The investor’s objective is to select a portfolio that maximizes expected return for a given level of risk (variance) or equivalently, to minimize variance for a given level of expected return (this is the dual optimization problem).
The classical approach is based upon Harry Markowitz’s ground-breaking work (1952) on Modern Portfolio Theory. Expected returns, volatilities and correlations used as input parameters in the model are generally estimated from historical data.
The classical mean-variance Markowitz framework is not suitable for all investors. Indeed, parameter uncertainty and the resulting estimation error have been found to substantially diminish the value of traditional theory-based portfolio models.
The recent finance literature has proposed alternative methods in portfolio construction that reduce estimation error, improve stability, and hence, increase the robustness of results. In the Black-Litterman model and its extensions, the investor’s views are combined with analysis of historical returns data to improve estimator efficiency.