Properties of returns r(Δt) defined as changes in a price p(t) of some financial asset over a time interval Δt, have been carefully studied by econophysicists for the last decade, see [1-3] for introduction and bibliography. The basic effort of investigations is aimed on the identification of some universal features in a time series of a financial asset hoping that these features may give us a better understanding of the underlying mechanism that drives the dynamics of the stock market. The main features that have been found are:
(i) an absence of short time correlation in a series of returns and a persistence of correlation when a series of absolute value of returns is investigated,
(ii) the wings of distributions of returns are characterized by the power law decay with the exponent value about 3. The listed properties are called stylized-facts because they are present independently of the kind of the financial asset: stock, money or derivative, and independently of the geographic location of a market: Tokyo, New York or London.
However, in the studies of Polish stock market (WSE) a local, emergent and inefficient market, we have found at least four characteristics that are different from the ones described above:
(A) The wings of distributions of returns decay faster. The exponent value of this decay is about 4, [4]
(B) The nonlinear short-time correlation in daily returns investigated by Artificial Insymmetrized Patterns (AIP in short) indicates at the Gaussian origin of the noise while the series from the mature markets exhibit self-similarity to the Levy noise [5]. Moreover, we show that the present state of this market in the AIP presentation is completely different from famous markets.
(C) The Polish market crash in April 2000 can be named the anti-bubble crash. Before that crash the Polish stock market had been a growing market since the Russian crash which happened in August of 1998. However, in contrast to the before-crash ordinary log-periodic price development, see [6], the price of Polish stocks developed in the log-periodic style as the market would suffer from the Russian crash. That is, the log-periodic oscillations were initiated by the Russian crash. This price dependence ended with the New Technology crash in April 2000. Such the after-crash behavior observed before the crash is called the anti-bubble crash, [7].
(D) The deficit in small returns is noticable. It appears that the zero-return peaks are accompanied with valleys on the left always and sometimes on the right side. This feature is observed not only in stocks of companies with low capital and low liquidity or on the verge of bankruptcy; the returns of liquid stocks from the top of the volume also exhibit the described property, [8].
On poorly developed markets, such as emergent and local markets, the investors deal with assets of little liquidity. For example, on Polish stock market the majority of stocks (about 2/3 out of 235) are with less than 20 transactions per session (data from 2002 [9]). In addition, the investors meet in their activity a strong political interference.
As the result, the investors could decide to:
- follow the leader: identify a "well-informed" agent: the leader, and form a team with the leader. If it is impossible then observe the leader deccisions to copy them as fast as it is possible, [10].
- follow the trend: the present decission of an investor is strongly conditioned by the last time step price change,[11]
In both models the synchronized decisions of many investors effect in a noticeable deficit in small returns. To our study purpose we choose the model of Cont and Bouchaud [12] modified to a lattice version by Stauffer et al. [13]. The intentional imitation mechanism can be easily applied to other market models as, for example, Lux-Marchesi [14] or Levy-Levy-Solomon [15]
Acknowledgement:
This work is supported by Gdansk University Project: BW/5400-5-0256-4
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