Faculty of Business Administration
Visiting Scholar Seminar
High-Dimensional Index Tracking based on the Adaptive Elastic Net
Dr. Fangquan Shi
School of Finance
Nanjing Audit University
Date: 2 July 2021 (Friday)
When a portfolio consists of a large number of assets, it generally incorporates too many small and illiquid positions and needs a large amount of rebalancing, which can involve large transaction costs. For financial index tracking, it is desirable to avoid such atomized, unstable portfolios, which are difficult to realize and manage. A natural way of achieving this goal is to build a tracking portfolio that is sparse with only a small number of assets in practice. The cardinality constraint approach by directly restricting the number of assets held in the tracking portfolio is a natural idea. However, it requires the pre-specification of the maximum number of assets selected, which is rarely practicable. Moreover, the cardinality constrained optimization problem is shown to be NP-hard. Solving such a problem will be computationally expensive, especially in high-dimensional settings. Motivated by this, this paper employs a regularization approach based on the adaptive elastic-net (Aenet) model for high-dimensional index tracking. The proposed method represents a family of convex regularization methods, which nests the traditional Lasso, adaptive Lasso (Alasso), and elastic-net (Enet) as special cases. To make the formulation problem more practical and general, we also take the full investment condition and turnover restrictions (or transaction costs) into account. An efficient algorithm based on coordinate descent with closed-form updates is derived to tackle the resulting optimization problem. Empirical results show that the proposed method is computationally efficient and has competitive out-of-sample performance, especially in high-dimensional settings.
Dr. Fangquan Shi is currently an Assistant Professor in School of Finance at Nanjing Audit University. He received his Bachelor degree in Computer Science and Technology in 2012 and Master degree in Financial Engineering in 2015 respectively, both from Southwestern University of Finance and Economics. He received his PhD in Decision Science from the Faculty of Business Administration at University of Macau in 2020. He won the Macao Scientific and Technological R&D Award for Postgraduates in 2020. His papers appear on Journal of Financial and Quantitative Analysis and Quantitative Analysis.