Using column generation to solve extensions to the Markowitz model

Abstract

We introduce a solution scheme for portfolio optimization problems with cardinality constraints. Typical portfolio optimization problems are extensions of the classical Markowitz mean–variance portfolio optimization model. We solve such types of problems using a method similar to column generation. In this scheme, the original problem is restricted to a subset of the assets resulting in a master convex quadratic problem. Then the dual information of the master problem is used in a subproblem to propose more assets to consider. We also consider other extensions to the Markowitz model to diversify the portfolio selection within given intervals for active weights.     

A Three-phase Approach to an Enhanced Index-tracking Problem with Real-life Constraints

Abstract

Enhanced index tracking is an emerging strategy for investing money in the stock market and is aimed at achieving outperformance over a given benchmark index while achieving a low tracking error. We consider the problem of rebalancing a portfolio for an enhanced index tracking strategy subject to various real-life constraints, including a lower bound and an upper bound on the expected tracking error. To solve this problem, we propose a three-phase approach consisting of preprocessing, optimization, and learning. In a computational experiment, we applied this approach to rebalance a given portfolio on a monthly basis over a time horizon of 10 years; the data for the S&P 500 benchmark index were provided by the investment company Principal Global Investors. Our approach generated portfolios that were provably close to optimality for all monthly rebalancing decisions. Over the entire horizon of 10 years, the portfolios devised by our approach yielded cumulative returns higher than the S&P 500 index after transaction costs with a moderate tracking error.     

GAN-MP hybrid heuristic algorithm for non-convex portfolio optimization problem

Abstract

During recent decades, the traditional Markowitz model has been extended for asset cardinality, active share, and tracking-error constraints, which were introduced to overcome the drawbacks of the original Markowitz model. The resulting optimization problems, however, are often very difficult to solve, whereas those of the original Markowitz model are easily solvable. In order to resolve the portfolio optimization problem for the new extensions, we developed a novel heuristic algorithm that combines GAN (Generative Adversarial Networks) with mathematical programming: the GAN-MP hybrid heuristic algorithm. To the best of our knowledge, this is the first attempt to bridge neural networks (NN) and mathematical programming to tackle a real-world portfolio optimization problem. Computational experiments with real-life stock data show that our algorithm significantly outperforms the existing non-linear optimization solvers.     

Variable neighborhood search heuristic for nonconvex portfolio optimization

Abstract

In this article we consider a portfolio optimization problem under multiple real-world constraints, such as: cardinality constraints, tracking error, active share, and turnover. We propose a heuristic based on variable neighborhood search (VNS) that effectively addresses additional constraints that introduce non-convexities. In the VNS-based heuristic, several neighborhood structures are introduced and fast local search is implemented. We develop a VNS portfolio rebalancing framework (VNS-PRF) with two rebalance strategies. Data sets provided by a financial investment firm are used to evaluate the validity and reliability of the proposed VNS-PRF. Computational experiments and different portfolio performance measures indicate that our approach is able to obtain solutions with competitive quality and can be applied on large-scale data sets.     

An extension to the classical mean–variance portfolio optimization model

Abstract

The purpose of this study is to find a portfolio that maximizes the risk-adjusted returns subject to constraints frequently faced during portfolio management by extending the classical Markowitz mean–variance portfolio optimization model. We propose a new two-step heuristic approach, GRASP & SOLVER, that evaluates the desirability of an asset by combining several properties about it into a single parameter. Using a real-life data set, we conduct a simulation study to compare our solution to a benchmark (S&P 500 index). We find that our method generates solutions satisfying nearly all of the constraints within reasonable computational time (under an hour), at the expense of a 13% reduction in the annual return of the portfolio, highlighting the effect of introducing these practice-based constraints.     

