Cointegration, causality and domestic portfolio diversification in the
Cyprus Stock Exchange
by
Eleni Constantinou1, Avo Kazandjian1, Georgios P. Kouretas3*
and Vera Tahmazian2
November 2005
Abstract
In this paper we provide an investigation on the potential benefits that may exist for
portfolio managers, private and institutional investors from domestic portfolio
diversification. We employ daily data for the period 1996-2002 from the Cyprus
Stock Exchange, recently established emerging market. Cointegration as well as linear
and nonlinear causality analysis is used in order to reveal whether there are benefits
from domestic portfolio diversification. The cointegration analysis leads to the
conclusion that we are unable to reject the null hypothesis of no cointegration in most
bivariate cases of the 56 pairs of sectoral indices and this finding is taken to imply that
the are benefits from portfolio diversification, when domestic investors construct
portfolios which include stocks from the sectors which are not cointegrated.
Furthermore, the application of linear and nonlinear Granger causality leads to a
pattern of causality between these pairs of sectoral indices which is almost identical
and therefore the linearity hypothesis is rejected. Furthermore, based on our causality
analysis we provide evidence that traders and investors in the CSE set up short-run
investment strategies. Moreover, this implies that the Cypriot investors do not adopt
contrarian and momentum investment strategies. Therefore, we argue that the
investors in the Cyprus stock market exhibit myopic investment behaviour.
1
Department of Business Studies, The Philips College, 4-6 Lamias Street, CY-2100, Nicosia, Cyprus.
Department of Accounting and Finance, The Philips College, 4-6 Lamias Street, CY-2100, Nicosia,
Cyprus.
3
Department of Economics, University of Crete, University Campus, GR-74100, Rethymno, Greece.
2
Keywords: cointegration, Granger causality, nonlinear causality, domestic portfolio
diversification.
JEL Classification: G15, G21, G32, G34
* This paper is part of the research project, Cyprus Stock Exchange: Evaluation, performance and
prospects of an emerging capital market, financed by the Cyprus Research Promotion Foundation
under research grant Π25/2002. We would like to thank the Cyprus Research Promotion Foundation for
generous financial support and the Cyprus Stock Exchange for providing us with its database. The
views expressed in this paper do not necessarily reflect those of either the CRPF or CSE. We would
also like to thank Panayiotis Diamandis, Anastasios Drakos, Dimitris Georgoutsos, Angelos Kanas and
Leonidas Zarangas for their comments on an earlier draft. Finally, we thank Angelos Kanas for
computational assistance. The usual disclaimer applies.
**Corresponding author: Fax (0831) 77406, email: kouretas@econ.soc.uoc.gr .
1. Introduction
Over the last fifteen years there has been a growing interest among portfolio
managers for the emerging capital markets as they provide opportunities for higher
asset returns compared to those of the developed markets. This was caused by the
substantial increase of capital flows from the mature markets to the emerging markets
of the South East Asia and the economies of transition of Central and Eastern
European countries. The purpose was to invest in portfolios consisting to a great
extent with securities from these new financial markets. Indeed, the study by Singh
and Weisse (1998) reports that, during the period 1989-1995 the inflow of funds in
emerging markets amounted to 107.6 billion US dollars as opposed to a mere 15.1
billion US dollars in the previous period 1983-1988. However, in the aftermath of the
financial crisis in Southeast Asia, Latin America and Russia in 1997-1998, we have
experienced a substantial increase in financial uncertainty as a result of the increased
volatility that stock returns of the mature markets but mainly of those of the emerging
markets exhibited.
Given these stylized facts academics and practitioners became aware of the
importance that a thorough study of the new markets had for portfolio managers and
institutional investors. Research has been focused on two independent issues which at
the same time belong to the class of issues that time series analysis encompasses,
namely existence of long-run relationships between stock markets (especially between
emerging markets and emerging and mature markets) and modeling the volatility of
stock returns in the emerging markets.
The main aim of the present paper is to investigate whether there are long-run
benefits from domestic portfolio diversification for the Cypriot investors who invest
in the Cyprus Stock Exchange (CSE) and what is the causality direction among the
2
sectors of the Cypriot economy whose firm equity are traded in this capital market.
Specifically, we examine the case of the Cypriot investor who invests on CSE and
he/she is interested for the stocks whose prices are expressed in Cyprus pounds.1 To
achieve our target we adopt the framework of cointegration theory and we statistically
examine whether cointegration exists for the following cases. First, between the
general price index and the volume of transactions. Second, among the twelve sectoral
price indices and finally between the sectoral indices in a bivariate framework giving
rise to 56 pairs to be examined.
Recent studies that deal with the issue of the multivariate analysis of the
relationship among the stock of different stock markets have applied cointegration
theory with the purpose of studying the long-run properties of stock prices. Most of
these studies have reached the conclusion that there is cointegration between two
stock prices or between two stock price indices and they have interpreted this finding
as evidence that there is a long-run linkage and therefore a long-run relationship.2
Equivalently, we could argue that the existence of cointegration between two or more
stock prices this could be seen as evidence of long-run relationships between these
series. With respect to the issue of portfolio diversification, existence of cointegration
between two or more stock prices implies that in the long run these prices are moving
together and therefore, the benefits from diversification with the construction of a
portfolio that consists of these stocks are limited. In contrast, lack of cointegration
implies that there are significant long-run benefits from the reduction of risk without
loss in the expected returns.
1
Therefore, in the present study we abstract from the issue of exchange rate volatility and the problems
which are tied with the international portfolio diversification.
2
Taylor and Tonks (1989), Arshanapalli and Doukas (1993), Byers and Peel (1993), Kasa (1992),
Richards (1995), Kanas (1998, 1999) και Georgoutsos and Kouretas (2003).
