Essays on fitting factor models for asset returns

Abstract

Factor models are used to describe the fundamental drivers of financial asset returns. There are 3 types: time-series factor, statistical factor and fundamental factor models. While factor models have existed for almost 60 years, industry-wide adoption with factor-based investing has surged in the last decade. This dissertation is centered on factorAnalytics, an open source R package co-developed with other UW students and faculty members, that demystifies the industry black-box models, making model fitting tools readily available for any interested academic or practitioner. Chapter 1 compares the characteristics of the three types of models in terms of model specification, estimation, interpretation and various in-sample and out-of-sample performance metrics using S&P 500 stock returns. Like Connor (1995), we find that the fundamental factor model outperforms the time-series and statistical factor models since it makes use of additional information on asset-specific characteristics. Moreover, we find that adding statistical factor(s) extracted from the residuals of time-series or fundamental factor models, or, fitting fundamental factors to the residuals of a time-series factor model, to create hybrid models, further improves performance. Investment management firms need to understand peer positioning for a variety of reasons, including risk management. Factor models provide a framework to estimate peer exposures, especially useful when holdings-based information is lacking. Chapter 2 presents a multi-asset time-series factor model constructed from long-short portfolios of asset class index returns, applied to peer-average returns from the Morningstar U.S. fund allocation categories. We show that factors are better than asset classes for assessing unknown exposures and decomposing risk in multi-asset portfolios. Furthermore, there is an opportunity to create more efficient, better risk-diversified portfolios using factors when making allocation decisions. We use the multi-factor model to construct equal-asset-risk and equal-factor-risk portfolios and compare them to the equal-weighted and minimum-variance portfolios. We also show that a zero-investment equal-factor-risk portfolio sleeve helps bridge the gap between pure risk parity and traditional portfolios, enhancing Sharpe ratio across all risk categories. Chapters 3-5 contain vignettes for each type of factor model that describe and demonstrate model fitting, factor risk (volatility, value-at-risk and expected shortfall) decomposition, and related S3 generic methods.