CHALLET Damien

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We apply the knockoff procedure to factor selection in finance. By building fake but realistic factors, this procedure makes it possible to control the fraction of false discovery in a given set of factors. To show its versatility, we apply it to fund replication and to the inference of explanatory and prediction networks.

Cleaning covariance matrices is a highly non-trivial problem, yet of central importance in the statistical inference of dependence between objects. We propose here a probabilistic hierarchical clustering method, named Bootstrapped Average Hierarchical Clustering (BAHC) that is particularly effective in the high-dimensional case, i.e., when there are more objects than features. When applied to DNA microarray, our method yields distinct hierarchical structures that cannot be accounted for by usual hierarchical clustering. We then use global minimum-variance risk management to test our method and find that BAHC leads to significantly smaller realized risk compared to state-of-the-art linear and nonlinear filtering methods in the high-dimensional case. Spectral decomposition shows that BAHC better captures the persistence of the dependence structure between asset price returns in the calibration and the test periods.

We propose a novel deep learning architecture suitable for the prediction of investor interest for a given asset in a given timeframe. This architecture performs both investor clustering and modelling at the same time. We first verify its superior performance on a simulated scenario inspired by real data and then apply it to a large proprietary database from BNP Paribas Corporate and Institutional Banking.

Recent empirical analyses have revealed the existence of the Zumbach effect. This discovery led to the development of the quadratic Hawkes process, adapted to reproduce this effect. Since this model does not relate to the price formation process, we extended it to the order book with a generalized quadratic Hawkes process (GQ-Hawkes). Using market data, we show that there is a Zumbach-like effect that decreases future liquidity. Microfounding the Zumbach effect, it is responsible for a potential destabilization of financial markets. Moreover, the exact calibration of a QM-Hawkes process tells us that markets are at the edge of criticality. This empirical evidence has therefore prompted us to analyze an order book model constructed with a Zumbach-type coupling. We therefore introduced the Santa Fe quadratic model and proved numerically that there is a phase transition between a stable market and an unstable market subject to liquidity crises. Thanks to a finite size analysis we were able to determine the critical exponents of this transition, belonging to a new universality class. Not being analytically solvable, this led us to introduce simpler models to describe liquidity crises. Putting aside the microstructure of the order book, we obtain a class of spread models where we have computed the critical parameters of their transitions. Even if these exponents are not those of the Santa Fe quadratic transition, these models open new horizons to explore the spread dynamics. One of them has a nonlinear coupling that reveals a metastable state. This elegant alternative scenario does not need critical parameters to obtain an unstable market, even if the empirical evidence is not in its favor. Finally, we looked at order book dynamics from another angle: reaction-diffusion. We modeled a liquidity that reveals itself in the order book with a certain frequency. Solving this model in equilibrium reveals that there is a stability condition on the parameters beyond which the order book empties completely, corresponding to a liquidity crisis. By calibrating it on market data, we were able to qualitatively analyze the distance to this unstable region.

The main objective of this thesis is to understand the various aspects of market impact. It consists of four chapters in which market impact is studied in different contexts and at different scales. The first chapter presents an empirical study of the market impact of limit orders in European equity markets. In the second chapter, we have extended the methodology presented for the equity markets to the options markets. This empirical study has shown that our definition of an options meta-order allows us to recover all the results highlighted in the equity markets. The third chapter focuses on market impact in the context of derivatives valuation. This chapter attempts to bring a microstructure component to the valuation of options by proposing a theory of market impact disturbances during the re-hedging process. In the fourth chapter, we explore a fairly simple model for metaorder relaxation. Metaorder relaxation is treated in this section as an informational process that is transmitted to the market. Thus, starting from the point of departure that at the end of the execution of a meta-order the information carried by it is maximal, we propose an interpretation of the relaxation phenomenon as being the result of the degradation of this information at the expense of the external noise of the market.

