CO-MOVEMENT OF
STOCK PRICES IN THE
CARICOM REGION
JOHN COZIER
AND
PAT R I C K WAT S O N
BBF5 CONFERENCE
M AY 2 - 3 , 2 013
OUTLINE OF PRESENTATION
Introduction
Methodology and Data
Empirical Analysis
Preliminary
Estimation of GARCH
Estimation of Copula
Conclusions
INTRODUCTION
Financial integration in the CARICOM
Region
Importance of stock price comovement
Baur (2003)
Stock price comovement in the literature
Developed markets
Kim and Langrin (CARICOM markets)
METHODOLOGY AND DATA
Preliminary Analysis
Correlation coefficients
oJanuary 1, 1998 – December 31, 2011
oJanuary 1, 1998 – March 31, 2008
oApril 1, 2008 – December 31, 2011
Sharpe Ratio
GARCH-Copula
oBollerslev (2008)
METHODOLOGY AND DATA
Data
 End of day values of the Composite Indices from
January 1, 1998 – December 31, 2011
BSE
JSE
TTSE
NYSE
 GARCH Copula: End of day values from April 1, 2008 –
December 31, 2011
TTSE
JSE
Ju
l
NYSE
BSE
ua
ry
Ja
n
01
2
8,
2
6
09
20
00
,2
18
l1
3,
y
3
1
00
20
0
2,
2
25
,
99
8
1,
1
ob
er
2
ry
A
pr
i
O
ct
Ja
nu
a
M
ay
20
40
60
80
100
120
FIGURE 1 – EVOLUTION OF COMPOSITE INDICES
(1998-2011)
120
40
60
80
100
FIGURE 2 - EVOLUTION OF COMPOSITE INDICES
(APRIL 1, 2008-DECEMBER 31, 2011)
(APRIL 1, 2008-DECEMBER 31, 2011)
November 30, 2007
April 13, 2009
TTSE
JSE
August 26, 2010
NYSE
BSE
January 8, 2012
TABLE 1 - CORRELATION COEFFICIENTS
FOR THE COMPOSITE INDICES
BSE
JSE
TTSE
BSE
1.0000
JSE
0.6275
1.0000
TTSE
0.6292
0.9211
1.0000
NYSE
0.2749
0.4528
0.38268
NYSE
1.0000
January 1998 – March 2008
BSE
1.0000
JSE
0.5267
1.0000
TTSE
0.6215
0.8196
1.0000
NYSE
-0.5432
-0.3648
-0.7255
1.0000
April 2008 – December 2011
BSE
1.0000
JSE
0.5849
1.0000
TTSE
0.5584
0.9501
1.0000
NYSE
-0.0212
0.5951
0.5464
1.0000
110,000
1,200
90,000
1,000
Index (JSE)
100,000
1,100
Figure 3 – BSE / TTSE
80,000
70,000
Figure 3 - TTSE/BSE
700
800
900
1,000
1,100
JSE/BSEIndex (BSE)
800
900
Index (TTSE)
1,000
900
800
Index (TTSE)
1,100
1,200
FIGURES 3 – 5: SCATTERPLOTS FOR THE RELATIONSHIPS
BETWEEN THE CARICOM COMPOSITE INDICES
Figure 4 - TTSE/JSE Figure 5 –
700
800
900
1,000
1,100
Index (BSE)
Figure 4 – JSE / TTSE
700
800
900
1,000
Index (BSE)
Figure 5 – BSE / JSE
1,100
1,200
1,000
70,000
400
80,000
600
800
Index (TTSE)
100,000
90,000
Index (JSE)
900
800
700
Index (BSE)
1,000
110,000
1,100
FIGURES 6 – 8: SCATTERPLOTS FOR THE
RELATIONSHIPS BETWEEN THE CARICOM
AND NYSE INDICES
4,000
6,000
8,000
Index (NYSE)
10,000
4,000
6,000
8,000
Index (NYSE)
Figure 6 - BSE/NYSE Figure 7 - JSE/NYSE
10,000
4,000
6,000
8,000
Index (NYSE)
Figure 8 - TTSE/NYSE
10,000
-2
0
-2
-6
-4
Daily Return (JSE)
0
2
2
4
4
FIGURES 9 – 12:
DAILY RETURNS (JANUARY 1998 – DECEMBER 2011)
FIGURE 9 – BSE
FIGURE 10 - JSE
May 1, 1998
Jan. 25, 2001 Oct. 22, 2003 July 18, 2006 April 13, 2009 January 8, 2012
Date
May 1, 1998
Jan. 25, 2001 Oct. 22, 2003 July 18, 2006 April 13, 2009 Jan. 8, 2012
Date
FIGURE 12 - NYSE
0
Daily Return (NYSE)
-5
-2
-1
0
1
5
2
FIGURE 11 - TTSE
May 1, 1998 Jan. 25, 2001 Oct. 22, 2003 July 18, 2006 April 13, 2009 Jan, 8, 2012
Date
