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A kinetic theory approach to consensus formation in financial markets

Jean-Gabriel Attali, Francesco Salvarani

TL;DR

The paper addresses whether sell-side consensus targets forecast or simply follow market prices. It shows, via Engle–Granger and Johansen analyses, that the SP500 level and the one-year consensus for the index are cointegrated and that price movements predominantly drive consensus in the short run, while peer influence wanes over time. The authors then develop a kinetic theory-based model describing the evolution of analysts' opinion distributions, deriving a simple three-parameter dynamic that links current price, sentiment, and mean-field effects, and demonstrate its predictive power on a training/testing split. Numerical results indicate the kinetic model captures long-run dynamics more faithfully and with stable errors, even in volatile periods, offering a distribution-aware alternative to traditional VAR/VECM approaches for forecasting consensus forecasts. The work highlights the robustness and practical relevance of kinetic approaches to financial opinion dynamics and market forecasting, with potential applicability to other indices through periodic recalibration.

Abstract

It is sometimes acknowledged that (sell-side) equity analysts' recommendations influence investors and therefore market prices. In particular, the S&P 500 is expected to decline (respectively rise) when analysts revise their targets downward (respectively upward). Our findings indicate not only that analysts' consensus exert no influence on market prices, but also that, conversely, analysts appear to set their target prices based on markets prices. Employing a kinetic theory framework, we model the dynamics of analysts' opinions, by taking into account both the mutual influences shaping price consensus and the dynamics of the actual S&P 500 index level. The model is calibrated on a training subset of data and tested on an independent set to assess its predictive power. Our tests show that just three free parameters are enough to accurately predict the one-year average price forecasts of analysts.

A kinetic theory approach to consensus formation in financial markets

TL;DR

The paper addresses whether sell-side consensus targets forecast or simply follow market prices. It shows, via Engle–Granger and Johansen analyses, that the SP500 level and the one-year consensus for the index are cointegrated and that price movements predominantly drive consensus in the short run, while peer influence wanes over time. The authors then develop a kinetic theory-based model describing the evolution of analysts' opinion distributions, deriving a simple three-parameter dynamic that links current price, sentiment, and mean-field effects, and demonstrate its predictive power on a training/testing split. Numerical results indicate the kinetic model captures long-run dynamics more faithfully and with stable errors, even in volatile periods, offering a distribution-aware alternative to traditional VAR/VECM approaches for forecasting consensus forecasts. The work highlights the robustness and practical relevance of kinetic approaches to financial opinion dynamics and market forecasting, with potential applicability to other indices through periodic recalibration.

Abstract

It is sometimes acknowledged that (sell-side) equity analysts' recommendations influence investors and therefore market prices. In particular, the S&P 500 is expected to decline (respectively rise) when analysts revise their targets downward (respectively upward). Our findings indicate not only that analysts' consensus exert no influence on market prices, but also that, conversely, analysts appear to set their target prices based on markets prices. Employing a kinetic theory framework, we model the dynamics of analysts' opinions, by taking into account both the mutual influences shaping price consensus and the dynamics of the actual S&P 500 index level. The model is calibrated on a training subset of data and tested on an independent set to assess its predictive power. Our tests show that just three free parameters are enough to accurately predict the one-year average price forecasts of analysts.

Paper Structure

This paper contains 21 sections, 2 theorems, 48 equations, 4 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Exploratory data analysis based on Engle and Granger approach
  3. Data
  4. Test for stationarity
  5. Cointegration test
  6. Short-run relationship
  7. Johansen procedure
  8. Tests for lags and cointegration
  9. Estimates
  10. Long-term relationship
  11. Short-run relationship with $D \ln (X(t))$ as the dependent variable
  12. Short-run relationship with $D\ln (s_{\text{meas}}(t))$ as the dependent variable
  13. Diagnostic tests for residuals
  14. Serial Correlation
  15. Check for normality
  16. ...and 6 more sections

Key Result

Theorem 2.3

Suppose $Y(t)$ and $Z(t)$ are cointegrated at the order 1. Then there exists an error-correction representation i.e. an (error-correction) model of the form: where $\varepsilon(t)$ is $I(0)$.

Figures (4)

  • Figure 1: Time series of the S&P 500 index $X(t)$ (dark grey line) and the one-year analysts' forecasts for the S&P 500 index (grey line), from May 26th, 2009, to June 2nd, 2025. Source: Bloomberg
  • Figure 2: Logarithm of one-year analysts' forecasts for the S&P 500 index (dark grey line) vs its long-term equilibrium level (grey line), from May 26th, 2009, to June 2nd, 2025.
  • Figure 3: Forecasts $s(t)$ of the kinetic model (black line), Forecasts $\exp{(\alpha\ln (X(t))+ \beta)}$ of the cointegration model (grey line) and the time series of the average of one-year analysts' forecasts for the S&P 500 index $s_{\text{meas}}(t)$ (light grey line), from January 3rd, 2017, to June 2nd, 2025.
  • Figure 4: Analysis of the relative error between the forecasts $s(t)$ of the model and the time series of the average of one-year analysts' forecasts for the S&P 500 index $s_{\text{meas}}$, from January 3rd, 2017, to June 2nd, 2025.

Theorems & Definitions (9)

  • Definition 2.1
  • Remark 2.2
  • Theorem 2.3
  • Remark 2.4
  • Remark 2.5
  • Remark 3.1
  • Remark 3.2
  • Theorem 5.1
  • proof