The Efficient Frontier from a LASSO Solver
Abstract
Schmelzer and Hastie prove that Markowitz's Critical Line Algorithm and the LASSO path trace the same curve. This companion note checks that result numerically with a stock LASSO solver, \texttt{lars\_path} from \texttt{scikit-learn}, and no portfolio software. It covers long--short portfolios under a leverage cap, fixed leverage with varying risk appetite, and the classical long-only, fully invested frontier. Every corner the path returns meets its own optimality conditions to about 10−13 and agrees with independent quadratic-programming solvers, on factor models of up to 500 assets, on the Fama--French size and book-to-market portfolios, and on daily returns of 494 S\&P~500 stocks. Called naively, the long-only 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. The script, its checks, the Fama--French returns and an R cross-check are published, with a locked environment, so that anyone can repeat them.
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BibTeX
@misc{schmelzer2026efficient,
title = {{The Efficient Frontier from a LASSO Solver}},
author = {Thomas Schmelzer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.37108},
eprint = {2609.37108},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37108},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Efficient Frontier from a LASSO Solver
AU - Thomas Schmelzer
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2609.37108
UR - https://arxiv.org/abs/2609.37108
AB - Schmelzer and Hastie prove that Markowitz's Critical Line Algorithm and the LASSO path trace the same curve. This companion note checks that result numerically with a stock LASSO solver, \texttt{lars\_path} from \texttt{scikit-learn}, and no portfolio software. It covers long--short portfolios under a leverage cap, fixed leverage with varying risk appetite, and the classical long-only, fully invested frontier. Every corner the path returns meets its own optimality conditions to about 10^−13 and agrees with independent quadratic-programming solvers, on factor models of up to 500 assets, on the Fama--French size and book-to-market portfolios, and on daily returns of 494 S\&P~500 stocks. Called naively, the long-only 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. The script, its checks, the Fama--French returns and an R cross-check are published, with a locked environment, so that anyone can repeat them.
ER -