May 1, 1998 Jan. 25, 2001 Oct. 22, 2003 July 18, 2006 April 13, 2009 Jan. 8, 2012
Date
TABLE 2 - CORRELATION COEFFICIENTS OF THE
RETURNS ON BSE, JSE, TTSE AND NYSE
1998 – 2011
BSE
JSE
TTSE
BSE
1.0000
JSE
0.0460
1.0000
TTSE
0.0512
0.1248
1.0000
NYSE
0.0170
0.0226
-0.0032
NYSE
1.0000
January 1998 - March 2008
BSE
1.0000
JSE
0.1208
1.0000
TTSE
0.1153
0.3724
1.0000
NYSE
-0.0216
0.0119
-0.0271
1.0000
April 2008 – December 2011
BSE
1.0000
JSE
0.0406
1.0000
TTSE
0.0483
0.0711
1.0000
NYSE
0.0173
0.0253
0.0003
1.0000
TABLE 3 - SUMMARY STATISTICS OF DAILY
RETURNS (APRIL 2008 – DECEMBER 2011)
Mean
Minimum Maximum
Standard
Deviation
Skewness
Kurtosis
Sharpe
Ratio
BSE
-0.01600
-1.74348
3.63590
0.19121
4.37807
167.153
-232.39
JSE
-0.0055
-2.74428
3.45594
0.09350
0.35179
32.18026
-81.17
TTSE
0.000927 -1.507199 0.66052
0.14517
-1.40828
20.20038
-225.01
NYSE
-0.00745
0.84153
-0.29779
8.367126
-46.46
-4.44373
5.00557
EMPIRICAL ANALYSIS
Estimation of the GARCH
The intercepts (𝑐0 ) and mean coefficients (𝑐1 ) for the markets are all
relatively close to zero.
 Two out of the four had negative intercepts (the BSE and the NYSE).
 Only the NYSE possessed a negative mean coefficient over the sample
period.
The GARCH coefficient (ω) for the BSE was the largest by a fairly
substantial margin.
 The remainder of the markets had relatively small GARCH coefficients.
The coefficient for α of the BSE is further evidence that there is very
little volatility within this market.
EMPIRICAL ANALYSIS
The β coefficient in the AR (1) – GJR (1, 1) model for the BSE
(0.4852) was much lower in value less than its three
counterparts (0.9347, 0.9285 and 0.9264) and it should
be noted that the β for these remaining three was relatively
similar to each other.
The degrees of freedom parameter υ was equal to two for all
the markets except the NYSE, where it was close to eight
(7.9466).
The parameter for asymmetry or skewness (λ) for the BSE and
the NYSE showed negative skewness in the returns over
the time period while the asymmetry parameter for the
TTSE (0.1071) was much larger than for the JSE (0.0043).
EMPIRICAL ANALYSIS
Estimation of the Copula
 Firstly, no results are available from the Symmetrized Joe
Copula vine.
 The estimated parameters for the remaining two Copula vines
suggest very little dependence among the four markets (Table
5).
 There also seems to be little difference in the estimated
parameters for the Clayton and the t methods under the
Canonical and the d-vines.
 The only glaring differences can be seen in the parameters
for 𝒂𝒕𝒕𝒔𝒆/𝒏𝒚𝒔𝒆 , 𝒂𝒃𝒔𝒆/𝒕𝒕𝒔𝒆|𝒋𝒔𝒆 and 𝒂𝒃𝒔𝒆/𝒏𝒚𝒔𝒆|𝒋𝒔𝒆/𝒕𝒕𝒔𝒆 .
EMPIRICAL ANALYSIS
The lack of a dependence structure is especially evident upon
closer examination of the structures involving the NYSE.
This could provide some understanding as to why there seems
to be relatively minimal fallout for the CARICOM stock
markets resulting from the sub-prime mortgage crisis,
which precipitated the global recession.
CARICOM stock markets are sufficiently underdeveloped that
they represent unattractive investment vehicles due to rigid
market illiquidity.
