Capital Fund Management (France)

The Nested factor model was introduced by Chicheportiche et al. to represent non-linear correlations between stocks. Stock returns are explained by a standard factor model, but the (log)-volatilities of factors and residuals are themselves decomposed into factor modes, with a common dominant volatility mode affecting both market and sector factors but also residuals. Here, we consider the case of a single factor where the only dominant log-volatility mode is rough, with a Hurst exponent $H \simeq 0.11$ and the log-volatility residuals are ''super-rough'' or ''multifractal'', with $H \simeq 0$. We demonstrate that such a construction naturally accounts for the somewhat surprising stylized fact reported by Wu et al. , where it has been observed that the Hurst exponents of stock indexes are large compared to those of individual stocks. We propose a statistical procedure to estimate the Hurst factor exponent from the stock returns dynamics together with theoretical guarantees of its consistency. We demonstrate the effectiveness of our approach through numerical experiments and apply it to daily stock data from the S&P500 index. The estimated roughness exponents for both the factor and idiosyncratic components validate the assumptions underlying our model.

Sociotechnical systems, where technological and human elements interact in a goal-oriented manner, provide important functional support to our societies. Here, we draw attention to the underappreciated concept of timeliness—i.e., system elements being available at the right place at the right time—that has been ubiquitously and integrally adopted as a quality standard in the modus operandi of sociotechnical systems. We point out that a variety of incentives, often reinforced by competitive pressures, prompt system operators to myopically optimize for efficiencies, running the risk of inadvertently taking timeliness to the limit of its operational performance, correspondingly making the system critically fragile to perturbations by pushing the entire system toward the proverbial “edge of a cliff.” Invoking a stylized model for operational delays, we identify the limiting operational performance of timeliness, as a true critical point, where the smallest of perturbations can lead to a systemic collapse. Specifically for firm-to-firm production networks, we suggest that the proximity to critical fragility is an important ingredient for understanding the fundamental “excess volatility puzzle” in economics. Further, in generality for optimizing sociotechnical systems, we propose that critical fragility is a crucial aspect in managing the trade-off between efficiency and robustness.

Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define and study an interesting new matrix ensemble with extensive correlations, generalising the elliptic ensemble. We determine analytically the boundary of its eigenvalue spectrum in the complex plane, as a function of the correlations determined by the model at hand. We solve numerically our equations in several cases of interest, and show that the resulting spectra can take a surprisingly wide variety of shapes.

This is the English version of my inaugural lecture at Collège de France in 2021. I reflect on the difficulty of multi-disciplinary research, which often hinges on unexpected epistemological and methodological differences, for example about the scientific status of models. What is the purpose of a model? What are we ultimately trying to establish: rigorous theorems or ad-hoc calculation recipes; absolute truth, or heuristic representations of the world? I argue that the main contribution of statistical physics to social and economic sciences is to make us realise that unexpected behaviour can emerge at the aggregate level, that isolated individuals would never experience. Crises, panics, opinion reversals, the spread of rumours or beliefs, fashion effects and the zeitgeist, but also the existence of money, lasting institutions, social norms and stable societies, must be understood in terms of collective belief and/or trust, self-sustained by interactions, or on the contrary, the rapid collapse of this belief or trust. The appendix contains my opening remarks to the workshop ‘More is Different’, as a tribute to Phil Anderson.

The mean first passage time (MFPT) of random walks is a key quantity characterizing dynamic processes on disordered media. In a random fractal embedded in the Euclidean space, the MFPT is known to obey the power law scaling with the distance between a source and a target site with a universal exponent. We find that the scaling law for the MFPT is not determined solely by the distance between a source and a target but also by their locations. The role of a site in the first passage processes is quantified by the random walk centrality. It turns out that the site of highest random walk centrality, dubbed as a hub, intervenes in first passage processes. We show that the MFPT from a departure site to a target site is determined by a competition between direct paths and indirect paths detouring via the hub. Consequently, the MFPT displays a crossover scaling between a short distance regime, where direct paths are dominant, and a long distance regime, where indirect paths are dominant. The two regimes are characterized by power laws with different scaling exponents. The crossover scaling behavior is confirmed by extensive numerical calculations of the MFPTs on the critical percolation cluster in two dimensional square lattices.

The economic shocks that followed the COVID-19 pandemic have brought to light the difficulty, both for academics and policy makers, of describing and predicting the dynamics of inflation. This paper offers an alternative modelling approach. We study the 2020-2023 period within the well-studied Mark-0 Agent-Based Model, in which economic agents act and react according to plausible behavioural rules. We include a mechanism through which trust of economic agents in the Central Bank can de-anchor. We investigate the influence of regulatory policies on inflationary dynamics resulting from three exogenous shocks, calibrated on those that followed the COVID-19 pandemic: a production/consumption shock due to COVID-related lockdowns, a supply-chain shock, and an energy price shock exacerbated by the Russian invasion of Ukraine. By exploring the impact of these shocks under different assumptions about monetary policy efficacy and transmission channels, we review various explanations for the resurgence of inflation in the United States, including demand-pull, cost-push, and profit-driven factors. Our main results are four-fold: (i) without appropriate fiscal policy, the shocked economy can take years to recover, or even tip over into a deep recession; {(ii) the success of monetary policy in curbing inflation is primarily due to expectation anchoring, rather than to the direct economic impact of interest rate hikes; (iii) however, strong inflation anchoring is detrimental to consumption and unemployment, leading to a narrow window of ``optimal'' policy responses due to the trade-off between inflation and unemployment;} (iv) the two most sensitive model parameters are those describing wage and price indexation. The results of our study have implications for Central Bank decision-making, and offers an easy-to-use tool that may help anticipate the consequences of different monetary and fiscal policies.