Anticipating client needs is crucial for any company - this is especially true for investment banks such as BNP Paribas Corporate and Institutional Banking given their role in the financial markets. This thesis focuses on the problem of predicting future customer interests in the financial markets, with a particular emphasis on the development of ad hoc algorithms designed to solve specific problems in the financial world.This manuscript consists of five chapters, divided as follows:- Chapter 1 presents the problem of predicting future customer interests in the financial markets. The purpose of this chapter is to provide the reader with all the keys necessary for a good understanding of the rest of this thesis. These keys are divided into three parts: a highlighting of the datasets available to us for solving the future interest prediction problem and their characteristics, a non-exhaustive overview of the algorithms that can be used to solve this problem, and the development of metrics to evaluate the performance of these algorithms on our datasets. This chapter closes with the challenges that can be encountered when designing algorithms to solve the problem of predicting future interests in finance, challenges that will be, in part, solved in the following chapters: - Chapter 2 compares some of the algorithms introduced in Chapter 1 on a dataset from BNP Paribas CIB, and highlights the difficulties encountered when comparing algorithms of different nature on the same dataset, as well as some ways to overcome these difficulties. This comparison puts into practice classical recommendation algorithms only considered from a theoretical point of view in the previous chapter, and allows us to acquire a more detailed understanding of the different metrics introduced in chapter 1 through the analysis of the results of these algorithms. Chapter 3 introduces a new algorithm, Experts Network, i.e., a network of experts, designed to solve the problem of heterogeneous behavior of investors in a given market through an original neural network architecture, inspired by research on expert mixtures. In this chapter, this new methodology is used on three distinct datasets: a synthetic dataset, an open access dataset, and a dataset from BNP Paribas CIB. Chapter 4 also introduces a new algorithm, called History-augmented collaborative filtering, which proposes to augment the classical matrix factorization approaches with the help of the interaction histories of the considered customers and products. This chapter continues the study of the dataset studied in Chapter 2 and extends the introduced algorithm with many ideas. Specifically, this chapter adapts the algorithm to address the cold start problem, i.e., the inability of a recommender system to provide predictions for new users, as well as a new application case on which this adaptation is tried.- Chapter 5 highlights a collection of ideas and algorithms, both successful and unsuccessful, that have been tried in the course of this thesis. This chapter closes with a new algorithm combining the ideas of the algorithms introduced in chapters 3 and 4.

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We introduce a $k$-fold boosted version of our Boostrapped Average Hierarchical Clustering cleaning procedure for correlation and covariance matrices. We then apply this method to global minimum variance portfolios for various values of $k$ and compare their performance with other state-of-the-art methods. Generally, we find that our method yields better Sharpe ratios after transaction costs than competing filtering methods, despite requiring a larger turnover.

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Cleaning covariance matrices is a highly non-trivial problem, yet of central importance in the statistical inference of dependence between objects. We propose here a probabilistic hierarchical clustering method, named Bootstrapped Average Hierarchical Clustering (BAHC) that is particularly effective in the high-dimensional case, i.e., when there are more objects than features. When applied to DNA microarray, our method yields distinct hierarchical structures that cannot be accounted for by usual hierarchical clustering. We then use global minimum-variance risk management to test our method and find that BAHC leads to significantly smaller realized risk compared to state-of-the-art linear and nonlinear filtering methods in the high-dimensional case. Spectral decomposition shows that BAHC better captures the persistence of the dependence structure between asset price returns in the calibration and the test periods.

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We report statistical regularities of the opening and closing auctions of French equities, focusing on the diffusive properties of the indicative auction price. Two mechanisms are at play as the auction end time nears: the typical price change magnitude decreases, favoring underdiffusion, while the rate of these events increases, potentially leading to overdiffusion. A third mechanism, caused by the strategic behavior of traders, is needed to produce nearly diffusive prices: waiting to submit buy orders until sell orders have decreased the indicative price and vice-versa.

