Simplified Mean-Variance Portfolio Optimisation

Abstract

We propose a simplified approach to mean-variance portfolio problems by changing their parametrisation from trading strategies to final positions. This allows us to treat, under a very mild no-arbitrage-type assumption, a whole range of quadratic optimisation problems by simple mathematical tools in a unified and model-independent way. We provide explicit formulas for optimal positions and values, connections between the solutions to the different problems, two-fund separation results, and explicit expressions for indifference values.

Keywords: mean-variance, portfolio choice, hedging, indifference valuation, Markowitz problem, two-fund separation, no approximate profits, minimum variance, Sharpe ratio

JEL Classification: G11, C61, D81