Hypothesis testing of Slovak capital market efficiency.

Transcription

1 Hypothesis testing of Slovak capital market efficiency. Mária Kanderová Jaroslav Barochovský - Abstract Contribution discusses the Slovak capital market efficiency topic. We tried to find out, whether Slovak capital market verifies assumptions of efficiency market, where we focused on testing of weak efficiency form. While testing Slovak capital market efficiency we came out from daily development of SAX index. To verify efficiency assumptions we used Dickey-Fuller test and correlation tests. Key words Efficiency Market Hypothesis, Random Walk Model, stationarity of profits, Dickey-Fuller test, Jarque Bera test. Introduction Theory of market efficiency considers the question, whether market prices fluctuate randomly, or their movements could be define by deterministic behavior forms. Market efficiency is condition of market, when all available information are included in market prices. As effective market, we can consider capital market, which is able to absorb all new information very quickly. Afterwards market price of stocks constitutes objective value. There are no overvalued or undervalued stocks on the market. Basic and primary hypothesis about capital market behavior is efficient markets hypothesis. Efficient market hypothesis assumes, that stock prices always and fully reflect expectations and information of all market participants whereupon stock prices are unpredictable. Market is efficient on the information set exactly at that time, if there is no way to gain abnormal profit using these information for making dealing decisions. According to types of information theory distinguish three forms of capital market efficiency. Weak form of efficiency Market is efficient in weak form, if market prices contain all information which are included in historical prices. It follows, that historical prices provide no information about future prices development, what imply uselessness of technical analyses on efficient markets. In the case of weak form efficiency price changes meet the terms of random walk model. Semi-strong form of efficiency Market is efficient in semi-strong form, if market prices contain all public available information. Market prices can adapt to new market information very quickly. Consequence of semi-strong form efficiency is impossibility of exploitation of the public available information to gain the profit. If the market is semi-strong effective, it is also weak effective, because historical prices are subset of all public available information. How close is the market to semi-strong efficiency, depends on ability to adapt to new market information and on the level of market competition. It is assumed, that different stocks have different level of efficiency depending on size of company. Stocks of small companies absorb information with lag in comparison with bigger companies. Strong form of efficiency Market is efficient in strong form, if market prices reflect all known and useful information including insider information. Consequence of this, investments can t reach above average profit neither using insider trading information. Results of tests show, that neither capital markets of economically advanced countries are not strongly efficient.

2 Methods and data Model, which is joined with theory of market efficiency, is known as Martingale. This model comes out from the definition of Fair Game. Stock market is the fair game, when systematic difference between real and expected profit doesn t exist. The main in term of Martingale model creation implies, that if P t is stock price in time t, then the best estimation of future stock price in time t+1 is price in time t, subject to all historical prices of this stock are known. If we consider stock price time series as discrete stochastic process {P t }, then martingale we can formulate as follows: or E[P t+1 P t, P t-1, P t-2, P 1 ] = P t, (1) E[P t+1 - P t P t, P t-1, P t-2, P 1 ] = 0. (2) Martingale model assumes, that nonoverlap price changes are linear independent in all time lags. In the past Martingale was considered as necessary assumption of efficient capital market. Martingale turned out to be only sufficient condition, because we can meet with nonzero correlation between present and prior prices or profits also on standard and effective capital markets. This fact could be explained by institutional market s factors as transactional costs or stock-exchange rules, which limit trading. It is assumed, that stocks of small companies, which are trading in lower volumes, absorb market information in delay comparing to bigger companies stocks. Those are trading in higher volumes, what can lead to nonzero autocorrelation of present and prior values of stock-exchange indexes, which involve both types of these stocks. These facts lead to creation of new model, which describes effective behavior of capital market Random walk model. [Diviš, 2004]. Random walk process is formulated as follows: X t = X t-1 + ε t (3) Where for ε t holds: E[ε t ] = 0, E[ε t, ε t-k ] = 0, where k 0 (4) E[ε t, ε t-k ] = σ 2, where k 0. P-P t t-1 Pt Let profit be defined as: r t = ln = lnp - lnp Pt Pt-1 t t-1 Then Random walk model (3) in logarithmic form could be formulated as follows: = lnp t. (5) lnp t = lnp t-1 + ε t. (6) From formula (6) results, that r t = ε t and in according to (4) profits are created by accumulated random errors, which are independent each other, normally distributed with zero mean and σ 2 dispersion. Formula (6) shows, that the best estimation of price in time t+1 is the price in time t. Random walk process is integrated process and if stock prices lnp t, meet random walk model, then profits lnp t make integrated process of zero level I(0), let us say stock prices lnp t make integrated process of the first level I(1). Stationarity of the ln stock market prices time series (SAX) we will test by ADF test of unit roots. (Augmented Dickey Fuller test). Testing statistics of this stationarity test can be written as [Gavliak, 2005]: where P t stock price difference (index SAX) in time t, P lagged difference - k periods, t k m Pt t Pt k P t k t k = 1 ln = β + β + δ ln + γ ln + ε, (7)

