The long memory of the efficient market

For the London Stock Exchange we demonstrate that the signs of orders obey a long-memory process. The autocorrelation function decays roughly as $\tau^{-\alpha}$ with $\alpha \approx 0.6$, corresponding to a Hurst exponent $H \approx 0.7$. This implies that the signs of future orders are quite predictable from the signs of past orders; all else being equal, this would suggest a very strong market inefficiency. We demonstrate, however, that fluctuations in order signs are compensated for by anti-correlated fluctuations in transaction size and liquidity, which are also long-memory processes. This tends to make the returns whiter. We show that some institutions display long-range memory and others don't.Comment: 19 pages, 12 figure

How markets slowly digest changes in supply and demand

In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly incorporated into prices. Because revealed market liquidity is extremely low, large orders to buy or sell can only be traded incrementally, over periods of time as long as months. As a result order flow is a highly persistent long-memory process. Maintaining compatibility with market efficiency has profound consequences on price formation, on the dynamics of liquidity, and on the nature of impact. We review a body of theory that makes detailed quantitative predictions about the volume and time dependence of market impact, the bid-ask spread, order book dynamics, and volatility. Comparisons to data yield some encouraging successes. This framework suggests a novel interpretation of financial information, in which agents are at best only weakly informed and all have a similar and extremely noisy impact on prices. Most of the processed information appears to come from supply and demand itself, rather than from external news. The ideas reviewed here are relevant to market microstructure regulation, agent-based models, cost-optimal execution strategies, and understanding market ecologies.Comment: 111 pages, 24 figure

The adaptive nature of liquidity taking in limit order books

In financial markets, the order flow, defined as the process assuming value one for buy market orders and minus one for sell market orders, displays a very slowly decaying autocorrelation function. Since orders impact prices, reconciling the persistence of the order flow with market efficiency is a subtle issue. A possible solution is provided by asymmetric liquidity, which states that the impact of a buy or sell order is inversely related to the probability of its occurrence. We empirically find that when the order flow predictability increases in one direction, the liquidity in the opposite side decreases, but the probability that a trade moves the price decreases significantly. While the last mechanism is able to counterbalance the persistence of order flow and restore efficiency and diffusivity, the first acts in opposite direction. We introduce a statistical order book model where the persistence of the order flow is mitigated by adjusting the market order volume to the predictability of the order flow. The model reproduces the diffusive behaviour of prices at all time scales without fine-tuning the values of parameters, as well as the behaviour of most order book quantities as a function of the local predictability of order flow.Comment: 40 pages, 14 figures, and 2 tables; old figure 12 removed. Accepted for publication on JSTA

A piecewise linear model for trade sign inference

We use transaction level data for twelve stocks with large market capitalization on the Australian Stock Exchange to develop an empirical model for trade sign (trade initiator) inference. The new model is a piecewise linear parameterization of the model proposed recently in Ref. [1]. The space of the predictor variables is partitioned into six regions. Signs of individual trades within the regions are inferred according to simple and interpretable rules. Across the 12 stocks the new model achieves an average out-of-sample classification accuracy of 74.38% (SD=4.25%), which is 2.98% above the corresponding accuracy reported in Ref. [1]. Two of the model's regions, together accounting for 16.79% of the total number of daily trades, have each an average classification accuracy exceeding 91.50%. The results indicate a strong dependence between the predictor variables and the trade sign, and provide evidence for an endogenous component in the order flow. An interpretation of the trade sign classification accuracy within the model's regions offers new insights into a relationship between two regularities observed in the markets with a limit order book, competition for order execution and transaction cost minimization.Order submission, Trade classification, Piecewise linear, Competition for order execution, Transaction cost minimization

Heterogeneous Agents Models: two simple examples, forthcoming In: Lines, M. (ed.) Nonlinear Dynamical Systems in Economics, CISM Courses and Lectures, Springer, 2005, pp.131-164.

These notes review two simple heterogeneous agent models in economics and finance. The first is a cobweb model with rational versus naive agents introduced in Brock and Hommes (1997). The second is an asset pricing model with fundamentalists versus technical traders introduced in Brock and Hommes (1998). Agents are boundedly rational and switch between different trading strategies, based upon an evolutionary fitness measure given by realized past profits. Evolutionary switching creates a nonlinearity in the dynamics. Rational routes to randomness, that is, bifurcation routes to complicated dynamical behaviour occur when agents become more sensitive to differences in evolutionary fitness.