Testing the Efficient Market Hypothesis for the Athens Stock Exchange

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Jul 14, 2007 - 4th AFE Samos: International Conference on Advances in Applied ..... Test statistics in Table 4 show that there is bidirectional causality ...

4th AFE Samos: International Conference on Advances in Applied Financial Economics, 12-14 July 2007

Testing the Efficient Market Hypothesis for the Athens Stock Exchange Tarkan Cavusoglu Assistant Professor Hacettepe University, Department of Public Finance 06532, Beytepe, Ankara, TURKIYE Tel: + 90 312 2978675, Fax: + 90 312 2992063 E-mail: [email protected]

Abstract In this paper, the weak form of the efficient market hypothesis is tested for the Athens Stock Exchange through approaches accounting for conditional heteroscedasticity. The paper contains also an analysis on the influence of changes in economic conditions on stock returns and on conditional volatility. Empirical findings do not support the weak form of the efficient market hypothesis while mixed evidence is obtained from the latter investigation. Introduction A vast literature on finance has been accumulated on the theory of efficient markets since the influential paper of Fama (1965). The theory asserts that a market is efficient if the successive price changes are independent and identically distributed following a random walk process. Market efficiency is classified in three forms with respect to differences in information subsets, namely the weak form, semi-strong form and the strong form. Owing to the data availability, the majority of the empirical studies on market efficiency is about testing the weak form through the random walk hypothesis, in which only historical prices constitute the information set. However, neither of these studies takes into account the time-varying conditional variance in random walk tests despite the volatility clustering and thick tails characterising the financial data. In this respect, while Kim and Schmidt (1993) show that small sample property of unit root tests is not affected by conditional heteroskedasticity, Seo(1999) claims that these tests ignore the information coming from conditional heteroscedasticity and propose the joint estimation of the unit root and the generalised autoregressive conditional heteroskedasticity (GARCH) equations. Following Seo (1999), also Ling et al. (2003) show that unit root tests based on the maximum likelihood estimator are more powerful and robust to size distortions than Dickey-Fuller (DF) tests based on the least squares estimator. In this paper, the weak form of the efficient market hypothesis is tested for the Athens Stock Exchange (ASE) by exploiting the unit root test suggested by Seo (1999) in addition to other tests in the literature. The empirical analysis covers the period between October 1999 and April 2007 using the daily FTSE/ASE-20 stock price index. Due to the trend break of April 2003, the analyses are carried out for two different samples. 217

4th AFE Samos: International Conference on Advances in Applied Financial Economics, 12-14 July 2007

Following parts of the paper contain brief information about the data and methodology of the empirical analyses, followed by the estimation results and the conclusion. Data and the Methodology Empirical investigations in this study are based on the daily closing FTSE/ASE20 stock price index (Pt) between October 1999 and April 2007. There are two main reasons for the choice of this sample period. One is the macroeconomic stability achieved in the Greek economy by the year 1999 which is initiated through the efforts of meeting the convergence criteria required for joining the euro area. The other is the econometric convenience owing to relatively few outliers and structural breaks observed in the stock price series. However, the trend break of April 2003 in the ASE requires a separate two-period analysis, where the downward trend turns into an upward one. In investigating the linkage between stock returns and future economic activity in the study, the latter is proxied by the daily spread between overnight deposit interest rates ( RtS ) and benchmark 10-year bond yields. A decrease in the spread indicates expectations of a slow down in the economy. Data series are from the Datastream statistical database. Stock returns are computed by the first differences of the stock price series in natural logarithms, denoted by ∆ln(Pt). The short- and long-term interest rates RtS and

R tL are transformed into natural logarithms by the formula ln(1+R/100) and denoted by rtS and rtL , respectively. The empirical part of the study begins with Perron’s (1997) unit root test, because the FTSE/ASE-20 series seems to be stationary around a broken trend. After that, ADF-type unit root tests are performed for the two different sample periods split with respect to the break date. On the general-to-specific basis, tests are based on the following broadest representation of a unit root model: k

∆ ln(Pt ) = µ + β t + α ln(Pt −1 ) + ∑ λ i ∆ ln(Pt −i ) + ε t i=1

(1)

