Paper: arXiv 2609.37108

Authors: Thomas Schmelzer

Abstract

In a recent paper, Schmelzer and Hastie argue that Markowitz’s Critical Line Algorithm and the LASSO path trace the same curve. Here we use that identity to compute efficient frontiers with a stock LASSO solver, \texttt{lars_path} from \texttt{scikit-learn}. It handles long–short portfolios under a leverage cap, fixed leverage with varying risk appetite, and the classical long-only, fully invested frontier. Called naively, the last path stops at the maximum-Sharpe portfolio. One shift of the response, by an amount computed in advance, lets a single call reach the minimum-variance portfolio.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a novel and practical application of the LASSO-CLA identity for efficient frontier computation, demonstrating strong empirical results with clear methodology. The mathematical underpinnings are solid, and the code availability significantly enhances reproducibility.

Research Flowchart

  flowchart TD
    A[Research Goal: Compute Efficient Frontiers] --> B{Key Identity: CLA = LASSO Path};
    B --> C[Methodology: Use LASSO Solver (lars_path)];
    C --> D[Inputs: Stock Data, Leverage Constraints];
    D --> E[Computational Process: Call lars_path, Shift Response];
    E --> F[Outcomes: Efficient Frontiers (Long-Short, Fixed Leverage, Long-Only), Max-Sharpe, Min-Variance];