# Covariance Matrix Estimation under Total Positivity for Portfolio Selection

arXiv: https://arxiv.org/abs/1909.04222 · HTML: https://mlsanity.com/paper/1909.04222/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2019.

## Built on by (most cited first, 8 of 8)

- [Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity](https://mlsanity.com/paper/2112.01939/) (2021)
- [Learning Large-Scale MTP2 Gaussian Graphical Models via Bridge-Block Decomposition](https://mlsanity.com/paper/2309.13405/) (2023)
- [Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistency](https://mlsanity.com/paper/2111.00590/) (2021)
- [Automated Efficient Estimation using Monte Carlo Efficient Influence Functions](https://mlsanity.com/paper/2403.00158/) (2024)
- [Adaptive Estimation of Graphical Models under Total Positivity](https://mlsanity.com/paper/2210.15471/) (2022)
- [Joint Network Topology Inference via Structured Fusion Regularization](https://mlsanity.com/paper/2103.03471/) (2021)
- [Learning Gaussian Graphical Models under Total Positivity via Spectral Graph Sparsification](https://mlsanity.com/paper/2605.17154/) (2026)
- [Variational Bayes Portfolio Construction](https://mlsanity.com/paper/2411.06192/) (2024)

## Abstract (arXiv)

Selecting the optimal Markowitz porfolio depends on estimating the covariance matrix of the returns of N assets from T periods of historical data. Problematically, N is typically of the same order as T, which makes the sample covariance matrix estimator perform poorly, both empirically and theoretically. While various other general purpose covariance matrix estimators have been introduced in the financial economics and statistics literature for dealing with the high dimensionality of this problem, we here propose an estimator that exploits the fact that assets are typically positively dependent. This is achieved by imposing that the joint distribution of returns be multivariate totally positive of order 2 (MTP2). This constraint on the covariance matrix not only enforces positive dependence among the assets, but also regularizes the covariance matrix, leading to desirable statistical properties such as sparsity. Based on stock-market data spanning over thirty years, we show that estimating the covariance matrix under MTP2 outperforms previous state-of-the-art methods including shrinkage estimators and factor models.