Volatility spillovers across major equity markets of Americas.
Adrangi, Bahram ; Chatrath, Arjun ; Raffiee, Kambiz 等
I. INTRODUCTION
The world financial markets have experienced increasing
integration, resulting in transmission of financial shocks across
connected markets. Equity markets have felt the effects positive as well
as negative shocks to economies and equity markets of all sizes around
the world. While this is not a surprising outcome of economic and
financial integration, the dynamics, the mode, and channels of contagion
and shock transmission continue to be subjects of interest and
investigation. Studying the spread of shocks, and financial crises
throughout global economies, pique the interest of academicians,
financial professionals, domestic and international regulators, and
central bank policy makers. The consensus among researchers is that the
globalization and expanding regional integration, through banking
systems, international trade, and other cross investments have been
instrumental in spreading economic and financial turmoil.
Events of the decades of 1990s and 2000, as well as financial
turmoil of Ireland, Greece, Portugal, and Spain in 2012-2013,
demonstrate how economies of even small size can play a significant role
in transmitting banking and equity market crises across world economies.
Furthermore, these events have reignited interest in this line of
research for all involved.
Researchers have gone to great lengths to investigate the channels
of contagion, shock transmission, and volatility spillovers among world
major markets, in emerging markets, and between them. There are some
obvious ramifications of the findings of such research. For instance,
evidence of volatility spillovers and dynamics would offer an
understanding on the degree of openness and economic co-dependence of
global economies. Many emerging markets have implemented policies that
have led to financial liberalization which has contributed to capital
inflows. Increased capital flows into emerging market securities by
portfolio managers and hedge funds have fueled renewed attention to
these equity markets. Given that rates of economic growth in emerging
markets dwarf those of developed economies, the attention given to them
is understandable. Given that equity market returns and GDP growth rates
are correlated, emerging market equities will only enter more fund
portfolios.
On the down side, concerns about the spread of financial crises
from emerging markets have raised the risk of exposure to these
economies. Portfolio managers want to understand the dynamic
interactions between all equity markets, including emerging, in order to
be able to evaluate market risk and hedging strategies. National and
international regulators and central bankers need information and
insight into these issues in order to be able to cope with spillovers of
volatility, especially during the periods of financial crises. In
particular, world's central bankers and other financial policy
makers would benefit from this line of research findings may become
better equipped to cope with contagious effects of shocks among markets.
Academic researchers are interested in contagion and dynamic
relationships among equity markets for intellectual curiosity, policy
ramification, and empirical evidence in support of theoretical paradigms
such as market efficiency, information arrival, price discovery, and
shock transmission mechanisms across markets.
The empirical research in the last few decades has recorded the
following findings. First, generally equity returns do not follow a
Gaussian distribution and their third and fourth moments confirm skewed
and leptokurtic distributions. Second, returns exhibit long memory and
nonlinearity, i.e., auto correlation of returns and squared returns are
statistically significant for high lag orders. This also leads to
volatility clustering, where high and low returns cluster for a period
of time. Third, conditional volatility reaction to positive and negative
innovations emanating from their own and other markets are asymmetric.
This creates the leverage effect because as equity values drop sharply
in response to negative news, debt to equity ratios rise.
In this paper we examine the behavior of the major equity markets
of the Americas. Our paper analyzes nonlinearities, volatility
spillovers, and causalities in these markets. We examine the daily
values of the Standard and Poor's 500 (S&P 500), Bolsa,
Bovespa, and Merval indices over the period 2000 to 2012. The assessment
of the feedback between the four markets will provide an opportunity for
a comparative analysis of spillovers between the major markets of the
Americas. An incidental though important contribution of the paper is
the examination of the possibly nonlinear, chaotic, and asymmetric
nature of the price dynamics following information arrival within each
of the three markets. We deploy tests of nonlinearity, chaos, GARCH
models, and Granger causality to investigate the behavior, dynamics and
bilateral causality between equity index pairs.
Three specific issues motivate the paper. Foremost, investigating
the role of the US market and its relationship to the markets of
Americas will be of obvious interest to the academics and policy makers.
Given the ongoing liberalization of the financial sector in the
transition economies such as Brazil, Mexico and Argentina, the
integration of financial markets of Americas is bound to increase. While
the comprehensive Free Trade Agreement of Americas has met serious
headwinds, the US and its Latin neighbors continue to be significant
trading partners. For instance, Mexico is the third largest trading
partner of the US, while Brazil ranks as the eighth. Furthermore,
findings of this research may be helpful in better understanding of the
spread of financial crises in general, and among markets under study, in
particular. Given the importance of the Latin American Equity markets
and country funds of Brazil, Mexico, and Argentina in portfolio
diversification, this study is quite timely. However, the
diversification benefits of LA markets may be limited by their dynamic
interdependence with the US equity markets. Furthermore, given the
wealth effect of equity markets, the dynamic interdependence between the
US and LA markets may have broader implications for economic recessions
and recoveries in their economies.
Second, contagion and dynamics of relationships among equity
markets in the globalized economic climate remain critical subjects of
research. Exploring the underlying linear and nonlinear complexities of
equity prices and indices and possible chaotic behavior may shed some
light on appropriate modeling of the dynamic relationship among equity
index series. Financial econometrics of time series and modeling
nonlinearity in the last few decades has gone through innovations that
offer researchers econometric capabilities conducive to non-linear
structures. A study of the price dynamics of the US equity prices with
Latin American equities in the context of nonlinearity would offer
further insights into possible nuances of market behavior and price
discovery.
Third, investigating volatility spillovers, information arrival,
asymmetric reactions to positive and negative news or economic shocks,
and approaches to proper modeling of these behaviors, are useful to
academicians, capital market managers, and policy makers.
Our paper complements the existing literature on the markets of
Americas, and furthers their methodologies by explicitly examining more
recent data for the sources of non-linear behavior of equity series and
deploying the proper methodologies based on the dynamics of the equity
series under question. The US policy makers and portfolio managers are
specifically interested in these bilateral relationships.