Log Likelihood value suggests that the t-distribution d-vine
method most effectively explains the relationships existing
between the CARICOM stock markets and the NYSE.
However, the Clayton d-vine appears to best explain these
relationships based on Akaike’s Information Criterion as
well as the Bayesian Information Criterion.
EMPIRICAL ANALYSIS
The bivariate copulas, especially the tDCC method, seem to display a
substantial degree of dependence among the respective market pairs.
The CARICOM stock markets exhibit substantial dependence structures with
each other.
The BSE-NYSE dependence structure is considerably lower than the other
two CARICOM markets (as evidenced by the β indicator in the tDCC and
the GDCC methods).
The TTSE-NYSE relationship is the most significant among the three
bivariate copulas involving the NYSE.
β indicator for the JSE/TTSE (approximately 0.98 under both the tDCC and
the GDCC methods) suggests a significant dependence between the JSE
and the TTSE.
The JSE and the TTSE are highly integrated with each other (with both
markets possibly close to being fully integrated with each other), which
has resulted in significant co-movement of prices for their listed
securities.
EMPIRICAL ANALYSIS
The BSE and the JSE (0.85 under the tDCC and 0.84 under
the GDCC).
There is some amount of integration between the BSE and
the JSE.
Based on the Log Likelihood criterion, the Gaussian
Dynamic Conditional Correlation model appears to be
the best fit for all except the TTSE/NYSE relationship,
which appears to be best explained by the Student’s t
copula (tDCC model).
The tDCC model seems to be the best fit under the Akaike’s
and the Bayesian Criteria.
EMPIRICAL ANALYSIS
Time varying Clayton (tvC) Copulas show relatively similar β
parameters for the three corresponding pairs for the CARICOM
stock markets (all within the 4.62 – 4.63 range) which could
mean dependence among the markets.
The result for the static SJC (SJC) copula show little difference
between the upper and lower tails as evidenced by its 𝑇 𝑈 − 𝑇 𝐿
parameter.
The time varying SJC (tvSJC) copula shows a significant difference in
the β parameters for the lower and upper tails for the BSE/JSE
relationship (0.3831 and 9.8648).
The BSE/TTSE show little disparity in this parameter.
EMPIRICAL ANALYSIS
There are some disparities in determining which of the three
models has the best goodness of fit indicator.
If the Log Likelihood criterion is used for this purpose, the
tvSJC copula is most appropriate for explaining the
dependence structures for the BSE/TTSE and the
JSE/TTSE.
The SJC copula is appropriate for the BSE/JSE.
The tvSJC copula is best for the BSE/JSE and the JSE/TTSE
structures under the Akaike’s Information Criterion (the tvC
copula for BSE/TTSE).
The tvSJC copula is arguably best fit for all three under the
Bayesian Information Criterion.
EMPIRICAL ANALYSIS
The copulas involving the NYSE (as seen in Table 8) yielded
some interesting results.
JSE/NYSE: Negative in all of its parameters for the time
varying Clayton copula (-7.4874, -1.7807 and -0.8482).
The estimations for the SJC copula show little to no
difference between the tails and little variance
occurring.
BSE/NYSE: The only one out of the three possible
relationships which shows relative closeness between
the β parameters for the lower and upper tails (2.2552
and 3.7025) when one analyses the tvSJC copula.
JSE/NYSE and the TTSE/NYSE: Significant differences
between these parameters (0.3859, 8.6022 for the
former and 0.7031, 4.0764 for the latter).
CONCLUSIONS
It can be argued that there appears to be comovement in stock prices within the CARICOM stock
markets.
This is evidenced by the derived bivariate copula
estimations.
The tDCC copula estimations suggest significant
dependence structures between the three CARICOM
stock markets, with the most significant being the
one between the JSE and the TTSE.
CONCLUSIONS
However, this does not seem to be fully the case for the
structures between each of the CARICOM markets and the
NYSE.
 The TTSE is argued to possess the most developed
dependence structure with the NYSE among the three
CARICOM stock markets studied.
 It can be argued that the level of dependence among the
CARICOM markets, both as a group and individually, with the
NYSE is underdeveloped and not as pronounced.
 This could be an explanation why the regional markets were
not as affected in the fallout from the U.S. originated
financial crisis.
CONCLUSIONS
Further research may be needed to
ascertain the factors which affect the
dependence among the regional
markets as well as whether it is
important for the regional markets to
strengthen the dependence structure
with the NYSE.
THE END
THANK YOU FOR YOUR
ATTENTION.