3
Since the early 1990s economists have paid attention to the analysis of mature
and emerging markets by applying cointegration theory in order to confirm whether
benefits from international portfolio diversification exist. Arshanapalli and Doukas
(1993) focused their analysis on the capital markets of the U.K., France, Germany and
U.S.A. and they performed statistical tests for the existence of bivariate cointegration
between the U.S. stock market with each of the other major markets. For the U.S.
investor this study finds out that there exists cointegration for all potential pairs and
therefore there are small benefits from the international portfolio diversification of the
American investors. Contrary to these findings, Taylor and Tonks (1989) found no
evidence of cointegration between the U.S. and the U.K. stock markets. Byers και
Peel (1993) as well as Kasa (1992) studied the case of three European of three
European stock markets and the those of Japan and Canada and they reached the
conclusion that there is partial evidence of cointegration. Kanas (1998) examined the
case of the six largest stock markets vis-à-vis the NYSE and found no evidence in
favour of cointegration leading to the conclusion that there may be substantial benefits
from the international portfolio diversification. Other studies like Gallagher (1995)
and DeFusco et al. (1996) which analyse the case of some of the major European
stock markets also confirmed that there is no evidence of cointegration between the
stock markets of Ireland, Germany and the U.K. Serletis and King (1997) examined
the issue within the European Union context and they failed to find on common
stochastic trend. They explained this evidence on the low integration of the Athens
Stock Exchange with the other European capital markets. Fraser and Oyefeso (2005)
also examined the long-run interrelationships of the European capital markets and
they concluded that although cointegration exists the gains from diversification are
short-lived since the adjustment to the common trend is very slow. Finally,
4
Georgoutsos and Kouretas (2003) analyzing the major stock markets argued that the
most significant cause for the lack of evidence in favour of cointegration among them
is the rejection of the long-run Purchasing Power Parity.
We also provide a Granger causality analysis between the 12 sectors of the
Cyprus economy which are included in the stock market in a bivariate context as we
do for the cointegration analysis. Cointegration analysis examines whether a long-run
relationship between two or more variables exists or not. Granger causality analysis is
adopted in order to investigate the causal dynamic relationships between the same set
of variables. We first conduct a linear Granger causality between the first differences
for every pair of the sectoral price indices by estimating a VAR model in each case.
We then employ the corrected statistical criterion due to Baek and Brock (1992) in
order to conduct a non-linear Granger causality analysis. We do that in order to
examine whether the results of the linear causality analysis depend of the linearity
hypothesis or not (robustness test).
The rest of the paper is organized as follows. Section 2 presents the
institutional and functional framework of the Cyprus Stock Exchange. Section 3
presents and discusses the data and preliminary empirical results. Section 4 discusses
cointegration analysis and the obtained results. Finally, section 5 provides the
summary and the concluding remarks.
2. The Cyprus Stock Exchange
The Cyprus Stock Exchange is the primary stock market in Cyprus. It is
considered to be a small emerging capital market with a very short history since it was
established in April 1993 when the inaugural Stock Exchange Law passed through the
Cypriot House of Representatives. In July 1995 the Cypriot House of Representatives
5
passed the laws for the stock exchange function and supervision, while additional
laws led to the establishment of the Central Securities Depository. On 29 March 1996
the first day of transactions took place. The Cyprus Stock Exchange S.A. is
supervised by the Ministry of Finance and the Minister of Finance is responsible for
choosing the seven member executive committee that runs CSE. Furthermore, the
Securities and Exchange Committee is mostly responsible for the well functioning of
the capital market of Cyprus. Trading takes place electronically through the
Automated Trade System. The main index is the CSE General Price Index that
reflects, approximately, 93% of the trading activity and 96% of the overall
capitalization. In November 2000 the FTSE/CySE 20 was constructed with the
cooperation of CSE, the Financial Times and the London Stock Exchange in order to
monitor closer the market. To highlight the increasing need for regional capital market
integration the FTSE Med 100 was created in June 2003 with the cooperation of CSE,
ASE and the Tel-Aviv Stock Exchange. Figure 1 shows the evolution of the CSE
general price index and its returns, (Chisostomidou et al. 2006 provide a
comprehensive analysis of the institutional framework of CSE).
The Cyprus accession in the European Union on 1st May 2004 it also
determines the starting period within which all required changes for the adjustment of
the financial system and the operation of the financial markets of Cyprus in order to
become an integral part of the European financial system and the European financial
markets. The capital market of Cyprus seeking to achieve its primary goal which is
the efficient allocation of sources in their alternative uses in the production and
investment process it has to adjust its institutional framework of operation by fully
incorporated all procedures that regulate the European capital markets.
6
The forthcoming European financial market integration implies that the
benefits from international portfolio diversification within Europe may be
substantially reduced and this provides a further motivation of the present study since
we are seeking for exploring intra-firm benefits from domestic portfolio
diversification. This argument provides a further motivation for the present study.
3. Data and preliminary empirical results
Our data consists of daily observations for the period 29 March 1996 (first day
of operation of the CSE) to 19 April 2002, excluding all weekends, holidays and days
during which the CSE was closed. The final sample consists of 1444 observations.
The data has been taken from DATASTREAM and all series have been transformed
to natural logarithms. The variables used for the present analysis are the following:
The general stock price index, Banks, Construction companies, Fisheries and
Fishtrading companies, Investment companies, Manufacturing, Insurance, Hotels,
Tourist services, Real Estate, Informatics, Financial Services, Other companies. We
also use the volume of transactions.