Model (1) is estimated with and without a lagged ∆ln(Pt) where the choice requires serially uncorrelated disturbances εt, tested by the Breusch-Godfrey Lagrange Multiplier (LM) statistic having a χ2 distribution. In addition to testing the unit root hypothesis α=0 in Model (1), non-rejection of the joint hypotheses µ=β=α=0 implies yt is generated by a pure random walk process while nonrejection of the restrictions β=α=0 implies a random walk with drift process1. However, the assumption of independent and identically distributed (i.i.d) residuals in Model (1) may be violated due to time-varying volatilities in stock prices. Therefore, the BDS test of Brock et al. (1996) and the ARCH LM test of Engle (1982) are exploited respectively to check for non-linear dependence and volatility clustering in residuals. Model (1), which is now assumed to have GARCH(1,1) errors, is estimated jointly with the parameters of the corresponding conditional variance (ht) equation, as suggested by Seo (1999). Estimations exploit both the 1

Critical values of the corresponding F-statistics are reported in Dickey and Fuller (1981).

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4th AFE Samos: International Conference on Advances in Applied Financial Economics, 12-14 July 2007

Maximum Likelihood Estimation with the Brendt-Hall-Hall-Hausman iterative algorithm and the heteroskedasticity consistent covariance matrix. The asymptotic distribution of the unit root test is a function of a nuisance parameter ρ, which decreases with the GARCH effect. Hence, the distribution is the standard normal when ρ=0 and the same as the Dickey-Fuller distribution when ρ=1 (Seo, 1999). Another widely used test for the random walk hypothesis is the Variance Ratio test, suggested by Lo and MacKinlay (1988). The test statistic, which has asymptotic standard normal distribution, has two versions. One is with homoskedastic disturbances, denoted by z(q), the other is with heteroskedasticity-robust disturbances, denoted by z*(q). Statistically significant test statistics indicate the rejection of the random walk hypothesis. Finally, for the empirical investigation of the linkage between stock returns and economic activity AR(1)-GARCH(1,1) and AR(1)-EGARCH(1,1) estimations are exploited. It is followed by the Granger causality analysis, which is carried out through detecting a causality between the conditional stock return volatility (ht) and the change in the interest rate spread ∆ rtS − rtL , and a

(

)

causality between stock returns ∆ln(Pt) and the change in the spread. Note that evidence from Granger causality tests is exploited as an indicator of the predictive capability of changes in economic conditions on stock returns and their volatility. Estimation Results Perron’s (1997) test statistic computed for ln(Pt) series results in the rejection of the unit root hypothesis with a test statistic t=-5.904 which is statistically significant at 1 % level. Endogenously selected break-date is found to be the 870th observation of the sample, coinciding with the date 3/28/2003, as expected. This break-date is exactly the turning point where the downward trend in ASE ends and an upward trend begins afterwards. In this respect, there seem to be two trend-stationary time paths that should be analysed separately. ADF-type unit root tests computed for the two sample periods are given in Table 1. The unit root hypothesis is rejected for both the non-augmented and augmented forms of the regressions in both samples, where augmentation with ∆ln(Pt-1) seems necessary due to rejections of the ‘no serial correlation’ hypothesis in non-augmented cases. Moreover, both the intercept and trend terms are statistically significant in unit root regressions. This is confirmed by the computed DF F-statistics where restrictions in favour of ‘random walk with drift’ and ‘pure random walk’ processes are rejected. However, as indicated by the computed BDS and ARCH LM test statistics, residuals of these unit root regressions depart from being i.i.d. and characterised significantly with firstorder ARCH effects. Therefore, these unit root tests should take into account the conditional heteroskedasticity.

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4th AFE Samos: International Conference on Advances in Applied Financial Economics, 12-14 July 2007

Table 1: Unit Root Analysis dependent variable: ∆ln(Pt) Intercept Trend ln(Pt −1 ) ∆ ln(Pt −1 )

10/01/1999 – 03/31/2003 (T=871) 0.254** 0.303** 0.275** (0.071) (0.071) (0.064) -5.1×10-5 ** -6.0×10-5 ** -5.4×10-5 ** (1.4×10-5) (1.4×10-5) (1.2×10-5) -0.032** -0.038** -0.034** (0.009) (0.009) (0.008) 0.167** 0.145** (0.034) (0.036)

4/01/2003 – 04/10/2007 (T=1007) 0.142** 0.139** 0.134** (0.034) (0.034) (0.033) 1.9×10-5** 1.9×10-5** 1.7×10-5** (5.3×10-5) (5.3×10-5) (5.2×10-6) -0.020** -0.020** -0.019** (0.005) (0.005) (0.005) 0.082** 0.115** (0.031) (0.032)

