Asset Allocation Strategies Using Covariance Matrix Estimators

Abstract

The covariance matrix is an important element of many asset allocation strategies. The widely used sample covariance matrix estimator is unstable especially when the number of time observations is small and the number of assets is large or when high-dimensional data is involved in the computation. In this study, we focus on the most important estimators that are applied on a group of Markowitz-type strategies and also on a recently introduced method based on hierarchical tree clustering. The performance tests of the portfolio strategies using different covariance matrix estimators rely on the out-of-sample characteristics of synthetic and real stock data.

Optimization of Asset Allocation Strategies in Major Categories—Theories, Indicators, Assets and Timing

“…However, the mean-variance method also has defects. First, the calculation results based on historical data have limitations; Secondly, the duration of each stage is relatively short, indicating that the number of time observations is small (László, 2022), so the distribution of asset return does not satisfy the normal distribution assumption; Finally, when there are only two assets in the portfolio, this method tends to give up the asset with lower return and higher volatility and pour all the funds into another asset. In practice, asset allocation can still be done based on the mean-variance model, but the input parameters should be the analyst's expected rate of return rather than the historical rate of return.…”

Positive Definiteness of the Sample Covariance Matrix of Multi-poisson Distribution

“…Covariance matrix is an important tool which is widely used in studying noise [1][2], direction-ofarrival [3][4][5], error distribution [6], allocation strategies [7], image analysis [8], power state estimation [9], local path planning [10], human activity recognition [11], geomagnetic jerk [12], the qualities of software and the sustainable innovation ability of enterprises [13][14][15], etc.. An important feature of the ML approach is that it has robust performance in noise environment by treating the covariance matrix of the additive Gaussian noise as a parameter [2]. In the image matching algorithm, The gradient magnitudes, direction, corrosion, expansion and information entropy and so forth, the feature of the target image can be reconciled with their covariance matrix to construct a new characteristic model [8].…”