A penalized expected risk criterion for portfolio selection

Under the classical mean-variance framework, the purpose of this paper is to investigate the properties of the instability of minimal variance portfolio and then propose a novel penalized expected risk criterion (PERC) for optimal portfolio selection.

The proposed method considers not only a portfolio’s expected risk, but also its instability that is quantified by the variance of the estimated portfolio weights. This study tests the out-of-sample performance of various portfolio selection methods on both China and US stock markets.

It is very useful to control portfolio stability in real application of portfolio selection. The empirical results on both US and China stock markets show that PERC portfolio effectively controls turnover and consequently the transaction cost, and that is why it is so competing compared with other alternative methods.

The findings suggest that the rebalancing turnover and the associated transaction cost that is usually ignored in theoretical analysis play a very important role in real investment.

For investors, especially institutional investors, the rebalancing turnover and corresponding transaction cost must be carefully addressed. The variance of the estimated portfolio weights is a good candidate to quantify portfolio instability.

This study addresses the important role of portfolio instability and proposes a novel expected risk criterion for portfolio selection after the quantitative definition of portfolio instability.