Generalised Mean-Variance Analysis and Robust Portfolio Diversification

This paper presents a new approach to portfolio optimisation that we call generalised mean-variance (GMV) analysis. One important case of this approach is based on the stocks m-tile (or quantile): if m = n, where n is the number of stocks, m-tile membership becomes rank. Our analysis is the rank equivalent of conventional Markowitz Mean Variance analysis. The first stage to generate rank probability statistics using, historic data, Monte Carlo analysis or direct user input. The second stage is optimisation based on those rank statistics to calculate recommended portfolio weights. Our optimisation uses state preference theory to derive an objective function that can be minimised using standard quadratic programming techniques. We deal with some advantages of this method including a more intuitive fully diversified (or minimum risk) position on the efficient frontier with all the portfolio holdings equally weighted.