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Article Title:
Developing an Application to Estimating a Covariance Matrix for Financial Risk Management (A Case of Portfolios Risk in Debts Dynamics, Sustainability and Management): Brazil and Ghana
by Prof. Dr. Emmanuel Opoku Ware, CPA and Rowland Dabi

Abstract:
An out-of-sample portfolio allocation study is undertaken. We find that our simple and positive-definite covariance matrix estimator yields strong empirical results under a variety of factor models and thresholding schemes. Conversely, and somewhat surprisingly, we find that the Fama-French factor model is only suitable for covariance estimation when used in conjunction with our proposed thresholding technique. Theoretically, we provide justification for the empirical results by jointly analyzing the in-fill and diverging dimension asymptotics. Moreover, we develop the central limit theory for the integrated risk of continuously rebalanced portfolio strategies. We analyze covariance matrix estimation from the perspective of market risk management, where the goal is to obtain accurate estimates of portfolio risk across essentially all portfolios ? even those with small standard deviations. We propose a simple but effective visualization tool to assess estimator bias. We employ a portfolio perspective to determine covariance matrix loss functions particularly suitable for market risk management. We introduce several specialized loss functions. Proper regularization significantly improves dynamic covariance models. These methods are applied to credit default swaps (CDS), for which covariance matrices are used to set portfolio margin requirements for central clearing. Among the methods we test, the graphical lasso estimator performs particularly well. The graphical lasso and a hierarchical clustering estimator also yield economically meaningful representations of market structure through a graphical model and a hierarchy, respectively. We find that credit default swap log-differences are driven by a strong market factor. The additional effect of natural candidates for other observable market factors is small, but there are latent factors and direct pairwise dependencies at play.

Keywords: covariance, portfolio, debt, sustainability, dynamic, matrix,risk

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