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Efficient Market Hypothesis in Times of the Financial Crisis: Evidence from the Central European Stock Market PETR SEĎA Department of Mathematical Methods in Economics VŠB - Technical University of Ostrava Sokolská třída 33, 701 21 Ostrava 1 CZECH REPUBLIC [email protected], http://www.vsb.cz/en/ Abstract: Efficient market hypothesis (EMH) is an integral part of financial economics for decades. Efficient market fully and accurately reflects all relevant information. Stock market efficiency with respect to a set of reliable information leads to the fact that it is not possible to achieve consistently abnormal returns by trading. The efficiency in the concept of efficient market hypothesis means that the information are fully reflected in stock prices, therefore it is the information efficiency. First it will be discussed the theoretical background of an efficient stock market hypothesis. Then, using data obtained from the Czech and Polish stock market it will be tested the weak form of efficient market hypothesis by linear and nonlinear statistical methods. The aim of this paper is to analyse an impact of the global financial crisis in 2008-09 on the weak form of efficiency of the Czech and Polish stock markets.

Key-Words: market efficiency, information, random walk, martingale, linear and nonlinear methods. rule and may face such instability sometime. Therefore, a special aim of our paper is to investigate a behavior of Czech and Polish stock markets before and during global financial crisis in 2008-09 from the point of view of weak form of EMH.

1 Introduction The behavior of stock prices has been a subject of many recent investigations. Most theories claim that stock markets are efficient and can’t be forecasted. Practitioners have never believed in it and try to maximize profit from the liquidity market using more and more forecasting methods. The EMH is almost certainly the right place to start when thinking about asset price formation and represents one of the basic analytic approaches that try to explain movements of securities in time. The basic idea of the EMH is determination of prices of shares by interaction of interested rational market agents. For details see [7]. This paper contributes to the discussion on the efficiency of newly emerged stock markets in transition economies. The aim of this paper is to test the weak-form of the EMH in Czech and Polish stock markets. First it will be discussed the theoretical basis for an EMH. Then, using data obtained from the most developed stock markets in transition, Czech and Polish stock market, namely the time series of the Czech PX index and Polish WIG20 index will be tested the weak form of EMH by linear and nonlinear statistical methods. Crashes and or crisis are not devoted to developed market and emerging markets includes Czech Republic and Poland isn’t excluded from this

ISBN: 978-1-61804-066-4

2 Theoretical backgrounds The EMH is an essential part of financial economics for many years. The stock market is considered to be efficient with regard to a specific set of information Ω if the shares are not affected by publication of information to all market participants. The effectiveness in efficient market means that the information is fully reflected in stock prices. The stock market is efficient with respect to a set of information Ω if it is not possible to achieve economic profit trading on the basis of this set of information, for details see [4]. The content of the information set determines the form of EMH. If it contains only historical information, then it is a weak form of the hypothesis. If the information set includes all public information available, then we can talk about semi weak form, and if the information set contains also insider information, then it is a strong form of EMH. The Czech and Polish equity markets are considered as emerging capital markets. Hence, we

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transactions to be constant, we can reduce the EMH testing in the form of equations with variable righthand side or with constant right hand side, namely: (3) E [ Rt +1 − rt | Ωt ] = const, which is already known formula for random walk or martingale model. The random walk model is more strict than the martingale model and requires that a rate of return is independent and have the same distribution. The martingale model assumes a rate of return is independent. In this paper we will assume that the yield rates are independent and have the same distribution.

will test the weak form of the EMH only. Thus, effort to analyze historical information therefore does not bring any additional results for analytics. Efficient market hypothesis is in essence based on these three basic assumes which are less restrictive compared with perfect market: a) investors are rational, their rationality lies in the fact that the decision correctly updated after the discovery of new information, b) any investment decision must satisfy the arbitrage condition, this decision is based on subjective beliefs about maximizing own wealth, c) the whole team of investors are rational, this means that the individual errors across the market are independent or correlated. Assuming rational expectations, the individuals must take into account the individual arbitrage conditions with regard to the information set available to all, their individual risk premium and its own transaction costs with regard to market conditions. It is expected that abnormal returns from holding shares must be equal the expected rate risk premium and information and transaction costs per unit of investment considering a set of information available to all investors, namely: (1) E [ Rt +1 − rt | Ωt ] = E ( λit + δ it | Ωt ) ,