We begin by providing a discussion of the financial developments in the
operation of the CSE. We divide the time period of the operation of CSE in three
periods. The first period (29/03/1996-30/06/1999) is characterized by low interest by
domestic and foreign investors, thin trading as well as low volatility and persistence
of the general price index around the 100 units. The second period (01/07/199931/10/2000) is characterized by the presence of a rational bubble. The stock market
bubble is an expected event in new and emerging markets, like the Cyprus capital
market, although this is a phenomenon that often appears in mature markets as well.
For the Cyprus case the appearance of the rational bubble was the result of the sudden
7
increased interest of a great number of domestic investors who, as it is always the case
in the new and emerging markets were not well informed about the workings of this
new market and the trading process in the CSE. We could partially attributed the
presence of the rational bubble to the rational bubble that existed in the Athens Stock
Exchange which is a market whose developments influence the investors’ behaviour
in the Cyprus capital market. This event occurred in a year before the one in Cyprus
and during its upward trend made domestic investors to believe that there will be a
continuous increase in stock prices. However, it is well known that there comes a time
period that the bubble burst leading to panic and continuous fall in the stock prices.
The leading view about the creation of a bubble in a financial market is that it occurs
when the price of financial instrument (stock price, exchange rate, etc.) deviates
substantially and systematically from the fundamentals (either of the corresponding
firm or the economy) for long time periods. The bubble in the CSE lasted for one and
a half years. Looking at the third and final period (01/11/2000 – 19/04/2002) we
clearly see that the general price index of CSE has gradually returned to its initial
level and for a long period its value was around the baseline of 100 while at the
present its value is a bit higher, steadily leading to reduced interest by investors and
low volume of transactions. Figure 1 presents the evolution of the general price index
as well as of the stock returns for the period under investigation. We clearly see the
bubble during the period 01/07/1999 – 31/10/2000.
Table 1 reports the results from unit root and stationarity tests for the CSE
general stock price index and its first difference in order to obtain a clear picture of
the stochastic properties of the series. It also report these test statistics for the 12
sectoral indices and the volume of transactions. Specifically, in order to test for the
presence of a unit root in the level of the series we apply a set of unit root tests
8
developed by Elliott et al. (1996) and Elliott (1999) as well as by Ng and Perron
(2001). These tests modify conventional ADF and Philips-Perron unit root tests in
order to derive tests that have better size and power. The use of these recently
developed tests lead to firmer conclusions with respect to the integration properties of
the stock price series since rejections of the null hypothesis of nonstationarity will not
be attributed to size distortions, whereas nonrejections is not the outcome of a low
probability of rejecting a false null hypothesis. The null hypothesis for the Elliot et al.
(1996) GLS augmented Dickey-Fuller test (DF-GLSu) and Ng and Perron (2001) GLS
version of the modified Phillips-Perron (1988) tests ( MZ aGLS and MZ tGLS ) is that of a
unit root against the alternative that the initial observation is drawn from its
unconditional distribution. These tests use the GLS-detrending technique proposed by
Elliott et al. (1996) and extended by Elliott (1999), to maximize power, and a
modified selection criterion to select the lag truncation parameter in order to minimize
size distortion. In the GLS procedure of Elliot et al. (1996), the standard unit root
tests (without trend) are applied after the series are first detrended under the local
alternative ρ = 1 + α / T . This methodology resulted to a substantial increase in power
for the DF-GLSu test deriving power functions that lie just under the asymptotic
power
envelope.
Ng
and
Perron
(2001)
find
similar
gains
for
the
MZ aGLS and MZ tGLS tests and they have also derived a modified version of the AIC
criterion (MIC) that give rise to substantial size improvements over alternative
selection rules such as BIC. Finally, we apply the Kwiatkowski et al. (1992) KPSS
test for the null hypothesis of level or trend stationarity against the alternative of nonstationarity and these additional results will provide robust inference. The overall
evidence for this set of tests is that all price indices as well as the trading volume are
nonstationary while their first difference is a stationary process.
9
Provided that the stock price index is a nonstationary variable we only
consider the first differences of the general price index:
∆pt = 100 * ( pt − pt −1 ) and ∆qt = 100 * (qt − qt −1 )
(1)
which corresponds to the approximate percentage nominal return on the stock price
series obtained from time t to t-1. Specifically, the daily returns have been calculated
by taking the first difference of the logarithms of two consecutive days. By the same
token the percentage daily changes in the volume of transactions is 100 times the first
difference of the logarithms of two consecutive trading values
Table 2 reports several descriptive statistics for the returns of the general
index as well as of the sectoral indices of the CSE. The descriptive statistics include
the mean, the variance, the asymmetry and kurtosis of the distribution of stock
returns. According to Table 2 almost all series exhibit asymmetry and kurtosis since
the respective statistics are statistically significant leading to the conclusion that we
observe statistically significant deviations from normality. Further analysis of these
descriptive statistics show that the stock market of Cyprus is not efficient which is
expected given that this market is an emerging one. These results are of importance
when we use the VAR models in order to examine the long-run properties of the stock
prices as well as when we conduct the linear and nonlinear Granger causality analysis
for the stock returns. Finally the value of the Q 2 statistic is statistically significant
which implies that there is evidence of strong second-moment dependencies
(conditional heteroskedasticity) in the distribution of the stock price changes. This
finding implies that there is strong evidence for the presence of non-linear dependence
between the different stock prices and we should take that into consideration when we
employ the non-linear models for Granger causality.
10
4. Cointegration analysis
To conduct the cointegration analysis between the sectoral indices we apply
the well known multivariate cointegration methodology developed by Johansen
(1988, 1991) and Johansen and Juselius (1990, 1992). Given the numerous application
of this methodology we only provide a short description of it.3
Johansen’s methodology (1988, 1991) is based on the estimation of an
autoregressive (VAR) system of n x 1 vectors of nonstationary variables Χt.