We introduce a simplified version (STvL) of the Talent versus Luck (TvL) model where only lucky events are present and verify that its dynamical rules lead to the same very large wealth inequality as the original model. We also derive some analytical approximations aimed to capture the mechanism responsible for the creation of such wealth inequality from a Gaussian-distributed talent. Under these approximations, our analysis is able to reproduce quite well the results of the numerical simulations of the simplified model. On the other hand, it also shows that the complexity of the model lies in the stochastic transformation of lucky events into an increase of capital, so that, when the talent heterogeneity of the population increases, the task of finding a formal analytical relationship between the distributions of capital, talent and luck in either the TvL or the STvL models becomes very hard.

We propose a novel deep learning architecture suitable for the prediction of investor interest for a given asset in a given timeframe. This architecture performs both investor clustering and modelling at the same time. We first verify its superior performance on a simulated scenario inspired by real data and then apply it to a large proprietary database from BNP Paribas Corporate and Institutional Banking.

Using more than 6.7 billions of trades, we explore how the tick-by-tick dynamics of limit order books depends on the aggregate actions of large investment funds on a much larger (quarterly) timescale. In particular, we find that the well-established long memory of market order signs is markedly weaker when large investment funds trade either in a directional way and even weaker when their aggregate participation ratio is large. Conversely, we investigate to what respect a weaker memory of market order signs predicts that an asset is being actively traded by large funds. Theoretical arguments suggest two simple mechanisms that contribute to the observed effect: a larger number of active meta-orders and a modification of the distribution of size of meta-orders. Empirical evidence suggests that the number of active meta-orders is the most important contributor to the loss of market order sign memory.

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We first investigate static properties of opening and closing auctions such as typical auction volume relative to daily volume and order value distributions. We then show that the indicative match price is strongly mean-reverting because the imbalance is, which we link to strategic behavior. Finally, we investigate how the final auction price reacts to order placement, especially conditional on imbalance improving or worsening events and find a large difference between the opening and closing auctions, emphasizing the role of liquidity and simultaneous trading in the pre-open or open-market order book.

We introduce a method to predict which correlation matrix coefficients are likely to change their signs in the future in the high-dimensional regime, i.e. when the number of features is larger than the number of samples per feature. The stability of correlation signs, two-by-two relationships, is found to depend on three-by-three relationships inspired by Heider social cohesion theory in this regime. We apply our method to US and Hong Kong equities historical data to illustrate how the structure of correlation matrices influences the stability of the sign of its coefficients .

This thesis is composed of four chapters.The first chapter is a preliminary description of the Factset Ownership database. The first chapter is a preliminary description of the Factset Ownership database. We give a statistical description of the database and present some stylized facts characterizing the portfolio structure of financial institutions and investment funds, as well as the market capitalization of the companies listed in the database.The second chapter proposes a method for statistically evaluating the similarity between pairs of financial institutions' portfolios. The second chapter proposes a method to statistically evaluate the similarity between pairs of portfolios of financial institutions. Since a statistically significant pair leads to the creation of a similarity link between these two entities, we are able to project an originally bi-partite network (between financial institutions and firms) into a mono-partite network (between institutions only) in order to study the evolution of its structure over time. Indeed, from an economic point of view, it is suspected that similar investment motives constitute an important risk factor of financial contagion that can be at the origin of bankruptcies with significant systemic consequences.The third chapter focuses on the collective behavior of investment fund managers and, in particular, on the way in which the structure of the portfolio of these funds optimally takes into account, on average, transaction costs in the presence of weak investment constraints. This phenomenon, where in many situations the median or average of a group of people's estimates is surprisingly close to the true value, is known as the wisdom of the crowd.The fourth chapter is devoted to the simultaneous study of market data. We use over 6.7 billion trades from the Thomson-Reuters Tick History database, and portfolio data from the FactSet Ownership database. We study the tick-to-tick dynamics of the order book as well as the aggregate action, i.e. on a much larger time scale, of investment funds. In particular, we show that the long memory of the sign of market orders is much shorter in the presence of the action, absolute or directional, of investment funds. Conversely, we explain to what extent a stock characterized by a weak memory is subject to directional trading due to the action of investment funds.

