City Research Online

Abstract

The field of investment management has experienced a profound transformation over the last half-century. The practice has evolved from one dominated by qualitative judgment and individual intuition to a discipline increasingly defined by systematic processes, quantitative analysis, and scientific rigor. This paradigm shift has been propelled by the exponential growth in computational power and the proliferation of financial data, giving rise to the domain of mathematical and quantitative finance. The central premise of this domain is that the application of sophisticated statistical models can be used to identify and systematically harvest market inefficiencies and risk premia.

However, this evolution has introduced a new set of formidable challenges. The sheer volume and complexity of modern financial data present significant obstacles, including the prevalence of noise, the curse of dimensionality, and non-stationarity in market dynamics. Researchers and practitioners must also contend with the ever-present danger of data mining and overfitting statistical models. In this complex landscape, classical portfolio theories, while foundational, often prove to be insufficient. Specifically, traditional diversification strategies can falter when faced with the low-rank nature of financial data, where the returns of thousands of securities are often driven by a small number of underlying common factors. Furthermore, static, single-state models of asset returns fail to capture the abrupt and persistent shifts in market behavior, known as ”regimes,” which are empirically observed throughout economic cycles. The relentless academic and industrial search for predictive signals has also created a factor zoo, a landscape of hundreds of potential return predictors. This proliferation makes the task of combining signals into a single, robust investment score a non-trivial challenge, fraught with the risks of signal redundancy and cancellation.

This thesis argues that overcoming these modern challenges requires a departure from conventional approaches that analyze securities and signals in isolation. It posits that more resilient, efficient, and scalable investment frameworks can be developed by focusing on the identification, modeling, and exploitation of the market’s latent structures. These underlying structures, whether they manifest as the implicit risk factors driving a covariance matrix, the unobservable macroeconomic regimes dictating return distributions, or the fundamental predictive waveforms hidden within noisy data, offer a more parsimonious and robust foundation for building investment portfolios. To this end, this thesis presents three distinct essays that leverage innovative methodologies from fields such as unsupervised machine learning, probabilistic modeling, and electrical engineering to address these critical limitations in modern portfolio construction.

Publication Type:	Thesis (Doctoral)
Subjects:	H Social Sciences > HG Finance Q Science > QA Mathematics
Departments:	Bayes Business School Bayes Business School > Bayes Business School Doctoral Theses Doctoral Theses

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