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

Anderssen, T & T. Bollerslev (1997). Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-run in High Frequency Returns. Journal of Finance. 52, 975 – 1005

Alexander, C. (2001). Market Models. A Guide to Financial Data Analysis. 1st ed. Chichester: John Wiley & Sons Ltd. 494 Bekaert, Geert & Campbell R. Harvey (1997). Emerging equity market volatility. Journal of Financial Economics. 43: 29-77 Bekaert, Geert & Guojun Wu. (2000). Asymmetric volatility and risk in equity markets. The Review of

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model. Journal of Empirical Finance. 1: 83-106

BIBLIOGRAPHY

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Granger, C.W.J., and Joyeaux, R. (1980), An introduction to long memory time series models and fractional diferencing., Journal of Time Series Analysis, 1, 15-39.

Johansen, S (1988). Statistical Analysis of Co-integration Vectors, Journal of Economic Dynamics and Control, 12, 231-254.

Johansen, S. & J. Katarina (1990). Maximum Likelihood Estimation and Inference on Co integration with Application to the Demand for Money, Oxford Bulletin of Economics and Statistics, 52, 169 210.

Mandelbrot, B. (1963). The variation of certain speculative prices. Journal of Business. 36: 394 – 419. Nelson, D (1990). ARCH models as diffusion approximations. Journal of Econometrics 45. 7 – 38. Porteba, James M. (1990). Linkages between equity markets. The Review of Financial Studies. 3: 1, 34-

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Thank you for your consideration!