena.
Figure 1 displays the impulse response functions to US market volatility shocks. The Canadian market reacts most noticeably to US volatility shocks. In addition, the equity markets belonging to France and the UK evidence notable responses. Not surprising is the fact that the Canadian volatility IRF is quite simi- lar. The apparent symmetry may be due to the integrated nature of the two North American markets.
The impulse response function of shocks to UK market volatility is displayed in Figure 2. Stock market volatilities of France and Japan are the most notable respondents to UK volatility shocks. Similarly, the UK market evidences a notice- able reaction to volatility shocks in the equity market of France. In the remaining European market, that of Germany, home-county market shocks and, to a much lesser degree, shocks to US market volatility generate the only noticeable responses.
The impact of shocks to equity return volatility of the US and Canada gener- ates the most sustained responses from foreign markets. In addition, a shock to the volatility of Japanese market returns continues to cause volatility in the domestic market to remain high well past one year. However, in general the impact of volatility shocks across markets taper off by the 12th month. This find- ing is consistent with the maximum half life of various market volatilities found in the GARCH models. It indicates that shocks tend to be much more persistent than those reported by Susmel and Engle.
Equity Market Return Volatility 37
IO
08
06
01
02
0.0
-02
c 96
0.80
0 64
048
0 32
0.16
000
-0 16
I t I t 1
t
t
t
t
1atp --- _-----
--\ --__----- _---
I I I I I I I r 11
0 2 4 6 El IO 12 14 16 IEI 20 2’2
Figure 1. IRF of a Shock to Market Volatility of the US
Figure 2. IRF of a Shock to Market Volatility of the UK
38 GLOBAL FINANCE JOURNAL 7(l), 1996
a1
02
0.0
-0 2
lot!Js -\ totco ---- ---.
.. --_ ----..__
Figure 3. IRF of a Shock to Market Volatility of Japan
As noted earlier, Hodrick and others argue that a time-varying risk premium represents a market fundamental. For time-varying risk premia to generate mar- ket volatility, shocks to vo~ti~~ must persist for prolonged periods of time. The results of the impulse response functions provide an avenue to address the per- sistence issue. The fact that the impulse response functions indicate that shocks to any single market generally take about six months to a year to be fully accom- modated by the others provides marginal support for the persistence of volatility. Poterba and Summers argue quite forcefully that shocks which do not persist for much longer time periods are not persistent enough to generate time- varying risk premia. Thus, it appears that time-varying risk premia are not the source of transmission of volatility across national equity markets.
Variance Decomposition
Although the set of impulse response functions allows one to trace out the dynamics within the system of variables, it does not allow the researcher to determine the relative importance of each market in generating fluctuations in the others. This is accomplished with the use of variance decomposition. The set of impulse response functions is decomposed into variation in the variables due to variation in the shocks or innovations. This decomposition is known as the forecast error variance (FEV). The FEV is equal to the sum of the variances and covariances of all innovation series. A summary of the fraction of the FEV for each variable attributable to each innovation or shock to all variables comprising the system is given by the VARD. By analyzing the way in which the variances
Equity Market Return Volatility 39
of each variable’s innovations affects the movement of all the variables in the system, one can determine relative importance and potentially causality.
The VARDs of the volatili ty
of the seven national stock markets are presented and summarized in Table 2. Clearly, innovations to domestic market volatility account for the single largest percentage of forecast error variance in each mar- ket, except possibly those belonging to the UK and the US, the two historically most open markets. Further, on average, each market, except for Italy’s, explains at least five percent of the FEV of one other market. This evidence is testament to the strength of the interdependency of capital markets in the post-Bretton- Woods era. In that there is not a single market in which home market innova- tions fully account for domestic variance, one must conclude that no market is clearly exogenous. This is consistent with the results of studies by King and Wadhwani, and Hamao et al., which show that volatility is transmitted intema- tionally among international equity markets.
Closer inspection of Table 2 indicates that the impact of volatility shocks in other markets on domestic return volatility varies widely among the markets represented. The volatility of the markets of Japan and Italy are least affected by innovations to foreign market volatility. Specifically, in no case is more than six percent of the FEV of Italian return volatility explained by volatility shocks to foreign markets. Moreover, shocks to Italian volatility on average explain less than two percent of the FEV of the other markets represented. Clearly, the Ital- ian market is the least interactive; an observation which is also supported by the impulse response functions.
In the case of the Japanese market return volatility, the results in Panel E of Table 2 indicate that it remains relatively unaffected by volatility shocks to for- eign markets. On average, no foreign market’s innovations explain more than three percent of the Japanese FEV. However, shocks to market return volatility in Japan are felt to a limited degree in other markets. Innovations in Japanese return volatility explain a high of approximately five percent of the FEV of Ger- man return volatility and a low of less than one percent of the FEV of Canadian market return volatility. The apparent isolation evidenced here may be attribut- able to the fact that Japan did not truly begin liberalization of its equity market until 1980.
