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Index tracking, also known as passive investing, has gained significant traction in financial markets due to its cost-effective and efficient approach to replicating the performance of a specific market index. This review paper provides a…

Portfolio Management · Quantitative Finance 2026-01-08 Vrinda Dhingra , Amita Sharma , Anubha Goel

An actively managed portfolio almost never beats the market in the long term. Thus, many investors often resort to passively managed portfolios whose aim is to follow a certain financial index. The task of building such passive portfolios…

Sparse index tracking is a prominent passive portfolio management strategy that constructs a sparse portfolio to track a financial index. A sparse portfolio is preferable to a full portfolio in terms of reducing transaction costs and…

Portfolio Management · Quantitative Finance 2024-03-19 Eisuke Yamagata , Shunsuke Ono

We address the problem of partial index tracking, replicating a benchmark index using a small number of assets. Accurate tracking with a sparse portfolio is extensively studied as a classic finance problem. However in practice, a tracking…

Portfolio Management · Quantitative Finance 2020-02-04 Yu Zheng , Timothy M. Hospedales , Yongxin Yang

Partial (replication) index tracking is a popular passive investment strategy. It aims to replicate the performance of a given index by constructing a tracking portfolio which contains some constituents of the index. The tracking error…

Portfolio Management · Quantitative Finance 2019-11-15 Yu Zheng , Bowei Chen , Timothy M. Hospedales , Yongxin Yang

In this paper, we study asset selection methods to construct a sparse index tracking portfolio. For its advantage over full replication portfolio, the concept of sparse index tracking portfolio has significant attention in the field of…

Computational Engineering, Finance, and Science · Computer Science 2024-05-10 Yutaka Sakurai , Daiki Wakabayashi , Fumio Ishizaki

Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward…

Portfolio Management · Quantitative Finance 2021-07-27 Spiridon Penev , Pavel Shevchenko , Wei Wu

We study the construction and rebalancing of sparse index-tracking portfolios from an operational research perspective, with explicit emphasis on uncertainty quantification and implementability. The decision variables are portfolio weights…

Computational Finance · Quantitative Finance 2025-12-29 Dimitrios Roxanas

We develop a methodology for index tracking and risk exposure control using financial derivatives. Under a continuous-time diffusion framework for price evolution, we present a pathwise approach to construct dynamic portfolios of…

Mathematical Finance · Quantitative Finance 2017-05-31 Tim Leung , Brian Ward

Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that…

Portfolio Management · Quantitative Finance 2018-07-31 Ali Al-Aradi , Sebastian Jaimungal

This paper studies the finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject capital into the portfolio account such that the total…

Portfolio Management · Quantitative Finance 2021-05-03 Lijun Bo , Huafu Liao , Xiang Yu

Among professionals and academics alike, it is well known that active portfolio management is unable to provide additional risk-adjusted returns relative to their benchmarks. For this reason, passive wealth management has emerged in recent…

Portfolio Management · Quantitative Finance 2022-03-28 Daniele Bufalo , Michele Bufalo , Francesco Cesarone , Giuseppe Orlando

In the practical business environment, portfolio managers often face business-driven requirements that limit the number of constituents in their tracking portfolio. A natural index tracking model is thus to minimize a tracking error measure…

Optimization and Control · Mathematics 2015-06-22 Fengmin Xu , Zhaosong Lu , Zongben Xu

Index funds are substantially preferred by investors nowadays, and market sensitivities are instrumental in managing index funds. An index fund is a mutual fund aiming to track the returns of a predefined market index (e.g., the S&P 500). A…

Portfolio Management · Quantitative Finance 2022-12-20 Yoonsik Hong , Yanghoon Kim , Jeonghun Kim , Yongmin Choi

In this research, we introduce a novel methodology for the index tracking problem with sparse portfolios by leveraging topological data analysis (TDA). Utilizing persistence homology to measure the riskiness of assets, we introduce a…

Computational Engineering, Finance, and Science · Computer Science 2023-10-17 Anubha Goel , Puneet Pasricha , Juho Kanniainen

An index tracker is a passive investment reproducing the return and risk of a market index, an enhanced index tracker offers a return greater than the index. We consider the selection of a portfolio of given cardinality to track an index,…

Portfolio Management · Quantitative Finance 2025-03-25 N. Meade , C. A. Valle , J. E. Beasley

The Total Portfolio Approach and Strategic Asset Allocation are widely viewed as competing frameworks for institutional portfolio management. We argue they differ in a single governance parameter: the tracking error constraint. Using U.S.…

Portfolio Management · Quantitative Finance 2026-03-04 Ashwin Alankar , Allan Maymin , Philip Maymin , Myron Scholes , Sujiang Zhang

Recently, $L_1$ regularization have been attracted extensive attention and successfully applied in mean-variance portfolio selection for promoting out-of-sample properties and decreasing transaction costs. However, $L_1$ regularization…

Optimization and Control · Mathematics 2015-06-22 Fengmin Xu , Zongben Xu , Honggang Xue

Tracking a financial index boils down to replicating its trajectory of returns for a well-defined time span by investing in a weighted subset of the securities included in the benchmark. Picking the optimal combination of assets becomes a…

Quantum Physics · Physics 2021-10-22 Samuel Fernández-Lorenzo , Diego Porras , Juan José García-Ripoll

While Indices, Index tracking funds and ETFs have grown in popularity during then last ten years, there are many structural problems inherent in Index calculation methodologies and the legal/economic structure of ETFs. These problems raise…

General Finance · Quantitative Finance 2020-05-05 Michael C. Nwogugu
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