We introduce a framework to infer lead-lag networks between the states of elements of complex systems, determined at different timescales. As such networks encode the causal structure of a system, infering lead-lag networks for many pairs of timescales provides a global picture of the mutual influence between timescales. We apply our method to two trader-resolved FX data sets and document strong and complex asymmetric influence of timescales on the structure of lead-lag networks. Expectedly, this asymmetry extends to trader activity: for institutional clients in our dataset, past activity on timescales longer than 3 hours is more correlated with future activity at shorter timescales than the opposite (Zumbach effect), while a reverse Zumbach effect is found for past timescales shorter than 3 hours. retail clients have a totally different, and much more intricate, structure of asymmetric timescale influence. The causality structures are clearly caused by markedly different behaviors of the two types of traders. Hence, market nano-structure, i.e., market dynamics at the individual trader level, provides an unprecedented insight into the causality structure of financial markets, which is much more complex than previously thought.

We introduce a method to infer lead-lag networks of agents’ actions in complex systems. These networks open the way to both microscopic and macroscopic states prediction in such systems. We apply this method to trader-resolved data in the foreign exchange market. We show that these networks are remarkably persistent, which explains why and how order flow prediction is possible from trader-resolved data. In addition, if traders’ actions depend on past prices, the evolution of the average price paid by traders may also be predictable. Using random forests, we verify that the predictability of both the sign of order flow and the direction of average transaction price is strong for retail investors at an hourly time scale, which is of great relevance to brokers and order matching engines. Finally, we argue that the existence of trader lead-lag networks explains in a self-referential way why a given trader becomes active, which is in line with the fact that most trading activity has an endogenous origin.

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We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, tests of goodness of parametric fit unambiguously reject backward event times, which implies that inferring kernels from time-symmetric quantities, such as the autocovariance of the event rate, only rarely produce statistically significant fits. Finally, we find that fitting financial data with many-parameter kernels may yield significant fits for both arrows of time for the same event time vector, sometimes favouring the backward time direction. This goes to show that a significant fit of Hawkes processes to real data with flexible kernels does not imply a definite arrow of time unless one tests it.

We first investigate static properties of opening and closing auctions such as typical auction volume relative to daily volume and order value distributions. We then show that the indicative match price is strongly mean-reverting because the imbalance is, which we link to strategic behavior. Finally, we investigate how the final auction price reacts to order placement, especially conditional on imbalance improving or worsening events and find a large difference between the opening and closing auctions, emphasizing the role of liquidity and simultaneous trading in the pre-open or open-market order book.

We first review empirical evidence that asset prices have had episodes of large fluctuations and been inefficient for at least 200 years. We briefly review recent theoretical results as well as the neurological basis of trend following and finally argue that these asset price properties can be attributed to two fundamental mechanisms that have not changed for many centuries: an innate preference for trend following and the collective tendency to exploit as much as possible detectable price arbitrage, which leads to destabilizing feedback loops.

We run an experiment to investigate the emergence of excess and synchronised trading activity leading to market crashes. Although the environment clearly favours a buy-and-hold strategy, we observe that subjects trade too much, which is detrimental to their wealth given the implemented market impact (known to them). We find that preference for risk leads to higher activity rates and that price expectations are fully consistent with subjects’ actions. In particular, trading subjects try to make profits by playing a buy low, sell high strategy. Finally, we do not detect crashes driven by collective panic, but rather a weak but significant synchronisation of buy activity.

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The total duration of drawdowns is shown to provide a moment-free, unbiased, efficient and robust estimator of Sharpe ratios both for Gaussian and heavy-tailed price returns. We then use this quantity to infer an analytic expression of the bias of moment-based Sharpe ratio estimators as a function of the return distribution tail exponent. The heterogeneity of tail exponents at any given time among assets implies that our new method yields significantly different asset rankings than those of moment-based methods, especially in periods large volatility. This is fully confirmed by using 20 years of historical data on 3449 liquid US equities.

