The Efficient Frontier from a LASSO Solver

Abstract: In a 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.