A Broad-Spectrum Computational Approach for Market Efficiency

The Efficient Market Hypothesis (EMH) is one of the most investigated questions in Finance. Nevertheless, it is still a puzzle, despite the enormous amount of research it has provoked. For instance, it is still discussed that market cannot be outperformed in the long run (Detry and Gregoire, 2001), persistent market anomalies cannot be easily explained in this theoretical framework (Shiller, 2003) and some talented hedge-fund managers keep earning excess risk-adjusted rates of returns regularly. We concentrate in this paper on the weak form of efficiency(Fama, 1970). We focus on the efficacity of simple technical trading rules, following a large research stream presented in Park and Irwin (2004). Nevertheless, we depart from previous works in many ways : we first have a large population of technical investment rules (more than 260.000) exploiting real-world data to manage a financial portfolio. Very few researches have used such a large amount of calculus to examine the EMH. Our experimental design allows for strategy selection based on past absolute performance. We take into account the data-snooping risk, which is an unavoidable problem in such broad-spectrum researches, using a rigorous Bootstrap Reality Check procedure. While market inefficiencies, after including transaction costs, cannot clearly be successfully exploited, our experiments present troubling outcomes inviting close re-consideration of the weak-form EMH.efficient market hypothesis, large scale simulations, bootstrap

Estimating the Algorithmic Complexity of Stock Markets

Randomness and regularities in Finance are usually treated in probabilistic terms. In this paper, we develop a completely different approach in using a non-probabilistic framework based on the algorithmic information theory initially developed by Kolmogorov (1965). We present some elements of this theory and show why it is particularly relevant to Finance, and potentially to other sub-fields of Economics as well. We develop a generic method to estimate the Kolmogorov complexity of numeric series. This approach is based on an iterative "regularity erasing procedure" implemented to use lossless compression algorithms on financial data. Examples are provided with both simulated and real-world financial time series. The contributions of this article are twofold. The first one is methodological : we show that some structural regularities, invisible with classical statistical tests, can be detected by this algorithmic method. The second one consists in illustrations on the daily Dow-Jones Index suggesting that beyond several well-known regularities, hidden structure may in this index remain to be identified

Testing double auction as a component within a generic market model architecture

Since the first multi-agents based market simulations in the nineties, many different artificial stock market models have been developped. There are mainly used to reproduce and understand real markets statistical properties such as fat tails, volatility clustering and positive auto-correlation of absolute returns. Though they share common goals, these market models are most of the time different one from another: some are based on equations, others on complex microstructures, some are synchronous, others are asynchronous. It is hence hard to understand which characteristic of the market model used is at the origin of observed statistical properties. To investigate this question, we propose a generic model of artificial markets architecture which allows to freely compose modules coming from existing market models. To illustrate this formalism, we implement these components to propose a model of an asynchronous double auction based on an order-book and show that many stylized facts of real stock markets are reproduced with our model.multi-agent; orderbook; double auction; simulation; financial markets; stylized facts

Algorithmic Complexity of Financial Motions

We survey the main applications of algorithmic (Kolmogorov) complexity to the problem of price dynamics in financial markets. We stress the differences between these works and put forward a general algorithmic framework in order to highlight its potential for financial data analysis. This framework is “general" in the sense that it is not constructed on the common assumption that price variations are predominantly stochastic in nature.algorithmic information theory; Kolmogorov complexity; financial returns; market efficiency; compression algorithms; information theory; randomness; price movements; algorithmic probability

Portfolio Performance Gauging in Discrete Time Using a Luenberger Productivity Indicator

This paper proposes a pragmatic, discrete time indicator to gauge the performance of portfolios over time. Integrating the shortage function (Luenberger, 1995) into a Luenberger portfolio productivity indicator (Chambers, 2002), this study estimates the changes in the relative positions of portfolios with respect to the traditional Markowitz mean-variance efficient frontier, as well as the eventual shifts of this frontier over time. Based on the analysis of local changes relative to these mean-variance and higher moment (in casu, mean-variance-skewness) frontiers, this methodology allows to neatly separate between on the one hand performance changes due to portfolio strategies and on the other hand performance changes due to the market evolution. This methodology is empirically illustrated using a mimicking portfolio approach (Fama and French 1996; 1997) using US monthly data from January 1931 to August 2007.shortage function, mean-variance, mean-variance-skewness, efficient portfolios, Luenberger portfolio productivity indicator

Insider trading, imitative behaviour and price formulation in a stimulated double-auction stock market

This paper presents the results of a series of experiments in a simulated double-auction stock market. Price formation was observed under various manipulations of asymmetric information and communication, including conditions intended to promote imitative behaviour and rumour. Inefficient prices were observed when the presence of insiders was completely disguised – that is, prices reflected the expectations of non-insiders. When the presence (but not the identity) of insiders was revealed there was a sharp increase in imitative behaviour that appeared to be one-sided – observed prices became efficient with respect to bad news but not with respect to good news. When subjects were allowed to communicate uncertain information to create a climate of rumour (they could lie, tell the truth and/or spread rumours but were forbidden to prove the veracity of any communication) there was a decrease in both efficiency and price volatility – that is, informational noise appeared to mask the signals of insiders. Price formation under these conditions was similar to the homogeneous expectations baseline, but there was also some evidence of speculative pricing

Testing double auction as a component within a generic market model architecture

Since the first multi-agents based market simulations in the nineties, many different artificial stock market models have been developped. There are mainly used to reproduce and understand real markets statistical properties such as fat tails, volatility clustering and positive auto-correlation of absolute returns. Though they share common goals, these market models are most of the time different one from another: some are based on equations, others on complex microstructures, some are synchronous, others are asynchronous. It is hence hard to understand which characteristic of the market model used is at the origin of observed statistical properties. To investigate this question, we propose a generic model of artificial markets architecture which allows to freely compose modules coming from existing market models. To illustrate this formalism, we implement these components to propose a model of an asynchronous double auction based on an order-book and show that many stylized facts of real stock markets are reproduced with our model