∆z t = Γ1 ∆z t −1 + ..... + Γk −1 z t −k +1 + Π z t − k + γDt + µ + ε t
(1)
where z t is a column vector of stochastic variables, ε t ~Niidp (0,Σ). The parameters
(Γ1,.........,Γk−1,γ ) define the short-run adjustment to the changes of the process, whereas
Π = αβ ' defines the short-run adjustment, α , to the cointegrating relationships, β . If
the short-run effects are basically different from the long-run effects, due for instance,
to costly arbitrage and/or imperfect information, the explicit specification of the shortrun effects is probably crucial for a successful estimation of the steady-state relations
of interest. Dt is a vector of nonstochastic variables, such as centered seasonal
dummies which sum to zero over a full year by construction and are necessary to
account for short-run effects which could otherwise violate the Gaussian assumption,
and/or intervention dummies; µ is a drift and T is the sample size.
Johansen (1991) shows that if Z t ~ I (1) , the following restrictions on model
(3) have to be satisfied:
Π = αβ '
(2)
where Π has reduced rank, r , α and β are ( pxr ) matrices, and
3
For a comprehensive and rigorous presentation of this methodology see Hamilton (1994).
11
Ψ = α ⊥ (−I + Γ1)β ⊥ = ϕη '
where
Ψ
is
a
( p − r )x( p − r )
(3)
matrix
of
full
rank,
ϕ
and
η
are
( p − r ) x ( p − r ) matrices, and α ⊥ and β ⊥ are px ( p − r ) matrices orthogonal to α and
β , respectively. The parameterization in (2) and (3) facilitates the investigation of, on
the one hand, the r linearly-independent stationary relations between the levels of the
variables and, on the other hand, the p − r linearly-independent non-stationary
relations. This duality between the stationary relations and the non-stationary common
trends is very useful for a full understanding of the generating mechanisms behind the
chosen data. While the AR representation of the model is useful for the analysis of the
long-run relations in the data, the MA representation is useful for the analysis of the
common stochastic and deterministic trends that have generated the data.
Using the maximum likelihood estimation method, Johansen developed two
statistical criteria to test the null hypothesis of no cointegration. The first test is the
maximum eigenvalue test and the second test is the Trace test.4 We apply the
multivariate cointegration methodology due to Johansen (1988, 1991) on the system
given by (1), while the lag structure of the system is determined with the use of a
Likelihood Ratio (LR) test developed by Sims (1980). In case that there are more than
two variables z t (n > 2), then there exists the likelihood that exist more than one
linear stationary cointegration vectors of the non-stationary time series. In principle,
the larger is the number of cointegration vectors the greater is the probability that a
long run relationship exists between the series.
We begin the cointegration analysis by examining the pair of the general price
index and the volume of transactions (GEN-VOL). Both the maximum eigenvalue and
4
The algebraic expressions of these two statistical criteria are given in Hamilton (1994). The critical
values of these two statistical criteria have been calculated by Osterwald-Lenum (1992) and extended
by MacKinnon et al. (1999).
12
the trace test statistics could not reject the null hypothesis of no cointegration and
therefore, we argue that there does not exist a long-run relationship between the
general price index and the volume of transactions in the CSE. The lack of
cointegration between these two variables does not necessarily imply the lack of
Granger causality, an issue which is examined in the next section. The results are
given in Table 3.
We next move to the cointegration analysis of the 12 sectoral indices within a
multivariate framework. Table 4 reports the results. Both statistics reject the null
hypothesis of no cointegration among the 12 sectors and thus, we argue that there is at
least one long-run relationship between the 12 sectoral indices. Specifically, with the
trace test we find nine cointegration vectors, while on the basis of the maximum
eigenvalue we confirm the existence of at most five cointegration vectors. Therefore,
given our discussion above, the fact that there exists a large number of cointegration
vectors leads to the conclusion that we can have at least one statistically significant
long-run relationship between the 12 sectoral indices. This finding is consistent with
our intuition that since all the sectors of the economy of Cyprus are subject to a
greater or lesser extent to common disturbances like macroeconomic disturbances
(inflation level, interest rate level, tax rates, monetary policy) as well as to various
political events. This statistically significant long-run relationship between the 12
sectoral indices implies that there are no benefits from portfolio diversification in
terms of reduction in risk for that portfolio which also includes stocks from these 12
sectors. Based on this evidence we can investigate the case of potential combinations
of portfolios which include stocks from some of the sectors and which could give to
the domestic investors benefits from the diversification.
13
Table 5 reports the results of the bivariate cointegration analysis for all 56
pairs of sectoral indices of the CSE. According to the cointegration analysis we
observe that there are indeed possible cases in which portfolio diversification can
result to long-run benefits for the Cypriot investor. Specifically, the banking index
ΒΑΝΚ appears to have a cointegrating vector with all other sectors besides BUILD,
INSUR, MANUF and REALESTATE. Based on these findings we could achieve a
risk reduction (without reduction of the expected returns), in case we construct a
portfolio which includes stocks of the banking sector with stocks either of the building
sector, the insurance sector, the manufacturing sector or the realestate sector.
Furthermore, we conclude that the building sector, BUILD, has no long-run
relationship with any of the other 11 sectoral indices and this implies that there will be
long-run benefits from the portfolio diversification. Respectively, the index of the
financial services companies, FINSERV as well as that of the fisheries companies,
FISH, appear to have a statistically significant cointegration vector only with the
banking sector index each one of them. Hence, any portfolio which includes stocks
from either the financial services sector or the fisheries sector and any of the other
sectors besides that of the banking sector will provide the opportunity to the investors
opportunities to accrue benefits from the reduction of risk.