3.1 Testing the efficient market hypothesis by linear methods Properties of Rt +1 will be tested by following linear tests: Box-Pierce test and Variance ratio test. 3.1.1 Box-Pierce test This test verifies whether all the autocorrelation coefficients are significantly different from zero. Sample autocorrelation coefficient of the k-th delayed returns is defined as follows: T −k

∑ ( R − R )( R

where E [ Rt +1 − rt | Ωt ] is an expected abnormal return

ρˆ k =

from holding shares, E ( λit + δit | Ωt ) is an expected rate risk premium and information and transaction costs, Ω t is an information set available at time t, λit is a rate of risk premium for investors, λit > 0 , δ it is information and transaction costs per unit of investment, δ it > 0 .

T

∑(

Rt − R

t =1

)

−R

)

2

,

(4)

1 T ∑ Rt , where T is number T t =1 of observation and Rt is return on shares at time t. If returns are independent, then all sample autocorrelation coefficients of returns should be zero. This hypothesis is tested by Portmanteau statistic proposed by Box and Pierce, see [1]:

where k = 1,2,...a and R =

The equation (1) shows that E ( λit + δit | Ωt ) is the same for all investors and therefore can be rewritten as: (2) E [ Rt +1 − rt | Ωt ] = E ( λit + δ it | Ωt ) = ρt ,

m

ˆ = T ρˆ 2 , Q ∑ k

where ρt is combined average rate of risk premium and transaction and information costs. Rationality and market discipline in this case outweigh the individual's preferences and provide arbitrage condition of a representative agent, which is the theoretical basis of the EMH, see [8].

(5)

k =1

where m is a selected number of autocorrelation. This statistic has asymptotically Chi-distribution with m degrees of freedom. The null hypothesis has in this case the following form: H 0 : ρ k = 0 for all k = 1, 2,...,m . 3.1.1 Variance ratio test Let Rt is the daily logarithmic rate of return and Rtk is k-day logarithmic rate of return of shareholdings. If the rates of return are independent, then the variance of their sum must be a linear function of time, namely: k (6) Var ( Rt ) = kVar ( Rt ) ,

3 Methodology In this paper will be tested only the weak form of EMH. We start from equation (3). According to LeRoy, please see [5], an influence of fluctuations in returns due to risk aversion is relatively small and in short term can be considered together with the costs associated with obtaining information and

ISBN: 978-1-61804-066-4

t +k

t

t =1

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conditional mean E (ε t +1 | Ωt ) = 0 and conditional

assuming that Rt has a constant variance. From the definition of autocorrelation coefficient in the k-th order linear dispersion and definitions of variance of linear combinations of random variables can be written: k

∑Var ( R ) + 2∑ cov ( R t,j

VR ( k ) =

t ,i

j =1

variance E (ε t2+1 | Ωt ) = ht +1 , where Ωt is information set available at time t. Those requirements are met by following model: (10) ε t = vt ht , where vt has unspecified probability

,Rt , j )

ip j

.

kVar ( Rt )

(7)

distribution F ( 0 ,1) . Hence it is clear that ε t and Rt is a nonlinear in the second moment. Engle assumed that ht = σ t2 is AR process expressed by:

The ratio of variances is a linear combination of the first k-1 autocorrelation return coefficients with linearly declining weights of corresponding autocorrelation coefficients. The null hypothesis of random walk is rejected, unless the share of variance is equal to 1 at any time of delay. For details see [6].

(11) σ t2 = α0 + α1ε t2−1 + ... + α pε t2− p . The null hypothesis for testing linearity in the second moment assumes that there is no correlation between σ t2 and ε t2 for j = 1,2,..., p , therefore H 0 : α1 = α 2 = ... = α p = 0 compared to H1 : it exist at least one α j ≠ 0 for j = 1,2,..., p .

