Comput Manag Sci
DOI 10.1007/s10287-016-0257-2
ORIGINAL PAPER
Bootstrap estimation of the efficient frontier
Begoña Font
1
Received: 30 January 2015 / Accepted: 9 May 2016
© Springer-Verlag Berlin Heidelberg 2016
Abstract In this paper, we propose a bootstrap resampling methodology to obtain
the confidence intervals for efficient portfolios weights and the sample characteristics
of the mean-variance efficient frontier. We provide an estimate of efficient portfo-
lios, compute the confidence region of the efficient frontier and get the prediction
densities of the future efficient portfolio returns without distributional assumptions
on returns. An extensive simulation study evaluates the finite-sample performance of
these bootstrap intervals and stresses the advantages of such approach. Interestingly,
the methodology can be easily modified to make inferences that incorporate our mod-
elling of returns in the predictive efficient frontier estimation with or without additional
managerial restrictions.
Keywords Asset allocation · Efficient frontier · Portfolio analysis · Mean-variance
portfolios · Resampling methods · Sharpe ratio optimal portfolio · Interval estimation
1 Introduction
The mean-variance analysis derived by Markowitz (1952) is a milestone in modern
finance theory for optimal portfolio construction, asset allocation and investment diver-
sification. According to his theory, the investor selects his optimal portfolio depending
on his risk aversion level on the Markowitz efficient frontier, i.e. the set of efficient
portfolios with minimum risk for a given level of the average portfolio return. Two
mean-variance efficient portfolios play an important role in asset allocation: the global
B Begoña Font
maria.b.font@uv.es
1
Department of Mathematics for Economics and Business, Faculty of Economics, University of
Valencia, Tarongers Campus, Av. dels Tarongers, s/n, 46022Valencia, Spain
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