Rebalancing an investment portfolio in the presence of convex transaction costs,including market impact costs

The inclusion of transaction costs is an essential element of any realistic portfolio optimization. We extend the standard portfolio optimization problem to consider convex transaction costs incurred when rebalancing an investment portfolio. Market impact costs measure the effect on the price of a security that result from an effort to buy or sell the security, and they can constitute a large part of the total transaction costs. The loss to a portfolio from market impact costs is often modelled with a convex function that can be expressed using second-order cone constraints. The Markowitz framework of mean-variance efficiency is used. In order to properly represent the variance of the resulting portfolio, we suggest rescaling by the funds available after paying the transaction costs. This results in a fractional programming problem, which we show can be reformulated as an equivalent convex program of size comparable to the model without transaction costs. We show that an optimal solution to the convex program can always be found that does not discard assets.     

Large scale portfolio optimization with piecewise linear transaction costs

We consider the fundamental problem of computing an optimal portfolio based on a quadratic mean-variance model for the objective function and a given polyhedral representation of the constraints. The main departure from the classical quadratic programming formulation is the inclusion in the objective function of piecewise linear, separable functions representing the transaction costs. We handle the non-smoothness in the objective function by using spline approximations. The problem is first solved approximately using a primal-dual interior-point method applied to the smoothed problem. Then, we crossover to an active set method applied to the original non-smooth problem to attain a high accuracy solution. Our numerical tests show that we can solve large scale problems efficiently and accurately.     

基于灵敏度分析的含比例型手续费的投资组合优化

研究含比例型手续费的离散时间投资组合优化问题. 基于马尔可夫决策过程模型和性能灵敏度分析方法, 推导两个不同投资策略之间的资产长期平均增值率的差分公式, 利用差分公式的结构特点, 证明了最优性方程, 并设计出可在线应用的策略迭代算法. 仿真实例验证了所提出算法的有效性.

     

Robust portfolio selection for index tracking

We develop a robust portfolio selection model for tracking a market index using a subset of its assets. The model is a 0-1 integer program that seeks to maximize similarity between selected assets and the assets of the target index. We allow uncertainty in the objective function by using a computationally tractable robust framework that can control the conservativeness of the solution. This protects against worst-case realizations of potential estimation errors and other deviations. Out-of-sample experiments using the S&P 100 demonstrate the advantages of the robust model. Compared to portfolios constructed with the nominal model, moderately conservative robust portfolios are shown to have lower tracking error and risk profiles that are more similar to the target index.     

多阶段均值–方差资产负债管理的随机控制

资产负债管理研究如何合理分配资产以到达最小化风险同时确保期望剩余财富(财富减去负债)达到一定水平.本文在均值–方差投资组合理论的框架下研究两类资产负债管理模型, 包括带有跨期均值–方差投资目标和带有非破产约束的模型. 由于在动态规划意义下, 方差不具有可分性质, 传统的随机最优控制方法难以直接应用. 如采用处理动态均值–方差优化问题的嵌入法来解决以上问题会带来计算上的困难. 本文借鉴平均场控制的思想对以上两类问题加以研究. 本文假设了非常宽泛的市场模型: 所有的资产都是风险资产; 债务和风险资产之间存在相关性. 在此市场假设模型下, 本文给出了最优投资策略(控制率)的解析表达式和均值–方差有效前沿的表达形式. 本研究成果为投资者提供了新的投资策略, 可应用于更复杂的资产负债管理中.     

A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs

A 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.     

Recursive portfolio management: Large-scale evidence from two Scandinavian stock markets

In the present study, we present evidence on the efficiency of a recursive linear portfolio management system. Extensive tests have been performed using data from two Scandinavian stock markets. The optimal ex-ante investment strategies generated by the system yield a yearly return on investment of 75 to 80% when using a forecasting horizon of three to five days. The computational efficiency of the system can be improved considerably by using a faster optimization algorithm.     

