The mean–variance model is widely acknowledged as the foundation of portfolio allocation because it provides a framework for analyzing the trade-off between risk and return for gaining diversification benefits. Despite the well-known shortcomings of the model, it is often the starting point for making asset allocation decisions. In this article, the authors briefly review mean–variance optimization and approaches for resolving its limitations by demonstrating backtest results on asset allocation. Feedback from asset managers is also included to explain how optimization methods are applied in practice. TOPICS:Quantitative methods, statistical methods, portfolio construction, performance measurement Key Findings ▪ Mean–variance optimization provides a framework for analyzing risk–return trade-offs when making asset allocation decisions. ▪ Sensitivity of the mean–variance model can be addressed with robust models, and the model generates candidate asset allocations that are informative in practice. ▪ Feedback from asset managers suggests that mean–variance optimization along with simulation and various robust methods are being applied in practice for asset allocation.

In quantitative portfolio management, combining optimization with estimation causes concern for asset managers because portfolio problems may be sensitive to deviations in their inputs, but obtaining accurate input estimates is a difficult task. Robust factor models address these concerns using factor models for estimating asset returns and worst-case approaches for gaining stability in portfolio performance. Recent studies on robust factor investing explore methods of incorporating factors into robust portfolio construction. In this article, the authors provide a survey that includes theoretical insight, empirical findings from historical data, and experience from practitioners in formulating and executing robust factor-based investment strategies.

In investment management, especially for automated investment services, it is critical for portfolios to have a manageable number of assets and robust performance. First, portfolios should not contain too many assets in order to reduce the management fees, transaction costs, and taxes. Second, portfolios should be robust as investment environments change rapidly. In this study, therefore, we propose two convex portfolio selection models that provide portfolios that are sparse and robust. We first perform semi-definite relaxation to develop a sparse mean-variance portfolio selection model, and further extend the model by using $L_2$-norm regularization and worst-case optimization to formulate two sparse and robust portfolio selection models. Empirical analyses with historical stock returns demonstrate the effectiveness of the proposed models in forming sparse and robust portfolios.

Machine learning has been widely used in the asset management industry to improve operations and make data-driven decisions. This article provides an overview of machine learning for asset management by presenting various machine learning models in the context of their applications, including general classification and regression, time series forecasting, natural language processing, dimension reduction, reinforcement learning, data generation, recommendation, and clustering. Additionally, it highlights the challenges of implementing machine learning in asset management, such as data quality and quantity, interpretability, and fairness.