We find evidence that stock index price series exhibit nonlinear
dependencies that are inconsistent with chaotic structure. Applying
nonlinear Granger causality tests, we find that the returns in US market
Granger cause the returns in Latin American (LA) markets, but there is
feedback. We identify GARCH (1,1) process as a model that satisfactorily
explains the nonlinearities in prices. We propose and estimate a set of
VAR-bivariate GARCH (1,1) models to ascertain the flow of information
between prices. The estimates indicate that the volatility spills in
both directions, i.e., there is feedback between markets. We also find
evidence of asymmetric market responses to negative and positive shocks.
We propose and estimate asymmetric bivariate VAREGARCH models for the
index pairs. These findings suggest the shock transmissions are
asymmetric and there is leverage effect. Specifically, volatility
responses to negative innovations are larger than to positive ones, no
matter where they occur. Our paper contributes to the existing work by
emphasizing and explicitly testing for the underlying nonlinearities and
deploying the nonlinear Granger causality tests.
The remainder of the paper is organized as follows. Section II
summarizes the related research. Section III discusses the methodology.
Data and summary statistics are contained in Section IV. Section V
describes our main empirical findings. Summary and conclusions are
presented in Section VI.
II. RELATED RESEARCH
There is a significant body of research on international spillover
effects across financial markets dating back to Morgenstern (1959).
Scholars have examined various aspects of intertwining of financial
markets under the categories of interdependence, contagion, comovement,
and volatility spillover.
We limit our review of the literature to the international
interrelationships among equity markets to three main categories. The
first comprises of papers that address contagion, spillovers, comovement
and causality among the world's mature economies and their equity
markets. The second category covers papers that also include equity
markets of the developing world. The last group of papers consists of
studies that involve Latin American markets.
Notable among papers in the first subset that investigate the
behavior of first and second moments of equity returns and their
spillovers across major equity markets are those by King and Wadhwani
(1990), Hamao, Masulis and Ng (1990), Lin et al. (1994), Ito and Lin
(1993), Koutmos and Booth (1995), Koutmos (1996), Longin and Solnik
(1995), Kaminsky and Reinhart (2000), Ledoit et al. (2003), Connolly and
Wang (2003), Baele (2005), Hakim and McAleer (2010), among others. These
studies mainly employ variation of GARCH models or equity markets
time-varying correlations, among others as their methodology.
These papers employ VARs and variations GARCH Models, to
investigate the topic. Taken together, the results from these studies
suggest increasing cross market correlations. Moreover, there appears to
be an important role for the interdependence of banking in international
financial market contagion.
Papers that examine contagion among markets of developing
countries, and between developed and developing markets comprise the
second category. Notable among these are Baig and Goldfajn (1999),
Chan-Lau et al. (2004), Bekaert, et al. (2005), Talla and Imad (2006),
Caporale et al. (2006), Kim et al. (2001), Christiansen (2007),
Worthington and Higgs (2004), Dungey et al. (2006), Lucey and Voronkova
(2008), Beirene et al. (2009), Diebold and Yilmaz (2009) Harrison and
Moore (2009), and Sok-Gee et al. (2010), among others. While summarizing
each of their findings in detail may not be appropriate in this paper,
it can be noted that these papers generally point out to spillover and
contagion effects in various degrees in the markets under study. They
deploy variations of GARCH modeling, VAR, Kalman filters, and variance
decomposition to investigate contagion and spillovers. The findings from
all of these studies suggest that there is a uni-directional spillover
of equity market volatility from major economies to others.
The third group of papers summarized in this section is devoted to
the emerging markets of Latin America. Some notable papers in this
subset are, Choudhry (1997), Christofi and Pericli (1999), Pagan and
Soydemir (2000), Chen et al. (2002), Johnson and Soenen (2003), Barari
(2004), Fujii (2005), Verma et al. (2008), Rivas et al. (2008), El Hedi
et al. (2010), Aloui (2011), among others. Following in the path of the
previous two categories, these researchers deploy the well-known
methodologies of previous papers to investigate the volatility contagion
among markets of Americas.
Methodologies applied run the gamut. They include cross-correlation
function analysis, vector autoregression models, constant and time
-varying correlation coefficients, cointegration, regime switching
models, stochastic volatility models, Kalman filters, univariate and
multivariate GARCH models (MGARCH), among others.
These researchers establish co-movement, cointegration, and
asymmetric volatility spillover among the markets of Latin America.
Their salient findings can be summarized as follows.
There is a notable trend toward increased regional integration
relative to global integration until the mid-1990s. However, the second
half of the 1990s, the global integration proceeds faster than regional
integration. Volatility in these markets shows asymmetry and long
memory. Furthermore, conditional correlations in these markets increased
in the face of the global as well as regional financial turmoil.
The cointegration tests show that there is a long-term comovement
among these neighboring economics. The conditional correlations are
largely affected by their own volatility shocks. However, regional and
international crises affect the interaction among these markets. The
cross-market comovements and integration are time- varying, and have
increased in the last two decades.
Latin American equity market volatility is more responsive to
negative news than positive news. Furthermore, due to globalization and
integration with the world economy, Latin American equity markets have
become more susceptible to contagion from the world financial crises.
There are asymmetric volatility spillovers and feedback among the Latin
equity markets.
The significance of findings of the past research may be that the
diversification benefits of investing in various Latin American equity
markets may be limited.
III. METHODOLOGY
To begin our analysis, we first examine the equity indices of the
markets under study for stationarity and non-linearities. Augmented
Dickey Fuller (ADF), Phillips- Peron (PP), and
Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests of stationarity are
employed for this purpose. To examine nonlinearities in the series under
study, we compute the Q and [Q.sup.2] statistics, and perform Wald test
for ARCH effects. To test for chaotic behavior, we apply the Brock,
Dechert, and Scheinkman (1987) test (BDS) and Correlation Dimension (CD)
tests of chaos. If nonlinearities are present, but we find no chaos, we
estimate appropriate variations of autoregressive GARCH (1,1) models to
capture the dynamic behavior of equity indices. We complete the analysis
with Granger causality test or its adaptation for nonlinear processes.