On the other hand, the UK market return volatility is most affected by volatil- ity shocks to other markets. More than half of the error variance of UK volatility is explained by foreign volatility shocks. In addition, Panels B and F of Table 2 reveal that there is a great deal of feedback (simultaneity) between market inno- vations in UK and French stock market volatility and to a lesser extent between the UK and US equity markets. This is seen by noting that the percent of the FEV in each market explained by a shock to the UK and French volatility varies between the two according to the ordering scheme. By similar reasoning, it appears that simultaneity may also be present between the UK and US markets.
Panel D of Table 2 indicates that the French market is relatively isolated. Spe- cifically, apart from its impact on the UK return volatility, innovations in French return volatility account for very little of the FEV of other markets except possi- bly Canada. Further, French innovations account for a minimum of approx-
FEV
of
Tab
le
2 F
ull
Sa
mpl
e V
aria
nce
Dec
ompo
sitio
n of
Mar
ket
Vol
itilit
ies
(197
3:4-
1993
:5)
Can
ada
Fran
ce
Ger
?Yla
n2/
, ”
&pa
n f_
lK
US
___-
..-
_-
A)
Can
ada
K=
l K
=6
K=
12
B) F
ran
ce
K=
l K
=6
K=
12
C)
Ger
man
y K
-l
K=
6 K
=12
D
) It
aly
K--
l K
=6
I(=
12
El J
apan
K
=l
K=
6 K
=lZ
F
) U
K
K=
l K
=6
K-1
2 G
) u
s K
=l
K=
6 K
=12
H
) C
olle
ctiv
e D
omes
tic
Col
lect
ive
For
eign
100.
00 (
45.0
8)
94.1
7 (4
5.49
) 92
.38
(46.
73)
0.00
(3
.40)
2.
24 (
4.36
) 4.
45
(7.0
7)
0.00
(2
2.18
) 2.
82
(22.
09)
2.82
(2
1.71
)
0.00
(0.
12)
4.20
(4.
19)
4.19
(4
.17)
0.00
(0.
06)
0.16
(0
.18)
0.
64
(0.8
2)
0.00
(1
.16)
3.
67 (
4.92
) 3.
95 (
5.19
)
0.00
(3
6.67
) 6.
73
(50.
74)
9.82
(52
.18)
92.3
8 (4
6.73
)
7.62
(5
3.27
)
0.00
(9
.34)
0.
78
(6.2
8)
0.83
(6
.52)
100.
00 (
76.4
5)
91.2
9 (6
1.66
) 86
.39
(57.
42)
0.00
(1
.48)
0.
20
(1.5
4)
0.22
(1.
54)
0.00
(0
.13)
0.
24
(0.3
7)
0.28
(0
.42)
0.00
(0
.05)
0.
43
(0.3
2)
0.62
(0
.68)
0.00
(1
1.05
) 36
.67
(50.
45)
36.3
0 (4
9.81
)
0.00
(0
.82)
0.
21
(0.8
1)
0.76
(1
.31)
86.3
9 (5
7.42
)
13.6
1 (4
2.58
)
0.00
(2
9.92
) 0.
00 (
0.19
) 1.
22 (
27.2
3)
1.06
(0.
83)
1.87
(2
6.11
) 1.
14
(0.8
5)
0.00
(0
.01)
0.
00
(0.0
1)
0.59
(0
.83)
0.
40
(0.3
2)
1.36
(1
.65)
0.
47
(0.4
0)
100.
00
(66.
74)
0.00
(0
.01)
90
.94
(61.
67)
1.15
(1.
17)
89.2
0 (6
0.45
) 1.
18 (
1.19
)
0.00
(0
.09)
10
0.0
(97.
86)
5.83
(6
.21)
86
.62
(85.
11)
5.82
(6
.20)
86
.21
(84.
71)
0.00
(0
.43)
0.
00
(0.8
3)
1.84
(0.
88)
0.59
(0
.28)
1.
69
(0.7
2)
0.88
(0
.27)
0.00
(0
.43)
0.
00
(0.9
6)
4.20
(5
.60)
1.
16
(1.3
1)
4.42
(5
.82)
1.
18
(1.3
4)
0.00
(0
.07)
0.
00
(0.0
0)
5.04
(4
.53)
0.
60
(0.6
4)
4.82
(4
.35)
0.
65
(0.6
9)
89.2
0 (6
0.45
) 86
.21
(84.
71)
10.8
0 (3
9.55
) 13
.79
(15.
29)
0.00
(0
.46)
0.
27
(0.6
2)
0.29
(0
.70)
0.00
(0
.10)
0.
53
(0.5
6)
1.49
(1
.43)
0.00
(0
.02)
3.
84
(3.8
7)
5.19
(5
.22)
0.00
(0
.64)
1.
74 (
2.13
) 2.
11
(2.5
0)
100.
00
(95.
13)
95.3
8 (9
4.08
) 91
.52
(92.
