2019/09/09 by Raj Agrawal, Agrawal, Raj, Uma Roy +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Applications (stat.AP) #FOS: Computer and information sciences #Financial Markets and Investment Strategies #Forecasting Techniques and Applications #Methodology (stat.ME) #Stock Market Forecasting Methods
paper · pdf · doi:10.48550/arxiv.1909.04222
openalex publication_date 2019/09/09 · openalex created_date 2022/07/24 · openalex updated_date 2026/07/28
Selecting the optimal Markowitz porfolio depends on estimating the covariance\nmatrix of the returns of N assets from T periods of historical data.\nProblematically, N is typically of the same order as T, which makes the\nsample covariance matrix estimator perform poorly, both empirically and\ntheoretically. While various other general purpose covariance matrix estimators\nhave been introduced in the financial economics and statistics literature for\ndealing with the high dimensionality of this problem, we here propose an\nestimator that exploits the fact that assets are typically positively\ndependent. This is achieved by imposing that the joint distribution of returns\nbe multivariate totally positive of order 2 (\MTP2). This constraint\non the covariance matrix not only enforces positive dependence among the\nassets, but also regularizes the covariance matrix, leading to desirable\nstatistical properties such as sparsity. Based on stock-market data spanning\nover thirty years, we show that estimating the covariance matrix under\n\MTP2 outperforms previous state-of-the-art methods including\nshrinkage estimators and factor models.\n