The Adaptive Multi-Factor Model and the Financial Market

Abstract

Modern evolvements of the technologies have been leading to a profound influence on the financial market. The introduction of constituents like Exchange-Traded Funds, and the wide-use of advanced technologies such as algorithmic trading, results in a boom of the data which provides more opportunities to reveal deeper insights. However, traditional statistical methods always suffer from the high-dimensional, high-correlation, and time-varying instinct of the financial data. In this dissertation, we focus on developing techniques to stress these difficulties. With the proposed methodologies, we can have more interpretable models, clearer explanations, and better predictions. We start from proposing a new algorithm for the high-dimensional financial data -- the Groupwise Interpretable Basis Selection (GIBS) algorithm, to estimate a new Adaptive Multi-Factor (AMF) asset pricing model, implied by the recently developed Generalized Arbitrage Pricing Theory, which relaxes the convention that the number of risk-factors is small. We first obtain an adaptive collection of basis assets and then simultaneously test which basis assets correspond to which securities. Since the collection of basis assets is large and highly correlated, high-dimension methods are used. The AMF model along with the GIBS algorithm is shown to have significantly better fitting and prediction power than the Fama-French 5-factor model. Next, we do the time-invariance tests for the betas for both the AMF model and the FF5 in various time periods. We show that for nearly all time periods with length less than 6 years, the $\beta$ coefficients are time-invariant for the AMF model, but not the FF5 model. The $\beta$ coefficients are time-varying for both AMF and FF5 models for longer time periods. Therefore, using the dynamic AMF model with a decent rolling window (such as 5 years) is more powerful and stable than the FF5 model. We also successfully provide a new explanation of the well-known low-volatility anomaly which pervades in the finance literature for a long time. We use the Adaptive Multi-Factor (AMF) model estimated by the Groupwise Interpretable Basis Selection (GIBS) algorithm to find those basis assets significantly related to low and high volatility portfolios. These two portfolios load on very different factors, which indicates that volatility is not an independent risk, but that it is related to existing risk factors. The out-performance of the low-volatility portfolio is due to the (equilibrium) performance of these loaded risk factors. For completeness, we compare the AMF model with the traditional Fama-French 5-factor (FF5) model, documenting the superior performance of the AMF model.