Of the various tests used in this research, a brief description of tests
of Chaos may be appropriate. We present more detail on the methodologies
used as we apply them.
We deploy two tests of chaos: (i) the Correlation Dimension of
Grassberger and Procaccia (1983) and Takens (1984), (ii) and the BDS
statistic of Brock, Dechert, and Scheinkman (1987) which are discussed
in detail in Adrangi et al. (2001a,b). The correlation dimension is
based on the following statistic:
S[C.sup.M] = {ln [C.sup.M]([[epsilon].sub.i]) - ln
[C.sup.M]([[epsilon].sub.i] - 1)} (1) { ln([[epsilon].sub.i]) -
ln([epsilon]i-1)}
for various levels of M (e.g., Brock and Sayers, 1988). The
S[C.sup.M] statistic is a local estimate of the slope of the [C.sup.M]
versus e function. Following Frank and Stengos (1989), we take the
average of the three highest values of SCM for each embedding dimension.
The BDS statistic is proposed by Brock, Dechert and Scheinkman
(1987), which is based on the correlation integral that has been quite
robust in discerning various types of nonlinearity as well as
deterministic chaos. BDS show that if [x.sub.t] is (i.i.d) with a
nondegenerate distribution,
[C.sup.M]([epsilon]) [right arrow] [C.sup.1][([epsilon]).sup.M], as
T [right arrow] infinity (2)
for fixed M and [epsilon]. Based on this property, BDS show that
the statistic
[W.sup.M](e) = [square root of (T)] {[[C.sup.M]([epsilon]) -
[C.sup.1][([epsilon]).sup.M]]/[[sigma].sup.M](e)} (3)
where [[sigma].sup.M], the standard deviation of [*], has a
limiting standard normal distribution under the null hypothesis of IID.
[W.sup.M] is termed the BDS statistic. Nonlinearity is indicated by a
significant [W.sup.M] for a stationary series with no linear dependence.
Chaos is rejected if there is evidence that the nonlinear structure
arises from a known nondeterministic system.
IV. DATA AND SUMMARY STATISTICS
We employ daily index values of Bolsa (Mexico), Bovespa (Brazil),
Merval (Argentina) and Standard & Poor's 500 (S&P500)
spanning the period of 2007 through October 2012. All series are
retrieved from the Bloomberg data base. Percentage changes (index
returns) are given by [R.sub.t] = (1n([P.sub.t]/[P.sub.t-1])) x 100,
where Pt represents the daily closing values.
The graphs of indices exhibit mean and covariance nonstationarity,
as well as volatility clustering. Percentage change, i.e., returns
([R.sub.t]) series for the four indices are mean-stationary, but may be
covariance non-stationary. These graphs are not presented here for the
purpose of brevity, however, justify formal statistical tests of
stationarities and possible nonlinearities in return series. We provide
the statistical evidence of behavior of these series in Table 1.
Panel A shows that index levels are nonstationary and there is
evidence of nonlinear behavior as evidenced by significant [Q.sup.2]
statistics. The [R.sub.t] series are found to be stationary employing
the Augmented Dickey Fuller (ADF), PP and KPSS statistics. There remain
linear and nonlinear dependencies as indicated by the Q and Q2
statistics, and Autoregressive Conditional Heteroskedasticity (ARCH)
effects are suggested by the ARCH (6) chi-square statistic. Whether
these dynamics are chaotic in origin is the question we turn to next.
To capture the linear structure, we estimate autoregressive models,
[R.sub.t] = [p.summation over (i = 1)] [[pi].sub.i][R.sub.t-1] +
[[epsilon].sub.t]. (4)
The lag length for each series is selected based on the Akaike
(1974) criterion. The residual ([[epsilon].sub.t]) represents the index
movements after filtering the linear relationships. The mean equation of
the GARCH model is the same as given in Equation (7), while the
conditional variance equation of the model is given by
[[sigma].sup.2.sub.i,t] = [[beta].sub.i] +
[[gamma].sub.i][u.sup.2.sub.i, t - 1] + [[phi].sub.i]
[[sigma].sup.2.sub.i, t - 1] i = 1, 4 (5)
where [[sigma].sup.2.sub.i, t] is the conditional variance,
[u.sub.i, t - 1] is the lagged innovations, and [[sigma].sup.2.sub.t -
1] is the lagged conditional volatility.
V. EMPIRICAL FINDINGS
A. Tests for Chaos
1. Correlation dimension estimates
Table 2 reports the Correlation Dimension (S[C.sup.M]) estimates
for the returns and logistic series. The values of the correlation
dimension for chaotic series and its filtered version shown in the first
two rows of the Table do not show an explosive trend. For instance,
S[C.sup.M] estimates for the logistic map stay around one as the
embedding dimension rises. Furthermore, the estimates for the logistic
series are insensitive to AR transformations, consistent with chaotic
behavior. For the return series, S[C.sup.M] estimates show inconsistent
behavior with chaotic structures. For instance, the S[C.sup.M] does not
settle. The estimates for the AR or GARCH transformation do not change
results much, but are mostly larger and do not settle with increasing of
the embedding dimension. These initial indicators suggest that the
series under consideration are not chaotic.
2. BDS test results
Tables 3 and 4 report the BDS statistics (Brock, Dechert, and
Scheinkman, 1987) for [AR(p)] series, and standardized residuals
([epsilon]/[square root of (h)]) from the GARCH (1,1) models,
respectively. The critical values for the BDS statistics are reported in
Adrangi et al. (2001a, b). The BDS statistics strongly reject the null
of no nonlinearity in the [AR(1)] errors for all of the return series.