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The average portfolio structure of institutional investors is shown to have properties which account for transaction costs in an optimal way. This implies that financial institutions unknowingly display collective rationality, or Wisdom of the Crowd. Individual deviations from the rational benchmark are ample, which illustrates that system-wide rationality does not need nearly rational individuals. Finally we discuss the importance of accounting for constraints when assessing the presence of Wisdom of the Crowd.

The main objective of this thesis is to provide new theoretical results concerning the performance of investments based on stochastic models. To do so, we consider the optimal investment strategy in the framework of a risky asset model with constant volatility and a hidden Ornstein Uhlenbeck process. In the first chapter, we present the context and the objectives of this study. We present, also, the different methods used, as well as the main results obtained. In the second chapter, we focus on the feasibility of trend calibration. We answer this question with analytical results and numerical simulations. We close this chapter by also quantifing the impact of a calibration error on the trend estimate and exploit the results to detect its sign. In the third chapter, we assume that the agent is able to calibrate the trend well and we study the impact that the non-observability of the trend has on the performance of the optimal strategy. To do so, we consider the case of a logarithmic utility and an observed or unobserved trend. In each of the two cases, we explain the asymptotic limit of the expectation and the variance of the logarithmic return as a function of the signal-to-noise ratio and the speed of reversion to the mean of the trend. We conclude this study by showing that the asymptotic Sharpe ratio of the optimal strategy with partial observations cannot exceed 2/(3^1.5)∗100% of the asymptotic Sharpe ratio of the optimal strategy with complete information. The fourth chapter studies the robustness of the optimal strategy with calibration error and compares its performance to a technical analysis strategy. To do so, we characterize, analytically, the asymptotic expectation of the logarithmic return of each of these two strategies. We show, through our theoretical results and numerical simulations, that a technical analysis strategy is more robust than the poorly calibrated optimal strategy.

Mean-field game theory is a powerful formalism recently introduced to study stochastic optimization problems with a large number of agents. After recalling the basic principles of this theory and presenting some typical applications, we study in detail a stylized model of a seminar, of the mean field type. We derive an exact equation that allows us to predict the start time of the seminar and analyze different limit regimes, in which we arrive at approximate expressions of the solution. Thus we obtain a "phase diagram" of the problem. We then turn to a more complex population model with attractive group effects. Thanks to a formal analogy with the nonlinear Schrödinger equation, we show general evolution laws for the mean values of the problem, that the system verifies certain conservation laws and we develop approximations of variational type. This allows us to understand the qualitative behavior of the problem in the regime of strong interactions.

Common asset holding by financial institutions (portfolio overlap) is nowadays regarded as an important channel for financial contagion with the potential to trigger fire sales and severe losses at the systemic level. We propose a method to assess the statistical significance of the overlap between heterogeneously diversified portfolios, which we use to build a validated network of financial institutions where links indicate potential contagion channels. The method is implemented on a historical database of institutional holdings ranging from 1999 to the end of 2013, but can be applied to any bipartite network. We find that the proportion of validated links (i.e. of significant overlaps) increased steadily before the 2007–2008 financial crisis and reached a maximum when the crisis occurred. We argue that the nature of this measure implies that systemic risk from fire sales liquidation was maximal at that time. After a sharp drop in 2008, systemic risk resumed its growth in 2009, with a notable acceleration in 2013. We finally show that market trends tend to be amplified in the portfolios identified by the algorithm, such that it is possible to have an informative signal about institutions that are about to suffer (enjoy) the most significant losses (gains).

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This contribution discusses in what respect Econophysics may be able to contribute to the rebuilding of economics theory. It focuses on aggregation, individual vs collective learning and functional wisdom of the crowds.

