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From Binary Screens to Continuous Compliance: A Shariah Screening Measure for Portfolio Design

Abdulrahman Qadi, Akash Sharma, Francesca Medda

Abstract

Islamic equity screening relies on multiple binary rulebooks that often classify the same firm differently. This paper develops a Continuous Shariah Compliance Index (CSCI) on $[0,1]$ that embeds the published business-activity and financial-ratio thresholds of six leading standards in a single transparent measure. Using CRSP/Compustat U.S. equities from 1999-2024 with lagged accounting inputs and monthly portfolio formation, we document four results. First, existing binary standards map to distinct regions of a common compliance scale, so firms that receive the same pass/fail label can still differ materially in compliance strength. Second, CSCI-threshold portfolios provide a transparent way to vary compliance intensity while retaining economically meaningful diversification, although baseline risk-adjusted performance declines modestly as thresholds tighten. Third, the September 2023 DJIM/S&P methodology change admits firms with materially lower CSCI scores than firms that remained compliant under both the old and new rules. Fourth, in cross-sectional return tests, CSCI is not reliably associated with higher expected returns once standard characteristics are controlled for. The main contribution of CSCI is therefore measurement and portfolio design rather than the discovery of a new priced factor.

From Binary Screens to Continuous Compliance: A Shariah Screening Measure for Portfolio Design

Abstract

Islamic equity screening relies on multiple binary rulebooks that often classify the same firm differently. This paper develops a Continuous Shariah Compliance Index (CSCI) on that embeds the published business-activity and financial-ratio thresholds of six leading standards in a single transparent measure. Using CRSP/Compustat U.S. equities from 1999-2024 with lagged accounting inputs and monthly portfolio formation, we document four results. First, existing binary standards map to distinct regions of a common compliance scale, so firms that receive the same pass/fail label can still differ materially in compliance strength. Second, CSCI-threshold portfolios provide a transparent way to vary compliance intensity while retaining economically meaningful diversification, although baseline risk-adjusted performance declines modestly as thresholds tighten. Third, the September 2023 DJIM/S&P methodology change admits firms with materially lower CSCI scores than firms that remained compliant under both the old and new rules. Fourth, in cross-sectional return tests, CSCI is not reliably associated with higher expected returns once standard characteristics are controlled for. The main contribution of CSCI is therefore measurement and portfolio design rather than the discovery of a new priced factor.
Paper Structure (46 sections, 3 theorems, 16 equations, 8 figures, 11 tables)

This paper contains 46 sections, 3 theorems, 16 equations, 8 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Institutional Background and Related Literature
  3. Shariah screening architecture and the standard-disagreement problem
  4. The September 2023 methodology change
  5. Islamic indices: performance, risk, and crisis resilience
  6. Towards continuous measures of Shariah compliance
  7. ESG and ethical investing: continuous scores, rating disagreement, and portfolio roles
  8. Sin stocks, exclusion, and the pricing of non-pecuniary constraints
  9. Gap and contribution
  10. Equilibrium Model with Heterogeneous Compliance Standards
  11. Setup
  12. Equilibrium characterisation
  13. Discussion and limitations
  14. Data and Measurement
  15. Sample and data sources
  16. ...and 31 more sections

Key Result

Proposition 1

In equilibrium, the set of investors who hold asset $i$ is exactly $\{\tau : \tau \leq \phi_i\}$. The equilibrium expected return $\mu_i$ is increasing in $\phi_i$ if $g(\cdot)$ places sufficient mass near $\phi_i$ and the resulting investor base is small relative to supply. Formally, for an asset w where $\int_0^{\phi_i} g(\tau) d\tau$ is the total wealth of investors for whom asset $i$ is admiss

Figures (8)

  • Figure 1: Timeline of accounting data availability and portfolio formation.
  • Figure 2: Cross-sectional distribution of the Continuous Shariah Compliance Index (CSCI) for all firms, 1999--2024. The large mass at zero reflects both sector exclusions and firms whose financial ratios breach the outer bounds on at least one dimension. Among firms with $\textrm{CSCI} > 0$, scores are concentrated in the upper range (0.7--1.0), reflecting the narrow gap between comfort and outer thresholds for the leverage and cash dimensions.
  • Figure 3: Cross-sectional CSCI distribution in permissible sectors (investable universe), 1999--2024. Restricting to firms not excluded by sector screens removes the large mass at zero from prohibited industries, but a substantial mass near zero remains from firms whose financial ratios exceed the outer thresholds.
  • Figure 4: Time-series of cross-sectional CSCI, 1999--2024. The solid line is the annual cross-sectional mean; the dashed line is the median; the shaded band shows $\pm 1$ standard deviation. Mean CSCI dips during the global financial crisis (2008--2009), consistent with rising leverage and liquidity stress temporarily pushing more firms below the outer bounds, and recovers in the subsequent decade.
  • Figure 5: Compliance--performance frontier. The left panel plots average CSCI against annualized Sharpe ratio; the right panel plots average CSCI against annualized FF5+MOM alpha. The conventional market benchmark (grey square) has the lowest compliance score. The binary Islamic benchmark (blue circle) moves up in compliance with lower Sharpe. The CSCI-threshold portfolios (red triangles) trace a frontier in which tighter compliance is associated with slightly lower Sharpe but higher average compliance.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Proposition 1: Segmented demand
  • Corollary 1: Muted pricing effect when thresholds cluster
  • Corollary 2: Methodology shock effects