However, BDS statistics for the standardized residuals from the
GARCH-type models are mostly insignificant at the 1 and 5 percent
levels. On the whole, the results provide compelling evidence that the
nonlinear dependencies in the series arise from GARCH-type effects,
rather than from a complex, chaotic structure. From the BDS statistics
presented in Table 4, it is apparent that the variations of the GARCH
model may explain the nonlinearities.
B. Bivariate GARCH Models
To model the relationship between the returns while accounting for
the GARCH effects, we estimate three VAR models in a bivariate GARCH
context. We summarize the findings of this model but do not report it in
the interest of brevity. Most model coefficients are statistically
significant at five or ten percent levels of significance, indicating
that a variation of GARCH model maybe well-suited for modeling the
interaction between markets under study. Examining sign bias tests show
that size bias and joint sign and size bias tests are statistically
significant pointing toward asymmetric volatility effects of positive
and negative shocks or news. This may also indicate that EGARCH model
may be better suited for modeling the volatility spillovers for Latin
American markets.
To account for asymmetric shock responses, we estimate bivariate
EGARCH models that are better suited to account for the asymmetric
volatility response within and across markets. This model is an
extension of the univariate EGARCH model of Nelson (1991). Koutmos
(1999), Cheung and Ng (1992), Hakim and McAleer (2010), Rivas et al.
(2008), among others, have documented this pattern of asymmetric
volatility transmission in financial markets. The following equations
represent the proposed VAREGARCH model:
[R.sub.it] = [[alpha].sub.i, 0] + [2.summation over (j = 1)]
[[alpha].sub.ij] [R.sub.i, t - 1] + [u.sub.i, t] (6)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
[[phi].sub.j]([z.sub.j, t - 1]) = ([absolute value of ([z.sub.j, t
- 1])] + [[delta].sub.j][z.sub.j, t - 1]) i.j = 1, 2 (8)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
where [z.sub.j, t] = ([absolute value of ([u.sub.j,
t]/[[sigma].sub.j, t])] - [square root of (2/[pi])]) +
[[delta].sub.j][u.sub.jt]/[[sigma].sub.j, t] and [z.sub.i, t] =
[[epsilon].sub.it]/[[sigma].sup.2.sub.i, t] t is the standardized
innovations of market i at time t. Volatility persistence is measure by
[gamma]. Nelson (1991) notes that unconditional volatility is finite and
measurable if [[gamma].sub.i] < 1 while [[gamma].sub.i] = 1 signals a
non-stationary and unconditional volatility is not well-defined. We
deploy a combination of the simplex method with the
Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to maximize the
likelihood function, L([OMEGA]) .
Table 5, reports the estimation results of the bivariate- EGARCH
models of equations (6)-(9) for the S&P500 and three LA indices. In
all equations [[delta].sub.1] and [[delta].sub.2] < 0 combined with
positive [[beta].sub.12] and [[beta].sub.21], confirm that volatility
transmission across markets is asymmetric. Negative shocks in each
market results in elevated conditional volatility in the other and there
is feedback in a similar manner. Statistically significant
[[delta].sub.j] < 0 shows the presence of asymmetric volatility
effects in each market. Thus, negative shocks in each market lead to
higher volatility than positive innovations. The size effect (the degree
of asymmetry) as measured by [absolute value of (-1 +
[[delta].sub.j])]/(1 + [[delta].sub.j]), are and have become known as
"leverage effect." The leverage effect occurs as the negative
shocks reduce the market capitalization and raise the debt to equity
ratio. The unconditional volatility in both cases is finite as indicated
by [[gamma].sub.1] and [[gamma].sub.2] < 1. Insignificant sign and
size bias tests reinforce the statistical validity of the Asymmetric
model even in the presence of significant joint test of size and sign
bias.
To summarize the impact of negative and positive shock transmission
among markets, we use the estimated [[delta].sub.j] and [[beta].sub.ij]
coefficients. For instance, a one unit negative shock to market j
affects the conditional volatility in market i by [[absolute value of
((-1 + [[delta].sub.j]))].sup.*] ([[beta].sub.ij]) for negative shocks
and [[absolute value of ((-1 + [[delta].sub.j]))].sup.*]
([[beta].sub.ij]) for positive shocks. Table 6 reports these effects for
a percentage positive and negative shock from market i on the percentage
change in volatility of market j. The notable conclusions are as
follows. First, the shock transmission is asymmetric. For instance, in
all cases positive shocks to the S&P500 futures have smaller
percentage impact on S&P500 and other indices relative to negative
shocks of the same size. Volatility reaction in all markets to own
negative innovations and cross market negative innovations is much
larger in all markets. Second, negative shocks to LA markets also show a
significant impact on the volatility of S&P500 relative to the same
size positive shocks. Finally, the largest impact of shocks to
S&P500 is felt in equity market of Argentina. This may be due to the
size of equity market there which is the smallest in dollar value
relative to Mexico and Brazil. The leverage effects reported in Table 6
confirm that the largest leverage effect of the S&P500 is on the
S&P500 and the magnitude is smaller on the LA equity markets.
C. Spillovers and Granger Causality
Having established volatility spillover, and low conditional
correlations between equities markets of Americas, we proceed to
investigate the possibility of nonsynchronous relationship-dynamics that
may be unobservable from returns' correlations. To this end, we
examine the causality deploying the nonlinear extension of the standard
Granger causality test between two variables (Granger, 1969; Geweke,
1984). In the standard Granger autoregressive and linear test, the null
hypothesis that an observed series [x.sub.t] does not Granger cause
another series, [y.sub.t], is to test the null hypothesis that
[[gamma].sub.1] through [[gamma].sub.n] = 0.
[y.sub.t] = [alpha] + [[beta].sub.1][y.sub.t - 1] + ...
[[beta].sub.k][y.sub.t - k] + [[gamma].sub.1][x.sub.t - 1] + ...
[[gamma].sub.n][x.sub.t - n] + [[epsilon].sub.t] (10)
where [[epsilon].sub.t] is normally and identically distributed
with mean of zero and constant variance under H0. Our variables exhibit
nonlinearities and therefore the linear framework may not be suitable.
