A comprehensive review and analysis of different modeling approaches for financial index tracking problem

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 comprehensive overview of the various modeling approaches and strategies developed for index tracking, highlighting the strengths and limitations of each approach. We categorize the index tracking models into three broad frameworks: optimization-based models, statistical-based models and machine learning based data-driven approach. A comprehensive empirical study conducted on the S\&P 500 dataset demonstrates that the tracking error volatility model under the optimization-based framework delivers the most precise index tracking, the convex co-integration model, under the statistical-based framework achieves the strongest return-risk balance, and the deep neural network with fixed noise model within the data-driven framework provides a competitive performance with notably low turnover and high computational efficiency. By combining a critical review of the existing literature with comparative empirical analysis, this paper aims to provide insights into the evolving landscape of index tracking and its practical implications for investors and fund managers.

Learning hidden cascades via classification

The spreading dynamics in social networks are often studied under the assumption that individuals' statuses, whether informed or infected, are fully observable. However, in many real-world situations, such statuses remain unobservable, which is crucial for determining an individual's potential to further spread the infection. While this final status is hidden, intermediate indicators such as symptoms of infection are observable and provide important insights into the spread process. We propose a partial observability-aware Machine Learning framework to learn the characteristics of the spreading model. We term the method Distribution Classification, which utilizes the power of classifiers to infer the underlying transmission dynamics. We evaluate our method on two types of synthetic networks and extend the study to a real-world insider trading network. Results show that the method performs well, especially on complex networks with high cyclic connectivity, supporting its utility in analyzing real-world spreading phenomena where direct observation of individual statuses is not possible.

Time-Series Foundation Model for Value-at-Risk

This study is the first to explore the application of a time-series foundation model for VaR estimation. Foundation models, pre-trained on vast and varied datasets, can be used in a zero-shot setting with relatively minimal data or further improved through finetuning. We compare the performance of Google's model, called TimesFM, against conventional parametric and non-parametric models, including GARCH, Generalized Autoregressive Score (GAS), and empirical quantile estimates, using daily returns from the S\&P 100 index and its constituents over 19 years. Our backtesting results indicate that, in terms of the actual-over-expected ratio, the fine-tuned TimesFM model consistently outperforms traditional methods. Regarding the quantile score loss function, it achieves performance comparable to the best econometric approach, the GAS model. Overall, the foundation model is either the best or among the top performers in forecasting VaR across the 0.01, 0.025, 0.05, and 0.1 VaR levels. We also found that fine-tuning significantly improves the results, and the model should not be used in zero-shot settings. Overall, foundation models can provide completely alternative approaches to traditional econometric methods, yet there are challenges to be tackled.

Sparse Portfolio Selection via Topological Data Analysis based Clustering

This paper uses topological data analysis (TDA) tools and introduces a data-driven clustering-based stock selection strategy tailored for sparse portfolio construction. Our asset selection strategy exploits the topological features of stock price movements to select a subset of topologically similar (different) assets for a sparse index tracking (Markowitz) portfolio. We introduce new distance measures, which serve as an input to the clustering algorithm, on the space of persistence diagrams and landscapes that consider the time component of a time series. We conduct an empirical analysis on the S\&P index from 2009 to 2020, including a study on the COVID-19 data to validate the robustness of our methodology. Our strategy to integrate TDA with the clustering algorithm significantly enhanced the performance of sparse portfolios across various performance measures in diverse market scenarios.