Robust hedging strategies

While investing in foreign assets may bring additional benefits in terms of risk diversification, it may also expose the portfolio to a further source of risk derived from changes in the value of the foreign currencies. Hedging strategies for international portfolios have usually focused on the use of forward contracts to mitigate the currency risk. We propose an alternative formulation aimed at the reduction of the overall portfolio risk by assuming the returns are uncertain and maximizing the portfolio return for the worst possible outcome of the returns. This technique known as robust optimization provides a first guarantee on the portfolio value thanks to the non-inferiority property. We further complement our approach with forward contracts on the foreign exchange rates and options on the assets. Because the total return on any asset will be the product of its local return and currency return, the models proposed are bilinear and non convex. A reformulation of both the uncertainty set and the objective function as a semidefinite problem will yield an approximate tractable model. We compare the hedging alternatives proposed with simulated and historical market data and conclude on their relative benefits.     

Robust optimization framework for cardinality constrained portfolio problem

One of the primary concerns on any asset allocation problem is to maintain a limited number of assets from the market. The problem becomes more complicated when the return of all risky assets are subject to uncertainty. In this paper, we propose a new portfolio modeling approach with uncertain data and it is also analyzed using different robust optimization techniques. The proposed formulations are solved using genetic algorithm. The implementation of the proposed method is examined on variety of well known benchmark data sets.     

基于PSO的考虑完整费用的证券组合优化研究

通过分析中国证券市场证券交易不可拆分、不能卖空的特点以及现存的各种交易费用,建立一个考虑完整交易费用的证券投资组合优化模型,同时给出一个应用粒子群算法(PSO)求解的实例。结果证明该证券投资组合优化模型的完整性和有效性,也表明PSO算法可以快速准确地求解证券投资组合优化问题。     

Continuous-time mean variance portfolio with transaction costs: a proximal approach involving time penalization

This paper proposes a new continuous-time optimization solution that enables the computation of the portfolio problem (based on the utility option pricing and the shortfall risk minimization). We first propose a dynamical stock price process, and then, we transform the solution to a continuous-time discrete-state Markov decision processes. The market behavior is characterized by considering arbitrage-free and assessing transaction costs. To solve the problem, we present a proximal optimization approach, which considers time penalization in the transaction costs and the utility. In order to include the restrictions of the market, as well as those that imposed by the continuous-time space, we employ the Lagrange multipliers approach. As a result, we obtain two different equations: one for computing the portfolio strategies and the other for computing the Lagrange multipliers. Each equation in the portfolio is an optimization problem, for which the necessary condition of a maximum/minimum is solved employing the gradient method approach. At each step of the iterative proximal method, the functional increases and finally converges to a final portfolio. We show the convergence of the method. A numerical example showing the effectiveness of the proposed approach is also developed and presented.     

A clustering-based review on project portfolio optimization methods

Project portfolio management and optimization constitutes a critical activity for organizations in different industrial sectors and business. The scientific literature in this subject is extremely vast, which makes it difficult to understand the connections among the existing approaches and perspectives. This paper provides a clustering map of the existing work on the subject, thus identifying the main trends and approaches from different scientific communities. After analyzing each of the identified clusters, the paper provides insights and emerging trends that can be useful both for researchers and practitioners in the area.     

Quadratic programming with transaction costs

We consider the problem of maximizing the mean-variance utility function of n$n$ assets. Associated with a change in an asset's holdings from its current or target value is a transaction cost. These must be accounted for in practical problems. A straightforward way of doing so results in a 3n$3n$-dimensional optimization problem with 3n$3n$ additional constraints. This higher dimensional problem is computationally expensive to solve. We present an algorithm for solving the 3n$3n$-dimensional problem by modifying an active set quadratic programming (QP) algorithm to solve the 3n$3n$-dimensional problem as an n$n$-dimensional problem accounting for the transaction costs implicitly rather than explicitly. The method is based on deriving the optimality conditions for the higher dimensional problem solely in terms of lower dimensional quantities and requires substantially less computational effort than any active set QP algorithm applied directly on a 3n$3n$-dimensional problem.     

