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Friday, June 5
Practice and Applications
Practice and Applications Posters, Part 2
Fri, Jun 5, 2:00 PM - 5:00 PM
TBD
 

On Using Graphical Models and Regularized Parameter Estimates: Practical Considerations and Applications (308359)

*Zhipu Zhou, University of California - Santa Barbara 
Sang-Yun Oh, University of California - Santa Barbara 

Keywords: sparse graphical model, regularized parameter estimates, portfolio selection

Graphs are indispensable for modern-day data analysis and modeling for its ability to intuitively represent underlying relationships. In statistics, for example, sparse estimation of the inverse covariance matrix is a popular way to capture the underlying pairwise dependency relationships through the resulting zero/non-zero pattern. Despite the usefulness of the sparsity pattern, the parameter estimates, i.e. the estimated non-zero values, have been largely ignored due to the bias introduced by L1-regularization. In this work, we show that the regularized parameter estimates outperform a number of other estimators (despite the bias) where the underlying relative conditional dependencies are important. Furthermore, we give applications of graphical models where the graph (i.e., the sparsity pattern), as well as the parameter estimates, are used in concert for solving the portfolio allocation problem. Our empirical study uses the Dow Jones Industrial Average (DJIA) component stocks over 22 years horizon with a periodic rebalancing strategy. Our results show that using sparse inverse covariance estimator in portfolio optimization produces an improved portfolio performance. Specifically, the empirical results present increased realized returns, Sharpe ratios, terminal wealth, and smaller realized-risk, turnover rate, and short side of the portfolio. In our empirical study, we develop a dynamic portfolio rebalancing strategy by detecting change points based on likelihood ratio test statistic for regularized sparse inverse covariance estimates. We verify the performance in finite sample through simulation. We show that the performance of our portfolio selection approach is improved while reducing realized-risk. In addition, a heuristic graph similarity measure is developed in order to compare two dependency structures by utilizing both the sparsity pattern and the parameter estimates simultaneously.