Beyond Binary Screens: A Continuous Shariah Compliance Index for Asset Pricing and Portfolio Design

ArXiv ID: 2512.22858 “View on arXiv”

Authors: Abdulrahman Qadi, Akash Sharma, Francesca Medda

Abstract

Binary Shariah screens vary across standards and apply hard thresholds that create discontinuous classifications. We construct a Continuous Shariah Compliance Index (CSCI) in $[“0,1”]$ by mapping standard screening ratios to smooth scores between conservative ``comfort’’ bounds and permissive outer bounds, and aggregating them conservatively with a sectoral activity factor. Using CRSP/Compustat U.S. equities (1999-2024) with lagged accounting inputs and monthly rebalancing, we find that CSCI-based long-only portfolios have historical risk-adjusted performance similar to an emulated binary Islamic benchmark. Tightening the minimum compliance threshold reduces the investable universe and diversification and is associated with lower Sharpe ratios. The framework yields a practical compliance gradient that supports portfolio construction, constraint design, and cross-standard comparisons without reliance on pass/fail screening.

Keywords: Shariah Compliance, Portfolio Construction, Screening Criteria, Investable Universe, Risk-Adjusted Performance, Equities

Complexity vs Empirical Score

  • Math Complexity: 4.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Street Traders
  • Why: The paper uses weighted geometric means and multiplicative aggregation for the compliance index, which involves algebraic functions but not advanced stochastic calculus or machine learning. However, it demonstrates strong empirical rigor with a comprehensive backtest using CRSP/Compustat data from 1999-2024, monthly rebalancing, and analysis of risk-adjusted returns, Sharpe ratios, and factor exposures.
  flowchart TD
    A["Research Goal: Continuous Shariah Compliance Index"] --> B["Methodology: Construct CSCI 0-1"]
    B --> C["Data: CRSP/Compustat US Equities<br>1999-2024, Monthly Rebalancing"]
    C --> D["Process: Map Ratios to Scores<br>Aggregate with Sectoral Factors"]
    D --> E["Analysis: CSCI-based Portfolios<br>vs. Binary Benchmark"]
    E --> F["Key Findings: Continuous Index<br>Enables Gradient Analysis & Optimization"]