We investigate the emergence of momentum and reversal anomalies in a general equilibrium model with complete markets and cognitively biased agents. General equilibrium and market completeness avoid spurious effects due to portfolio composition or price stickiness. Taking inspiration from and merging different strands of empirical literature, we try to identify anomalies in the most general way, studying return autocorrelation patterns, price gaps following sequences of specific events, and relative performances of suitably defined portfolios. We show that these three characterizations are not equivalent. They capture different aspects of mispricing and relate differently to the behavioral characteristics of the agents. Often, similar anomalous patterns struggle to coexist under seemingly related biases. Overall, the model is generically able to reproduce the empirical evidence of momentum profits that subsequently revert.

The degree of uncertainty associated with the value of a company plays a relevant role in valuation analysis. We propose an original and robust methodology for company market valuation, which replaces the traditional point estimate of the conventional Discounted Cash Flow model with a probability distribution of fair values that convey information about both the expected value of the company and its intrinsic uncertainty. Our methodology depends on two main ingredients: an econometric model for company revenues and a set of firm-specific balance sheet relations that are estimated using historical data. We explore the effectiveness and scope of our methodology through a series of statistical exercises on publicly traded U.S. companies. At the firm level, we show that the fair value distribution derived with our methodology constitutes a reliable predictor of the company’s future abnormal returns. At the market level, we show that a long-short valuation (LSV) factor, built using buy-sell recommendations based on the fair value distribution, contains information not accessible through the traditional market factors. The LSV factor significantly increases the explanatory and the predictive power of factor models estimated on portfolios and individual stock returns.

This paper studies market selection in an Arrow-Debreu economy with complete markets where agents learn over misspecified models. In this setting, standard Bayesian learning loses its formal justification and biased learning processes may provide a selection advantage. Studying two cases of model misspecification and four learning processes, our analysis reveals that, differently from correctly specified settings, the ecology of traders populating the market crucially affects selection dynamics and, thus, long-run asset valuation. In fact, model misspecification implies a general difficulty in ranking learning behaviors with respect to their survival prospects. For instance, prediction averaging shows an advantage when the true data generating process belongs to the same family of models that agents use to learn. This advantage partially disappears when the true model belongs to a more general class, as a trade off emerges between approximating the projection of the true model on the space on which the agents learn and adapting to the part of the true model that cannot be represented in that space. Rules that guarantee survival are possible, but they exploit imitative mechanisms that require information about all the other market participants.

A crucial aspect of every experiment is the formulation of hypotheses prior to data collection. In this paper, we use a simulation-based approach to generate synthetic data and formulate the hypotheses for our market experiment and calibrate its laboratory design. In this experiment, we extend well-established laboratory market models to the two-asset case, accounting at the same time for heterogeneous artificial traders with multi-asset strategies. Our main objective is to identify the role played in the price-bubble formation by both self-impact (i.e., how trading orders affect the price dynamics) and cross-impact (i.e., the price changes in one asset caused by the trading activity on other assets). To this end, we vary across treatments the possibility of traders of diverting their capital from one asset to the other, thereby artificially changing the amount of liquidity in the market. To simulate different scenarios for the synthetic data generation, we vary along with the liquidity the type of trading strategies of our artificial traders. Our results suggest that an increase in liquidity increases the cross-impact, especially when agents are market-neutral. Self-impact, however, remains significant and constant for all model specifications.

We introduce a new methodology to investigate the degree of persistence in firm growth dynamics, based on Conditional Quantile Transition Probability Matrices (CQTPMs) and exact inferential tests derived from two well-known mobility indexes. We apply the methodology to study manufacturing firms in the UK and four major European economies over the period 2010–2017. We find that CQTPMs display more persistence than under a fully independent firm growth process, albeit considerable turbulence and significant bouncing effects are detected. Exploiting the inferential statistics within a regression framework, we show that productivity, openness to trade, and business dynamism are the primary sources of firm growth persistence across sectors, while country-specific and time-specific factors play a second-order role.

We provide sufficient conditions for the persistence or transience of stochastic processes on the real line based on the behavior of the first and second moment of their conditional increments at the boundaries. Our findings extend previous results in the literature (Lamperti, 1960) to the large class of discrete-time processes with bounded increments. We present some examples of application by studying survival and dominance of agents trading in complete financial markets.

This note analyzes some properties of the Pareto Type III distribution. A three parameter version of the original two parameter distribution proposed by Pareto is introduced and both its density and characteristic function are derived. The analytic expression of the inverse distribution function is also obtained, together with an explicit expression of its moments of any order. Finally, a simple statistical exercise is proposed, designed to show the reliability of the Pareto Type III distribution in describing asymptotically dumped power-like behaviors.

We consider a market economy where two rational agents are able to learn the distribution of future events. In this context, we study whether moving away from the standard Bayesian belief updating, in the sense of under-reaction to some degree to new information, may be strategically convenient for traders. We show that, in equilibrium, strong under-reaction occurs, thus rational agents may strategically want to bias their learning process. Our analysis points out that the underlying mechanism driving ex-ante strategical decisions is diversity seeking. Finally, we show that, even if robust with respect to strategy selection, strong under-reaction can generate low realized welfare levels because of a long transient phase in which the agent makes poor predictions.

This chapter investigates whether a behaviourally biased agent is able to persistently maintain a positive consumption share when trading in the market with a Bayesian agent. The question is addressed by recasting a popular model of investor sentiment in a general equilibrium framework. Our evolutionary stability analysis complements standard Behavioural Finance studies, where a biased representative agent is usually considered to explain deviations from rational pricing. In fact, if the biased agent asymptotically disappears from the market, then misvaluation patters generated by its behaviour do not survive in the long term. We find that, despite the existence of generic cases in which the biased agent succumbs, the learning process with behavioural biases displays a good degree of evolutionary stability.