-7.2×10-5 ** (2.1×10-5) 0.229** (0.069) 0.569** (0.106) -5.453 -5.414 2376.2

1.0×10-5 ** (3. 7×10-5) 0.117** (0.030) 0.845** (0.039) -6.199 -6.165 3121.9

dependent variable: ht Intercept

ε 2t−1 h t −1

AIC -5.299 -5.324 -6.142 SBC -5.283 -5.302 -6.128 log-L 2308.4 2317.5 3092.7 H0: unit root -3.59* -4.28** -4.10** H0: random walk with drift 6.69* 9.39** 9.78** H0: pure random walk 7.17** 8.27** 10.84** H0: no serial correlation 24.05** 2.54 6.89** H0: no ARCH effect 15.04** 14.56** 0.53 4.99* H0: independence m1 5.83** 5.31** 0.31 2.12* m2 8.46** 7.73** 0.85 4.21** 9.21** m3 8.53** 0.58 5.19** H0: unit root – GARCH -4.27** (nuisance parameter ρˆ ) (0.02) Asterisks * and ** denote 5 % and 1 % levels of significance, respectively.

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-6.147 -6.128 3093.1 -4.03** 9.14** 9.61** 0.77 7.93** 1.64 3.91** 5.01**

1.56 -2.04* -1.21 -1.02 -3.96** (0.01)

4th AFE Samos: International Conference on Advances in Applied Financial Economics, 12-14 July 2007

Table 2: Variance Ratio Test VR Test q=2

q=3 q=4 q=5 10/01/1999 – 03/31/2003 VR(q) 1.147 1.163 1.167 1.192 z(q) (3.23)*** (2.27)** (1.81)* (1.78)* z*(q) (4.34)*** (3.23)*** (2.63)*** (2.59)*** 4/01/2003 – 04/10/2007 VR(q) 1.081 1.132 1.143 1.138 z(q) (2.26)** (2.36)** (1.99)** (1.63) z*(q) (2.55)** (2.80)*** (2.43)** (1.99)** Asterisks *, ** and *** denote 10 %, 5 % and 1 % levels of significance, respectively.

When the BDS test statistics are computed from the standardised residuals of the unit root regressions with GARCH(1,1) errors, the null of independence cannot be rejected in both samples. This shows that including GARCH(1,1) errors can account for the non-linear dependence present in the residuals of the unit root regressions. Although the unit root hypotheses are rejected even with GARCHerror considerations, the aptness of Seo’s unit root testing procedure is reflected in the estimated nuisance parameters. They are very close to zero in both samples (ρ=0.02 and ρ=0.01) indicating a significant departure from the Dickey-Fuller distribution. When the Variance Ratio (VR) test is used to test the random walk hypothesis, the above conclusions are confirmed. In Table 2, where the computed variance ratios and the associated test statistics up to an aggregation value q=5 are given, the z(q) and z*(q) statistics both indicate the rejection of the random walk hypothesis. In order to carry out the investigation of the linkage between stock returns and economic activity, an AR(1)-GARCH(1,1) model is fitted to stock returns and estimated, the results of which are given in Table 3. To learn about the influence of the changes in economic activity on the conditional stock return volatility, ∆ rtS − rtL is included as an explanatory variable in the conditional variance of the AR(1)-GARCH(1,1) model. The corresponding regression coefficient is positive but statistically significant only in the first sample period. When the same procedure is repeated with an AR(1)-EGARCH(1,1) model, which is also assumed to have nonnormal errors, a significant asymmetric effect of shocks on conditional volatility is detected in the first sample period. To elaborate more on this, Granger causality tests are performed between the estimated conditional variance hˆt and ∆ rtS − rtL . Test statistics in Table 4 show that there is bidirectional causality between hˆ and

(

)

(

t

), however, only in the first sample period. On the other hand, while the causality tested between ∆ln(P ) and ∆ (r − r ) shows no evidence supporting the ∆

(

)

rtS

− rtL

t

S t

L t

predictive power of the past values of the changes in the spread on the current value of the stock returns, past values of the latter appear to effect the current value of the former in the second sample.