3.2 Testing the efficient market hypothesis by nonlinear methods

3.2.2 BDS test The BDS test is based on the basis of the correlation integral of time series return C (T ,m,ε ) with T observations and it is calculated for embedding dimension m as follows: T −1 1 C (T ,m,ε ) = H ( ε − Rt − Rs ) , (12) ∑ T (T − 1) m≤t ≠ s ≤n

The validity of weak form of EMH should be tested not only by linear methods, but also by nonlinear methods, because the linear methods cannot detect any nonlinear relations generating returns in time. When testing by nonlinear methods we verify whether it is possible to express the rate of return as follows: (8) Rt = gt ( r1 ) + ε t ht ( r2 )

where ε is a pre-selected and sufficiently small number, H ( z ) is so called Heaviside function that takes value 1 when its argument is positive and 0 if the argument is negative. The symbol . denotes the distance between two selected points. The correlation integral is the percentage return of pairs Rt , Rs , such that they are close to each other. Brock, Dechert and Scheikman [2] constructed a test, which is nonparametric, to assess the null hypothesis that the time series of returns Rt is independent and distributed equally with regard to non-specific alternative hypothesis. It was found that the BDS statistic is computed as:

where ε t is random noise which has a specified distribution F, thus ε t ~ F ( 0 ,1) . Functions gt and ht are nonlinear functions containing historical and are information in itself, r1 r2 vectors of independent variables. It is obvious that 2

Et −1 ( Rt ) = gt ( r1 ) and Et −1 ( Rt − Et −1 ( Rt ) ) = ht2 ( r2 ) .

If we find a gt or ht , or both functions simultaneously, we can say that returns are nonlinear in the first moment, or are nonlinear in the second moment, or are nonlinear in both moments. There is a wide range of tests to detect nonlinearities in the returns. In this paper the following tests were selected: Engel’s test and BDS test.

Wmn ( ε ) =

3.2.1 Engel’s test Engle [3] constructed a test that explicitly examines the non-linearity in the second moment and proposed autoregressive conditional heteroskedasticity model. Let the return from shares for one period is expressed by the equation: (9) Rt = f ( Rt − j ) + ε t ,

σ m (ε )

m

),

(13)

where Wmn ( ε ) converges to normal distribution N ( 0 ,1) when T approaches to infinity. In practice, the BDS statistic is asymptotically normal distribution even then, when investigated series have more than 500 observations.

where ε t is conditional heteroskedastic process with

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(

N Cnm ( ε ) − ( C1m ( ε ) )

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Thus Fig. 2 and Fig. 3 show volatility clustering where large returns tend to be followed by small returns leading to continuous periods of volatility and stability.

4 Data Empirical analysis is performed on daily data of indexes PX and WIG20 as representatives of Czech and Polish stock markets in period from 2004 till 2010 and was based on closing prices. It includes total of 1825 observations. This period was chosen purposely, to investigate changes of the Czech and Polish equity markets behavior during time with a special emphasis on behavior of respective indexes in the time before and during financial crisis. The returns Rt at time t were defined in the logarithm of PX and WIG20 indices P, that is: Rt = log ( Pt − Pt −1 ) . (14)

WIG20_RETURN .100 .075 .050 .025 .000 -.025 -.050 -.075

Following the spread of bad news about U.S financial crisis the Central European equity markets, Czech and Polish ones included, we have seen more than 60 percent decline in both selected indexes, please see Fig. 1. This happened primarily due to the withdrawal by foreign portfolio investors between September and December 2008. W IG20_VALUE

4,000

-.100 250

500

750

1000

1250

1500

1750

Fig. 3: WIG20 returns (2004-2010) Since the volatility was highest in 2008 when the values of both indexes reached the minimum values during investigated period we divided the basic period 2004-2010 into two testing period. First period was defined from 2004 to the end of June 2007 and the second one started at the beginning of July 2007 and finished by the end of 2010. Our goal is to investigate and compare the weak form of EMH of investigated markets in both periods.

PX_VALUE

3,500 3,000 2,500 2,000 1,500

5 Empirical results

1,000

In this chapter the results of empirical testing the efficiency of both analyzed indexes in both investigated periods using linear and nonlinear methods as defined in Chapter 3 will be performed.

