UC Santa Barbara

In recent years, the L-1 regularization has been extensively used to estimate a sparse precision matrix and encode an undirected graphical model. Because the regularized estimates are biased, the application of the graphical models has largely been restricted and has been ignored in many areas. In this work, we show that graphical models and their regularized estimates can be useful in the area of finance. We present our discussion in three parts. First, we propose a graphical representation model for the asset returns. The model captures observed variance in the equity market endogenously and offers a new perspective on the covariance estimation for asset returns. We show that such a model may provide a straightforward interpretation for investors regarding investment decision making. Second, we show that regularized estimates of graphical models, though biased, are useful to estimate the minimum variance portfolio and determine the portfolio rebalancing strategy. Third, we discuss the algorithms of solving one of the graphical models -- the graphical Concord. We present the software development process for the graphical Concord and illustrate the usage of the packages with some examples.