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4th AFE Samos: International Conference on Advances in Applied Financial Economics, 12-14 July 2007

Table 3: Modeling Stock Returns with GARCH Errors 10/01/1999 – 03/31/2003 (T=871) 4/01/2003 – 04/10/2007 (T=1007) dependent variable: ∆ln(Pt) -0.0014** -0.0013** -0.0021** 0.0013** 0.0013** 0.0012** intercept (0.0005) (0.0005) (0.0005) (0.0003) (0.0003) (0.0003) 0.1516** 0.1562** 0.1442** 0.1025** 0.1029** 0.0892** ∆ ln(Pt −1 ) (0.0412) (0.0412) (0.0348) (0.0321) (0.0321) (0.0330) ht ht ln(h t ) ht ht ln(h t ) dependent variable: -5 -5 -6 -6 -1.1296** -0.4040** 5.5×10 ** 4.0×10 4.8×10 ** 4.0×10 ** intercept (0.3320) (0.1427) (2.1×10-6) (1.1×10-5 ) (9.3×10-6) (2.0×10-6) 0.2023** 0.2193** 0.0738** 0.0745** 2 ε t−1 (0.0289) (0.0344) (0.0245) (0.0248) 0.6323** 0.5919** 0.8933** 0.8926** h t −1 (0.0567) (0.0551) (0.0334) (0.0340) 0.8946** 0.9678** ln(h t −1 ) (0.0371) (0.0142) -0.1034** -0.0221 ε t −1 h t −1 (0.0375) (0.0199) 0.3556** 0.1429** ε t −1 h t −1 (0.0612) (0.0353) 0.0108** 38.158* 0.0023 10.853 S L ∆ r t − rt (0.0036) (18.543) (0.0038) (37.437) 5.1549** 12.067** t-distribution (ν) (0.9839) (4.2466) AIC -5.452 -5.457 -5.521 -6.230 -6.229 -6.234 SBC -5.424 -5.425 -5.477 -6.206 -6.199 -6.194 log-L 2373.9 2377.0 2407.0 3135.7 3135.9 3140.4 (1) Asterisks * and ** denote 5 % and 1 % levels of significance, respectively. (2) Estimations are based on the BollerslevWooldridge heteroskedasticity consistent covariance matrix. (3) Figures in parenthesis in the row titled ‘t-distribution (ν)’ denote the degree of freedom (ν) that controls the tail behavior of the conditional distribution of the GARCH errors, where the t-distribution approaches the standard normal as ν tends to infinity.

(

)

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4th AFE Samos: International Conference on Advances in Applied Financial Economics, 12-14 July 2007

Table 4: Granger Causality Test ∆ r S − r L → hˆ hˆ → ∆ r S − r L t

(

t

t

)

(

t

t

)

t

(

∆ ln(Pt ) → ∆ rtS − rtL

)

(

)

∆ rtS − rtL → ∆ ln(Pt )

10/01/1999 – 03/31/2003 14.49**(6) 2.573 (4) 4.981 (4) 4/01/2003 – 04/10/2007 8.924 (6) 2.203 (6) 18.04**(7) 2.357 (7) (1) ** and * denote 5 % and 10 % levels of significance respectively. (2) The symbol → between the two variables denotes that the first variable Granger causes the second, where the corresponding causality test statistic is distributed with a χ2 distribution. (3) Lag length of the VAR model selected by the information criteria. 13.14**(6)

Conclusion No empirical support is found for the weak form of market efficiency in the Athens Stock Exchange, even tests accounting for conditional heteroskedasticity are used. Although this finding implies the predictability of stock returns with past information, a macroeconomic indicator, which is considered capable of reflecting expectations on economic activity, does not lend support for any predictive power on stock returns. It only exhibits predictability on the conditional return-volatility for the October 1999 - March 2003 period, during which ASE experienced a downward trend due to the unfavourable global economic environment. References Brock, W. A., Dechert, W., Scheinkman, J. & LeBaron, B. (1996). A tetst for independence based on the correlation dimension. Econometric Reviews, 15(3), 197-235. Dickey, D. & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, 1057-1072. Fama, E. F. (1965). The behavior of stock-market prices. The Journal of Business, 38(1), 34-105. Kim, K., & Schmidt, P. (1993). Unit root tests with conditional heteroskedasticity. Journal of Econometrics, 59, 287-300. Ling, S., Li, W. K., & McAleer, M. (2003). Estimation and testing for unit root processes with GARCH (1,1) errors: theory and Monte Carlo evidence. Econometric Reviews, 22(2), 179-202. Lo, A., & MacKinlay, A.C. (1988). Stock market prices do not follow random walks: evidence from a simple specification test. Review of Financial Studies, 1, 41–66. Perron, P. (1997). Further evidence on breaking trend functions in macroeconomic variables. Journal of Econometrics, 80, 355-385. Seo, B. (1999). Distribution theory for unit root tests with conditional heteroskedasticity. Journal of Econometrics, 91, 113-144.

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