Celebrating Harry Markowitz’s legacy of mean–variance optimization, this paper reviews the history of MVO and proposes a Bayesian approach to estimating inputs for expected return.
Abstract
We celebrate the life, work, and intellectual legacy of Harry Markowitz (1927–2023). Professor Markowitz’s philosophy and math have guided portfolio construction and asset allocation for 71 years. Markowitz optimization (MVO) was set forth in his 1952 University of Chicago Ph.D. dissertation. We trace the links from his work to William Sharpe’s CAPM and the investment giants who followed. MVO has been challenged and enhanced and has endured. But Markowitz did leave us the task of figuring out how to estimate the “stage one” inputs for MVO, which are expected return and risk. (Stage two is running the optimizer.) We propose a Bayesian approach to crafting those inputs.