Mean-variance portfolio optimization when means and covariances are
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.