Using unpublished high-frequency data, this thesis studies three types of clustering present in the foreign exchange market: the concentration of orders on certain prices, the concentration of transactions over time and the existence of groups of investors making the same decisions. We start by studying the statistical properties of the EBS order book for the EUR/USD and USD/JPY currency pairs and the impact of a reduction in tick size on its dynamics. A large proportion of limit orders are still placed on the old authorized prices, leading to the appearance of barrier prices, where the best limits appear most of the time. This congestion effect can be seen in the average shape of the book where peaks are present at full distances. We show that this concentration of prices is caused by manual traders who refuse to use the new price resolution. We then raise the question of the ability of Hawkes processes to capture market dynamics. We analyze the accuracy of such processes as the calibration interval is increased. Different kernels constructed from sums of exponentials are systematically compared. The FX market that never closes is particularly suitable for our purpose, as it avoids the complications due to the nightly closing of equity markets. We find that the modeling is valid according to the three statistical tests, if a two-exponential kernel is used to fit one hour, and two or three for a full day. Over longer periods the model is systematically rejected by the tests because of the non-stationarity of the endogenous process. The estimated self-excitation time scales are relatively short and the endogeneity factor is high but subcritical around 0.8. Most agent-based models implicitly assume that agents interact through asset prices and trading volumes. Some explicitly use a network of interaction between traders, on which rumors are propagated, while others use a network that represents groups making common decisions. Unlike other types of data, such networks, if they exist at all, are necessarily implicit, which makes their detection complicated. We study the transactions of customers of two liquidity providers over several years. Assuming that the links between agents are determined by the timing of their activity or inactivity, we show that interaction networks exist. Moreover, we find that the activity of some agents systematically leads to the activity of other agents, thus defining lead-lag relationships between agents. This implies that the flow of customers is predictable, which we verify using a sophisticated statistical learning method.

The goal of this thesis is to answer the real need to predict future stock price fluctuations. Indeed, the randomness governing these fluctuations constitutes for financial actors, such as market makers, one of the greatest sources of risk. Throughout this study, we highlight the possibility of reducing the uncertainty on future prices by using appropriate mathematical models. This study is made possible thanks to a large financial database and a powerful computational grid made available to us by the Automatic Market Making team of BNP Paribas. In this paper, we only present the results of the research concerning high frequency trading. The results concerning the low-frequency part are of less scientific interest to the academic world and are also confidential. In the first chapter, we present the context and the objectives of this study. We also present the different methods used, as well as the main results obtained. In chapter 2, we focus on the contribution of technological superiority in high frequency trading. For this purpose, we simulate an ultra-fast, omniscient, and aggressive trader, and then we calculate his total gain over 3 years. The gains obtained are very modest and reflect the limited contribution of technology in high frequency trading. In chapter 3, we study the predictability of prices based on order book indicators. Using conditional expectations, we present empirical evidence of statistical dependencies between prices and the different indicators. The importance of these dependencies results from the simplicity of the method, eliminating any risk of overlearning the data. We then focus on the combination of the different indicators by a linear regression and we analyze the different numerical and statistical problems related to this method. Finally, we conclude that prices are predictable for a time horizon of a few minutes and we question the market efficiency hypothesis.In chapter 4, we focus on the price formation mechanism based on the arrival of events in the order book. We classify the orders into twelve types whose statistical properties we analyze. We then study the dependencies between these different types of orders and propose an order book model in line with empirical observations. Finally, we use this model to predict prices and we support the hypothesis of the non-efficiency of markets, suggested in chapter 3.

Trust is a collective, self-fulfilling phenomenon that suggests analogies with phase transitions. We introduce a stylized model for the build-up and collapse of trust in networks, which generically displays a first order transition. The basic assumption of our model is that whereas trust begets trust, panic also begets panic, in the sense that a small decrease in trust may be amplified and ultimately lead to a sudden and catastrophic drop of trust. We show, using both numerical simulations and mean-field analytic arguments, that there are extended regions of the parameter space where two equilibrium states coexist: a well-connected network where confidence is high, and a poorly connected network where confidence is low. In these coexistence regions, spontaneous jumps from the well-connected state to the poorly connected state can occur, corresponding to a sudden collapse of trust that is not caused by any major external catastrophe. In large systems, spontaneous crises are replaced by history dependence: whether the system is found in one state or in the other essentially depends on initial conditions. Finally, we document a new phase, in which agents are connected yet distrustful.

