Price return autocorrelation and predictability in agent-based models of financial markets

Abstract

We demonstrate that minority mechanisms arise in the dynamics of markets because of price impact; accordingly the relative importance of minority and delayed majority mechanisms depends on the frequency of trading. We then use mixed majority/minority games to illustrate that a vanishing price return auto-correlation function does not necessarily imply market efficiency. On the contrary, we stress the difference between correlations measured conditionally and unconditionally on external patterns.Whether financial markets are predictable or not is a debate whose origin can be traced back to Bachelier's hypothesis that prices follow a random walk [1]. Later work, in particular by Fama [2] and Samuelson [3] aimed at proving mathematically that markets are efficient, i.e. unpredictable, grounding their theories on perfect rationality. This is indeed the simplest view of a financial market, and a very convenient one. There are however good reasons to believe that markets are not perfectly efficient. The well-known January effect is a systematic deviation from efficiency and has been observed in real markets for many years, but is reportedly disappearing; other examples include the predictive power of moving averages [4]. According to more recent theoretical studies, the cost of acquiring information [5] or the presence of noise traders [6] prohibits perfect efficiency, as perfect information can only be achieved at an infinite cost, or by accepting a considerable risk; this leads to the hypothesis of marginally efficient markets, where most of the easily detectable predictability is removed by traders.Market efficiency is often illustrated by the fact that the price return auto-correlation function is essentially zero. Denoting the log-price at time t by p(t), the price return is defined as r(t) = p(t + 1) − p(t), and assuming that r(t) is a stationary process, its auto-correlation readsHere · · · stands for averages over time; note that we normalise by the average magnitude of returns. The units of time are arbitrary in this paper. If C(τ ) = 0, statistically significant predictions of future price changes are possible on time-scales τ , that is, the knowledge of r(t) allows to make probabilistic statements about r(t + τ ). The analysis of real market data shows that C(τ ) ≈ 0 typically for τ larger than a few minutes [7,8,9]. However, the existing correlations on shorter time-scales are not exploitable in reality because of transaction costs [9]. This apparent efficiency however does not deter some practitioners from making statistically abnormal profits. In this paper we argue that the correlation function as defined in Eq. (1) is a poor measure of predictability. It is indeed an unconditional measure of correlation and does not differentiate between technical analysis patterns, states of the market or of the economy. Finding and exploiting relevant information patterns generates arbitrage opportunities. As a consequence, correlation functions conditional on these patterns have to be used.In the following we will...

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