In nature, many simple objects interacting with each other can self-organize into behaviors that seem unexpectedly complex. A well-documented example is the stock market. The market’s emergent behavior results from the interactions among all participants with their very own incentives to be there, also playing very different roles. It is possible to identify indicators for nonlinearities in financial markets – characteristic of complex systems. For instance, we can see the autocatalytic behavior in how quickly panic can spread in market losses, that is when small perturbations can be strongly amplified due to its internal dynamic.
Another property observed in the stock market which makes it classified as a complex system is the absence of any equilibrium’ stable state.
One observation on the stock market‘s emergent properties is the disappearance of “anomalies,” demonstrating the concept of adaptative decision rules -Evolution-. Another observation is on feedback loops. For instance, some investors use “momentum” strategies, which use stock price changes as a buy/sell signal source, allowing the whole system to have a self-reinforcing behavior.
Initially, a set of predictors is assigned to each trader at random, along with a detailed history of stock prices, interest rates, and dividends. The traders then select one of their rules, based on its weight, and use it to start the buying-and-selling process. As a result of what happens in the first round of trading, the traders modify their collection of weighted rules, generate new rules (possibly), and then choose the best set of rules for the next round of trading. And so the process goes, period after period, buying, selling, placing money in bonds, modifying and generating rules, estimating how good the rules are, and, in general, acting analogously to traders in real financial markets.
Another emergent property occurring in financial markets arises from the collective behavior observed during typical and extreme market events. This is resulting from the interactions among the agents and the environment.
Typical and extreme days are different concerning the statistical properties of the ensemble return distribution. It is observed that, in addition to the first moment (mean return), higher-order moments (variance, skewness, and kurtosis) govern the shape of ensemble return distribution during extreme market events (rallies or crashes).
The change of shape of the ensemble return distribution is not fully arbitrary. Rather, it is possible to detect statistical regularities for extreme events occurring after a long time interval. The shape of the ensemble return distribution is found to be symmetrical o the normal trading day, while on extreme days, the distribution turns out to be skewed -asymmetrical-.
After many trading periods (and modification of the traders’ decision rules), what emerges is a kind of ecology of predictors, with different traders employing different practices to make their decisions. Furthermore, the stock price always settles down to a random fluctuation about its fundamental value. But within these fluctuations, price bubbles and crashes, psychological market “moods,” overreactions to price movements, and all the other things associated with speculative markets in the real world can be observed. In summary, every buying and selling transactions of equity create a series of complex possibilities.
Stylized facts (Empirical observations that are consistent and accepted as truths, to which theories must fit ) may be interpreted as emergent properties of a complex system – the Stock Market. They are:
- Absence of autocorrelation of asset returns.
- Slow decay of autocorrelation in absolute returns. A sig of Long-range dependence.
- Fat tails: Return distribution appears to display a power-law or Pareto-life tail with a tail index that is finite and greater than two (positive excess kurtosis).
- Excess Volatility: It is not easy to justify the observed level of volatility in asset returns by considering variations in the fundamental economic variables. The new information in the market cannot always explain both large positive ad negative returns.
- Volatility Clustering: It means that different volatility measures display a positive autocorrelation over periods of time, which indicates that high and low volatility events tend to cluster in time. In other words, periods of intense and mild fluctuations tend to cluster together.
- Volatility Persistence: It is also known as long memory. It represents the dependence between stock market returns at different times. Volatility has slowly decaying autocorrelation, and there is nonlinear dependence.
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