Mobile Edition
Print
Get the Mag
Weekly UpdatesAbstract The Warsaw Stock Exchange (WSE) has been operating in present form for 15 years. WSE is regarded as an "emerging market". We can observe that it is still developing (in order to become "developed market"). The level of development is often analyzed with reference to the efficiency of the market. We can say that the capital market is efficient if the prices at the market fully reflect all available information. The aim of the presented research is to analyze the current situation at the Warsaw Stock Exchange. Particularly we investigate the weak form of efficiency using selected statistical tests. The research is based on actual data concerning daily observations of shares at the Warsaw Stock Exchange transformed to the logarithmic rates of return, considering the period 2000-2006 and subperiods: the bear market, stagnation and the bull market.
Keywords Warsaw Stock Exchange * Weak form of capital market efficiency . Runs test * Variance ratio test
JEL C10 * G10
Introduction
The history of the capital market in Poland contains facts that have been collected for nearly 200 years. The new Warsaw Stock Exchange (WSE) started in 1991 and it has been developing rapidly ever since (Table 1).
The changes and activity of the stock exchange is described by market indexes. Stock indexes are composite index numbers that measure the relative changes in values of several variables, taken as a combination. According to the list of stocks that are taken for the index calculation, the certain index describes the situation of the whole capital market or the particular part of it. The Warsaw Stock Exchange publishes several market indexes. These indexes are:
* Evaluated for the economic branches: TechWIG (the price index of all companies from the segment for innovative technologies--SiTech), WIGbanking, WIGconstruction, WIGit, WIGmedia, WIGoil&gas, WIGfood and WIGtelecom are the total return indexes that contains all companies from the selected branches.
Since WSE seems to represent the developed capital market, it is necessary to introduce several changes into the market index calculations. Thus, starting on March 19, 2007 new stock indexes as well as the rules of calculation of the existing ones was introduced. Here the question arises how to recognize the developed market. In our research it is defined as efficient one.
The research on the stock securities has long history. The study of Bachelier (1900) is considered to be first pioneering contribution in this area. The next important step in examining the financial market was calling upon the Cowles Commission. Over 30 years later, E. Fama formulated EMH--Efficient Market Hypothesis (see Fama 1970, 1991) which was a summarization of ideas that the prices at the capital market fully reflect available information so that market could be called efficient (see i.e. Campbell et al. 1995, p. 20). Three forms of the capital market efficiency can be distinguished (Campbell et al. 1995, p. 22):
* Weak-Form Efficiency when prices reflect all information contained in past trading,
* Semistrong-Form Efficiency when prices reflect all publicly available information,
* Strong-Form Efficiency when prices reflect all relevant information including inside information.
Efficient Market Hypothesis implies that:
* a stock price is always at the fair level (fundamental value),
* a stock price reacts to news immediately
* a stock price changes only when the fair level changes
Therefore, stock price changes are unpredictable because no one knows tomorrow's news. In other words, one cannot forecast securities prices successfully using their historical values and one cannot have profits higher than average profits. This means that stock price can be defined as a random walk (RW) process.
In literature, three types of random walk processes are recognized. When it is assumed that increments of analyzed process are independently and identically distributed (IID), the process is RW1. Practically, this assumption is rarely fulfilled. Therefore, it can be assumed that random walk include processes with independent, but not identically, distributed (INID) increments (RW2). The most general version of random walk is the processes with dependent but uncorrelated increments that are called (RW3).
The efficiency of the Warsaw Stock Exchange was investigated, among others, by: Czekaj et al. (2001), Buczek (2005), Szyszka (2003), Papla (2001) Jajuga (2000).
In this paper, we investigate the Warsaw Stock Exchange efficiency in weak-form using the most popular tests: runs test and variance ratio test [Lo and MacKinlay 2002, Karemera et al. 1999, Smith and Ryoo 2003, Buguk and Brorsen 2003].
Data Description
During a trading session of The Warsaw Stock Exchange, data is available on line. Official trading results such as (1) open, close, maximal, minimal and average prices; (2) volume of transactions (number of shares) and (3) turnovers are published after the close of a trading session.
In our investigation we consider stock exchange indexes and share prices:
* WIG, WIG20 and MIDWIG--all in traditional composition and
* close prices of selected gold companies that composed index WIG20 in February 2007.
