An asymptotic analysis of the mean-variance portfolio selection

This paper gives an asymptotic analysis of the mean-variance ( Markowitz-type) portfolio selection under mild assumptions on the market behavior. Theoretical results show the rate of under performance of the risk aware Markowitz-type portfolio strategy in growth rate compared to the log-optimal portfolio strategy, which does not have explicit risk control. Statements are given with and without full knowledge of the statistical properties of the underlying process generating the market, under the only assumption that the market is stationary and ergodic. The experiments show how the achieved wealth depends on the coefficient of risk aversion measured on past NYSE data.