Thus, we employ a nonlinear version of the test as suggested by Skalin
and Svirta (1999), based on smooth transition regression (STR).
Motivated by the linear causality regression, when [y.sub.t] (under the
null hypothesis of non-causality) is generated by the STAR model, this
test is based on the non-existent predictive power of lagged values of
another variable, [x.sub.t], where the sequence {[x.sub.t]} is assumed
to be stationary. The non-linear causality from x to y is modeled by an
additive smooth transition component. Consider the following additive
smooth transition regression model
[y.sub.t] = [[pi].sub.10] + [[pi].sub.1]'[w.sub.1] +
([[pi].sub.20] + [[pi].sub.2][w.sub.t])F([y.sub.t - d]) +
[[delta].sub.1]'[v.sub.t] + ([[delta].sub.20] +
[[delta]'.sub.2][u.sub.1])G([x.sub.t - e]) + [u.sub.t] (11)
where [[delta].sub.j] = ([delta]j1 ... [delta]jq)', j = 1, 2,
v t = (xt-1 ... xt-q)' and G (.) is a transition function.
Non-causality is tested as H0: G = 0 & [delta]1i=0, i = 1, ... q. It
can be shown that the relevant approximation to the above equation is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
where K'= (k1 ... kq), and non-causality is supported by
[k.sub.i] = 0, [[phi].sub.ij] = 0 and [[psi].sub.i] = 0 i = 1 ... q, j =
1 ... q. Under H0 the resulting test statistic has an asymptotic [chi
square] distribution with (q*(q + 1)/2) + 2q degrees of freedom.
Alternatively, as in this paper, one may perform the test based on F
distribution.
Table (7) presents the results of the nonlinear Granger Causality
tests for q = 5 .... 10. The reported F statistics in Table 7 test the
joint null hypotheses of no causality, i.e. that [k.sub.i] = 0,
[[phi].sub.ij] = 0 and [[psi].sub.i] =0. Therefore, at some lag levels
of variable x the null may not be rejected. FolloWing previous research
(Skalin and Svirta, 1999), We estimate Equation (12) for a range of lag
order to ensure that causality test results are robust at longer lags.
For all cases and all lag levels the P-values of F statistics are
virtually equal to zero, showing that the H0 is rejected and there is
evidence of causality from the S&P 500 to equity markets of Latin
America. However, there is also feedback, i.e., LA equity market
volatilities also cause volatility in S&P500. This finding
emphasizes that the globalization of financial markets has enhanced the
role of "small" economies in the world financial markets. For
instance, volatility and shocks to a Latin American equity markets,
would send volatility waves to the US equity markets. These strong
causality results confirm and support the findings of bivariate VAR-
EGARCH models. They go beyond establishing shock spillovers from one
equity market to another in Americas, and point to a concrete causality
and feedback among equity markets of Americas. Indirectly, our findings
confirm that financial turmoil in smaller markets could trigger
headwinds for major economies of the world. As events of the year 2012
in Greece showed, US Federal Reserve Open Market Committee and equity
and bond fund managers were duly and seriously concerned with the
potential deleterious effects of banking and financial markets of Greece
on the US economic recovery. The Fed bond buying thus continued robustly
through 2012 and 2013 to partially countervail those events.
The known channels of volatility spillovers across markets are
trade and banking system. Trade among major economies of Americas is
expected to grow. However, there have been no serious attempts toward
coordinating banking regulation, monetary policy, or interest rate
targets. Unlike the Euro zone and the European Central Bank (ECB), there
is no such coordinating financial body in Americas. Furthermore, the
establishment of a Central Bank of Americas is far from reality, and is
not even discussed at the time of this research. Thus, it is incumbent
upon Central banks of Latin American economies and the Fed to coordinate
policies that foster trade and economic growth without promoting
instability in financial markets. For instance, tapering the
quantitative easing by the Fed in the late 2013 throughout 2014,
affected returns in various asset classes in the US, across the world,
and Americas. Latin American equity markets suffered losses due to
capital flight. Continued downturn in these markets and its effects on
economic growth and trade among Americas could potentially have ripple
effects on the economies of all partners, including the US.
The findings of this research also suggest that for the US money
managers, Latin American equity markets may not be the best vehicles of
portfolio diversification. Negative shocks to the LA markets studied in
this paper result in volatility in the US of more than 4 percent in two
out of three cases. The effects of positive shocks to these markets, on
the other hand, are negligible. Therefore, US investors will not be able
to reduce their portfolio risk by investing in LA equities. Events of
the late 2012 and 2013 in European economies such as Greece shed light
on the potential effects of negative shocks to the Brazilian economy,
for instance. Negative shocks to LA equity markets are certain to
trigger volatility in the US equity markets and potentially create
economic growth obstacles at least in the short-run.
On the other hand, negative shocks to LA markets may also create
temporary opportunities to purchase equities inexpensively. For
instance, if negative shocks are seen as transitory, then the effects of
these shocks on the US equities maybe short-lived. In these cases, the
deep market drops due to LA negative shocks, may provide profitable
buying opportunities given the significant negative effects of these
shocks on equity markets. It is well known that negative news impart
temporary shocks to equity markets caused by investor jitters. Equity
returns are mean-reverting and in the medium and long-run revert back to
long-run trends.
VI. SUMMARY AND CONCLUSIONS
This paper investigates the volatility spillovers in a dynamic
framework between the Standard and Poor's 500 (S&P500), and the
indices of markets of Argentina (Merval), Brazil (Bovespa) and Mexico
(Bolsa). Several issues motivated the paper. Foremost, investigating the
intermarket dynamics among the US equities and major emerging markets of
Americas is important given the ongoing financial liberalization and
integration with the US market. Investigating volatility spillovers and
potentially asymmetric reactions to positive and negative shocks
emanating in each of these connected markets are informative to capital
market players and political policy makers in Americas.