This paper studies the occurrence of price momentum and reversal in a general equilibrium setting, with complete markets and expected utility maximizing agents. We show that price anomalies can generically emerge when agents derive their individual probabilities from reinforcing and progressive learning processes defined over misspecified models.

In this paper we study the impact of non-performing loans (NPLs) on financial stability using a network based approach. We start by combining loan-level data from DealScan and firm-level data from Orbis to reconstruct the global financial network in 1991-2016 and identify a series of stylized facts. We show that many regularities found at national level by the literature hold also at international level. Based on our empirical findings, we develop a simple network model in which banks and firms are linked by their reciprocal claims and study how an exogenous increase in NPLs affects the stability of the system. We investigate the model using Monte Carlo simulations and show that there exists a critical threshold of NPLs beyond which a systemic crisis occurs. This implies that small variations in the magnitude of the initial shock can have very different consequences at the aggregate level.

This paper presents two stocks recommendation systems based on a stochastic characterization of firm present value that extends the conventional discounted cash flow analysis. In the Single-Stock Quantile recommendation system, the market price of a company's stocks is compared with the estimated distribution of the company fair value to obtain an individual measure of mispricing, while in the Cross-Sectional Quantile system, a relative measure of mispricing is built using the fair value distribution of all firms at the same time. Both systems use mispricing information to build sell side and buy side portfolios. We provide a series of statistical exercises that show how these portfolios can consistently deliver significant excess returns, also when rebalancing costs are accounted for.

This paper studies whether, and to what extent, trading in an incomplete competitive market rewards the CAPM portfolio rule over alternative rules. We find that, if a mean-variance trader faces an agent who invests in each asset proportionally to expected relative payoffs, in the long-run only two scenarios are possible: either the mean-variance trader vanishes or both agents survive with fixed and constant wealth shares. In both cases, asymptotic prices are proportional to assets’ expected payoff, and the relation between prices and returns implied by the CAPM does not generally hold. Conversely, when a mean-variance trader faces a generic fixed-mix investor, several long-run outcomes are possible, such as dominance of one trader, survival of both, and generic path-dependency. We provide sufficient conditions to assess such outcomes. We find that the different outcomes can be effectively discussed in terms of the effective risk aversion of the trading strategies, as implied by their portfolio choices conditional on prevailing market prices. In general, a larger effective risk aversion constitutes a survival advantage.

We consider a repeated betting market populated by two agents who wage on a binary event according to generic betting strategies. We derive new simple criteria, based on the difference of relative entropies, to establish the relative wealth of the two agents in the long-run. Little information about agents' behavior is needed to apply the criteria: it is sufficient to know the odds traders believe fair and how much they would bet when the odds are equal to the ones the other agent believes fair. Using our criteria, we show that for a large class of betting strategies, it is generically possible that the ultimate winner is only decided by luck. As an example, we apply our conditions to the case of Constant Relative Risk Averse (CRRA) and quantal response betting.

We propose an aggregate growth index that explicitly accounts for fat tails in the firm size distribution and for the negative scaling relation between the size of the firm and the volatility of its growth rates. Using Compustat data on US publicly traded company, we show that the new index tracks aggregate fluctuations much better than simpler measures of central tendency of the dynamics of firms, like the growth rates sample average, confirming that the statistical properties characterizing the micro-economic dynamics of firms are relevant for the dynamics of the aggregate. To better characterize the origins of aggregate fluctuations, we decompose the index in two parts, describing, respectively, the modal (typical) value of log growth rates and the tilt (asymmetry) of their distribution. Regression analysis shows that models based on this decomposition, despite their simplicity, possess a remarkable explanatory and predictive power with respect to the aggregate growth.

We investigate market selection and bet pricing in a repeated prediction market model. We derive the conditions for long-run survival of more than one agent (the crowd) and quantify the information content of prevailing prices in the case of fractional Kelly traders with heterogeneous beliefs. It turns out that, apart some non-generic situations, prices do not converge, neither almost surely nor on average, to true probabilities, nor are they always nearer to the truth than the beliefs of all surviving agents. This implies that, in general, prediction market prices are not maximum likelihood estimators of the true probabilities. However, when more than one agent survives, the average price emerging from a prediction market approximates the true probability with lower information loss than any individual belief.

We consider a repeated betting market populated by two agents who wage on a binary event according to generic betting strategies. We derive new simple criteria to establish the relative wealth of the two agents in the long run, only based on the odds they believe fair and how much they would bet when the odds are equal to the ones the other agent believes fair. Using our criteria, we show that for a large class of betting strategies it is generically possible that the ultimate winner is only decided by luck. As an example, we apply our conditions to the case of CRRA betting.

This paper investigates whether short-term momentum and long-term reversal may emerge from the wealth reallocation process taking place in speculative markets. We assume that there are two classes of investors who trade long-lived assets by holding constantly rebalanced portfolios based on their beliefs. Provided beliefs, and thus portfolios, are sufficiently diversified, all investors survive in the long-run and, due to waves of mispricing, the resulting equilibrium returns exhibit long-term reversal. If, moreover, asset dividends are positively correlated, investors' profitable trades become positively correlated too, thus generating short-term momentum in equilibrium returns. We use the model to replicate the performance of the Winners and Losers portfolios highlighted by the empirical literature and to provide insights on how to improve upon them. Finally, we show that dividend positive autocorrelation is positively related to momentum and negatively related to reversal while diversity of beliefs is positively related to both momentum and reversal.