mean_variance_solvers

LaTeX source for a set of companion working papers on fast, matrix-free solvers for the long-only minimum-variance / mean-variance portfolio problem, by Thomas Schmelzer (Jebel Quant Research), Martin Stoll (TU Chemnitz), and Michael Wolf (University of Zurich / ADIA Lab):

• Matrix-Free Methods for Long-Only Portfolio Optimization — under matrix_free/. Casts the long-only minimum-variance problem so that covariance shrinkage acts as a preconditioner, and solves it with matrix-free iterative methods that never form the dense covariance matrix.
• From Marchenko–Pastur to Woodbury: Direct Solvers for Long-Only Mean-Variance Portfolios — under rmt/. Uses random-matrix theory (Marchenko–Pastur) to motivate a low-rank-plus-diagonal covariance model that a Woodbury identity turns into a fast direct solver.
• Non-Negative Conjugate Gradients — under non_negative_cg/. A domain-neutral technical note that isolates the computational kernel shared by the two papers above: solving the bound-constrained SPD quadratic min_{x≥0} ½xᵀAx − bᵀx (and its least-squares / equality-augmented variants) by wrapping matrix-free conjugate gradients in a primal-dual active-set loop, with an unconditional finite-termination guarantee and an operator abstraction that admits dense, Gram, factor/Woodbury, and regularised backends. It contains no finance material; the other two papers are, in its terms, two backends of one solver.

All three papers share one bibliography (matrix_free/bib/refs.bib). The two finance papers draw every figure and table from the same numerical experiments in experiment/; the non-negativity note is self-contained and draws its synthetic-study figures and tables from its own non_negative_cg/experiment/ (NumPy only, no finance data).

Building

A Makefile at the repository root drives everything; run make (or make help) for the list of targets:

make compile   # build every paper (minvar_paper.pdf, rmt_paper.pdf, nncg_paper.pdf)
make figures   # regenerate every paper's figures and tables (finance experiment + nncg study)
make arxiv     # assemble a self-contained arXiv source tarball per paper
make clean     # remove both papers' LaTeX build artifacts (keeps the PDFs)

make compile runs pdflatex → bibtex → pdflatex → pdflatex per paper: the first pass records the citations, BibTeX turns them into a formatted bibliography, and the final two passes fold it in and resolve all cross-references. The minimum-variance paper uses the standard siam bibliography style; the RMT paper uses plain. Both ship with any full TeX Live install, so no class or style files need to be vendored.

make figures delegates to experiment/, whose scripts are self-contained PEP 723 programs run with uv; their pinned dependencies include the fast-minimum-variance package, resolved directly from its git repository. The committed figure PDFs and table .tex files mean the papers compile without ever running the experiment.

Layout

Makefile                 root entry point: delegates to the per-paper Makefiles
common.mk                shared build logic (compile / arxiv / clean)
matrix_free/
  Makefile               builds minvar_paper.pdf (include ../common.mk)
  minvar_paper.tex       main file: preamble + \input of the sections
  sections/              one .tex per section (s0_abstract … s8_conclusions)
  bib/refs.bib           shared BibTeX database
  siam/                  vendored SIAM class/style (reference copy)
  graphs -> ../experiment/graphs    figure PDFs (symlink)
  tables -> ../experiment/tables    table .tex fragments (symlink)
rmt/
  Makefile               builds rmt_paper.pdf (cites ../matrix_free/bib/refs.bib)
  rmt_paper.tex          main file: preamble + \input of the sections
  sections/              one .tex per section (s0_abstract … s8_conclusions)
  graphs -> ../experiment/graphs
  tables -> ../experiment/tables
non_negative_cg/
  Makefile               builds nncg_paper.pdf (cites ../matrix_free/bib/refs.bib)
  nncg_paper.tex         main file: preamble + \input of the sections
  sections/              one .tex per section (s0_abstract … s8_conclusions)
  experiment/            self-contained synthetic study (nncg.py + experiment_nncg.py,
                         NumPy only) and an external-solver benchmark
                         (experiment_nncg_bench.py; SciPy + Clarabel); the algorithms
                         are released as the pip package
                         https://github.com/Jebel-Quant/nncg
  graphs/                generated figure PDFs (committed; `make figures`)
  tables/                generated table + \newcommand fragments (committed)
experiment/              numerical experiments that generate graphs/ and tables/
  experiment*.py         PEP 723 scripts (real-data, synthetic, OOS, RMT)
  fetch_*.py             download the raw S&P 500 / FTSE 100 return data
  data/                  committed return data (*.parquet)
  graphs/                generated figure PDFs (committed)
  tables/                generated table .tex fragments (committed)
  util/                  shared table/timing helpers

Adding a new paper is a matter of dropping in a folder with a Makefile that sets DOC and include ../common.mk; the root Makefile discovers it automatically (the experiment/ folder is excluded).

Continuous integration

GitHub Actions workflows (.github/workflows/):

• build — compiles both papers (make compile) and publishes minvar_paper.pdf and rmt_paper.pdf to the pdf branch; on tags it also attaches the PDFs and the arXiv source tarballs to a GitHub release.
• arxiv — assembles a self-contained arXiv source tarball for each paper (make arxiv) and publishes both to the arxiv branch.

Branches

• main — primary development branch.
• pdf — orphan branch holding the compiled PDFs; never merged into main.
• arxiv — orphan branch for arXiv submission artifacts; never merged into main.