We deploy tests of nonlinearity and chaos to determine the behavior
of the indices under question and appropriate models to test the dynamic
bilateral interaction between the S&P500 and each of the indices.
Our statistical tests establish that every index exhibits nonlinear
patterns that are not consistent with chaotic behavior. We propose and
estimate two variations of bivariate VAR-GARCH models. The estimated
bivariate VAR-EGARCH models capture nonlinearities in both index series.
Furthermore, this model is well positioned to reflect the asymmetric
reaction in each market to negative and positive shocks to the other
equity market in the model. Bivariate EGARCH models also show that the
volatility spills in both directions, i.e, there is bivariate feedback
between equity indices of Americas.
To further investigate the nonlinear interaction the S&P500
with each market under study, we employ the nonlinear version of Granger
causality test. The findings of Granger causality test strongly support
the bivariate VAR-EGARCH model findings and show the causality runs in
both directions, i.e., there is feedback. These findings taken together
are notable for policy makers and central banks, as well as hedge
funders and money managers. They provide evidence that equity market
downturns (negative shocks) in the US may have serious effects on equity
markets and economies of Latin America. Therefore, diversification
benefits from major equity markets of Americas may be limited for all
investors across Americas. More importantly for US Fed, the US economy
may face headwinds that may emanate from negative shocks to Latin
American equity markets.
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Bahram Adrangi (a), Arjun Chatrath (b), Kambiz Raffiee (c)
(a) W. E. Nelson Professor of Financial Economics, University of
Portland 5000 N. Willamette Blvd., Portland, Oregon 97203 adrangi @up.
edu
(b) Schulte Professor of Finance, University of Portland 5000 N.
Willamette Blvd., Portland, Oregon 97203 chatrath@up. edu
(c) Foundation Professor of Economics, College of Business,
University of Nevada, Reno, Nevada 89557 raffiee@unr. edu
Table 1
Diagnostics
Returns are given by [R.sub.t] = ln([P.sub.t][P.sub.t - 1])T00, where
[P.sub.t] represents closing index values on day t.
ADF represents the Augmented Dickey Fuller
tests (Dickey and Fuller (1981)). The [Q.sup.2](12)
and [Q.sup.2](12) statistics represent the Ljung-
Box (Q) statistics for autocorrelation of the
[R.sub.t] and [R.sub.t.sup.2] series respectively. The ARCH(6)
statistic is the Engle (1982) test for ARCH
(of order 6) and is [chi square] distributed with 6
degrees of freedom.
Panel A: Price Levels
S&P 500 MERVAL BOVESPA BOLSA
Interval: 7/2007-7/2012 (N = 127)
ADF_trend -1.900 -1.266 -2.015 -2.075
PP_trend -1.851 -1.337 -1.872 -2.011
KPPS_trend 0.797 0.531 0.282 0.560
Q(24) 23177.00 23858.00 22283.00 24001.00
[Q.sup.2] 23020.00 23703.00 22011.00 23985.00
(24)
LM_ARCH (6) 255.975 98.945 180.985 104.720
Panel B: Percentage Changes
S&P 500 MERVAL BOVESPA BOLSA
Interval: 7/2007-7/2012 (N = 1271)
ADF_trend -28.735 (a) -33.725 (a) -36.190 (a) -33.338 (a)
PP_trend -40.564 (a) -33.836 (a) -36.345 (a) -33.279 (a)
KPPS_trend 0.315 0.164 0.084 0.153
Q(24) 69.766 (a) 32.162 (a) 44.134 (a) 48.046 (a)
[Q.sup.2] 1655.010 (a) 867.480 (a) 1801.400 (a) 1249.700 (a)
(24)
LM_ARCH 333.589 (a) 223.859 (a) 339.309 (a) 201.050 (a)
(6)
Notes: S&P500, MERVAL, BOVESPA, and BOLSA,
represent equity indices of the US, Argentina,
Brazil and Mexico. Q(12) and [Q.sup.2](12) are the Ljung
Box statistics for AR(1) residuals and their
squared values. a, b, and c, represent
significance at .01, .05, and .10, respectively.
Panel C: Summary descriptive statistics for model
variables. All variables are in level.
S&P 500 MERVAL BOVESPA BOLSA
Interval: 7/2007-7/2012 (N = 1271)
Mean 1199.577 2279.117 59190.331 31050.240
Stand Dev 191.634 658.409 9219.429 5306.679
Skewness -0.439 0.025 -0.975 -0.669
Kurtosis 2.520 2.730 3.341 2.811
J-B 52.33789 (a) 3.917 204.302 (a) 97.135 (a)
Notes: S&P500, MERVAL, BOVESPA and BOLSA represent
equity indices of the US, Argentina, Brazil and
Mexico.
a represents significance level of .01.
Table 2
Correlation dimension estimates
The Table reports SCM statistics for the Logistic
series (w = 3.750, n = 2000), daily percentage changes
in index values over four embedding dimensions: 5,
10, 15, 20. AR(1) represents autoregressive order
one residuals. GAR( 1,1) represents standardized
residuals from a AR1--GARCH( 1,1) model.
M= 5 10 15 20
Logistic 1.02 1.00 1.03 1.06
Logistic AR 0.96 1.06 1.09 1.07
BOLSA AR(1) 2.198 3.601 4.458 5.549
BOVESPA AR(1) 2.472 4.218 5.706 7.153
MERVAL AR(1) 2.384 4.576 6.451 8.519
S&P AR(1) 2.145 3.440 4.340 5.107
BOLSA _ GAR(1,1) 3.591 7.000 1.0225 15.149
BOVESPA _ GAR(1,1) 3.697 7.312 10.602 11.460
MERVAL _ GAR(1,1) 3.142 6.909 10.767 Infinity
S&P _ GAR(1,1) 3.515 6.701 9.070 11.258
Notes: S&P500, MERVAL, BOVESPA and BOLSA represent
equity indices of the US, Argentina, Brazil and
Mexico. AR(1) indicates AR(1) model residuals
fitted to each index, and GAR(1,1) represents
standardized residuals of GARCH(1,1) model fitted
to the indices under study.