23)
0.00
(1
.66)
1.
11
(1.2
6)
1.63
(1.
82)
0.00
(1
.05)
1.
27 (
1.57
) 3.
13
(3.3
6)
91.5
2 (9
2.23
)
0.00
(1
.62)
1.
00 (
1.59
) 1.
53
(1.8
5)
0.00
(1
7.45
) 1.
82
(24.
28)
1.70
(2
2.90
)
0.00
(0
.04)
0.
60
(0.6
1)
0.60
(0
.61)
0.00
(1
.10)
0.
84
(1.4
1)
0.85
(1
.42)
0.00
(0
.80)
0.
47
(1.8
7)
0.75
(2
.53)
100.
00
(77.
22)
48.1
9 (2
2.92
) 47
.45
(22.
53)
0.00
(1
.77)
0.
29
(1.8
4)
0.34
(1
.75)
47.4
5 (2
2.53
)
0.00
(1
4.38
) 1.
50 (
17.9
7)
1.97
(1
7.24
)
0.00
(2
.52)
3.
13
(7.9
9)
4.13
(9
.14)
0.00
(9
.52)
0.
45
(9.0
6)
0.79
(9
.27)
0.00
(0
.06)
0.
53
(0.5
8)
0.54
(0
.59)
0.00
(2
.71)
1.
13
(2.3
9)
3.90
(2
.76)
0.00
(7
.52)
5.
00
(13.
54)
5.07
(1
3.49
)
100.
00 (
59.6
3)
85.8
5 (3
9.86
) 80
.47
(36.
36)
80.4
7 (3
6.36
)
8.48
(7.
77)
52.5
5 (7
7.47
) 19
.53
(63.
64)
Equity Market Return Volatility 41
imately 57 percent of its own error variance. Hence, the volatility of French mar- ket returns is limited to bilateral interactions.
Table 2, Panel C presents the VARD of German volatility. Between 60 and 89 percent of its error variance is explained by domestic volatility shocks. Oddly, Canadian and German innovations evidence results consistent with feedback effects between the two markets. In addition, the evidence contained in the VARDs along with the impulse response functions indicate that feedback also exists between Germany and the US. Volatility shocks to European markets, however, have relatively little impact on German volatility. This is surprising considering that the European countries belonging to the G-7 are also members of the European Monetary System. It may reflect the German dominance hypothesis.
Turning our attention to the North American markets, we focus on the VARDs of the US and Canada presented in Table 2, Panels G and A, respectively. The results indicate that there is substantial feedback between the volatilities of these two markets. This is evidenced by the shifts in explanatory power attribut- able to shocks to both the US and Canada under the different ordering schemes. Outside of the contemporaneous correlation with Canadian volatility shocks, volatility of US market returns is marginally impacted by shocks to Japanese and German volatility. Similarly, in the Canadian equity market, return volatility is contemporaneously correlated with US volatility shocks and German volatility, as noted earlier. The symmetry and simultaneity evidenced in the VARDs of the US and Canada indicate a high degree of integration between these two markets. Thus, it may be that the integration of these two markets is the driving force behind the Canadian impact in the German market as well as others.
As pointed out in the introduction, volatility transmission may result from the presence of fads and/or bubbles. Although support for the presence of fads has received general acceptance, the issue of the presence of bubbles has been much more controversial. Earlier studies did not find support for the presence of spec- ulative bubbles. However, the recent study by Froot and Obstfeld finds that rational bubbles may exist. More importantly they model the bubbles as deter- ministic functions of exogenous fundamentals. These “intrinsic bubbles,” as the authors call them, can cause asset prices to overreact to changes in fundamentals. Thus, intrinsic bubbles are a plausible source of stock market volatility and expla- nation of the response patterns of the markets to shocks to one another.
Other sources of fundamental impacts, such as monetary policy coordination or competition and time varying risk premiums, are also noted above. Roll notes that market variation might be the result of changing inflationary expectations brought about by discretionary monetary policy activity. While the utilization of real returns can be expected to reduce volatility through the reduction of the impact of changing inflationary expectations, the presence of market volatility at the lower data frequency used in this study is consistent with real impacts of monetary policy. When one extends this line of thought, the volatility transmis- sion evidence above is consistent with monetary policy coordination or competition affecting economic fundamentals.
42 GLOBAL FINANCE JOURNAL 7(l), 1996
The Plaza Accord
Real exchange rate effects have some theoretical and empirical support as a possible source of equity market volatility and linkages (Bekaert & Hodrick, 1992; Dwyer & Haller, 1990). Stochastic policy coordination or competition has been shown to affect both real and nominal exchange rates. Thus, an avenue exists through which stochastic monetary policy can affect equity market volatility. To assess this as a possible source of international volatility transmission, the sample is partitioned in September, 1985 (the month in which the Plaza Accord was reached) and the models re-estimated. Degrees of freedom limitations in the more recent subperiod necessitate restricting the VAR to a lag length of one in both periods.