We also observe that index FIN is cointegrated with the banking index, ΒΑΝΚ
and the index of hotels, HOTELS and therefore any portfolio of two assets which
include stocks from the financial sector FIN, should not also include stocks from the
banking sector and from the hotels sector on the basis of the benefits criterion of
portfolio diversification. Furthermore, we find that there exists a long-run relationship
between the index of the tourist services sector, HOTELCOMP, and the index of the
manufacturing and banking sectors. Therefore, a combination of the index
14
HOTELCAMP, and either of these two indices will not offer long-run benefits to the
domestic investors from diversification of their portfolios. The sectoral index of
hotels, HOTELS, has a statistically significant cointegration vector with the index of
all other companies, MISC, as well as with the index of the banking sector, whereas
the index of the informatics, INFORM, has a long-run comovement with the banking
sector and the realestate sector. Finally, the index of the insurance sector, INSUR, is
found to have a statistically significant cointegrating vector with the manufacturing
sector and with the realestate vector.
To summarise, we argue that there exists a rich variety of results stemming
from our cointegration analysis with respect to the behaviour and predictability of the
general price index and all 12 sectoral indices. Our bivariate systems lead to the
conclusion that the CSE offers the opportunity for making long-run profits from the
portfolio diversification.5
5. Linear and nonlinear Granger causality analysis
Cointegration analysis examines whether or not a long-run relationship
between two or more variables. Granger causality analysis is adopted in order to
investigate the existence of causal dynamic relationships between the same variables.
The linear Granger causality analysis is conducted by regressing the first
differences between two sectoral indices at a time through the estimation of a VAR
model. The complete set of results is presented in Table 6. Given the large number of
cases and therefore the extensive length of results we provide a summary of them.
According to the estimated pairwise cases we observe that in most cases we are
5
To save space we only report the quantitative results given that there is an extensive set of tables for
all 56 bivariate cases. These tables are available upon request.
15
unable to reject the null hypothesis of no-Granger causality between any two pairs of
sectoral indices.
With the purpose to examine whether the results obtained from the linear
Granger causality analysis is independent of the linearity hypothesis we also apply the
non-linear Granger causality analysis (robustness test). The application of the nonlinear Granger causality is based on the corrected statistical criterion developed by
Baek and Brock (1992).
Consider two strictly stationary and weakly dependent scalar time series {Wt}
and {Zt}. We denote the m-length lead vector of Wt with W mt , and the Lw-length and
Lz
Lz-length lag vectors of Wt and Zt, respectively, by W tLw
− Lw and Z t − Lz :
W mt = (Wt , Wt+1, ..., Wt+m-1), m = 1, 2, ..., t=1, 2, ...
W tLw
− Lw = (Wt-Lw, Wt-Lw+1, ..., Wt-1), Lw = 1,2,..., t = Lw+1, Lw+2,
(4)
Z tLz− Lz = (Zt-Lz, Zt-Lz+1, ..., Zt-1), Lz = 1,2,..., t = Lz+1, Lz+2, ...
For given values of m, Lw, and Lz ≥ 1 and for e >0, Z does not strictly Granger cause
W if
Lz
Lz
Lw
Pr{|| W mt - W ms || < e ⏐|| W tLw
− Lw - W s − Lw || < e, || Z t − Lz - Z s − Lz || < e } =
Lw
= Pr {|| W mt - W ms || < e ⏐|| W tLw
− Lw - W s − Lw || < e }
(5)
where Pr{.} denotes probability and || . || denotes the maximum norm. The probability
on the left hand side of equation (5) is the conditional probability that two arbitrary mlength lead vectors of {Wt} are within a distance e of each other, given that the
corresponding Lw-length lag vectors of {Wt} and Lz-length lag vectors of {Zt} are
within a distance e of each other. The probability on the right hand side of equation
16
(5) is the conditional probability that two arbitrary m-length lead vectors of {Wt} are
within a distance e of each other, given that their corresponding Lw-length lag vectors
are within a distance e of each other. It can be shown6 that, given values for m, Lw, Lz
and e >0, under the null hypothesis that {Zt} does not strictly nonlinearly Granger
cause {Wt}, the statistic
C1(m+Lw, Lz, e, n)
C3(m+Lw, e, n)
n { ------------------------ - ------------------- } ~ AN (0, σ2(m, Lw, Lz, e))
C2(m + Lw, e, n)
(6)
C4(Lw, e, n)
where C1(m+Lw, Lz, e, n), C2(m + Lw, e, n), C3(m+Lw, e, n), and C4(Lw, e, n) are
correlation-integral estimators of the point probabilities corresponding to the left hand
side and right hand side of equation (5). This test has remarkably good power
properties against a variety of nonlinear Granger causal and noncausal relations, and
its asymptotic distribution is the same if the test is applied to the estimated residuals
from a vector autoregressive (VAR) model (Hiemstra and Jones, 1994).
In carrying out the modified Baek and Brock tests, values for the lead length
m, the lag lengths Lw and Lz, and the scale parameter e must be chosen. On the basis
of the Monte Carlo results of Hiemstra and Jones (1994), we set for all cases, m=1, Lw
= Lz using common lag lengths of 1 to 5 lags. Moreover, for all cases, we set e = 1.0σ,
where σ = 1 denotes the standard deviation of each series.
The results of the non-linear Granger causality analysis are presented in Table
7 for all bivariate cases of the sectoral indices. The overall findings lead to the
conclusion that the causality direction is almost identical to the one found in the linear
6
For more details on the derivations, see Hiemstra and Jones (1994).
17
Granger causality analysis and therefore we argue that the causality direction is given
and it does not depend on the linearity hypothesis.