Table 3
BDS statistics for AR(1) residuals
The figures are BDS statistics for the AR(p). (a),
(b), and (c) represent the significance levels of .01,
.05, and .10, respectively.
M
[epsilon]/[sigma] 2 3 4 5
BOLSA AR(1)
0.50 6.905 9.941 13.174 16.597
1 6.324 9.281 11.884 14.276
1.5 6.538 9.228 11.105 11.266
2 7.605 9.976 11.152 12.083
BOVEPA AR(1)
0.50 2.877 5.218 7.380 9.109
1 53.244 7.771 9.514 11.198
1.5 7.415 10.093 11.375 12.471
2 8.678 12.075 13.219 14.006
MERVAL AR(1)
0.50 3.225 6.309 8.205 9.481
1 4.609 8.119 10.023 11.400
1.5 5.946 9.601 11.314 12.523
2 6.340 10.153 11.592 12.615
S&P500 AR(1)
0.50 4.292 8.644 123.711 17.225
1 5.501 9.262 11.790 14.319
1.5 7.441 10.532 12.363 13.957
2 8.480 11.764 13.403 14.742
Notes: S&P500, MERVAL, BOVESPA and BOLSA represent
equity indices of the US, Argentina, Brazil and
Mexico. AR(1) indicates AR(1) model residuals
fitted to each index. All BDS statistics are
significant at 1 and 5 percent levels.
Table 4
BDS statistics for GARCH (1.1) standardized residuals
The figures are BDS statistics for the
standardized residuals from GARCH(1,1) models. The
BDS statistics are evaluated against critical
values obtained from Monte Carlo simulations
(Appendix 1). (a), (b), and (c) represent the
significance levels of .01, .05, and .10,
respectively.
M
[epsilon]/[sigma] 2 3 4 5
BOLSA_gar11
0.50 -1.355 -0.914 -0.896 -1.225
1 -1.432 -1.220 -1.207 -1.159
1.5 -1.592 -1.404 -1.444 -1.416
2 -1.078 -0.693 -0.765 -0.889
BOVESPA gar11
0.50 -2.166 -1.209 -0.559 -0.0004
1 -2.318 -1.624 -1.286 -1.027
1.5 -2.289 -1.314 -1.066 -0.859
2 -1.814 -0.572 -0.409 -0.370
MERVAL garll
0.50 -1.880 -0.342 0.142 0.068
l -2.103 -0.539 -0.079 0.199
1.5 -1.805 -0.310 -0.021 0.244
2 -1.499 0.115 0.233 0.435
S&P500 garll
0.50 -3.931 (a) -1.973 -9.580 (a) -0.308
l -4.260 (a) -2.561 (a) -1.760 -1.084
1.5 -4.438 (a) -3.141 (a) -2.534 (a) -2.090 (a)
2 -4.082 (a) -2.785 (a) -2.442 (a) -2.125 (a)
Notes: S&P500, MERVAL, BOVESPA and BOLSA represent
equity indices of the US, Argentina, Brazil and
Mexico. GAR(1,1) represents standardized residuals
of GARCH(1,1) model fitted to the indices under study.
Table 5
Bivariate asymmetric VAR-EGARCH model with
volatility spillovers Americas and S&P 500 Index
Mean Equation S&P500 BOLSA
Intercept [alpha]10, [alpha]20 0.028 0.005
(0.022) (0.012)
Lagged Return SP [alpha]11 [alpha]21 -0.108 (a) -0.039
(0.025) (0.0257)
Lagged Return other [alpha]12, [alpha]22 0.026 0.309 (a)
(0.023) (0.019)
Variance Equation S&P500 BOLSA
Intercept [beta]10, [beta]20 0.017 (a) 0.010
(0.005) (0.004)
Asymmetric Effect [beta]11, [beta]21 0.113 (a) 0.047 (a)
(0.024) (0.014)
Asymmetric Effect [beta]12, [beta]22 0.198 (a) 0.075 (a)
(0.020) (0.019)
Lagged stand. Shock [delta]1 [delta]2 -1.093 (a) -0.660 (a)
(0.246) (0.195)
Lagged Conditional 0.969 (a) 0.977 (a)
Variance [gamma]1 [gamma]2 (0.005) (0.004)
[absolute value of (/1 + 0.785
[delta]j)]/(1 +
[delta]j]) Correlation
Diagnostics on Standardized Residuals
Q (12), [epsilon]t/[sigma] 9.452 6.698
Q (24), [epsilon]t/[sigma] 13.620 13.876
Q2 (12), [epsilon]t2/[sigma] 37.342 (a) 17.020
Q2 (24), [epsilon]t2/[sigma] 49.359 (a) 30.432 (a)
Q(12), [epsilon]t/[sigma] 42.117 (a)
[epsilon]t/[sigma]/
[sigma]i[sigma]j
Q(24), [epsilon]it[epsilon] 60.841 (a)
it/[sigma]I[sigma]j]
Sign Bias t-Statistic
Sign bias 0.919 1.598
Size bias 1.394 -0.374
Joint sign and size bias 18.399 (a) 5.514
([chi square])
System Log Likelihood -2402.079
Mean Equation S&P500 BOVESPA
Intercept [alpha]10, [alpha]20 -0.142 -0.122
(0.028) (0.036)
Lagged Return SP [alpha]11 [alpha]21 -0.127 (a) -0.096 (a)
(0.037) (0.048)
Lagged Return other [alpha]12, [alpha]22 0.069 (a) 0.040
(0.029) (0.038)
Variance Equation S&P500 BOVESPA
Intercept [beta]10, [beta]20 0.159 (a) 0.019 (a)
(0.004) (0.006)
Asymmetric Effect [beta]11, [beta]21 0.071 0.005
(0.026) (0.015)
Asymmetric Effect [beta]12, [beta]22 0.054 (a) 0.110 (a)
(0.019) (0.025)
Lagged stand. Shock [delta]1 [delta]2 -1.321 (a) -0.769 (a)
(0.359) (0.159)
Lagged Conditional 0.992 (a) 0.989 (a)
Variance [gamma]1 [gamma]2 (0.003) (0.004)
[absolute value of (/1 + 0.741
[delta]j)]/(1 +
