High-Dimensional Minimum Variance Portfolio Estimation Based on High-Frequency Data

High-Dimensional Minimum Variance Portfolio Estimation Based on High-Frequency Data
Author: Tony Cai
Publisher:
Total Pages: 31
Release: 2019
Genre:
ISBN:

This paper studies the estimation of high-dimensional minimum variance portfolio (MVP) based on the high frequency returns which can exhibit heteroscedasticity and possibly be contaminated by microstructure noise. Under certain sparsity assumptions on the precision matrix, we propose estimators of the MVP and prove that our portfolios asymptotically achieve the minimum variance in a sharp sense. In addition, we introduce consistent estimators of the minimum variance, which provide reference targets. Simulation and empirical studies demonstrate the favorable performance of the proposed portfolios.

Sparse Precision Matrices for Minimum Variance Portfolios

Sparse Precision Matrices for Minimum Variance Portfolios
Author: Gabriele Torri
Publisher:
Total Pages: 36
Release: 2018
Genre:
ISBN:

Financial crises are typically characterized by highly positively correlated asset returns due to the simultaneous distress on almost all securities, high volatilities and the presence of extreme returns. In the aftermath of the 2008 crisis, investors were prompted even further to look for portfolios that minimize risk and can better deal with estimation error in the inputs of the asset allocation models. The minimum variance portfolio à la Markowitz is considered the reference model for risk minimization, due to its simplicity in the optimization as well as its need for just one input estimate: the inverse of the covariance estimate, or the so-called precision matrix. In this paper, we propose a data-driven portfolio framework that relies on two regularization methods, glasso and tlasso. They provide sparse estimates of the inverse of the covariance matrix by penalizing the 1-norm of the precision matrix relying on asset returns normality or t-Student assumptions, respectively. Simulation and actual data results support the proposed methods compared to state-of-art methods, such as random matrix and Ledoit-Wolf shrinkage.

High-Dimensional Covariance Estimation

High-Dimensional Covariance Estimation
Author: Mohsen Pourahmadi
Publisher: John Wiley & Sons
Total Pages: 204
Release: 2013-06-24
Genre: Mathematics
ISBN: 1118034295

Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.

Statistical Portfolio Estimation

Statistical Portfolio Estimation
Author: Masanobu Taniguchi
Publisher: CRC Press
Total Pages: 389
Release: 2017-09-01
Genre: Mathematics
ISBN: 1466505613

The composition of portfolios is one of the most fundamental and important methods in financial engineering, used to control the risk of investments. This book provides a comprehensive overview of statistical inference for portfolios and their various applications. A variety of asset processes are introduced, including non-Gaussian stationary processes, nonlinear processes, non-stationary processes, and the book provides a framework for statistical inference using local asymptotic normality (LAN). The approach is generalized for portfolio estimation, so that many important problems can be covered. This book can primarily be used as a reference by researchers from statistics, mathematics, finance, econometrics, and genomics. It can also be used as a textbook by senior undergraduate and graduate students in these fields.

Recent Advances in Theory and Methods for the Analysis of High Dimensional and High Frequency Financial Data

Recent Advances in Theory and Methods for the Analysis of High Dimensional and High Frequency Financial Data
Author: Norman R. Swanson
Publisher: MDPI
Total Pages: 196
Release: 2021-08-31
Genre: Business & Economics
ISBN: 303650852X

Recently, considerable attention has been placed on the development and application of tools useful for the analysis of the high-dimensional and/or high-frequency datasets that now dominate the landscape. The purpose of this Special Issue is to collect both methodological and empirical papers that develop and utilize state-of-the-art econometric techniques for the analysis of such data.

Random Matrix Theory with Applications in Statistics and Finance

Random Matrix Theory with Applications in Statistics and Finance
Author: Nadia Abdel Samie Basyouni Kotb Saad
Publisher:
Total Pages:
Release: 2001
Genre: University of Ottawa theses
ISBN:

This thesis investigates a technique to estimate the risk of the mean-variance (MV) portfolio optimization problem. We call this technique the Scaling technique. It provides a better estimator of the risk of the MV optimal portfolio. We obtain this result for a general estimator of the covariance matrix of the returns which includes the correlated sampling case as well as the independent sampling case and the exponentially weighted moving average case. This gave rise to the paper, [CMcS]. Our result concerning the Scaling technique relies on the moments of the inverse of compound Wishart matrices. This is an open problem in the theory of random matrices. We actually tackle a much more general setup, where we consider any random matrix provided that its distribution has an appropriate invariance property (orthogonal or unitary) under an appropriate action (by conjugation, or by a left-right action). Our approach is based on Weingarten calculus. As an interesting byproduct of our study - and as a preliminary to the solution of our problem of computing the moments of the inverse of a compound Wishart random matrix, we obtain explicit moment formulas for the pseudo-inverse of Ginibre random matrices. These results are also given in the paper, [CMS]. Using the moments of the inverse of compound Wishart matrices, we obtain asymptotically unbiased estimators of the risk and the weights of the MV portfolio. Finally, we have some numerical results which are part of our future work.

On the Estimation of the Global Minimum Variance Portfolio

On the Estimation of the Global Minimum Variance Portfolio
Author: Alexander Kempf
Publisher:
Total Pages: 20
Release: 2003
Genre:
ISBN:

The implementation of the Markowitz optimization requires the knowledge of the parameters of the return distribution. These parameters cannot be observed, but have to be estimated. Merton (1980) and Jorion (1985) point out that especially the expected returns are hard to estimate from time series data. The estimation risk is huge. The global minimum variance portfolio is the only efficient stock portfolio whose weights do not depend on the expected returns. Therefore, one can avoid extreme estimation risk by investing into this portfolio. Nevertheless, there remains a considerable estimation risk with respect to the covariance matrix. This article deals with the estimation of the weights of the global minimum variance portfolio. The literature suggests a two-step approach to determine the optimal portfolio weights. In the first step one estimates the return distribution parameters, and in the second step one optimizes the portfolio weights using the estimated parameters. The main contribution of our paper is to suggest new one-step approaches to estimate optimal portfolio weights. Our paper has four main results: 1) Our one-step regression approach is the best unbiased weight estimator. 2) The estimation risk for this best unbiased estimator is large. 3) (Biased) shrinkage estimators lead to portfolios with smaller out-of-sample return variances. 4) Our one-step shrinkage estimator beats the two step shrinkage approach proposed by Ledoit and Wolf (2003) significantly. The results 1 and 2 are shown analytically. The results 3 and 4 are derived from an extensive simulation study.

Improving Portfolios Global Performance with Robust Covariance Matrix Estimation

Improving Portfolios Global Performance with Robust Covariance Matrix Estimation
Author: Jay Emmanuelle
Publisher:
Total Pages: 5
Release: 2018
Genre:
ISBN:

This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but the same improvements apply also in the other optimisation problems such as the Minimum Variance Portfolio. We assume that the most important information (or the latent factors) are embedded in correlated Elliptical Symmetric noise extending classical Gaussian assumptions. We propose here to focus on a recent method of model order selection allowing to efficiently estimate the subspace of main factors describing the market. This non-standard model order selection problem is solved through Random Matrix Theory and robust covariance matrix estimation. The proposed procedure will be explained through synthetic data and be applied and compared with standard techniques on real market data showing promising improvements.