Abstract
We compare the performance of multiple covariance matrix estimators for the purpose of portfolio optimization. This evaluation studies the ability of estimators like Sample Based Estimator (SCE), Ledoit-Wolf Estimator (LWE), and Rotationally Invariant Estimators (RIE) to estimate covariance matrix and their competency in fulfilling the objectives of various portfolio allocation strategies. In this paper, we have captured the effectiveness of strategies such as Global Minimum Variance (GMVP) and Most-Diversified Portfolio (MDP) to produce optimal portfolios. Additionally, we also propose a new strategy inspired from MDP: Most-Diversified Portfolio (MMDP), that enables diversification upon minimizing risk. Empirical evaluations show that by and large, MMDP furnishes the maximum returns. LWE are relatively more robust than SCE and RIE but RIE performs better under certain conditions.
Highlights
The covariance matrix is, arguably, the second most important object in all of statistics. [1] It can be used to analyze the movement of random variables like two stocks or compute how the return of two assets move together
We propose a new strategy called Modified Maximum Diversification Portfolio strategy (MMDP) to evaluate covariance estimation methods, which is inspired from the Most-Diversified Portfolio (MDP) strategy
The prime objective of our project was to evaluate the performance of various covariance estimators in fulfilling the goals of portfolio optimization strategies
Summary
The covariance matrix is, arguably, the second most important object in all of statistics. [1] It can be used to analyze the movement of random variables like two stocks or compute how the return of two assets move together. [1] It can be used to analyze the movement of random variables like two stocks or compute how the return of two assets move together. Apart from that, it facilitates the application of Principal Component Analysis for robust pattern recognition, which further helps with Exploratory Data Analysis (EDA). When one deals with very large random matrices (such as covariance matrices), one expects the spectral measure of the matrix under scrutiny to exhibit some universal properties, which are independent of the specific realization of the matrix itself. It is composed of columns comprising returns , wherein every vector (for i ∈ [1, ..., N] )
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