A Combination Rule for Portfolio Selection with Transaction Costs

AuthorSangwon Suh
Date01 September 2016
Published date01 September 2016
A Combination Rule for Portfolio
Selection with Transaction Costs*
School of Economics, Chung-Ang University, Seoul, Korea
We propose a new portfolio rule for portfolio selection problems in the
presence of transaction costs. The new portfolio rule is formed by combining
an extant portfolio rule with the no-rebalancing portfolio rule, which species
the currentportfolio weights beforerebalancing as the desired portfolioweights.
The new portfolio rule can be applied into most extant portfolio rules.
Simulation and out-of-sample evidence show that the new portfolio rule can
greatly improveportfolio performance, in comparison with the extantportfolio
rules to be combined.
JEL classication: G11; G12
Although the mean-variance framework proposedby Markowitz (1952) is still the
most widely used model in asset allocation and active portfolio management, it
has several shortcomings. One notable problem is the issue of parameter uncer-
tainty or estimation errors. Several approaches have been proposed to improve
portfolio performance in the presence of parameter uncertainty. For example,
Brown ((1976)); Bawa and Klein (1976); Bawa, Brown, and Klein (1979); and
Jorion (1986) utilized a Bayesian approach for portfolio selection to explicitly ac-
count for parameter uncertainty.
More recently, MacKinlay and Pástor (2000),
Kan and Zhou (2007), and Tu and Zhou (2011)provided alternative portfolio rules
to address estimation error problems.
On the other hand, DeMiguel, Garlappi, and Uppal (2009) found that many
sophisticated portfolio rules incur signicant transaction costs. Therefore, the
evaluation of portfolio performance may depend greatly on whether transaction
costs are included. However, the mean-variance rule and alternative portfolio
* The author is grateful for helpful comments from an anonymous referee, the editor (Huining Cao),
Guangsug Hahn, Nhung Le, and other seminar participants from the 2015 meeting of the Korean Se-
curities Association and 2015 World Finance and Banking Symposium.
1 Fabozzi, Huang, and Zhou (2010) and Avramov and Zhou (2010) reviewed recent Bayesian
studies on the parameter uncertainty problem, such as Pástor (2000), Pástor and Stambaugh
(2000), Avramov (2004), Harvey, Liechty, Liechty, and Müller (), Tu and Zhou (2004, 2010),
and Wang (2005).
© 2016 International Review of Finance Ltd. 2016
International Review of Finance, 16:3, 2016: pp. 393420
DOI: 10.1111/ir.12087
rules do not consider transaction costs. Thus, in this paper, we propose a new
portfolio rule to improve performance in the presence of transaction costs.
Investorstypically hold their investablewealth as a form of diversied portfolios.
Rebalancing their portfolio weights from their current portfolio incurs transaction
costs. Becausemost portfolio rules do not account for transactioncosts, accounting
for them within extantportfolio rules may help to improveportfolio performance.
The no-rebalancingportfolio rule species the desired portfolio weights as the
current weights before rebalancing. These are equivalent to the prior-period
portfolio weights after adjustments for price changes during the period between
the previous and current points in time. Therefore, this no-rebalancing rule is the
zero-transaction costrule without incurring any trade. We intend to incorporate
the concerns with transaction costs into extant portfoliorules by combining them
with the zero-transaction costrule. Specically, we construct a new portfolio rule
as a linear combination of an extant benchmark rule with the no-rebalancing rule
and attempt to improve portfolio performance by appropriately combining both
rules. This new method can also be applied to any extant portfolio rule.
Several studies have explicitly included transaction costs in a dynamic setting.
While they typically include quadratic transaction costs for analytical tractability
(e.g., Gârleanu and Pedersen (2013) and DeMiguel et al. (2016)), proportional-
type transaction costs are also studied in several works, such as those of
Constantinides (1986), Davis and Norman (1990), and Liu (2004). However, this
strand of literature mainly intends to qualitatively characterize an optimal policy
of consumption and portfolio selection with a multiperiod horizon and ignores
the issue of parameter uncertainty, which differs from our paper.
Our paper is closely related to that of Tu and Zhou (2011) because both studies
commonly propose a combined portfolio rule. However, Tu and Zhou (2011)pro-
pose to combine a benchmark rule with the equal-weight portfolio rule as a way
to reduce estimation errors, whereas we propose to combine a benchmark rule
with the no-rebalancingportfolio rule in order to incorporate transaction costs.
Although we adopt the idea of a previously proposed combination portfolio rule,
we extend its application by using it with a different motivation and in a differ-
ent way. More recently, DeMiguel et al. (2016) propose multiperiod shrinkage
portfolio rules to mitigate parameter uncertainty problem. Even though the idea
of shrinkage in forming portfolio rules is similar to the idea of combination, our
paper differs from that of DeMiguel et al. (2016) because they take quadratic
transaction costs and shrink only the mean-variance (and the minimum-
variance) portfolios, whereas our paper takes proportional-type transaction costs
and considers various portfolio rules to combine.
We applied the new portfolio rule to several popular benchmark rules and
conducted not only simulation analysis but also out-of-sample performance
comparisons using real datasets. We found that even though several sophisti-
cated and popular benchmark portfolio rules exhibit performance improvements
in a setting without transaction costs, they fail to show outperformance with
returns net of transaction costs. Conversely, this new portfolio rule signicantly
improves performance in the presence of transaction costs in many cases.
International Review of Finance
© 2016 International Review of Finance Ltd. 2016394

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