My PhD Thesis
As you may have noticed, my posting activity on this site over the past several years has been effectively non-existent. I originally created this blog to encourage myself to “finish” mini-projects I was using to learn Python and find a career in quant investment management, but it has now morphed somewhat into my personal landing page. In 2019 I began a part-time PhD, where I maintained my full-time career as a quant equity research whilst spending my nights and weekends doing academic research. Naturally this meant the more “fun” data/learning projects posted here went to the bottom of the priority pile.
In November 2023 I was officially conferred my Doctor in Philosophy, capping off a fairly intense life period of work, work, and more work. The benefit of this is that now I have an emerging body of research which I’m allowed to share publicly (no secret sauce from the firms I’ve worked at!). This post will give you a simple overview of the core projects from my thesis. I’ll possibly do a follow-up on some of the tips/tricks I learnt along the way for managing a part-time PhD + full-time work.
You can access the full thesis here and I’ve dropped the Introduction of the thesis below.
Introduction
Academics and practitioners utilize commonly accepted views, paradigms, and “rules of thumb” in their everyday work. These consensus views often exist in response to the inherent challenge in modeling real-world financial markets. Empirical models are often not sophisticated enough to fully capture the complex behavior of financial markets, often leading to empirical anomalies: contradictions between real-world behavior and the behavior predicted by financial models. In financial markets, a dogmatic approach to many of the existing puzzles and anomalies has generally been adopted. Longstanding results, while not standing up to empirical evidence, persist to this day due to their acceptance as “easy to understand” and “easy to explain.” A canonical example is the capital asset pricing model (CAPM), independently proposed in the 1960s by several researchers. Despite the continuous challenges and criticism of the CAPM, it remains commonplace in finance curricula and empirical practice.
The blending of natural and social sciences is at the heart of this adherence to commonly accepted paradigms. The study of financial economics aims to develop and apply mathematical models to the real-world of financial markets. On one hand, financial economics is a social science studying the behavior of financial markets, which are themselves derivatives of human behavior and design. As humans change, the assets and markets they create and interact with also evolve. On the other hand, humans like to impose longstanding “laws” and “theories” to model real-world behavior. Nevertheless, the mathematical tools available are often not sophisticated enough to fully model ever-changing human behavior. This complexity leads to the core challenge of financial economics. Humans want to perfectly model real-world observations, yet perfectly modeling financial markets is impossible. This conflict ultimately leads to longstanding, and often dogmatic, adherence to commonly held views, whereas in reality, the evolving nature of financial markets requires constant challenging and re-evaluation of such perspectives.
This thesis examines biases and puzzles in empirical finance that arise from both traditional and modern modeling approaches. Chapters 2–4 of this thesis each explore a different topic in empirical finance research where commonly held beliefs are prevalent. Chapter 2 resolves the CAPM beta anomaly by fully accounting for time-series asynchronicity using dynamic time warping (DTW). Chapter 3 challenges the notion that the Standard and Poor’s (S&P) index effect has disappeared, finding that the S&P index effect is still present for subsets of index change announcements. Finally, Chapter 4 questions the current discipline when applying machine learning in asset pricing by demonstrating how empirical anomalies can arise from seemingly innocuous arbitrary modeling decisions.
Asynchronicity between financial time series
Asynchronicity is at the core of time-series models in financial econometrics. As markets have become faster, a prevailing view is that asynchronicity has become less problematic in empirical modeling, but this is far from accurate Although asynchronicity at lower frequencies (such as daily observations) has undoubtedly reduced, as long as latency between trading venues exists, latency will exist between common assets. The persistent nature and varying manifestations of asynchronicity continue to plague time-series models and have undue influence on model inference. Therefore, it is necessary to continue to explore methods for measuring and correcting for asynchronicity in financial models.
Chapter 2 proposes using DTW to measure asynchronicity between financial time series. DTW has a distinct advantage over prevailing methods: it estimates the lead-lag between time series for every observation in the estimation window. This key advantage allows DTW to be used in novel ways to correct for asynchronicity when comparing financial time series and to explore new ways of studying existing problems. I first use a simulation framework to demonstrate that DTW is effective at capturing stylized lead–lag structures between two time series. I subsequently use DTW to align stock returns with market returns, and then measure a stock’s beta to the market on these DTW-aligned time series. By fully incorporating the dynamic asynchronicity between stock returns and market returns, the DTW-estimated betas helps resolve the longstanding beta anomaly. I also use DTW to study intraday price leadership patterns between global futures contracts. Using DTW, I uncover rich intraday lead–lag dynamics between U.S. and U.K. equity index futures that are centered around significant market operation events in the underlying equity markets. Existing price discovery models miss such dynamics, as they are unable to provide sufficient granularity in the estimation window to uncover such patterns.
