El Karoui, N. (2010) High-Dimensionality Effects in the Markowitz Problem and Other Quadratic Programs with Linear Constraints: Risk Underestimation. The Annals of Statistics, 38, 3487-3566.
http://dx.doi.org/10.1214/10-AOS795

has been cited by the following article:

• TITLE: High Dimensionality Effects on the Efficient Frontier: A Tri-Nation Study

  AUTHORS: Rituparna Sen, Pulkit Gupta, Debanjana Dey

  KEYWORDS: High Dimensional Covariance Matrix Estimation, Minimum-Variance Portfolio, Norm Con-Strained Portfolio

  JOURNAL NAME: Journal of Data Analysis and Information Processing, Vol.4 No.1, February 15, 2016

  ABSTRACT: Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.