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.