Portfolio Optimization for Index Tracking with Constraints on Downside Risk and Carbon Footprint

Paper: arXiv 2512.21092

Authors: Suparna Biswas, Rituparna Sen

Abstract

Historically, financial risk management has mostly addressed risk factors that arise from the financial environment. Climate risks present a novel and significant challenge for companies and financial markets. Investors aiming for avoidance of firms with high carbon footprints require suitable risk measures and portfolio management strategies. This paper presents the construction of decarbonized indices for tracking the S & P-500 index of the U.S. stock market, as well as the Indian index NIFTY-50, employing two distinct methodologies and study their performances. These decarbonized indices optimize the portfolio weights by minimizing the mean-VaR and mean-ES and seek to reduce the risk of significant financial losses while still pursuing decarbonization goals. Investors can thereby find a balance between financial performance and environmental responsibilities. Ensuring transparency in the development of these indices will encourage the excluded and under-weighted asset companies to lower their carbon footprints through appropriate action plans. For long-term passive investors, these indices may present a more favourable option than green stocks.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 6.0/10 (capped from 6.5: transaction costs not modelled; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper adapts standard parametric VaR and ES optimization framework to carbon-constrained index tracking using Fama-French multi-factor risk models. It provides a solid, clear empirical formulation applied to both US (S&P 500) and Indian (NIFTY 50) equity markets, though it builds heavily on established tracking-error and optimization techniques.

Research Flowchart

  flowchart TD
    A[Research Goal: Construct Decarbonized Indices Tracking S&P-500 & NIFTY-50] --> B[Inputs: Financial Stock Data & Carbon Footprint Metrics]
    B --> C[Methodology: Portfolio Optimization via Mean-VaR & Mean-ES Models]
    C --> D[Computational Process: Minimize Downside Risk subject to Carbon Reduction Constraints]
    D --> E[Key Findings: Balanced Portfolio Performance, Lowered Climate Risk & Incentive for Corporate Decarbonization]