Demand outstrips available resources in most situations, which gives rise to competition, interaction and learning. In this article, we review a broad spectrum of multi-agent models of competition and the methods used to understand them analytically. We emphasize the power of concepts and tools from statistical mechanics to understand and explain fully collective phenomena such as phase transitions and long memory, and the mapping between agent heterogeneity and physical disorder. As these methods can be applied to any large-scale model made up of heterogeneous adaptive agent with non-linear interaction, they provide a prospective unifying paradigm for many scientific disciplines.

Many fits of Hawkes processes to financial data look rather good but most of them are not statistically significant. This raises the question of what part of market dynamics this model is able to account for exactly. We document the accuracy of such processes as one varies the time interval of calibration and compare the performance of various types of kernels made up of sums of exponentials. Because of their around-the-clock opening times, FX markets are ideally suited to our aim as they allow us to avoid the complications of the long daily overnight closures of equity markets. One can achieve statistical significance according to three simultaneous tests provided that one uses kernels with two exponentials for fitting an hour at a time, and two or three exponentials for full days, while longer periods could not be fitted within statistical satisfaction because of the non-stationarity of the endogenous process. Fitted timescales are relatively short and endogeneity factor is high but sub-critical at about 0.8.

Using non-linear machine learning methods and a proper backtest procedure, we critically examine the claim that Google Trends can predict future price returns. We first review the many potential biases that may influence backtests with this kind of data positively, the choice of keywords being by far the greatest culprit. We then argue that the real question is whether such data contain more predictability than price returns themselves: our backtest yields a performance of about 17bps per week which only weakly depends on the kind of data on which predictors are based, i.e. either past price returns or Google Trends data, or both.

Using non-linear machine learning methods and a proper backtest procedure, we critically examine the claim that Google Trends can predict future price returns. We first review the many potential biases that may influence backtests with this kind of data positively, the choice of keywords being by far the greatest culprit. We then argue that the real question is whether such data contain more predictability than price returns themselves: our backtest yields a performance of about 17bps per week which only weakly depends on the kind of data on which predictors are based, i.e. either past price returns or Google Trends data, or both.

A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for Gaussian and uniformly distributed variables, and more powerful than the sign and Wilcoxon signed-rank statistics as long as the data are not too heavy-tailed. Three two-sample parametric r-statistics are proposed, one with a higher specificity but a smaller sensitivity than Mann-Whitney U-test and the other one a higher sensitivity but a smaller specificity. A nonparametric two-sample r-statistic is introduced, whose power is very close to that of Welch statistic for Gaussian or uniformly distributed variables.

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Using non-linear machine learning methods and a proper backtest procedure, we critically examine the claim that Google Trends can predict future price returns. We first review the many potential biases that may influence backtests with this kind of data positively, the choice of keywords being by far the greatest culprit. We then argue that the real question is whether such data contain more predictability than price returns themselves: our backtest yields a performance of about 17bps per week which only weakly depends on the kind of data on which predictors are based, i.e. either past price returns or Google Trends data, or both.

Using the transaction history of all the clients of an on-line broker, we analyse the daily aggregated investment fluxes of individual investors, companies, and asset managers. Computing the probability that price returns and daily investment fluxes have the same sign provides a robust characterisation of contrarian behaviour. The three categories are found to be contrarian, but with widely different intensities. Individual investors are by far the most contrarian of the three, followed by companies. Asset managers are only mildly contrarian with respect positive price returns.

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We check the claims that data from Google Trends contain enough data to predict future financial index returns. We first discuss the many subtle (and less subtle) biases that may affect the backtest of a trading strategy, particularly when based on such data. Expectedly, the choice of keywords is crucial: by using an industry-grade backtesting system, we verify that random finance-related keywords do not to contain more exploitable predictive information than random keywords related to illnesses, classic cars and arcade games. We however show that other keywords applied on suitable assets yield robustly profitable strategies, thereby confirming the intuition of Preis et al. (2013).