Author: Zhaokun Cai
Advisor: Dr. Ionut Florescu, Dr. Chihoon Lee
Date: October 1, 2024
Department: Financial Engineering
Degree: Doctor of Philosophy
Advisory Committee:
Dr. Ionut Florescu, Chairman
Dr. Chihoon Lee, Chairman
Dr. Rong Liu,
Dr. Zachary Feinstein,
Dr. Jia Xu
Abstract: Portfolio theory typically presumes that the decision-maker possesses complete information about the underlying assets ex-ante. However, it is well-established that ex-post performance is sensitive to estimation risk. This proposal outlines three approaches designed to reduce the severe impact of estimation errors in portfolio optimization, focusing on the mean-variance approach introduced by Markowitz. The first essay, ”Partial Index Tracking Enhanced Mean-Variance Portfolio” proposes a shrinkage-based rule that leverages the idea of partial index-tracking. The proposed rule attains a higher ex-post mean-variance efficiency than the sample approach. The proposed approach replaces the portfolio variance in the mean-variance optimization with a linear combination of portfolio variance and its tracking error. To determine the optimal tuning parameter, we take advantage of the Expected Outof-sample Utility (EOOSU) framework proposed by Kan & Zhou (2007, JFQA) and minimize the mean squared error (MSE) with respect to the utopian mean-variance rule. Empirical findings underscore the efficacy of this proposed rule, showcasing not only comparable performance to widely adopted shrinkage-based methods prevalent in existing literature but also a distinct advantage in terms of lower turnover and reduced tracking error. The second essay, titled ”The Economic Value of MSE: Evidence from Portfolio Selection” proceeds by examining the importance of MSE in portfolio selection. The essay focuses on bridging utility loss and MSE disparity using the EOOSU framework, establishing a theoretical link between the two metrics. This connection forms the iv basis for advocating MSE minimization in addition to EOOSU maximization, leading to improved performance, as seen in the first project. Our findings collectively emphasize the significant role of MSE and its widespread use as a loss metric for refining standard machine learning models in the finance sector. The third essay delves into explainable artificial intelligence (XAI) within the mean-variance framework. While recent literature shows that the mean-variance optimization is equivalent to unconstrained ordinary least square (OLS) regression, contemporary machine-learning algorithms forge a more potent link between target returns and portfolio weights. Despite their effectiveness, these algorithms remain complex to interpret. Drawing from game theory, the Shapley values (SHAP) framework emerges, offering a novel method to demystify black-box machine learning. SHAP’s lens breaks down projected outcomes into components, enhancing our grasp of optimizing portfolio weights. Furthermore, this framework becomes a valuable tool for assessing the portfolio weights from its observable performance.
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