More specifically, in the case of the nonlinear Granger causality we observe
we were able to reject the null hypothesis of no causality between the indices in few
cases. The fact that in only few cases we found existence of linear or nonlinear
Granger causality between the sectoral indices can provide some interpretations with
respect to the behaviour of the investors who are active in the stock market of Cyprus.
Specifically, it is clear that there are no short run dynamic interrelationships between
the indices. This finding implies that overtime the sectoral indices are independent.
Furthermore, this evidence leads to the conclusion that traders and investors in the
CSE set up short-run investment strategies. Moreover, this implies that the Cypriot
investors do not adopt contrarian and momentum investment strategies. Therefore, we
argue that the investors in the Cyprus stock market exhibit myopic investment
behaviour. 7
6. Summary and concluding remarks
In this paper we provide a comprehensive analysis of the potential benefits
that may be realized from domestic portfolio diversification. Specifically, we use
daily data for the period 1996-2002 for the Cyprus Stock Exchange a recently
established emerging market.
We employ two well known econometric methodologies to accomplish our
aim. First, we use the Johansen (1988, 1991) and Johansen and Juselius (1990, 1992)
multivariate cointegration methodology to examine whether there are long-run
relationships among the 12 sectors of the Cyprus economy. Looking into the
7
To save space we only report the quantitative results given that there is an extensive set of tables for
all 56 bivariate cases. These tables are available upon request.
18
relationships between sectors can also be justified on the grounds that the recent
enlargement of the European Union may eventually result to minimum benefits from
international portfolio diversification whereas substantial benefits from risk reduction
due to exercise of domestic portfolio diversification may still existed. We also provide
a linear and nonlinear Granger causality to reveal any short-run dynamics between the
sectoral indices.
Our cointegration analysis provided us with a rich variety of results with
respect to the behaviour and predictability of the general price index and all 12
sectoral indices. First, we found no cointegration between the general price index and
the volume of transactions. Second, within a multivariate context we showed that
there is at least one statistically significant long-run relationship between the 12
sectoral indices. Based on this finding, we finally examine all bivariate systems of
sectoral indices and we can conclude that the CSE offers the opportunity for making
long-run profits from the portfolio diversification
The linear and nonlinear Granger causality analysis has led to very similar
pattern of causality with only few cases of causality between the bivariate cases of all
sectoral indices. Therefore, the linearity hypothesis was rejected while it is clear that
there are no short run dynamic interrelationships between the indices. This finding
implies that overtime the sectoral indices are independent. Furthermore, this evidence
leads to the conclusion that traders and investors in the CSE set up short-run
investment strategies. Moreover, this implies that the Cypriot investors do not adopt
contrarian and momentum investment strategies. Therefore, we argue that the
investors in the Cyprus stock market exhibit myopic investment behaviour.
The results of the present paper are particularly useful to private and
institutional investors as well to the financial institutions, for the evaluation and
19
management of their portfolios which include stocks of companies which are listed in
the CSE. These results are also useful to the pension funds (when they will be allowed
to invest part of their reserves in stocks traded in the CSE), to the insurance
companies and to the mutual funds (whose establishment and introduction to the CSE
is expected).
20
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23
Table 1. Unit root and stationarity tests
A. Levels
Variables
DF-GLSu
tµ
GENERAL
INDEX
VOLUME
BANK
BUILD
FIN
FINSERV
FISH
HOTEL
COMP
HOTELS
INFORM
INSUR
MANUF
MISC
REAL
ESTATE
-0.60
[4]
-0.41
[5]
-0.22
[1]
-0.41
[0]
-0.21
[2]
-1.41
[1]
-0.98
[2]
-0.43
[2]
-0.91
[0]
-1.46
[4]
-0.29
[1]
-1.02
[3]
-0.78
[4]
-0.33
[6]
KPSS
tτ
-0.34
[4]
-0.51
[5]
-0.31
[1]
-0.38
[0]
-0.77
[2]
-1.11
[1]
-1.12
[2]
-0.56
[2]
-0.88
[0]
-1.55
[4]
-0.56
[1]
-1.12
[3]
-0.63
[4]
-0.67
[6]
MZ aGLS
-0.14
[1]
-0.37