[delta]j]) Correlation
Diagnostics on Standardized Residuals
Q (12), [epsilon]t/[sigma] 13.706 14.547
Q (24), [epsilon]t/[sigma] 19.417 22.634
Q2 (12), [epsilon]t2/[sigma] 40.640 (a) 28.682
Q2 (24), [epsilon]t2/[sigma] 59.885 (a) 43.655 (a)
Q(12), [epsilon]t/[sigma] 42.130 (a)
[epsilon]t/[sigma]/
[sigma]i[sigma]j
Q(24), [epsilon]it[epsilon] 58.149 (a)
it/[sigma]I[sigma]j]
Sign Bias t-Statistic
Sign bias 0.128 1.198
Size bias 1.343 0.273
Joint sign and size bias 6.129 (a) 3.279
([chi square])
System Log Likelihood -2372.984
Mean Equation S&P500 MERVAL
Intercept [alpha]10, [alpha]20 -0.150 -0.173
(0.0214) (0.037)
Lagged Return SP [alpha]11 [alpha]21 -0.167 (a) -0.289 (a)
(0.015) (0.035)
Lagged Return other [alpha]12, [alpha]22 0.094 (a) 0.167 (a)
(0.021) (0.034)
Variance Equation S&P500 MERVAL
Intercept [beta]10, [beta]20 0.018 (a) 0.036 (a)
(0.005) (0.011)
Asymmetric Effect [beta]11, [beta]21 0.125 (a) 0.023
(0.023) (0.022)
Asymmetric Effect [beta]12, [beta]22 0.026 0.173 (a)
(0.020) (0.037)
Lagged stand. Shock [delta]1 [delta]2 -0.787 (a) -0.409 (a)
(0.175) (0.080)
Lagged Conditional 0.990 (a) 0.980 (a)
Variance [gamma]1 [gamma]2 (0.004) (0.008)
[absolute value of (/1 + 0.659
[delta]j)]/(1 +
[delta]j]) Correlation
Diagnostics on Standardized Residuals
Q (12), [epsilon]t/[sigma] 12.192 16.241
Q (24), [epsilon]t/[sigma] 27.757 24.336
Q2 (12), [epsilon]t2/[sigma] 60.723 (a) 13.690
Q2 (24), [epsilon]t2/[sigma] 65.579 (a) 19.384
Q(12), [epsilon]t/[sigma] 34.158 (a)
[epsilon]t/[sigma]/
[sigma]i[sigma]j
Q(24), [epsilon]it[epsilon] 43.784 (a)
it/[sigma]I[sigma]j]
Sign Bias t-Statistic
Sign bias 0.275 0.131
Size bias 0.901 0.242
Joint sign and size bias 8.213 (a) 0.424
([chi square])
System Log Likelihood -4109.342
Notes: Returns and conditional variance equations
are estimated in a system assuming variance
correlations are constant. Q and Q2 are the Ljung/Box
statistics of the autocorrelation in the
standardized residuals ([[[epsilon].sub.it]/[square root
of ([[sigma].sub.it)]) and their
squared values. The sign bias test shows whether
positive and negative innovations
affect future volatility differently from the
model prediction (see Engle and Ng (1993)). a, b,
and c, represent significance at .01, .05, and
.10, respectively.
Table 6
Impact of cross market shocks on the percentage
change in volatility and leverage effects
Shock Origin (t-1) S&P Bolsa Bovelsa Merval
S&P (-) 0.113 0.125 0.195 0.244
S&P (+) 0.005 0.026 0.025 0.102
Bolsa (-) 0.078
Bolsa (+) 0.004
Bovlesa (-) 0.011
Bovlesa (+) 0.002
Merval (-) 0.041
Merval (+) 0.005
Leverage Effects 12.715 4.882 7.658 2.384
Notes: The responses of S&P and the leverage
effect are the average for the three markets.
Table 7
Nonlinear Granger causality test: F statistics for
the Ho of no nonlinear Granger causality
The reported F values in Table 6 test the joint null
hypotheses of no causality, i.e. that [k.sub.i] = 0,
[[phi].sub.ij] = 0 and [[psi].sub.i] = 0. Therefore, at some
lag levels of variable x the null may not be rejected. For
instance, the computed F values for bilateral nonlinear
Granger causality tests show that the former causes the
latter for lags of 5, 6,7,8, 9 and 10 days, but not
consistently for all lags. The degrees of freedom in the
numerator and the denominator of the F/test of causality are
q *(q + 1)/2+2q and T//n//q *(q + 1)/2-2q, respectively,
where q is the number of lags, n is the dimension of the
gradient vector and T is the number of
observations.
Panel A
Causing Variable Caused Variables
Lags S&P500 MERVAL BOVESPA BOLSA
5 2.842 3.674 1.773
6 2.658 3.010 2.458
7 3.179 3.190 2.920
8 3.688 4.168 3.145
9 3.444 4.429 3.594
10 3.717 4.072 3.593
Panel B
Causing Variable Caused Variables
Lags S&P500 MERVAL BOVESPA BOLSA
5 2.801 3.830 2.656
6 3.174 3.371 3.480
7 3.834 4.220 3.484
8 2.591 4.411 4.104
9 2.756 4.402 4.030
10 3.704 4.675 4.007
Notes:All F statistics are significant at less than 1
percent significance level, with P-values virtually equal to
0. Degrees of freedom in the numerator of the F statistics
are 25, 32, 42, 52, 63, and 75 for q=5 through 10
respectively.
