Mean-variance portfolio optimization when means and covariances are estimated

Zehao Chen (Stanford)

Markowitz's celebrated mean-variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plug them into the efficient frontier that assumes know parameters leads to the so-called "Markowitz enigma", which states that portfolio with the "plug-in" efficient frontier can behave badly and be counter-intuitive. We first review different approaches and explains why they fall short of their good. We then describe a new approach with ideas in stochastic adaptive control, bootstrap resampling and consistent estimates of high-dimensional covariance matrice with certain sparsity assumption. Applications of the new approach in simulated and real data are also given.

This is joint work with T. L. Lai and Haipeng Xing.