Three concepts: stochastic discount factors, multi-beta pricing and mean-variance efficiency, are at the core of modern empirical asset pricing. This chapter reviews these paradigms and the relations among them, concentrating on conditional asset-pricing models where lagged variables serve as...

Implied expected returns are the expected returns for which a supposedly mean-variance efficient portfolio is effectively efficient given a covariance matrix. We analyze the statistical properties of monthly implied expected return estimates and study their sensitivity to the choice of a...

We use firm characteristics to estimate the enduring momentum probabilities for past winners (losers) to continue to be future winners (losers). The enduring momentum probability is significantly related to stock return persistence and explains cross-sectional expected returns. In addition, it...

Graphical models have shown remarkable performance in uncovering the conditional dependence structure across a set of given variables. In this paper, we introduce two new graphical modelling approaches—called Gslope and Tslope—to the portfolio selection literature for directly estimating the...

Investors sometimes have strong convictions that a distinctive economic regime will prevail in the period ahead and therefore would like to form a portfolio that reflects the expected returns, standard deviations, and correlations of assets during such a regime. To do so, they typically isolate...

We analyze the performance of investable portfolios built using predicted stock returns from machine learning methods and attribute their performance to linear, marginal non-linear and interaction effects. We use a large set of features including price-based, fundamental-based, and...