The article "Markowitz Portfolio Construction at Seventy" by Stephen Boyd, Kasper Johansson, Ronald Kahn, Philipp Schiele, and Thomas Schmelzer revisits and extends Harry Markowitz's original 1952 paper on portfolio selection. Markowitz's method, which optimizes the trade-off between expected return and risk, has been a cornerstone of modern portfolio theory. Despite criticisms, such as sensitivity to data errors and estimation uncertainty, the method remains dominant in practice due to its practical extensions and robust optimization techniques. The authors address these criticisms by proposing an extension of Markowitz's method that includes practical constraints and objective terms, such as transaction costs and leverage limits. This extension maintains the convex optimization nature of the original method, ensuring reliable and efficient solutions. The paper also discusses the historical context, the evolution of portfolio construction methods, and the role of software in facilitating practical implementation. Key contributions include: 1. **Robust Optimization and Regularization**: Techniques to mitigate sensitivity to input data, such as robust optimization and regularization, are discussed. 2. **Convex Optimization**: The paper highlights the advancements in convex optimization, including solvers and domain-specific languages (DSLs) that make it easier to specify and solve complex optimization problems. 3. **Practical Extensions**: The authors propose a generalized Markowitz trading problem, referred to as Markowitz++, which includes additional objective terms and constraints to handle practical issues and improve robustness. The article provides a comprehensive overview of the theoretical foundations, practical applications, and recent developments in Markowitz portfolio construction, making it a valuable resource for both practitioners and researchers in the field.The article "Markowitz Portfolio Construction at Seventy" by Stephen Boyd, Kasper Johansson, Ronald Kahn, Philipp Schiele, and Thomas Schmelzer revisits and extends Harry Markowitz's original 1952 paper on portfolio selection. Markowitz's method, which optimizes the trade-off between expected return and risk, has been a cornerstone of modern portfolio theory. Despite criticisms, such as sensitivity to data errors and estimation uncertainty, the method remains dominant in practice due to its practical extensions and robust optimization techniques. The authors address these criticisms by proposing an extension of Markowitz's method that includes practical constraints and objective terms, such as transaction costs and leverage limits. This extension maintains the convex optimization nature of the original method, ensuring reliable and efficient solutions. The paper also discusses the historical context, the evolution of portfolio construction methods, and the role of software in facilitating practical implementation. Key contributions include: 1. **Robust Optimization and Regularization**: Techniques to mitigate sensitivity to input data, such as robust optimization and regularization, are discussed. 2. **Convex Optimization**: The paper highlights the advancements in convex optimization, including solvers and domain-specific languages (DSLs) that make it easier to specify and solve complex optimization problems. 3. **Practical Extensions**: The authors propose a generalized Markowitz trading problem, referred to as Markowitz++, which includes additional objective terms and constraints to handle practical issues and improve robustness. The article provides a comprehensive overview of the theoretical foundations, practical applications, and recent developments in Markowitz portfolio construction, making it a valuable resource for both practitioners and researchers in the field.