Modern portfolio theory started with Harry Markowitz’s 1952 seminal paper “Portfolio Selection,” for which he would later receive the Nobel prize in 1990. He put forth the idea that risk-adverse investors should optimize their portfolio based on a combination of two objectives: expected return and risk. Until today, that idea has remained central in portfolio optimization. However, the vanilla Markowitz portfolio formulation does not seem to behave as expected in practice and most practitioners tend to avoid it.
During the past half century, researchers and practitioners have reconsidered the Markowitz portfolio formulation and have proposed countless of improvements and variations, namely, robust optimization methods, alternative measures of risk (e.g., CVaR or ES), regularization via sparsity, improved estimators of the covariance matrix via random matrix theory, robust estimators for heavy tails, factor models, mean models, volatility clustering models, risk-parity formulations, etc.
This course will explore the Markowitz portfolio optimization in its many variations and extensions, with special emphasis on R programming. Each week will be devoted to a specific topic, during which the theory will be first presented, followed by an exposition of a practical implementation based on R programming.