The GARCH (1,l) models are reestimated for the pre- and post-Plaza period as is the VAR system of market volatilities. In Table 3, we present the goodness of fit statistics of our VAR systems for the 1973:4 to 1985:9 and 1985:lO to 1993:5 subperiods. Chow test statistics indicate that only the VARs of US and Japanese equity market volatilities are significantly different in the pre- and post-Plaza periods. However, in most cases the VARDs evidence noticeable differences. In general, the R2 of the system of equations are higher for the later subperiod. In fact, the average R2 is 0.56 for the post-Plaza period compared to a value of 0.45 for the pre- Plaza period. Table 3 indicates that the return volatilities of all mar- kets are significantly affected by at least one other market’s volatility in the post- Plaza period. Thus, much like the full sample results, bilateral relationships appear to be the norm in the more recent subperiod. These later period results relative to those of the pre-Plaza era intimate that interplay between foreign and domestic markets is rising as we move toward the present. Finally, it is interest- ing to note that the volatility of the Japanese stock market evidences much closer ties to volatility in the European equity markets in the pre- versus the post-Plaza period.
Table 4 contains the VARDs of the system for the 1973:4 to 1985:9 and 1985:lO to 1993:5 subperiods. Comparisons of the results indicate that, in general, simul- taneity increases in the post-Plaza years. This is evidenced by the shifts in explanatory power attributable to the domestic market under the alternative ordering schemes. In addition, the European markets are noticeably more inter- active in the post-1985 sample. Germany displays more foreign influence, as do France and the US, while Canadian foreign impact is somewhat diminished in this later period.
Table 4 indicates that the earlier results intimating that US and UK equity markets are the most open are not specific to a particular subperiod. This result is interpreted as further evidence of the integrated nature of these markets into the global marketplace. Surprisingly, although the Chow test statistic indicates that the VAR representation differs significantly between the two subperiods, the subperiod VARDs of Japanese return volatility do not evidence pronounced dif- ferences in terms of internal or external influence. However, the results of the remaining countries’ VARDs indicate that domestic volatility shocks are transmit- ted to a greater degree and/or are more concurrent in the post-Plaza era.
Tab
le
3A
1973
:4
TO
198
5:9
Vec
tor
Aut
oreg
ress
ion
Res
ults
; R
%, C
oeff
icie
nt
Est
imat
es,
and
Blo
ck F
Sta
tistic
s of
VA
R L
ags
Dep
ende
nt
Var
.
lnd
Var
. C
anad
a
X2
0.39
60
Fran
ce
0.58
41
Ger
man
y
0.16
18
Ital
y
0.01
43
Japa
n
0.64
55
UK
us
0.65
46
0.69
29
Canada
B,,
= 0.6247
-0.0294
-0.0101
(7.6835)
(-0.1263)
(-1.0238)
59.0368*
0.0159
1.0482
-0.0571
-0.0150
0.1565
(-0.6074)
(-0.7646)
(0.8539)
0.3689
0.5846
0.7291
0.0265
(2.1043)
4.4282+
FB
=
France
B,.,
=
-0.0170
0.7640
0.0020
(-0.5576)
(8.7421)
(0.5519)
0.3109
76.4235*
0.3046
0.0637
(1.8038)
3.2537*
0.0190
(2.5892)
6.7039*
0.5770
0.0075
(8.3851)
(1.5947)
70.3104*
2.5430
F=
Germany
B,.,
=
0.9453
0.1262
(1.5737)
(0.0734)
2.4765
0.0054
0.3970
(5.4543)
29.7498'
0.4127
0.2392
(0.5942)
(1.6540)
0.3531
2.7658*
3.8991
0.1740
(2.8792)
(1.8716)
8.2898*
0.6349
F=
Italy
B,,
= 0.0193
0.1761
-0.0012
(0.2660)
(0.8487)
(-0.1332)
0.0708
0.7204
0.0177
0.1468
0.0121
-0.0669
1.7515
(0.6914)
(-0.4095)
3.0676*
0.4780
0.1677
0.0089
(0.7968)
3.5028*
F=
(con
tinu
ed)
Tab
le 3
A
Con
tinu
ed
Dep
ende
nt
Var
.