[3]
-0.59
[2]
-0.98
[2]
-0.20
[4]
-1.19
[3]
-0.34
[3]
-0.78
[4]
-1.16
[1]
-0.88
[3]
-0.78
[2]
-0.34
[0]
-0.23
[5]
-1.11
[3]
MZ
GLS
t
-0.15
[1]
-0.57
[3]
-0.63
[2]
-1.03
[2]
-0.19
[4]
-1.03
[3]
-0.29
[3]
-0.54
[4]
-1.02
[1]
-0.89
[3]
-0.68
[2]
-0.45
[0]
-0.37
[5]
-1.15
[3]
24
ηµ
ητ
2.251*
0.619*
0.889*
0.736*
2.333*
2.261*
1.167*
1.127*
1.098*
1.111*
1.209*
1.034*
2.145*
0.786*
0.989*
0.546*
1.333*
0.338*
1.654*
0.790*
1.335*
1.003*
1.991*
0.675*
1.565*
0.454*
2.160*
1.656*
B. First Differences
Variables
GENERAL
INDEX
VOLUME
BANK
BUILD
FIN
FINSERV
FISH
HOTEL
COMP
HOTELS
INFORM
INSUR
MANUF
MISC
REAL
ESTATE
DF-GLSu
tµ
tτ
-16.75*
[3]
-19.57*
[2]
-26.44*
[5]
-33.92*
[0]
-44.23*
[2]
-15.66*
[7]
-13.22*
[2]
-20.11*
[3]
-30.11*
[4]
-12.55*
[6]
-17.33*
[3]
-52.17*
[1]
-38.11*
[2]
-23.11*
[5]
-16.63*
[3]
-18.90*
[2]
-29.88*
[5]
-34.55*
[0]
-40.19*
[2]
-12.29*
[7]
-14.25*
[2]
-19.18*
[3]
-25.12*
[4]
-14.79*
[6]
-19.25*
[3]
-45.33*
[1]
-40.12*
[2]
-26.12*
[5]
MZ
GLS
a
-424.52*
[3]
-20.13*
[4]
-11.33*
[5]
-49.22*
[2]
-31.12*
[3]
-25.11*
[8]
-18.92*
[4]
-33.90*
[5]
-18.24*
[2]
-18.03*
[5]
-21.05*
[4]
-33.05*
[1]
-19.77*
[3]
-14.93*
[11]
MZ
GLS
t
-14.56*
[3]
-9.77*
[4]
-8.98*
[5]
-15.99*
[2]
-9.01*
[3]
-7.44*
[8]
-10.03*
[4]
-12.03*
[5]
-9.01*
[2]
-6.22*
[5]
-10.11*
[4]
-8.88*
[1]
-7.56*
[3]
-2.70*
[11]
ηµ
KPSS
ητ
0.221
0.136
0.198
0.078
0.233
0.067
0.335
0.105
0.178
0.077
0.201
0.035
0.099
0.111
0.103
0.099
0.201
0.105
0.198
0.034
0.095
0.077
0.122
0.056
0.088
0.044
0.244
0.067
Notes:
The DF-GLSu is due to Elliot et al. (1996) and Elliott (1999) is a test with an unconditional
alternative hypothesis. The standard Dickey-Fuller tests are detrended (with constant or constant
and trend). The critical values for the DF-GLSu test at the 5% significance level are:-2.73 (with
constant) and -3.17 (with constant and trend), respectively (Elliott,1999).
MZ a and MZ t are the Ng and Perron (2001) GLS versions of the Phillips-Perron tests. The
critical values at 5% significance level are: -8.10 and -1.98 (with constant), respectively (Ng and
Perron, 2001, Table 1).
ηµ and ητ are the KPSS test statistics for level and trend stationarity respectively (Kwiatkowski et
al. 1992). For the computation of theses statistics a Newey and West (1994) robust kernel estimate
of the "long-run" variance is used. The kernel estimator is constructed using a quadratic spectral
kernel with VAR(l) pre-whitening and automatic data-dependent bandwidth selection [see, Newey
and West, 1994 for details]. The 5% critical values for level and trend stationarity are 0.461 and
0.148 respectively, and they are taken from Sephton (1995, Table 2).
(*) indicates significance at the 95% confidence level.
25
Table 2. Desciptive statistics – Daily returns
mean
(x 102)
variance
General Index
0.001
0.003
Transactions Volume
0.20
0.068
Banks
0.011
0.0004
Building Materials
-0.17
0.0004
Fisheries
-0.40
0.0007
Investment
-0.007
0.0005
Financial Services
-0.4
0.0007
Insurance
-0.069
0.0006
Manufacturing
-0.03
0.0005
Other
0.000
0.004
Tourist Services
-0.02
0.0006
Hotels
-0.12
0.0008
Realestate
-0.09
0.0008
-0.7
0.0014
Informatics
m3
m4
JB
Q(8)
Q2(8)
1.88 *
[0.00]
-0.38 *
[0.00]
3.03 *
[0.00]
-1.81 *
[0.00]
0.17 *
[0.15]
0.91 *
[0.00]
-0.14
[0.25]
0.02
[0.70]
1.13 *
[0.00]
-0.13 *
[0.03]
-0.08
[0.17]
0.19
[0.12]
0.06
[0.35]
0.32 *
[0.01]
25.91 *
[0.00]
28.37 *
[0.00]
47.94 *
[0.00]
2.92 *
[0.00]
3.05 *
[0.00]
10.75 *
[0.00]
5.09 *
[0.00]
8.20 *
[0.00]
11.62 *
[0.00]
80.35 *
[0.00]
9.13 *
[0.00]
16.13 *
[0.00]
23.15 *
[0.00]
14.48 *
[0.00]
45120.0 *
[0.00]
52823.0 *
[0.00]
153685.0 *
[0.00]
146.83 *
[0.00]
158.9 *
[0.00]
7836.0 *
[0.00]
438.4 *
[0.00]
4429.9 *
[0.00]
9227.3 *
[0.00]
425071.0 *
[0.00]
5491.1 *
[0.00]
4385.0 *
[0.00]
35280.0 *
[0.00]
3540.0 *
[0.00]
89.25*
[0.00]
176.5 *
[0.00]
49.92 *
[0.00]
24.17 *
[0.00]
5.14 *
[0.74]
230.8 *
[0.00]
34.30 *
[0.00]
80.40*
[0.00]
77.81*
[0.00]
174.4 *
[0.00]
159.0 *
[0.00]
17.50 *
[0.02]
43.87 *
[0.00]
8.22
[0.41]
103.85 *
[0.00]
303.8 *
[0.00]
149.0 *
[0.00]
77.60 *
[0.00]
49.98 *
[0.00]
439.47 *
[0.00]
4.45
[0.81]
192.05 *
[0.00]
373.7 *
[0.00]
328.08 *
[0.00]
339.8 *
[0.00]
37.99 *
[0.00]
278.1 *
[0.00]
56.52 *
[0.00]
Notes: The average return is expressed in terms of x10 2 ; m3 and m 4 are the
coefficients of skewness and kurtosis of the standardized residuals respectively; JB is
the statistic for the null of normality; Q (8) and Q 2 (8) are the Ljung-Box test statistics
for up to 8th-order serial correlation in the ∆pt and ∆pt2 series, respectively. (*)
denotes statistical significance at the 5 percent critical level.