Growth optimal investment in discrete-time markets with proportional transaction costs

We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d. discrete-time two-asset markets under proportional transaction costs. We then extend our analysis to cover markets having more than two stocks. The market is modeled by a sequence of price relative vectors with arbitrary discrete distributions, which can also be used to approximate a wide class of continuous distributions. To achieve the optimal growth, we use threshold portfolios, where we introduce a recursive update to calculate the expected wealth. We then demonstrate that under the threshold rebalancing framework, the achievable set of portfolios elegantly form an irreducible Markov chain under mild technical conditions. We evaluate the corresponding stationary distribution of this Markov chain, which provides a natural and efficient method to calculate the cumulative expected wealth. Subsequently, the corresponding parameters are optimized yielding the growth optimal portfolio under proportional transaction costs in i.i.d. discrete-time two-asset markets. As a widely known financial problem, we also solve the optimal portfolio selection problem in discrete-time markets constructed by sampling continuous-time Brownian markets. For the case that the underlying discrete distributions of the price relative vectors are unknown, we provide a maximum likelihood estimator that is also incorporated in the optimization framework in our simulations.     

A linear programming algorithm for optimal portfolio selection with transaction costs

We study the optimal portfolio selection problem with transaction costs. In general, the efficient frontier can be determined by solving a parametric non-quadratic programming problem. In a general setting, the transaction cost is a V-shaped function of difference between the existing and the new portfolio. We show how to transform this problem into a quadratic programming model. Hence a linear programming algorithm is applicable by establishing a linear approximation on the utility function of return and variance.     

Multi-period portfolio optimization with linear control policies

This paper is concerned with multi-period sequential decision problems for financial asset allocation. A model is proposed in which periodic optimal portfolio adjustments are determined with the objective of minimizing a cumulative risk measure over the investment horizon, while satisfying portfolio diversity constraints at each period and achieving or exceeding a desired terminal expected wealth target. The proposed solution approach is based on a specific affine parameterization of the recourse policy, which allows us to obtain a sub-optimal but exact and explicit problem formulation in terms of a convex quadratic program.In contrast to the mainstream stochastic programming approach to multi-period optimization, which has the drawback of being computationally intractable, the proposed setup leads to optimization problems that can be solved efficiently with currently available convex quadratic programming solvers, enabling the user to effectively attack multi-stage decision problems with many securities and periods.     

A dynamic capabilities perspective of IS project portfolio management

Organizations use information systems project portfolio management (IS PMM) to reconfigure their IS resources and capabilities to match changing market and economic conditions. IS PPM can therefore be characterised as a dynamic capability. We investigate how firms developed and adapted IS PPM to match the turbulent recessionary conditions witnessed after 2008–2009. This study contributes to an understanding of IS PPM by identifying the constituent dynamic capabilities and providing empirical examples of adaptation. To our knowledge, the study is the first to apply the notion of second order dynamic capabilities to the IS domain and also makes an important contribution to the more general concept of dynamic capabilities by providing empirical evidence and theoretical justification of the increased detailed, centrally controlled and analytical nature of IS PPM dynamic capabilities in recessionary conditions.     

Evolutionary multi-objective portfolio optimization in practical context

This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.     

Optimal portfolio selection of assets with transaction costs and no short sales

In this paper we study the optimal portfolio selection problem for assets. A double-objective programming model is first formulated for selecting optimal portfolios of asserts with transaction costs and taxes, where short sales and borrowings are not allowed. Some properties of efficient portfolios and the efficient frontier to the model are then derived. Based on these results, an interactive method that requires only paired preference comparison from the investor is established for solving the optimal portfolio selection problem. A numerical example is also presented to illustrate this method.     

Application portfolio management: a decision-oriented view of enterprise architecture

Today large companies operate 100s of computer-based information systems (IS), also called applications, to support their businesses. Enterprise Architecture (EA) is regarded as a promising concept to cope with the complexity caused by large application portfolios (AP). This article focuses on senior IT managers’ decision-making with regard to their AP, and EA’s role therein. Through multiple case studies in large companies, we found that these managers consider and balance a set of aspects, each of which is supported by partial EA models maintained by specific groups within their IT departments. These models are, however, not sufficiently integrated. Based on the empirical findings, we propose indicators for each of the partial EA models to aggregate the AP-relevant characteristics per application, which are then integrated into an AP dashboard to support senior IT managers’ holistic AP management. Consequently, a decision-oriented view is created of the overall EA, which the managers of the case studies companies deemed to be very helpful for steering their AP.