Robust Growth-Optimal Portfolios
File(s)
Accepted version
Author(s)
Rujeerapaiboon, N
Kuhn, D
Wiesemann, W
Type
Journal Article
Abstract
The growth-optimal portfolio is designed to have maximum expected log-return over the next rebalancing
period. Thus, it can be computed with relative ease by solving a static optimization problem. The growthoptimal
portfolio has sparked fascination among finance professionals and researchers because it can be
shown to outperform any other portfolio with probability 1 in the long run. In the short run, however, it is
notoriously volatile. Moreover, its computation requires precise knowledge of the asset return distribution,
which is not directly observable but must be inferred from sparse data. By using methods from distributionally
robust optimization, we design fixed-mix strategies that offer similar performance guarantees as the
growth-optimal portfolio but for a finite investment horizon and for a whole family of distributions that share
the same first and second-order moments. We demonstrate that the resulting robust growth-optimal portfolios
can be computed efficiently by solving a tractable conic program whose size is independent of the length
of the investment horizon. Simulated and empirical backtests show that the robust growth-optimal portfolios
are competitive with the classical growth-optimal portfolio across most realistic investment horizons and for
an overwhelming majority of contaminated return distributions
period. Thus, it can be computed with relative ease by solving a static optimization problem. The growthoptimal
portfolio has sparked fascination among finance professionals and researchers because it can be
shown to outperform any other portfolio with probability 1 in the long run. In the short run, however, it is
notoriously volatile. Moreover, its computation requires precise knowledge of the asset return distribution,
which is not directly observable but must be inferred from sparse data. By using methods from distributionally
robust optimization, we design fixed-mix strategies that offer similar performance guarantees as the
growth-optimal portfolio but for a finite investment horizon and for a whole family of distributions that share
the same first and second-order moments. We demonstrate that the resulting robust growth-optimal portfolios
can be computed efficiently by solving a tractable conic program whose size is independent of the length
of the investment horizon. Simulated and empirical backtests show that the robust growth-optimal portfolios
are competitive with the classical growth-optimal portfolio across most realistic investment horizons and for
an overwhelming majority of contaminated return distributions
Date Issued
2016-07
Date Acceptance
2015-04-11
Citation
Management Science, 2016, 62 (7), pp.2090-2109
ISSN
1526-5501
Publisher
INFORMS (Institute for Operations Research and Management Sciences)
Start Page
2090
End Page
2109
Journal / Book Title
Management Science
Volume
62
Issue
7
Copyright Statement
© 2015, INFORMS
Subjects
Social Sciences
Science & Technology
Technology
Management
Operations Research & Management Science
Business & Economics
portfolio optimization
growth-optimal portfolio
distributionally robust optimization
value-at-risk
second-order cone programming
semidefinite programming
VARIANCE-EFFICIENT PORTFOLIOS
WORST-CASE VALUE
VALUE-AT-RISK
EXPECTED UTILITY
OPTIMIZATION
EQUILIBRIUM
INFORMATION
CRITERIA
MODELS
CHOICE
Operations Research
08 Information and Computing Sciences
15 Commerce, Management, Tourism and Services
Publication Status
Published
Date Publish Online
2015-11-13