(An) empirical study of principal portfolio analysis using prediction matrix in the Korean stock market

Abstract

In this paper, the construction of a prediction matrix using signals from a specific time period and subsequent returns is discussed. The prediction matrix is then subjected to singular value decomposition, leading to the formation of Principal Portfolios (PPs). These portfolios enable return prediction and the development of optimal portfolio strategies. The PPs are further decomposed into symmetric and antisymmetric parts, facilitating the analysis of factor exposure (beta) and alpha components, respectively. The prediction matrix possesses the properties of a positive semidefinite matrix. Furthermore, the analysis of PPs leverages the eigenvalues of the prediction matrix, akin to Principal Portfolios Analysis (PPA) with the covariance matrix, enabling dimension reduction and bolstering the robustness of the strategies. To empirically validate the approach, the PPA strategy is applied to the Korean stock market using the Fama-French 5-factor model, with momentum employed as the signal. The robustness of the methodology was verified not only under basic conditions but also under various additional conditions. As a result, significant findings were observed under specific conditions, revealing the characteristics of applying this methodology to the Korean stock market.