lnd Var
. Canada
Fran
ce
Germany
ltal
y la
pan
UK
U
S -_
-_
X2
0.3960
0.5841
0.1618
---
0.0143
0.6455
0.6546
0.6929
Japa
n B,
1 =
0.0401
1.0848
0.0234
0.1888
0.7495
0.0770
0.0840
(0.1485)
(1.4027)
(0.7149)
(0.6046)
(11.5261)
(0.1264)
(2.0079)
F=
0.0221
1.9675
0.5110
0.3656
132.8518*
0.0160
4.0316*
UK B
,, =
-0.0248
-0.1402
-0.0027
-0.0621
-0.0243
0.0836
-0*0109
(-0.6828)
(1.3476)
(-0.6110)
(-1.4786)
(-2.7812)
(1.0203)
(-1.9332)
F=
0.4662
1.8160
0.3734
2.1861
7.7350*
1.0410
3.7373"
US B
i.1 =
0.3471
1.3301
0.0255
-0.5067
0.1543
0.7005
0.6587
(0.7592)
(1.0162)
(0.4601)
(-0.9586
(1.4024)
(0.6796)
(9.3068)
F=
0.5764
1.0327
0.2117
0.9189
1.9666
0.4619
86.6172"
Ch
ow
Tes
P 1.3225
.8850
1.0560
0.6729
1.7989*
1.3305
2.0709*
Statistic
No
te:
ATh
e C
how
te
st s
tatis
tic
test
s th
e nu
ll hy
poth
esis
th
at
the
equa
tions
ar
e th
e sa
me
for
both
sa
mpl
e pe
riod
s.
The
cal
cula
ted
valu
e is
def
ined
by
: F
= [(
ESS,
-
ESS,
,)/K
]/
[ESS
&(n
+
m -
ZK)]
whe
re
ESSR
=
e
rror
bur
ns
of s
quar
es
in t
he
rest
rict
ed
mod
el
(i.e
., th
e m
odel
es
timat
ed
over
th
e fu
ll sa
mpl
e),
ESS
UH
= t
he
sum
of
the
err
or
sum
s of
sq
uare
s of
the
mod
el
indi
vidu
ally
re
estim
ated
fo
r th
e pe
riod
s 19
735
to 1
9859
an
d 19
85:lO
to
1993
:5, K
= t
he n
umbe
r of
par
amet
ers,
n
= th
e nu
mbe
r of
obs
erva
tions
in
the
fi
rst
subp
erio
d an
d m
= t
he n
umbe
r of
obs
erva
tions
in
the
lat
er s
ubpe
riod
. T
he c
ritic
al v
alue
is
giv
en
by F
g,,a
j.
Tab
le
3B
1985
:10-
1993
:5
Vec
tor
Au
tore
gres
sion
R
esu
lts;
R%
, C
oeff
icie
nt
Est
imat
es,
and
Blo
ck F
-Sta
tist
ics
of V
AR
Lag
s
lhen
dent
V
ar.
R2
Can
ada
B,_
j =
F=
F
ran
ce
B,l
=
F
Ger
nzn
y B
,_l
=
F=
Ital
y B,_
l =
F=
Japa
n B
,_,
=
F=
UK
B,.1
=
F=
us Bt
_l =
F=
0.73
26
0.92
81
0.10
09
0.50
46
0.74
17
0.77
53
0.16
94
0.74
02
0.02
17
0.59
99
-0.2
333
0.32
11
-0.1
663
0.38
33
(10.
9511
) (0
.1~
9)
~0.
9738
~
(-0.
4995
) (1
.385
7)
(-0.
4053
) (1
.326
3)
119.
9274
* 0.
0259
0.
9484
0.
2495
1.
9202
0.
1643
1.
7590
-0.0
503
0.96
75
0.55
15
0.12
14
0.03
29
0.08
19
OS
629
(-3.
3036
) (3
1.89
43)
(3.9
777)
(1
.154
6)
(0.6
315)
(0
.887
5)
(2.5
049)
10
.913
9*
1017
x47*
15
.822
1*
1.33
31
0.39
88
0.78
77
6.27
44”
0.00
81
-0.1
376
-0.0
699
0.32
14
0.12
86
0.93
24
0.22
95
(0.5
519)
(-
4.72
47)
(-0.
5251
) (3
.183
6)
(2.5
684)
(1
0.51
81)
(3.6
742)
0.
3046
22
.322
5”
0.27
57
10.1
355*
6.
5967
* 11
0.63
06*
13.4
996”
0.00
96
-0.0
276
0.01
11
0.64
23
-0.0
614
-0.2
265
-0.0
412
(0.8
531)
(-
1.22
72)
(0.1
079)
(8
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9)
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5893
) (-
3.31
36)
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8559
) 0.
7278
1.
5061
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0116
68
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4*
2.52
59
10.9
799*
0.
7325
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142
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209
0.20
34
0.02
46
0.84
77
0.02
01
0.03
23
(-0.
8482
) (-
0.62
80)
(1.3
345)
(0
.213
2)
(14.
7806
) (0
.197
8)
(0.4
579)
0.
7194
0.
3944
1.
7808
0.
0454
21
8.46
76*
0.03
91
0.20
42
-0.0
012
0.01
62
0.01
93
-0.0
548
(-0.
1218
) (0
.798
8)
(0.2
086)
(-
0.78
22)
0.01
48
0.63
80
0.04
35
0.61
19
-0.0
431
-0.1
143
0.17
66
-0.0
465
(-1.
4674
) (-
1.95
28)
(0.6
602)
(-
0.22
90)
2.15
32
3.81
36*
0.43
59
0.05
25
0.01
21
10.3
477)
0.
1209
-0.1
049
(-1.