3 β1, β 2 parameters of constant and deterministic trend. It holds, that time series in non-stationary if δ = 0. We are testing the following hypothesis that: H : δ = 0 0 H : δ < 0 1 Consequently, applying ADF test we can include constants, deterministic trend and time lagged differences into the test statistic. Fundamental rule recommends includuing additional lagged differences until elimination of residual autocorrelation (7). If we reject non-stationarity profits hypothesis, we will test, if profits are not correlated. Next we will test normality distribution of profits using Jarque Bera test, which compares kurtosis and skewness of analyzed time series with kurtosis and skewness of normal distributed time series. The instruments variable set contains daily values of SAX index (SAX), logarithmic values of SAX index (LNSAX) and profits of SAX index (DLNSAX). Empirical results Slovak capital market belongs to less developed capital markets and therefore we focused on testing of weak form market efficiency. We tested efficiency of Slovak capital market using Slovak stock index SAX, which is official index of BCPB. Time series contain daily values of SAX index in period since until SAX is performance index, which shows global change of wealth resulting from stocks investments included in SAX. SAX index is capital weighted index it compares market capitalization of set of stocks with market capitalization of the same set of stocks in reference day. No investment funds are included in basis of SAX index, because price changes of basis issues are already involved in prices. Issues included in basis of SAX index are weighted according to their market value. Index value is calculated as follows: act P i Gi i SAX act = 100, r P G F i i i i where F i correction factor, P i act close price of i share in specific day, P i r close price of i share in reference day. Formula of SAX index is flexible and allows changing the number included stocks of particular companies according to their trading volumes. (8) 600 Chart 1 : SAX index development SAX

4 On the basis of this chart is obvious that development of the SAX index is non-stationary and variability of values is higher especially at the end of the time series..12 Chart 2: Development of SAX index profits DLNSAX Figure 1: Standard Descriptive Statistics and Histogram of profits Series: DLNSAX Sample 7/26/1995 1/27/2005 Observations Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability On Figure 1 we can see, that distribution of profit values of SAX index are skewed and kurtosis compared to normal distribution. Jarque Bera test rejected hypothesis about profits normality distribution. Stationarity of SAX index profits was tested by Augmented Dickey-Fuller test. We estimated the model based on regression stated in (7). Results are depicted in Figure 2. Figure 2: ADF test of stationarity: the logarithm of stock market prices of SAX time series

5 Figure 2 shows, that on all levels of confidence we can t reject H 0 about nonstationarity of logarithmic prices of SAX index time series. However, on all significance levels we reject H 0 about nonstationarity of first difference of logarithmic prices. Applied statistics includes constant unit and also deterministic trend. However, inclusion of constant unit and deterministic trend was not critical for final result. ADF test rejected hypothesis about nonstationarity of profits and this result is in accordance with weak form efficiency. We also tested, if particular profits are not correlated. We calculated coefficients of autocorrelation and partial autocorrelation for 10 lagged profits. We used Ljunq-Box Q statistics for testing. The Q-statistics at lag k is the test statistics for the null hypothesis that there is no autocorrelation up to order k. Statistical significance of profits autocorrelation was not proved. Testing results of Slovak capital market efficiency leads to rejection of hypothesis about Slovak capital market inefficiency. Table 1: Autocorrelation analyses lag AC PAC Q-Stat Prob Chart 3: Correlogram ,06-0,04-0,02 0,00 0,02 0,04 0,06 Conclusion Market liquidity, market environment with a lot of investors and reachable information belong to basic assumptions of efficient market. Liquidity was biggest problem of Slovak capital market. Only 5 to 10 stocks are really trading, rest of the market is illiquid. Low liquidity has negative effects on potential investors, which move their money into foreign markets due to mentioned reasons. Turnover of the Slovak capital market is one of the lowest in Europe. Another problem of Slovak market is low transparency. Majority of transactions was negotiated directly between business partners, without generating objective price on the market. Typical is also information asymmetry among particular investors. Mentioned facts lead to results, that Slovak capital markets doesn t meet assumptions of effective capital market. Results of statistical tests lead to contradictory deduction. According to them Slovak capital market satisfies assumptions of weak form efficiency. This result is caused by lack of investors interest for Slovak stocks because of its low liquidity and lack of available information. Prices of stock are stagnate and therefore it looks like profits of SAX index meet Random walk model. References [1] Artl, J.- Antlová, M.: Finanční časové rady. GRADA, Praha 2003 [2] Blake, D. : Analýza finančných trhů. GRADA, Praha, [3] Brealey, R. A. Myers, J. C.: Teórie a praxe firemných financí. East Publishing, Praha [4] Diviš, K.-Teplý,P.: Informační efektívnost burzovních trhů v střední Evropě. In: Working papaer UK FSV IES, No. 52, Praha [5] Filáček,J.-Kapička,M.- Vošvrda, M.: Testování hypotézy efektívního trhu na BCPP. In: Finance a úvěr, roč. 48, č. 9, 1998.s

6 [6] Gavliak, R. Hrudkay, M. Možnosti modelovania volatility v podmienkach SR. In: Evropské finanční systémy Zborník príspevkov z medzinárodnej vedeckej konferencie. Brno : ESF MU, 2005, s [7] Gavliak, R. Úradníček, V. Zimková, E. Testovanie kointegrácie nestacionárnych časových radov. In: Forum Statisticum Slovacum 1/2005. Bratislava : SŠDS, 2005, s [8] Chocholatá, M. : Analýza denných hodnôt výmenných kurzov národných mien krajín V4 voči euru. In: Forum Statisticum Slovacum 2/2006. Bratislava : SŠDS, 2006, s [9] Musílek, P.: Trhy cenných papíru. EKOPRESS, Praha 2002 [10] Príhodová I.: Nelineárne modely Slovenského akciového indexu SAX. In: Forum Statisticum Slovacum 2/2006. Bratislava : SŠDS, 2006, s Mária Kanderová Faculty of Economics Matei Bel University Banská Bystrica Department of Quantitative Methods and Informatics Tajovského Street Banská Bystrica Slovak Republic maria.kanderova@umb.sk Jaroslav Barochovský Faculty of Economics Matei Bel University Banská Bystrica Department of Quantitative Methods and Informatics Tajovského Street Banská Bystrica Slovak Republic jaroslav. barochovsky@umb.sk