Related papers: Noisy Covariance Matrices and Portfolio Optimizati…
Modern portfolio optimization is centered around creating a low-risk portfolio with extensive asset diversification. Following the seminal work of Markowitz, optimal asset allocation can be computed using a constrained optimization model…
We study the feasibility and noise sensitivity of portfolio optimization under some downside risk measures (Value-at-Risk, Expected Shortfall, and semivariance) when they are estimated by fitting a parametric distribution on a finite sample…
In this paper, we explore the portfolio allocation problem involving an uncertain covariance matrix. We calculate the expected value of the Constant Absolute Risk Aversion (CARA) utility function, marginalized over a distribution of…
The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in…
Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance…
An investment portfolio consists of $n$ algorithmic trading strategies, which generate vectors of positions in trading assets. Sign opposite trades (buy/sell) cross each other as strategies are combined in a portfolio. Then portfolio…
We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…
We enhance the Universal Portfolio Shrinkage Approximator (UPSA) of Kelly et al. (2023) by making it more robust with respect to estimation noise and covariate shift. UPSA optimizes the realized Sharpe ratio using a relatively small…
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…
The comovement phenomenon in financial markets creates decision scenarios with positively correlated asset returns. This paper addresses covariance matrix estimation under such conditions, motivated by observations of significant positive…
Modeling and managing portfolio risk is perhaps the most important step to achieve growing and preserving investment performance. Within the modern portfolio construction framework that built on Markowitz's theory, the covariance matrix of…
Portfolio optimization approaches inevitably rely on multivariate modeling of markets and the economy. In this paper, we address three sources of error related to the modeling of these complex systems: 1. oversimplifying hypothesis; 2.…
We consider the problem of mean-variance portfolio optimization for a generic covariance matrix subject to the budget constraint and the constraint for the expected return, with the application of the replica method borrowed from the…
In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to…
The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…
Estimation of high dimensional covariance matrices is an interesting and important research topic. In this paper, we propose a dynamic structure and develop an estimation procedure for high dimensional covariance matrices. Asymptotic…
We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the…
We present a comparison between various algorithms of inference of covariance and precision matrices in small datasets of real vectors, of the typical length and dimension of human brain activity time series retrieved by functional Magnetic…
This paper investigates the large sample properties of the variance, weights, and risk of high-dimensional portfolios where the inverse of the covariance matrix of excess asset returns is estimated using a technique called nodewise…
In practice, observations are often contaminated by noise, making the resulting sample covariance matrix to be an information-plus-noise-type covariance matrix. Aiming to make inferences about the spectra of the underlying true covariance…