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.

This paper plays a part in two branches of the asset pricing literature, the multi-factor literature built on the Arbitrage Pricing Theory (APT) from Ross (1976) [1] and the Inter-temporal Capital Asset Pricing Model (ICAPM) from Merton (1973) [2] and to the growing literature related to the low-risk anomaly. First, we use the Adaptive Multi-Factor (AMF) model framework developed in Zhu et al. (2018) [3] in which both the APT and ICAPM are special cases under weaker conditions with three main added benefits: 1) It allows for a large number of risk factors to explain returns even though empirically a smaller subset of them is needed to explain returns, 2) The set of risk factors is different for different securities, and 3) The risk factors are Exchange Traded Funds (ETF) which are tradeable instruments. Second, the low-risk anomaly is an empirical asset pricing observation in which stocks with lower risk yield higher returns than stocks with higher risk. The two main measures for characterising risk in this context are volatility of returns and β derived from the Capital Asset Pricing Model (CAPM). Therefore, when mentioning the low-risk anomaly, we are referring to the low-volatility and the low-beta anomaly interchangeably.