0418
) 1.
0854
0.21
91
0.01
60
(3.5
592)
(0
.369
4 12
.668
0*
0.13
64
0.45
77
-0.1
440
(2.5
691)
(-
1.14
71)
6.60
05*
1.31
58
Not
es:
Bj t-
l is
the
coe
ffic
ient
es
timat
e of
vol
atili
ty
in t
hefn
m
arke
t at
lag
t _
1.
?‘ st
atis
tics
are
in p
aren
thes
is.
* in
dica
tes
sign
ific
ance
at
a
= 0.
10
B T
he F
-sta
tistic
tes
ts t
he n
ull
hypo
thes
is
H,:
B, f
_l =
0
FEVof
Canada
Tab
le
4A
Var
ianc
e D
ecom
posi
tion
of
Mar
ket
Vol
itili
ties
{1
973:
4198
5:9~
Fra
nce
Ger
man
v lta
lv
-.L
Japa
n
A) C
anad
a K
=1
K=6
K=12
B)France
K=l
K=6
K=12
C)Germany
K=l
K=6
K=12
D)Italy
K=l
K=6
K=12
E) Ja
pan
K-I
K=6
K=12
F)UK
K=l
K=6
K=12
G)US
K=l
K=6
K=12
100.00
(65.61)
94.98 (62.02)
94.34 (61.69)
0.00 (7.23)
0.00 (6.66)
0.00 (6.23)
0.00
(0.11)
0.79 (1.10)
0.81 (1.11)
0.00 (0.29)
0.41 (0.68)
0.44 (0.71)
0.00
(1.67)
1.08 (0.82)
1.30 (0.79)
0.00 (0.35)
5.15 (4.67)
4.94 (4.48)
0.00 (25.50)
4.83 (38.29)
4.66 (37.09)
0.00 (11.28)
1.78 (8.63)
2.28 (8.86)
100.00
(68.06)
91.45 (64.50)
87.22 (61.54)
0.00 (2.86)
0.13 (3.31)
0.15 (3.31)
0.00 (0.19)
1.21 (1.26)
1.23 (1.28)
0.00 (0.77)
2.29 (4.81)
2.16 (4.64)
0.00 (14.55)
32.09 (41.89)
31.14 (39.90)
0.00 (1.21)
0.43 (l&4)
0.53 (1.77)
0.00 (0.39)
0.00 (0.52)
2.33 (1.56)
0.05 (0.76)
2.42 (0.62)
0.05 (0.75)
0.00 (0.80)
0.00 (0.44)
0.14 (1.25)
0.99 (0.53)
0.30 (1.43)
1.12 (0.63)
100.00
(95.51) 0.00 (0.99)
98.03 (92.04) 0.03 (0.88)
97.63 (91.65) 0.04 (0.89)
0.00 (0.96) 100.00
(97.28)
0.25 (1.28) 95.94 (93.64)
0.27 (1.29) 95.83 (93.54)
0.00 (0.28)
0.00 (0.02)
1.60 (2.92)
0.73 (0.92)
1.65 (3.01)
0.83 (1.03)
0.00 (2.82)
0.00 (12.85)
4.65 (8.22)
1.45 (6.04)
4.65 (8.09)
3.58 (7.70)
0.00 (0.00)
0.00 (3.08)
2.93 (2.88)
4.43 (9.73)
3.15 (3.10)
6.75 (12.46)
UK
us
_.
..._
__ -
. -
0.00 (3.43)
0.15 (3.97)
0.18 (3.99)
0.00 (2.62)
4.27 (3.10)
6.95 (5.39)
0.00 (1.06)
0.63 (2.02)
0.86 (2.25)
0.00 (0.30)
0.13 (0.42)
0.14 (0.43)
l~.OO (75.61)
88.98 (73.30)
87.91 (72.87)
0.00
(0
.44)
0.41 (0.53)
0.52 (0.65)
0.00
(0
.08)
0.74 (0.55)
0.81 (0.61)
0.00 (2.99)
0.14 (3.88)
0.14 (3.86)
0.00 (16.97)
0.18 (13.55)
0.18 (13.04)
0.00 (0.30)
0.31 (0.40)
0.36 (0.45)
0.00 (0.98)
0.98 (1.64)
0.98 (1.64)
0.00 (17.51)
3.85 (8.26)
4.19 (7.64)
100.00
(64.33)
47.31 (24.80)
44.76 (23.95)
0.00 (0.85)
2.38 (1.52)
2.75 (1.80)
0.00 (15.77)
0.57 (19.19)
0.61 (19.22)
0.00 (3.87)
2.96 (10.39)
4.23 (11.65)
0.00 (0.15)
0.07 (0.26)
0.16 (0.34)
0.00 (0.01)
1.09 (1.08)
1.12 (1.11)
0.00 (4.13)
1.47 (8.96)
1.95 (10.02)
0.00 (4.65)
8.93 (13.86f
10.42 (15.23)
100.00
(69.29)
84.26 (45.19)
81.34 (43.16)
Tab
le
4B
Var
ianc
e D
ecom
posi
tion
of M
arke
t V
oliti
litie
s 19
85:lO
To
1993
:5
Can
ada
Fran
ce
Germany
-
. ..~
My
~....
la
pan
..___
___
UK
-.