Index fund optimization using a hybrid model: genetic algorithm and mixed-integer nonlinear programming

Abstract

Index funds consist of a subset of stocks, an index tracking portfolio, included in the market index. The index tracking portfolio aims to match the performance of the benchmark index. In this paper, we propose a hybrid model for solving the multiperiod index tracking problem, which includes rebalancing concerns, transaction costs, limits on the number of stocks, and diversification by sector, market capitalization, and stock weight. Our hybrid model combines the genetic algorithm (GA) to select stocks of the index tracking portfolio and mixed-integer nonlinear programming (MINLP) to estimate its weights. Finally, we apply our proposed hybrid model to the S&P500 to find an index tracking portfolio that includes those constraints. The results show that our hybrid model is able to create an index fund whose return rate is similar to the market index with significantly lower risk.     

Resource ambidexterity through alliance portfolios and firm performance

Research summary : Partner resources can be an important alternative to internal firm resources for attaining dual and seemingly incompatible strategic objectives. We extend arguments about managing conflicting objectives typically made at the firm level to the level of a firm's alliance portfolio. Specifically, will a balance between revenue enhancement and cost reduction attained collectively through partner resources accessed via a firm's various alliances be similarly beneficial for firm performance? Additionally, how do strategic attributes of alliance portfolio configuration, specifically alliance portfolio size and partner resource scope, condition the balance‐performance relationship? Based on data from the global airline industry, we find support for the balance‐performance relationship, though such balance is less beneficial for firms in the case of access to a broader resource scope per partner . Managerial summary : Increasing revenue and reducing costs simultaneously can potentially enhance firm competitiveness. We highlight that an alliance strategy can be an important alternative to internal resources for attaining such dual strategic objectives, particularly when partner resources accessed through alliances are treated collectively as portfolios. We examine the importance of balancing product‐market extending and efficiency‐improving partner resources in the global airline industry as well as the impact of two alternate strategies for accessing resources through alliances: fewer partners with more resources per partner or more partners with fewer resources per partner. We find that resource balance at the portfolio level helps airlines improve performance. Our results also suggest that managers should be cautious of accessing too many resources through just a few partners . Copyright © 2015 John Wiley & Sons, Ltd.     

Crypto-assets portfolio optimization under the omega measure

Abstract

Crypto-currencies, or crypto-assets, represent a new class of investment assets. The traditional portfolio analysis approach of Markowitz is not appropriate for use with portfolios containing crypto-assets, as the model requires that the investor have a quadratic utility function or that the returns be normally distributed, which isn’t the case for crypto-assets. We develop a portfolio optimization model based on the Omega measure which is more comprehensive than the Markowitz model, and apply this to four crypto-asset investment portfolios by means of a numerical application. The results indicate that these portfolios should favor traditional market assets over crypto-assets. In the case of portfolios formed only by crypto-assets, there is no clear preference in favor of any crypto-asset in particular.     

Venture capitalists' decision to withdraw: The role of portfolio configuration from a real options lens

When does a venture capital firm withdraw from an investment project prior to its completion? This study offers a real options view on this decision by examining the contingent effects of portfolio configuration. We explore how project withdrawal can be influenced by two distinct dimensions of portfolio configuration, portfolio focus in a strategic domain and portfolio diversity across multiple domains. The empirical analysis shows that while portfolio focus weakens the negative effect of industry‐level uncertainty on a venture capitalist's propensity to withdraw from a project, portfolio diversity strengthens the effect of uncertainty. This study informs current research on the boundary of real options theory and sheds light on the behavior of venture capitalists in financing entrepreneurship. Copyright © 2013 John Wiley & Sons, Ltd.     

Logistics scheduling to minimize inventory and transport costs

We study a logistics scheduling problem where a manufacturer receives raw materials from a supplier, manufactures products in a factory, and delivers the finished products to a customer. The supplier, factory and customer are located at three different sites. The objective is to minimize the sum of work-in-process inventory cost and transport cost, which includes both supply and delivery costs. For the special case of the problem where all the jobs have identical processing times, we show that the inventory cost function can be unified into a common expression for various batching schemes. Based on this characteristic and other optimal properties, we develop an O(n) algorithm to solve this case. For the general problem, we examine several special cases, identify their optimal properties, and develop polynomial-time algorithms to solve them optimally.     

