I’ll be presenting my (preprint) paper, “Online Probabilistic Estimation of Carbon Beta and Carbon Shapley Values for Financial and Climate Risk,” at the 18th FINANCIAL RISKS INTERNATIONAL FORUM, hosted by Institut Louis Bachelier (link to the preprint at the end of the post).

As climate change becomes a key financial risk factor, investors seek reliable ways to measure the exposure of stocks to climate transition risks. This paper introduces methods to estimate Carbon Beta and Carbon Shapley values dynamically and probabilistically.

  • Carbon Beta measures how stock returns react to a Brown Minus Green (BMG) portfolio, which holds long positions in carbon-intensive (brown) stocks and short positions in climate-friendly (green) stocks.
  • Carbon Shapley values, inspired by game theory, quantify the additive contribution of input factors to model predictions, helping explain stock return sensitivities.

Context: From CAPM to Carbon Beta

The Capital Asset Pricing Model (CAPM) (Sharpe, 1964) introduced Beta as a measure of stock risk relative to the market. Over time, more sophisticated approaches—machine learning (ML), neural networks, and game-theoretic Shapley values—have emerged.

Carbon Beta extends this concept, capturing climate risk by analyzing how a stock’s returns move with a BMG portfolio. A high Carbon Beta means a stock is highly exposed to the risks of transitioning to a low-carbon economy.

Proposed Methodology

Unlike traditional methods that assume a fixed, linear relationship between stock and market returns, the approach is described in the paper in **nonlinear**, **adaptive, nonparametric, and uncertainty-aware**.

My study introduces a machine learning (ML)-based, online estimation of Carbon Beta and Carbon Shapley values. Key innovations include:

  1. No assumption of a “true” Carbon Beta
    • Uses numerical derivatives instead of a fixed linear model.
  2. Uncertainty quantification
    • Employs conformal prediction to provide confidence intervals around estimates.
  3. Model-agnostic Shapley values
    • Computes dynamic Shapley values to understand the influence of climate risk factors on stock returns.

Link to the preprint:

https://www.researchgate.net/publication/387577137_Online_probabilistic_estimation_of_carbon_beta_and_carbon_Shapley_values_for_financial_and_climate_risk

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