The WIG20 index is based on 20 gold companies from WSE (Table 2). This index is of particular significance to investors for two reasons. Firstly, it brings together the largest companies listed on the Warsaw Stock Exchange, which also generates the largest turnover during trading. Secondly, the WIG20 index is the underlying instrument for derivatives, which for several years has enjoyed great interest on the part of investors. We selected five securities that share an index that is more than 5% and have been quoted at WSE at least since January 2000. The five securities are PEKAO, TPSA, BPH, KGHM and ORLEN.
The research is based on actual data concerning daily observations of the quotations at the Warsaw Stock Exchange from January 2000 to December 2006. The original data of close share prices ([Y.sub.t]) are transformed into daily logarithmic rate of return ([y.sub.t]).
Methodology and Research Organization
The investigation is organized in several stages. At the beginning logarithmic rates of return are calculated:
[y.sub.t] = ln([Y.sub.t]/[Y.sub.t - 1]) (1)
where:
[y.sub.t] logarithmic daily rate of return (calculated for every day),
[Y.sub.t] close shares prices or values of indexes,
t the number of observations (t = 1, 2, ..., T).
The next step of the research is the statistical description of calculated rates of return. We employ such measures as: mean [bar.y], variance [S.sup.2] and standard deviation S, skewness measure (Dobosz 2004):
A = [T/[(T - 1) * (T - 2)]] * [[[T.summation over (t = 1)][([y.sub.t] - [bar.y]).sup.3]]/[S.sup.3]] (2)
* Standardized skewness measure:
SA = A[(6/T).sup.-[1/2]] (3)
* Kurtosis:
K = {[[T * (T + 1)]/[(T - 1) * (T - 2) * (T - 3)]] * [T.summation over (t = 1)][[([y.sub.t] - [bar.y]).sup.4]/[S.sup.4]]} - [[3 * [(T - 1).sup.2]]/[(T - 2) * (T - 3)]] (4)
* Standardized kurtosis:
SA = K * [(24/T).sup.-[1/2]] (5)
where:
[y.sub.t] is a rate of return calculated due to formula 1.
The third stage of the research is the hypothesis verification in order to find out if the expected value of the analyzed rates of return significantly differs from zero. Thus the null hypothesis is (Aczel 1989):
[H.sub.0]: E(y) = 0 (6)
and the test statistic is:
u = [[bar.y]/S][square root of T] (7)
Regardless, central tendency measures the hypotheses about variability measures. Differences of variance estimated for two populations are also verified. The null hypothesis is (Aczel 1989):
[H.sub.0]:[D.sup.2]([y.sub.1]) = [D.sup.2]([y.sub.2]) (8)
and the test statistics are as follows:
F = [[max([S.sub.1.sup.2];[S.sub.2.sup.2])]/[min([S.sub.1.sup.2];[S.sub.2.sup.2])]] = [[S.sub.1.sup.2]/[S.sub.2.sup.2]] (9)
The fifth step of the investigation is verification of the hypothesis about random changes of the securities (runs test). The null hypothesis [H.sub.0] says that the changes of securities prices are random, and the test statistics are as follows:
U = [[K - E([~.K])]/[S([~.K])]] (10)
where:
K count of empirical runs,
E(~.K) expected number of runs that could be estimated, when two series are defined, as follows:
E([~.K]) = [[2[n.sub.1][n.sub.2] + n]/n] (11)
or for three defined series, the expected value is given by the following formula:
E([~.K]) = n + 1 - [[[3.summation over (j = 1)][n.sub.j.sup.2]]/n] (12)
S (~.K) standard deviation of the number of runs, which for two series, is given by:
[S.sup.2]([~.K]) = [[2[n.sub.1][n.sub.2](2[n.sub.1][n.sub.2] - n)]/[(n - 1)[n.sup.2]]] (13)
and for three defined series, standard deviation is given by the following formula:
[S.sup.2]([~.K]) = [[[3.summation over (j = 1)][n.sub.j.sup.2]([3.summation over (j = 1)][n.sub.j.sup.2] + n + [n.sup.2]) - 2n[3.summation over (j = 1)][n.sub.j.sup.3] - [n.sup.3]]/[n([n.sup.2] - 1)]] (14)
The statistics U (10) is normally distributed (~N(0,1)). If the null hypothesis is rejected one can claim that the prices of securities do not change randomly; thus, this is evidence that the market is not efficient.
In the last stage of the investigation the variance ratio test was used. As it was mentioned, this test is the most popular test that is used for verification for the weak-form efficiency market hypothesis. Variance ratio test was proposed by Lo and MacKinlay (1988). The test based on the assumption that the variance of the increments in a random walk is linearly time-dependent. The null hypothesis claims that the series of securities follow random walk. Variance ratio statistics are evaluated as the following:
FEED