-___
$
0.00 (22.96)
$
0.96 (26.91)
2
0.95 (22.77)
T
& r;
0.00 (18.43)
Q
8.40 (40.00)
d
7.73 (37.80)
0.00 (0.23)
0.64 (0.84)
0.66 (0.86)
0.00 (0.09)
4.24 (3.92)
7.21 (6.89)
0.00 (1.38)
2.03 (1.23)
3.44 (1.93)
0.00 (0.11)
18.72 (19.06)
18.51 (18.83)
100.00 (53.32)
83.47 (42.68)
82.92 (42.06)
rf;
FEV
of
A) C
anad
a K=l
K=6
K=12
B)France
K=l
K=6
K=12
C)Germany
K=l
K=6
K=12
D)Italy
K=l
K=6
K=12
E) Ja
pan
K-l
K=6
K=12
F)UK
K=l
K=6
K=12
G)US
K=l
K=6
K=12
100.00
(25.73)
83.81 (23.87)
73.10 (20.35)
0.00 (1.38)
0.13 (0.40)
0.48 (0.46)
0.00 (68.50)
0.69 (67.17)
0.72 (66.87)
0.00 (1.44)
0.02 (1.25)
0.03 (1.16)
0.00 (0.15)
1.35 (0.84)
2.25 (1.58)
0.00 (0.06)
0.25 (0.26)
0.26 (0.27)
0.00 (9.97)
0.54 (9.18)
0.54 (9.09)
0.00 (24.19) 0.00 (21.65)
10.03 (19.96) 0.86 (16.24)
16.75 (28.14) 2.30 (14.65)
0.00 (4.39)
3.74 (11.70)
5.84 (12.23)
0.00 (2.58)
0.39 (3.42)
0.82 (4.32)
0.00 (0.00)
0.20 (0.21)
0.29 (0.30)
100.00
(88.39)
85.15 (80.13)
78.51 (73.82)
0.00 (2.03)
3.41 (1.31)
3.92 (1.45)
0.00 (1.52)
8.35 (7.91)
8.17 (7.75)
0.00 (0.01)
0.66 (0.69)
0.70 (0.72)
0.00
(0.01)
0.43 (0.53)
0.77 (0.88)
0.00 (1.05)
0.18 (0.79)
0.30 (0.98)
LOO.00
(65.36)
80.61 (27.36)
79.69 (26.14)
0.00 (11.14)
8.50 (26.15)
8.05 (25.07)
0.00 (0.26)
1.83 (2.55)
5.07 (6.12)
0.00 (0.86)
0.14 (0.12)
0.17 (0.10)
0.00
(1.24)
3.13 (4.72)
3.55 (5.26)
100.00
(29.56)
94.68 (25.86)
93.97 (25.40)
0.00
(0
.44)
0.63 (1.14)
0.77 (1.23)
0.00 (0.03)
0.03 (0.06)
0.03 (0.07)
0.00 (4.61)
2.26 (4.30)
4.72 (6.34)
0.00
(0
.64)
7.21 (5.79)
8.77 (7.39)
0.00 (2.41)
0.34 (3.17)
0.41 (3.06)
0.00 (2.41)
0.37 (1.43)
0.35 (1.34)
0.00
(0
.64)
2.89 (2.10)
3.71 (2.60)
0.00 (2.65)
1.59 (2.23)
1.63 (2.95)
100.00
(92.82)
88.61 (92.15)
84.90 (89.36)
0.00 (0.33)
0.13 (0.14)
0.15 (0.72)
0.00 (3.47)
22.06 (24.80)
23.77 (26.48)
0.00 (0.02)
25.46 (25.61)
25.01 (25.16)
0.00 (0.06)
0.30 (0.34)
0.45 (0.49)
100.00
(94.76)
24.86 (22.01)
23.82 (21.02)
0.00 (0.62)
2.24 (2.95)
2.38 (3.10)
0.00 (34.40)
12.98 (43.04)
13.20 (43.41)
0.00 (1.65)
0.10 (1.41)
0.25 (1.57)
0.00 (0.04)
0.01 (0.05)
0.02 (0.05)
48 GLOBAL FINANCE JOURNAL 7(l), 1996
The preceding results indicate that the Plaza Accord affected the international transmission of domestic market return volatilities and heightened the interde- pendence of return volatility among the G-7 countries. Specifically, volatilities of all countries’ stock markets are better represented by the VAR system after adop- tion of the Plaza Accord. Additionally, shocks evidence a greater degree of simultaneity as well as international impact in the post-Plaza sample. Height- ened simultaneity, as opposed to lagged causal responses, is necessary to demonstrate rising interdependence. These findings are consistent with those of Von Furstenberg and Jeon (1989), which show that national stock markets have displayed an increase in international sensitivity since the early 1980s.
