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Academy of Economic Studies Doctoral School of Finance and Banking - DOFIN

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Title: Academy of Economic Studies Doctoral School of Finance and Banking - DOFIN


1
Academy of Economic Studies Doctoral 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
2
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

3
WHAT MOVES VOLATILITY?
  • NEWS
  • RESEARCH STRATEGIES
  • VOLATILITY MODELS
  • INTER-LINKAGES IN MARKET VOLATILITY

4
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 mid80s, used by (Granger, 1986 Engle and
    Granger, 1987 Johansen, 1988 Johansen and
    Juselius, 1990)

5
VOLATILITY MODELS
  • GARCH
  • TGARCH
  • EGARCH

6
COMPONENT GARCH MODEL
The conditional variance in the GARCH(1,1) model
can be written as
gt
Allowing for the possibility that s2 is not
constant over time, but a time-varying trend qt,
yields
Dt is a slope dummy variable that takes the value
Dt 1 for et lt 0 and Dt 0 otherwise, in order
to capture any asymmetric responses of volatility
to shocks.
7
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 gt ? gt (aß), ß gt F gt 0, a gt 0, ß
    gt 0, F gt 0, ? gt 0.

8
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

9
DATA STATISTICS FOR BET SERIES
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.
10
DATA STATISTICS FOR DAX SERIES
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.
11
DATA STATISTICS FOR WIG20 SERIES
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.
12
CONDITIONAL VOLATILITY FOR GARCH MODELS
BET Index
13
CONDITIONAL VOLATILITY FOR GARCH MODELS
DAX Index
14
CONDITIONAL VOLATILITY FOR GARCH MODELS
WIG20
15
CGARCH Components Chart
BET Index
16
CGARCH Components Chart
DAX Index
17
CGARCH Components Chart
WIG20 Index
18
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
  • rt2a b st2ut
  • Trying to avoid the strongly influenced extreme
    values on rt2 , the following model is used log
    rt2 a b log ht2 ut
  • l

19
BET stock market forecasted volatility


20
DAX stock market forecasted volatility

21
WIG20 stock market forecasted volatility
22
COINTEGRATION ANALYSIS
Cointegration requires the variables to be
integrated of the 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
23
COINTEGRATION ANALYSIS
  • Further we estimate a VAR and the lag length
    using AIC and SC Yt c ??yt-1 et
  • The information criteria selects a VAR(2)
  • Next step is the determination of the number of
    cointegrating relations in VAR

24
COINTEGRATION ANALYSIS
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.
VECM estimated results
25
CONCLUDING REMARKS
  • GARCH models showed evidence of asymmetric effect
    for DAX and WIG20, but not for BET
  • The autoregressive parameters in the trend
    equations, ?, 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

26
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 Financial Studies. 13 1, 1-42.
  • Bollerslev, T., R.Y. Chou Kroner K. F. (1992).
    ARCH-Modeling in Finance A
  • review of the theory and empirical
    evidence. Journal of Econometrics. 52 5-59.
  • Brooks, C. (2002). Introductory Econometrics for
    Finance. 1st ed. Cambridge Cambridge University
    Press. 701
  • Campbell John Y. (1990). Measuring the
    persistence of expected returns. The American
    Economic Review. 80 2, 43-47.
  • Dickey, D. W. Fuller(1979) Distribution of the
    estimators for the autoregressive Time series
    with a unit root. Journal of the American
    Statistical Association 74. 427 431.
  • Ding, Z., Granger C. W. Engle R. F. (1996). A
    long memory property of stock returns and a new
    model. Journal of Empirical Finance. 1 83-106

27
BIBLIOGRAPHY
  • Fama, E. (1970). Efficient capital markets A
    review of theory and empirical work. The Journal
    of Finance. 25 383-432. 
  • Glosten, L., Jagannathan, R D. Runkle (1993).
    On the relation between expected value and the
    volatility of the nominal excess returns on
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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
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  • Johansen, S. J. Katarina (1990). Maximum
    Likelihood Estimation and Inference on Co
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  • 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
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  • Porteba, James M. (1990). Linkages between equity
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  • Zakoian, J-M (1994). Threshold heteroskedastic
    models. Journal of Economic Dynamics and Control
    18. 931 955.

28
  • Thank you for your consideration!
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