Small fish,big fish: The performance effects of the relative standing in partners' affiliate portfolios

This study examines whether the value a venture derives from an affiliation depends on its relative standing in the portfolio of all affiliations held by its partner. Relative standing refers to how the venture ranks among other ventures in the partner's portfolio with respect to expected returns. The relative standing of a venture in its partner's portfolio influences the venture's access to the partner's resources and the venture's performance. We also argue that a venture's relative standing becomes more important to performance when the partner has a larger portfolio or higher status. In addition to a field study, we test the effect of a venture's relative standing in a venture capital portfolio on its exit likelihood, controlling for endogeneity. We find support for our hypotheses. Copyright © 2014 John Wiley & Sons, Ltd.     

Vertical integration,innovation, and alliance portfolio size: Implications for firm performance

We examine the consequences of alliance portfolio configuration by focusing on contingencies that affect the impact of alliance portfolio size on innovation and financial performance. While increasing alliance portfolio size is expected to positively impact innovation and financial performance, we propose that, at high levels of innovation of the focal firm, increasing alliance portfolio size dampens financial performance. We also propose that firm boundaries moderate the impact of alliance portfolio size on innovation and financial performance differently. Specifically, vertically integrated firms benefit less (more) than their vertically specialized counterparts in leveraging higher innovation (financial) performance with increasing alliance portfolio size. Our analysis suggests that both vertical scope and innovation levels of the firm play an important role in understanding how alliance portfolios impact performance. Copyright © 2013 John Wiley & Sons, Ltd.     

Alliance Concentration in Multinational Companies: Examining Alliance Portfolios,Firm Structure,and Firm Performance

Research summary: This article explores the distribution of alliances across firms' internal structure. Focusing on multinational companies, we examine the impact of alliance portfolio concentration—i.e., the extent to which alliances are concentrated within a limited number of geographic units—on focal firms' performance. Relying on Knowledge‐Based View (KBV) insights, we hypothesize that an increase in alliance portfolio concentration positively influences firm performance and that alliance portfolio size negatively moderates this relationship. Our empirical results enrich the emerging capability perspective on alliance portfolios, point to the relevance of conceptualizing focal firms in alliance portfolio research as polylithic entities instead of monolithic ones, and provide new insights into how firms create value by potentially recombining externally accessed knowledge. Managerial summary: In the setting of multinational companies, we examine whether alliance activities are concentrated in a limited number of subsidiaries or are highly dispersed across multiple subsidiaries. We find that, over time, firms exhibit different patterns in terms of alliance portfolio concentration. In addition, the results show that, for MNCs with a relatively small alliance portfolio, an increase in alliance portfolio concentration is positively related to their financial performance. However, when MNCs' alliance portfolios are relatively large, the relationship between alliance portfolio concentration and firm performance becomes negative. Jointly, these findings suggest that the distribution of alliances across firms' internal structure is an important factor in shaping potential knowledge recombination benefits from alliance portfolios. Copyright © 2017 John Wiley & Sons, Ltd.     

Unpacking functional alliance portfolios: How signals of viability affect young firms' outcomes

This article investigates how alliance portfolio composition affects young firms' outcomes. Drawing on signaling theory, we propose how alliance portfolio composition—number, functional domains (R&D, manufacturing, and marketing), and single‐purpose or multi‐purpose nature of alliances within the portfolio—may affect a firm's likelihood of achieving a liquidity event (IPO or acquisition). We study 8,600 U.S.‐based, VC‐backed firms during the period of 1990 to 2002 from 10 industry sectors. We find that alliance portfolios (to a certain extent) increase a firm's liquidity event likelihood. Further, firms with heterogeneous alliance portfolios, including portfolios emitting greater efficiency signals versus endorsement signals, are more likely to experience an IPO versus acquisition. Our findings lend support to the value of multi‐function alliances within portfolios. