Academy of Economic StudiesDoctoral School of Finance and Banking - DOFIN
VOLATILITY AND LONG TERM RELATIONS IN EQUITY MARKETS:
Empirical Evidence from
Romania, Germany and Poland
MSc. Student: Mircia Ana-Maria Supervisor: PhD. Professor Moisa Altar
July, 2009
GOALS
COMPARE SEVERAL GARCH MODELS for - modeling and forecasting conditional variance of Romania, Germany and Poland stock market indexes
LONG RUN RELATIONS BETWEEN THESE MARKETS
WHAT MOVES VOLATILITY?
NEWS RESEARCH STRATEGIES
– VOLATILITY MODELS INTER-LINKAGES IN MARKET
VOLATILITY
REVIEW OF PREVIOUS RESEARCH
Asymmetric effect to past information: Koutmos (1998) using TGARCH on 9 countries, Chen (2001) using EGARCH on 9 countries
Cointegration analysis, regarded as perhaps the most revolutionary development in econometrics since mid’80s, used by (Granger, 1986; Engle and Granger, 1987; Johansen, 1988; Johansen and Juselius, 1990)
VOLATILITY MODELS
GARCH
TGARCH: EGARCH:
q
iiti
r
iititi
p
iitit d
1
2
1
2
1
22
q
jjtj
p
i it
itr
k kt
ktkt
1
2
11
2 loglog
q
jiti
p
iitit
11
2
COMPONENT GARCH MODEL
=>
The conditional variance in the GARCH(1,1) model can
be written as:)()()1( 2
12
122
1122 ttttt hhh
Allowing for the possibility that σ2 is not constant over time, but a time-varying trend qt, yields:
ttty ),0(~| 12
1 ttt NI
1112
112
1122 )()()( ttttttttt Dqqqq
)()( 12
12
1 tttt qq Dt is a slope dummy variable that takes the value Dt = 1 for εt < 0 and Dt = 0 otherwise, in order to capture any asymmetric responses of volatility to shocks.
DECOMPOSITION IN PERMANENT AND TRANSITORY COMPONENTS
The long run component equation:
The short run component equation:
Stationarity of the CGARCH model and non-negativity of the conditional variance are ensured if the following inequality constraints are satisfied: 1 > ρ > (α+β), β > Φ > 0, α > 0, β > 0, Φ > 0, ω > 0.
)()( 12
12
1 tttt qq
1112
112
1122 )()()( ttttttttt Dqqqq
DATA
DAILY DATA FROM 2000 THROUGH 2009
FIRST 2200 observations for each stock market index were used for modeling
LAST 125 were kept out of sample to be used for forecasting volatility
Returns were computed using the prices log difference:
)ln()ln( 1 ttt PPr
DATA STATISTICS FOR BET SERIES
-.15
-.10
-.05
.00
.05
.10
.15
00 01 02 03 04 05 06 07 08
bet qq plot
BET Index the main indicator on the progression of Bucharest Stock Exchange, is a free float weighted capitalization index of the most liquid 10 companies listed on the BSE regulated market. It was launched in September 19, 1997, when its value stood at 1,000 points.
DATA STATISTICS FOR DAX SERIES
2000
3000
4000
5000
6000
7000
8000
9000
00 01 02 03 04 05 06 07 08
DAX
-.12
-.08
-.04
.00
.04
.08
.12
00 01 02 03 04 05 06 07 08
RDAX
DAX Index, is the most commonly cited benchmark for measuring the returns posted by stocks on the Frankfurt Stock Exchange. Started in 1984 with a value of 1000, the index is comprised of the 30 largest and most liquid issues traded on the exchange.
DATA STATISTICS FOR WIG20 SERIES
800
1200
1600
2000
2400
2800
3200
3600
4000
00 01 02 03 04 05 06 07 08
WIG20
-.12
-.08
-.04
.00
.04
.08
.12
00 01 02 03 04 05 06 07 08
RWIG20
0
50
100
150
200
250
300
350
-0.05 0.00 0.05 0.10
Series: RWIG20Sample 1/05/2000 5/13/2009Observations 2324
Mean -8.94e-06Median 4.52e-06Maximum 0.108016Minimum -0.084428Std. Dev. 0.017161Skewness -0.007015Kurtosis 5.326857
Jarque-Bera 524.3004Probability 0.000000
WIG20 Index, the main index of Warsaw Stock Exchange is calculated based on a portfolio comprised of shares in the 20 largest and most traded companies..
The index base date is April 16, 1994; and its base value is 1, 000 points.
CONDITIONAL VOLATILITY FOR GARCH MODELS
BET Index
MODEL TGARCH EGARCH AGARCH GARCH
TREND INTERCEPT ω 2.02E-05 -1,22179 0.000570 2.00E-05
0.0000 (0.0000) (0.2437) (0.0000)
ARCH Term α 0.236796 0.473249 0.172367 0.271573
(0.0000) (0.0000) (0.0015) (0.0000)
ASYMETRIC TERM γ 0.059174 -0.031814 0.106582
(0.2062) (0.1705) (0.0639)
GARCH TERM β 0.688264 0.896458 0.402559 0.685640
(0.0000) (0.0000) (0.0001) (0.0000)
TREND AR TERM ρ 0.985973
(0.0000)
FORECAST ERROR φ 0.139454
(0.0003)
CONDITIONAL VOLATILITY FOR GARCH MODELS
DAX Index
MODEL TGARCH EGARCH AGARCH GARCH
TREND INTERCEPT ω 2.56E-06 -0.261206 0.000308 1.95E-06
` (0.0000) (0.1342) (0.0036)
ARCH Term α -0.016944 0.114533 -0.155120 0.098332
(0.1592) (0.0000) (0.0000) (0.0000)
ASYMETRIC TERM γ 0.168519 -0.125316 0.136207
(0.0000) (0.0000) (0.0003)
GARCH TERM β 0.917642 0.980665 -0.660962 0.896633
(0.0000) (0.0000) (0.0000) (0.0000)
TREND AR TERM ρ 0.992817
(0.0000)
FORECAST ERROR φ 0.100209
(0.0000)
CONDITIONAL VOLATILITY FOR GARCH MODELS
WIG20
MODEL TGARCH EGARCH AGARCH GARCH
TREND INTERCEPT ω 3.47E-06 -0.220649 0.000298 2.44E-06
(0.0032) (0.0000) (0.0029) 0.0216
ARCH Term α 0.032397 0.112596 -0.083685 0.054110
(0.0020) (0.0000) (0.0001) (0.0000)
ASYMETRIC TERM γ 0.042952 -0.028651 0.087146
(0.0015) (0.0085) (0.0048)
GARCH TERM β 0.933931 0.984017 0.820285 0.937811
(0.0000) (0.0000) (0.0000) (0.0000)
TREND AR TERM ρ 0.989790
(0.0000)
FORECAST ERROR φ 0.067163
(0.0000)
CGARCH Components Chart
-.001
.000
.001
.002
.003
.004
00 01 02 03 04 05 06 07 08
SHORT_RUN_BET LONG_RUN_BET
BET Index
CGARCH Components Chart
-.002
-.001
.000
.001
.002
.003
00 01 02 03 04 05 06 07 08
SHORT_RUN_DAX LONG_RUN_DAX
DAX Index
CGARCH Components Chart
-.0004
.0000
.0004
.0008
.0012
.0016
00 01 02 03 04 05 06 07 08
SHORT_RUN_WIG20 LONG_RUN_WIG20
WIG20 Index
FORECASTING VOLATILITY
I used out-of-sample data in order to forecast volatility by using the last 125 observations
GARCH models are measured by the coefficient of determinations R2 coming from regressing squared returns on the volatility forecast:
rt2=a + b σt
2+ut
Trying to avoid the strongly influenced extreme values on rt
2 , the following model is used: log rt2 =a + b log ht
2 + ut
l
BET stock market forecasted volatility
.000
.001
.002
.003
.004
.005
.006
08M11 08M12 09M01 09M02 09M03 09M04
FOTBETEG
.000
.001
.002
.003
.004
.005
.006
.007
.008
08M11 08M12 09M01 09M02 09M03 09M04
FOTBETAG
.000
.001
.002
.003
.004
.005
.006
08M11 08M12 09M01 09M02 09M03 09M04
FOBETTG
.000
.001
.002
.003
.004
.005
.006
08M11 08M12 09M01 09M02 09M03 09M04
TBETGARCH
DAX stock market forecasted volatility
.0000
.0004
.0008
.0012
.0016
.0020
.0024
.0028
.0032
08M11 08M12 09M01 09M02 09M03 09M04
FOTDAXAG
.0000
.0002
