8,270 research outputs found
A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs
This is the author’s version of a work that was accepted for publication in Applied Soft Computing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Soft Computing, Vol 36 (2015) DOI 10.1016/j.asoc.2015.06.053A memetic approach that combines a genetic algorithm (GA) and quadratic programming is used to address the problem of optimal portfolio selection with cardinality constraints and piecewise linear transaction costs. The framework used is an extension of the standard Markowitz mean–variance model that incorporates realistic constraints, such as upper and lower bounds for investment in individual assets and/or groups of assets, and minimum trading restrictions. The inclusion of constraints that limit the number of assets in the final portfolio and piecewise linear transaction costs transforms the selection of optimal portfolios into a mixed-integer quadratic problem, which cannot be solved by standard optimization techniques. We propose to use a genetic algorithm in which the candidate portfolios are encoded using a set representation to handle the combinatorial aspect of the optimization problem. Besides specifying which assets are included in the portfolio, this representation includes attributes that encode the trading operation (sell/hold/buy) performed when the portfolio is rebalanced. The results of this hybrid method are benchmarked against a range of investment strategies (passive management, the equally weighted portfolio, the minimum variance portfolio, optimal portfolios without cardinality constraints, ignoring transaction costs or obtained with L1 regularization) using publicly available data. The transaction costs and the cardinality constraints provide regularization mechanisms that generally improve the out-of-sample performance of the selected portfolios
Portfolio selection problems in practice: a comparison between linear and quadratic optimization models
Several portfolio selection models take into account practical limitations on
the number of assets to include and on their weights in the portfolio. We
present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset
Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional
Value-at-Risk (LACVaR) models, where the assets are limited with the
introduction of quantity and cardinality constraints. We propose a completely
new approach for solving the LAM model, based on reformulation as a Standard
Quadratic Program and on some recent theoretical results. With this approach we
obtain optimal solutions both for some well-known financial data sets used by
several other authors, and for some unsolved large size portfolio problems. We
also test our method on five new data sets involving real-world capital market
indices from major stock markets. Our computational experience shows that,
rather unexpectedly, it is easier to solve the quadratic LAM model with our
algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of
the best commercial codes for mixed integer linear programming (MILP) problems.
Finally, on the new data sets we have also compared, using out-of-sample
analysis, the performance of the portfolios obtained by the Limited Asset
models with the performance provided by the unconstrained models and with that
of the official capital market indices
Combining Alpha Streams with Costs
We discuss investment allocation to multiple alpha streams traded on the same
execution platform with internal crossing of trades and point out differences
with allocating investment when alpha streams are traded on separate execution
platforms with no crossing. First, in the latter case allocation weights are
non-negative, while in the former case they can be negative. Second, the
effects of both linear and nonlinear (impact) costs are different in these two
cases due to turnover reduction when the trades are crossed. Third, the
turnover reduction depends on the universe of traded alpha streams, so if some
alpha streams have zero allocations, turnover reduction needs to be recomputed,
hence an iterative procedure. We discuss an algorithm for finding allocation
weights with crossing and linear costs. We also discuss a simple approximation
when nonlinear costs are added, making the allocation problem tractable while
still capturing nonlinear portfolio capacity bound effects. We also define
"regression with costs" as a limit of optimization with costs, useful in
often-occurring cases with singular alpha covariance matrix.Comment: 21 pages; minor misprints corrected; to appear in The Journal of Ris
A Unified Approach to Portfolio Optimization with Linear Transaction Costs
In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the problem within our unified framework.portfolio choice, transaction costs, stochastic singular control, stochastic impulse control, computational methods
Multi-Period Trading via Convex Optimization
We consider a basic model of multi-period trading, which can be used to
evaluate the performance of a trading strategy. We describe a framework for
single-period optimization, where the trades in each period are found by
solving a convex optimization problem that trades off expected return, risk,
transaction cost and holding cost such as the borrowing cost for shorting
assets. We then describe a multi-period version of the trading method, where
optimization is used to plan a sequence of trades, with only the first one
executed, using estimates of future quantities that are unknown when the trades
are chosen. The single-period method traces back to Markowitz; the multi-period
methods trace back to model predictive control. Our contribution is to describe
the single-period and multi-period methods in one simple framework, giving a
clear description of the development and the approximations made. In this paper
we do not address a critical component in a trading algorithm, the predictions
or forecasts of future quantities. The methods we describe in this paper can be
thought of as good ways to exploit predictions, no matter how they are made. We
have also developed a companion open-source software library that implements
many of the ideas and methods described in the paper
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