Chapter 2 also demonstrates how applying new techniques can challenge long-held consensus views around empirical results. Asynchronicity effects in trading drive the manifestation of stock betas, resulting in the beta anomaly in historical data. Although previous approaches for incorporating this asynchronicity into the measurement of beta improve the base result, they do not fully account for the dynamic nature of asynchronicity. By fully accounting for the dynamic lead–lag effects, a more accurate beta estimate can be obtained. Ultimately, DTW is shown to be a suitable method for measuring and correcting for dynamic asynchronicity between financial time series.
Is the S&P index effect dead?
One of the core features of financial markets is their self-learning nature. As academics and practitioners collectively learn and disseminate research around financial markets, participants incorporate this information into their behavior when operating in these markets. Academic literature can reveal an empirical observation in historical data, but there is no guarantee that this observation will manifest in the future realizations of the data. The commonly known S&P index effect is a key example of this phenomenon. Initial research (Harris and Gurel, 1986; Shleifer, 1986; Jain, 1987; Dhillon and Johnson, 1991; Lynch and Mendenhall, 1997; Chen, Noronha, and Singal, 2004) showed that stocks experience abnormal returns when added to or deleted from the S&P 500 index and that this pattern could be exploited for profit. New results (Kamal, Lawrence, McCabe, and Prakash, 2012; Kim, Li, and Perry, 2017; Bender, Nagori, and Tank, 2019; Bennett, Stulz, and Wang, 2020), using an updated sample of index announcements, find that the S&P index effect has disappeared. Stocks no longer experience statistically significant abnormal returns when added to or deleted from the S&P 500 index. However, this claim of the death of the S&P index effect has coincided with the enormous growth in passive investing and the amount of assets passively following the S&P 500 index. With such a significant growth in assets that mechanically track the S&P 500 index, the economic prior suggests that the S&P index effect should still exist, creating a puzzling observation of the death of the index effect.
Chapter 3 examines the S&P index effect by collecting a complete sample of S&P 500, S&P 400, and S&P 600 index change announcements and tracking the internal movements that occur between these indexes. By jointly considering the abnormal return responses of stocks to index change announcements for the three S&P indexes, I show that the S&P index effect is not dead. Rather, it is the migrations between S&P indexes that no longer experience significant abnormal price responses when index changes are announced. Stocks that are added from outside the broader S&P 1500 universe to one of the three S&P indexes still experience significant abnormal return responses when such a change is announced. By measuring the changing distribution in passive ownership between large capitalization and small capitalization stocks, I show that the S&P index effect is alive and well.
Chapter 3 further demonstrates that different approaches to studying the same problem can yield different conclusions. By replicating original studies with newer data, the original results on the existence of the S&P index effect can be discarded if the market context of the new results is not acknowledged. However, by considering how changes in market structure (such as the growth of passive investing) could impact index changes, richer insights on the S&P index effect can be obtained, complementing, and extending earlier results.
Biases and overfitting in cross-sectional machine learning models
The application of machine learning models across numerous disciplines has seen significant success in recent years. Seminal papers applying machine learning to asset pricing demonstrate the strength and superiority of machine learning models when using large sets of cross-sectional asset pricing characteristics to predict future excess returns across various asset classes. However, with such rapid growth in the literature, and the applied approach of trial-and-error for estimating these models, a rigorous understanding of how these models operate in the asset pricing domain has been understudied.
Chapter 4 critically examines the current application of machine learning models in the asset pricing literature. By imposing an economic prior on the relationship between market capitalization and future excess returns, economically significant improvements over existing approaches are obtained. By training group-specific machine learning models to predict stock returns, these model predictions outperform those trained on the entire cross-section of stocks. This result is counter-intuitive to the commonly held belief that “the more data, the better” for machine learning models. I show how this performance improvement should not be fully attributed to the imposed economic prior around group-specific asset pricing characteristics. Instead, the gain arises predominantly from a lack of regularization in the standard machine learning model design for predicting stock returns. This lack of regularization induces overfitting toward predicting returns for small stocks in cross-sectional machine learning models. By recognizing and correcting for this lack of regularization, similar performance gains as group-specific machine learning models can be achieved without the added computational complexity of training separate models.
Chapter 4 also demonstrates that even for more modern techniques, commonly held views and practices around these techniques should be challenged and continuously evaluated. It is detrimental to adhere to widely set empirical methods, particularly in machine learning, without questioning the economic rationale backing each decision inherent to the method. The high dimensionality of modeling decisions in machine learning means that a cautious and guided approach to investigating and comparing results from the use of machine learning in asset pricing is fundamental to its ongoing success.