Out-of-Sample Performance of Norm-Constrained Portfolios

Abstract

This paper extends the academic research around the Norm-Constrained Portfolio Strategies introduced by DeMiguel et al. in 2009 in terms of out-of-sample performance evaluation on the German Stock Market (DAX) for the years 2003 – 2020. Therefore, four different variations of the Norm-Constrained Portfolios are used that are: 1) 1-Norm Constrained Portfolio calibrated for low variance, 2) 1-Norm Constrained Portfolio calibrated for maximum return, 3) 2-Norm Constrained Portfolio calibrated for low variance, and 4) 2-Norm Constrained Portfolio calibrated for maximum portfolio return. A rolling window approach is applied to evaluate out-of-sample performance. Thereby Return, Variance, and Sharpe Ratio are taken as performance measurements. Empirical results show that the 1-Norm Constrained Portfolio calibrated for low variance is able to provide a significantly lower variance than the DAX given same return. However, this result may be viewed with a grain of salt since the corresponding Sharpe Ratio is not superior as it should be compared to the DAX’ one. Hence the result may suffer from a calculation error which I was not able to locate.