A Combination Rule for Portfolio Selection with Transaction Costs

• Date: 01 September 2016
• DOI: http://doi.org/10.1111/irfi.12087
• Published date: 01 September 2016

A Combination Rule for Portfolio

Selection with Transaction Costs*

SANGWON SUH

School of Economics, Chung-Ang University, Seoul, Korea

ABSTRACT

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 specifies

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 classification: G11; G12

I. INTRODUCTION

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.

1

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 significant 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. 393–420

DOI: 10.1111/irfi.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 diversified 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-rebalancing’portfolio rule specifies 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 cost’rule without incurring any trade. We intend to incorporate

the concerns with transaction costs into extant portfoliorules by combining them

with the ‘zero-transaction cost’rule. Specifically, 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-rebalancing’portfolio 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 significantly

improves performance in the presence of transaction costs in many cases.

International Review of Finance

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