.0004
.0006
.0008
.0010
.0012
.0014
.0016
08M11 08M12 09M01 09M02 09M03 09M04
FOTDAXEG
.0000
.0004
.0008
.0012
.0016
.0020
08M11 08M12 09M01 09M02 09M03 09M04
FOTDAXTG
.0000
.0004
.0008
.0012
.0016
.0020
.0024
08M11 08M12 09M01 09M02 09M03 09M04
TDAXGARCH
WIG20 stock market forecasted volatility
.0002
.0004
.0006
.0008
.0010
.0012
.0014
.0016
.0018
08M11 08M12 09M01 09M02 09M03 09M04
FWIG20AGARCH
.0004
.0006
.0008
.0010
.0012
.0014
.0016
08M11 08M12 09M01 09M02 09M03 09M04
FOTWIG20EG
.0004
.0006
.0008
.0010
.0012
.0014
.0016
.0018
08M11 08M12 09M01 09M02 09M03 09M04
FOTWIG20TG
.0002
.0004
.0006
.0008
.0010
.0012
.0014
08M11 08M12 09M01 09M02 09M03 09M04
TWIG20GARCH
COINTEGRATION ANALYSIS
Cointegration requires the variables to be integrated ofthe same order. Unit root tests are performed on each of the price index series in log first differences through the ADF test and the Phillips-Peron test:
ADF Test Phillips-Perron Testt-statistic P-value t-statistic P-value
LBET -1,862333 0.3505 -1,910636 0.3276LDAX -1,539064 0.5137 -1,509632 0.5288LWIG20 -1,103595 0.7166 -1,140560 0.7017RBET -41,63764 0.0000 -41,91274 0.0000RDAX -50,51171 0.0001 -50,51171 0.0001RWIG20 -46,58198 0.0001 -46,58614 0.0001
Unit Root test with intercept
COINTEGRATION ANALYSIS
Further we estimate a VAR and the lag length using AIC and SC: Yt = c + ∑Δyt-1 + εt
The information criteria selects a VAR(2) Next step is the determination of the number of
cointegrating relations in VAR
H0 H1 λtrace CV(trace, 5%) λmax CV(max,5%)r=0 r>0 50,639 29,797 36,800 21,132r≤1 r>1 13,839 15,495 7,609 14,265r≤2 r>2 6,230 3,841 6,230 3,841
COINTEGRATION ANALYSIS
Variables ΔBET ΔDAX ΔWIG20Error correction term 0.000830 -0.004414 0.002647
[ 0.95547] [-5.39971] [ 3.18883] R-squared 0.022918 0.024692 0.006948 F-statistic 7,754 8,369 2,313
Log likelihood 18394.88AIC -15,821SC -15,754
VECM estimated results:
Primary finding is that a stationary long-run relationship exists between the three equity markets.Further a VECM is created and the parsimonious model according to AIC and SC was found to be a VECM (4) with the cointegration rank =1.
CONCLUDING REMARKS
GARCH models showed evidence of asymmetric effect for DAX and WIG20, but not for BET
The autoregressive parameters in the trend equations, ρ, is very close to one for all indices, so the series are very close to being integrated
Error correction parameter is not significant for BET Index, Romania market will be the first one to react to the external shocks, while Germany is the one who impose shocks
It could be interesting to detect how much the exchange rate is important for investors who operate in this markets and how stock market and economic variables react
BIBLIOGRAPHY
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Thank you for your consideration!