Ph.D. Defense: Duyeol Lee
Public Presentation via ZOOM
Join URL: https://unc.zoom.us/j/955324595
Precision Finance and BERET
Ongoing advances in financial theory, from modern portfolio theory to valuation of complex financial derivatives, have heavily relied on statistical methodologies. In particular, portfolio theory has become a basic model that must be considered by a variety of market participants, from large financial institutions to individual investors. Another important statistical topic in financial modeling is measuring the dependency among various risk factors and testing independence among them. In this dissertation, we introduce new methods contributing to these topics.
The first concerns the problem of precision finance, particularly constructing individual investors’ portfolios. Conventional models that financial advisors use to construct individual investors’ portfolios are known to be based on the level of investor risk preference to some extent. However, relatively little is known about how advisors allocate their client wealth. Furthermore, recent studies show that investors’ portfolios depend more on advisor effect than investor characteristics. We propose an optimal portfolio strategy in which the estimate of investor risk preference plays the most important role. It is not only consistent with economic theory but also suitable for practical implementation. Simulation results indicate that the proposed method provides a good estimator of the optimal portfolio weights that maximizes investor’s expected utility.
The second part of the dissertation considers tests of independence of random vectors. Recently, the binary expansion testing framework was introduced to test the independence of two continuous random variables by utilizing symmetry statistics that are complete sufficient statistics for dependence. We develop a new test by an ensemble method that uses the sum of squared symmetry statistics and distance correlation. Simulation studies suggest that this method improves the power while preserving the clear interpretation of the binary expansion testing. We extend this method to tests of independence of random vectors in arbitrary dimension. By random projections, the proposed binary expansion randomized ensemble test transforms the multivariate independence testing problem into a univariate problem. Simulation studies and data example analyses show that the proposed method provides relatively robust performance compared with existing methods.