Collectively, these results are consistent with monetary policy’s having real effects on national equity markets through exchange rates. Although there is some doubt as to the importance of the role of stochastic policy coordination in volatility spillovers (Ito et al., 1992), there are two major channels through which coordinated central bank intervention such as enacted at the Plaza Agreement can impact on asset markets. They are the portfolio balance channel and the sig- nalling channel. Earlier studies of the portfolio channel do not find support for portfolio balance effects (Obstfeld, 1989). However, more recent studies find evi- dence of the effectiveness of both channels (Ghosh, 1992). Although this study cannot distinguish between the two channels as to the source of volatility spill- over across markets, at the very least the finding that results are different in the pre- and post- Plaza Agreement sample periods is consistent with stochastic pol- icy coordination’s having some effect on the transmission of capital market volatility.
VI. CONCLUSION
In this paper, volatility of returns of national stock price indices of the G-7 coun- tries is explicitly modeled with GARCH specifications. Then, via VAR analysis, the structure and timing of volatility transmission between the equity markets of these countries are examined.
Results indicate that a substantial level of interaction, albeit asymmetrical, of return volatility between national equity markets is present. These findings show that the volatility of the equity markets of the US, the UK, and to a much lesser extent Germany are the most interlinked, possibly reflecting a high degree of integration of those markets into the global economy. Japan and Italy, on the other hand, display the most internal isolation in conjunction with marginal external impacts. Volatilities of the equity markets of Canada and France evi- dence bilateral interaction with the US and UK respectively.
The dynamics of volatility shocks displayed by the system of seven markets in the full sample indicate that, with the exception of Japanese stock market volatil- ity, shocks to domestic and foreign markets are fully accommodated within six months to a year. Moreover, in smaller markets, such as Canada and Italy, vola- tility shocks taper off quickly while to varying degrees the impacts of shocks in larger markets are somewhat more persistent. Thus, these results do not provide
Equity Market Return Volatility 49
strong support for the time varying risk premium explanation of volatility trans- mission. However, they do provide evidence that volatility spillovers are much more persistent than previous studies have shown.
The partitioning of the sample around the signing of the Plaza Accord indi- cates that this event impacted volatility transmission. Given that the Plaza Agreement heralded the beginning of an era of policy coordination aimed at exchange rate management in the post-Bretton-Woods period of floating exchange rates, our results are consistent with the conjecture that stochastic pol- icy coordination has heightened national stock market linkages through exchange rate effects. Possible explanations of the pre-Plaza volatility transmis- sion might be the presence of intrinsic bubbles and/or varying information dissemination across markets. Although information flow as a source of volatility transmission is not addressed, the use of monthly data makes this source of vola- tility spillover unlikely. In fact, the lower data frequency is consistent with the conjecture that changing fundamentals may generate volatility and its interna- tional transmission.
These results suggest that future investigations of the relationship between domestic risk premium and market volatility should focus on incorporating international influences on domestic asset risk. Another possible direction of future research is to ascertain the specific cause(s) of the transmission of domes- tic market volatility internationally.
NOTES
1. Engle, Ito, and Lin (1990) and Ito, Engle, and Lin (1992), among others, have investigated this phenomenon in the foreign exchange market.
2. A multivariate GARCH model would produce more efficient parameter esti- mates than the two- stage procedure used in this paper. However, a multi- variate GARCH approach would not enable the researcher to obtain impulse response functions or perform variance decompositions, which is the pri- mary focus of this analysis. Note that the parameter estimates obtained with this procedure are consistent, which is more important than efficiency, given the objective.
3. The table of sample moments is available from the authors on request. 4. The table of autocorrelations is available from the authors on request. 5. Likelihood ratio statistics are available from the authors on request. 6. Although et is serially uncorrelated by construction, components of et may be
contemporaneously correlated. Therefore, it is necessary to transform the error terms through orthogonalization of the matrix of innovations. This pro- cedure can be implemented several different ways, depending upon the ordering of the variables in the system. Ordering is determined by the rela- tive sizes of the cross correlation coefficients between the system of markets. Figures l-3 correspond to the following ordering: US, Canada, France, the UK, Germany, Japan, and Italy. Results are generally consistent across all
50 GLOBAL FINANCE JOURNAL 7(l), 1996
7.
ordering schemes. Figures corresponding to alternative orderings are avail- able from the authors on request. Initial VAR orderings are based on the cross correlation matrix of the series. Here again it is important to note that contemporaneous correlation of the variables necessitates orthogonalization and the procedure can be imple- mented a number of ways depending upon variable ordering. Therefore, all VARDs are estimated for every possible ordering scheme. Generally, results are consistent across orderings. In order to facilitate interpretation, only the VARD results for each variable when it is ordered first and last (the two extremes) are presented.
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