This thesis explores innovative approaches to factor investing by examining the dynamics of factor portfolios and introducing novel methodologies for constructing and utilizing characteristic-based equity factors. Chapter 1 addresses the predictability of factor portfolios within the context of factor timing. This is achieved by extending stock return predictability to a portfolio level and using various dimension reduction techniques in both the characteristics and returns space. The analysis demonstrates that factor portfolios are predictable based not only on their own but also on other characteristics, highlighting the significant potential for asset return prediction. This finding also suggests that different portfolios share similarities in terms of signal sources or underlying factors.

Chapter 2 introduces a new technique for constructing characteristic-based equity factors, termed \say{power sorting}. This method leverages the non-linearities and asymmetries inherent in characteristic-return relationships while maintaining computational simplicity and avoiding excessive weighting. Empirical analysis shows that power sorting consistently delivers superior out-of-sample performance compared to traditional quantile sorting and other factor portfolio construction methods. The approach proves robust across different factors and time periods, with its effectiveness not attributable to increased turnover or tail risk. Moreover, power-sorted versions of well-known asset pricing factor models outperform their original counterparts.

Extending the power sorting methodology to the multivariate level, Chapter 3 investigates the evolution of portfolio dynamics when multiple characteristics are jointly considered. While Chapter 2 shows that, in a univariate context, individual characteristics drive portfolio performance primarily through the short side, the analysis in Chapter 3 reveals a shift in importance to the long side when characteristics are jointly analyzed. The multivariate power sorting approach achieves two key objectives: the development of multifactor strategies with significantly enhanced risk-adjusted performance and the construction of a six-factor model that effectively spans the tangency portfolio.