500 250

500

750

1000

1250

1500

1750

Fig. 1: WIG20 and PX values (2004-2010) It can be seen that from Fig. 2 and Fig. 3 that return fluctuates around mean value that is close to zero. Volatility is low for certain time periods and high for other periods. The movements are in the positive and negative territory and larger fluctuations tend to cluster together separated by periods of relative calm. The volatility of PX and WIG20 indexes was highest in 2008.

5.1 The results of testing the efficient market hypothesis by linear methods The values of autocorrelation coefficients and the Box-Pierce test statistics were calculated for the first ten lags and selected results are presented in Table 1. Table 1 shows the value of first three order autocorrelation coefficients, the values of Q statistics and p-value, i.e. the level of significance to which the null hypothesis is rejected. The results of the Box-Pierce test show that in the case of PX index there was significant autocorrelation in both investigated periods, i.e. in the pre-crisis period and during the global financial crisis period as well. Moreover it can be argued that in period of financial crisis a significance of that correlation increased. In the case of the WIG20 index the results differ significantly. In both periods a statistically

PX_RETURN .15 .10 .05 .00 -.05 -.10 -.15 -.20 250

500

750

1000

1250

1500

1750

Fig. 2: PX returns (2004-2010)

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significant autocorrelation wasn´t observed at all, suggesting a lack of linear dependence in returns. lag PX_1 1 2 3 WIG20_1 1 2 3 PX_2 1 2 3 WIG20_2 1 2 3 Table 1: Results WIG20 returns

5.2 The results of testing the efficient market hypothesis by nonlinear methods The p-values of Engle´s test are shown in Table 3. Null hypothesis that returns are linear in the second moment, is clearly rejected in case of PX returns. The results of this test show that returns are not independent in the second moment.

Q-statistic p-value ρ 0,084 6,509 0,011 0,008 6,565 0,038 -0,027 7,239 0,065 0,030 0,847 0,357 0,021 1,256 0,534 -0,020 1,633 0,652 0,081 6,026 0,014 -0,092 13,705 0,001 -0,067 17,833 0,001 0,037 1,238 0,266 -0,073 6,158 0,056 0,016 6,359 0,095 of Box-Pierce test for PX and

Lags 1 2 3 PX_1 0,003 0,000 0,000 WIG20_1 0,525 0,197 0,088 PX_2 0,000 0,000 0,000 WIG20_2 0,031 0,0002 0,000 Table 3: Results of Engel´s ARCH test for WIG20 returns

0,000 0,092 0,000 0,000 PX and

In the case of WIG20 the results are again different. While in the pre-crises period there wasn´t confirmed a statistically significant dependence in the second order in the crisis period the dependence in the second moment was clearly confirmed. BDS test was performed for the investigated time series. There have been calculated z-statistics for embedding dimensions 2 and 5 and also respective p-values, on which the null hypothesis is rejected when returns are independent and equally distributed. The results are given in Table 4.

Overall, the behavior of the Polish stock market is significantly more efficient than in the case of Czech market, which was already inefficient in the pre-crisis period. Table 2 shows variance ratio, test statistics and p-values of all respective series. This test statistic has a normal distribution; the critical value for a 5% significance level is ±1,96. If the test statistic lies within the interval ( −1,96, 1,96 ) , we don´t reject a null hypothesis that daily returns are independent. Otherwise, the alternative hypothesis that daily returns are mutually dependent is confirmed.

embedding z-statistic p-value dimension PX_1 2 3,801 0,000 5 7,342 0,000 WIG20_1 2 0,086 0,931 5 0,586 0,558 PX_2 2 6,887 0,000 5 13,355 0,000 WIG20_2 2 2,859 0,004 5 8,876 0,000 Table 4: Results of BDS test for PX and WIG20 returns

p-value Variance ratio z-statistic PX_1 0,542 -7,039 0,000 WIG20_1 0,505 -10,893 0,000 PX_2 0,595 -5,341 0,000 WIG20_2 0,558 -9,809 0,000 Table 2: Results of Variance ratio test for PX and WIG20 returns In used variance ratio test we assumed heteroskedasticity in residuals which is less restrictive than the assumption of homoscedasticity in residual component. Sufficiently significant for rejecting random walk or martingale hypotheses is a fact that the proportion of variance is not equal to 1 at any time delay. The variance ratio test results are very clear and show that in all investigated series we cannot reject hypothesis that daily returns are mutually dependent.

