# Mean-variance portfolio optimization: methods for superior estimates of returns

Leaving aside the aspects related to the estimation of the variance component (all the latest techniques to compute a stable covariance matrix of a given set of assets such as simple shrinkage, Ledoit-Wolf shrinkage, Oracle shrinkage, MCD (minimum covariance determinant), EWMA covariance etc.) how is it possible to improve the optimization results considering the estimation of the mean return component or rather what methods happened to be more effective and efficient in estimating the returns (both from the empirical and practical point of view)?

Of course the simple linear model (expectation = mean return over the last n years) is quite simplistic.

$$\omega = \frac{\Sigma^{-1}\iota}{\iota^{\top}\Sigma^{-1}\iota}$$