26
Table 3. Johansen-Juselius cointegration analysis-(general index-volume)
5% Critical Values
Trace
R
Trace
λmax
λmax
r=0
5.75
5.08
18.11
15.02
r=1
0.66
0.66
8.19
8.19
Notes: r denotes the number of eigenvectors. Trace and λmax denote, respectively,
the trace and maximum eigevalue likelihood ratio statistics. The 5% critical values are
taken from MacKinnon et al. (1999; Table III). A structure of nine lags was chosen
according to a likelihood ratio test, corrected for the degrees of freedom (Sims, 1980)
and the Ljung-Box Q statistic for detecting serial correlation in the residuals of the
equations of the VAR. A model with an unrestricted constant in the VAR equation
was estimated following the Johansen (1992a,b; 1994) testing strategy.
(*) denotes statistical significance at the five percent critical level.
27
Table 4. Johansen-Juselius cointegration analysis-(All sectoral indices)
5% Critical Values
Trace
R
Trace
λmax
λmax
r=0
552.9938*
103.7403*
336.22
76.61
r=1
449.2535*
85.80932*
286.39
70.59
r=2
363.4442*
81.59040*
240.58
64.56
r=3
281.8538*
60.80931*
198.72
58.51
r=4
221.0444*
59.72142*
160.87
52.41
r=5
161.3230*
42.03399
127.05
46.31
r=6
119.2890*
35.69364
97.26
40.19
r=7
83.59539*
30.56815
71.44
34.03
r=8
53.02724*
22.93630
49.64
27.80
r=9
30.09094
20.29929
31.88
21.49
r=10
9.791651
9.733150
18.11
15.02
r=11
0.058501
0.058501
8.19
8.19
Notes: r denotes the number of eigenvectors. Trace and λmax denote, respectively,
the trace and maximum eigevalue likelihood ratio statistics. The 5% critical values are
taken from MacKinnon et al. (1999; Table III). A structure of ten lags was chosen
according to a likelihood ratio test, corrected for the degrees of freedom (Sims, 1980)
and the Ljung-Box Q statistic for detecting serial correlation in the residuals of the
equations of the VAR. A model with an unrestricted constant in the VAR equation
was estimated following the Johansen (1992a,b; 1994) testing strategy.
(*) denotes statistical significance at the five percent critical level.
28
Table 5. Johansen-Juselius bivariate cointegration analysis
BANK
BUILD
FIN
FINSERV
FISH
HOTELCOMP
HOTELS
INFORM
INSUR
MANUF
MISC
REALESTATE
BANK
BUILD
FIN
FINSERV
FISH
HOTELCO
MP
HOTELS
INFORM
INSUR
MANUF
MISC
REALE
STATE
YES
NO
YES
YES
YES
YES
YES
NO
NO
YES
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
NO
NO
YES
NO
NO
NO
NO
NO
YES
NO
NO
NO
NO
YES
YES
NO
YES
NO
NO
NO
-
Notes: Yes=the null hypothesis of nocointegration is rejected; No=the null hypothesis of nocointegration could not be rejected. The level of
significance is five percent.
29
Table 6. Linear Granger causality
BANK
BANK
BUILD
FIN
FINSERV
FISH
HOTELCOMP
HOTELS
INFORM
INSUR
MANUF
MISC
REALESTATE
NO
YES
NO
NO
YES
YES
NO
YES
NO
NO
YES
YES
NO
YES
YES
YES
YES
NO
NO
YES
YES
YES
BUILD
FIN
FINSERV
FISH
HOTELC
OMP
HOTELS
INFORM
INSUR
MANU
F
MISC
REALE
STATE
YES
YES
YES
NO
YES
YES
YES
NO
YES
NO
NO
NO
YES
NO
YES
NO
YES
YES
YES
NO
NO
NO
NO
YES
NO
NO
NO
NO
NO
YES
NO
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
YES
YES
YES
NO
NO
YES
YES
YES
YES
NO
NO
NO
YES
YES
NO
YES
NO
NO
NO
YES
NO
YES
NO
YES
NO
YES
NO
YES
NO
NO
NO
NO
NO
NO
YES
YES
NO
NO
NO
YES
NO
NO
NO
NO
NO
NO
NO
NO
YES
YES
NO
NO
NO
NO
NO
NO
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
-
Notes: NO = F is not statistically significant at the 5% level of significance. YES = F is statistically significant at the 5% level of significance.
30
Table 7. Nonlinear Granger causality
BANK
BANK
BUILD
FIN
FINSERV
FISH
HOTELCOMP
HOTELS
INFORM
INSUR
MANUF
MISC
REALESTATE
YES
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
NO
YES
NO
YES
YES
NO
NO
NO
YES
YES
NO
BUILD
FIN
FINSERV
FISH
HOTELCOMP
HOTELS
INFORM
INSUR
MANUF
MISC
REALESTATE
YES
NO
NO
NO
NO
NO
NO
NO
YES
NO
NO
NO
YES
YES
YES
NO
YES
YES
YES
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
NO
YES
YES
YES
NO
NO
NO
YES
NO
NO
NO
NO
YES
NO
NO
NO
NO
NO
NO
YES
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
YES
YES
NO
NO
NO
YES
NO
YES
NO
NO
NO
YES
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
YES
YES
NO
NO
NO
NO
NO
NO
YES
NO
-
Notes: NO = F is not statistically significant at the 5% level of significance. YES = F is statistically significant at the 5% level of significance.
31
Figure 1. CSE General Price Index and Returns
32