ISBN: 978-1-61804-066-4

4

The results are similar to Engel’s test. While in the case of PX returns null hypothesis that returns are independent and equally distributed in both analyzed period was rejected a behavior of WIG20 series differs. In the pre-crisis period the null hypothesis wasn´t rejected at 5% significance level. In the crisis period was behavior of WIG20 returns similar to PX series.

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reject null hypothesis of efficiency in the pre-crisis period. Although in crisis period linear Box-Pierce test didn´t reject null hypothesis of efficiency on the other hand according the nonlinear methods we observed nonlinear dependency in returns of WIG20 series. When assessing the overall effectiveness of the Czech and Polish stock market, it is necessary to take into consideration that the above conclusions are verified by statistical tests, but it is also necessary to examine their economic significance, because the tests have not taken into account information and transaction costs. Moreover we have abstracted from risk premium. In the case of inefficiency is therefore possible to build a prediction model, which forecasts are more accurate than the predictions of random walk model.

6 Conclusion EMH is often associated with the idea of random walks, which is used in financial literature as a tool to describe the phenomenon where the future price changes are random deviations from past prices. Since arrival of new information is unpredictable, then price changes will also be unpredictable and random. As a consequence, prices fully and immediately reflect the price-fixing information; no investor can get above average yield, without himself taking on more risk. The form of this hypothesis is determined by the character set information available to the investor. Table 5 gives an overview of the results of testing the weak form of EMH of the Czech and Polish stock market in the period before and during the global financial crisis, with both linear and nonlinear methods.

References: [1] Box, G. E. P., Pierce, D., Distribution of Residual Autocorrelations in Autoregressive Moving Average Time Series Models, Journal of American Statistical Association, Vol. 65, 1970, pp. 1509-26. [2] Brock, W. A., Dechert, W. D., Scheikman, J. A., A Test for Independence Based on the Correlation Dimension, University of Wisconsin at Madison, University of Houston, University of Chicago, 1987.

PERIOD PERIOD (2004-2007) (2007-2010) PX WIG20 PX WIG20 BoxNot Not rejected rejected Pierce t. rejected rejected Variance rejected rejected ratio test

rejected rejected

Engel´s test

rejected rejected

rejected

Not rejected

Not rejected rejected rejected Table 5: Null hypothesis in relation to specific tests

[3] Engle, R. F., Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, Vol. 50, No. 4, 1982, pp. 987-1007.

BDS test rejected

The results of testing the efficiency of the Czech market have shown that if the weak form of EMH is being tested by linear methods we can reject it clearly in both testing periods. PX returns are not independent, and therefore shares do not follow a random walk or martingale. In addition to linear dependence, which was confirmed by the Box-Pierce test and variance ratio test, using nonlinear methods shows that there is relatively strong nonlinearity present in returns, which affects the behavior of returns over time, as well as the behavior of the variance in time. This finding implies that there may be linear or nonlinear model that using historical data can successfully describe the behavior of returns in the stock market and predict future returns from investing in shares on the Czech stock market at least for a relatively short time horizon. Testing the efficiency of Polish stock markets has given different results. Except from variance ratio test results all the tests show that we cannot

ISBN: 978-1-61804-066-4

[4] Fama, E. F., Efficient Capital Markets: A Review of Theory and Empirical Work, Journal of Finance, Vol. 25, 1970, pp. 383-417. [5] LeRoy, S. F., Risk Aversion and the Martingale Property of Stock Prices, International Economic Reviews, Vol. 14, No. 2, 1973, pp. 436-446. [6] Lo, A., Campbell, J. Y., Mackinlay, C. A., The Econometrics of Financial Markets, 2nd Ed. New York: Princeton University Press, 1997. [7] Malkiel, B., Efficient Market Hypothesis, New Palgrave Dictionary of Money and Finance. London: Macmillan. 1992. [8] Tran, V. Q., Testing the Weak Form of Efficiency on Czech Stock Market, Politická ekonomie, Vol. 6, 2007, pp. 751-772.

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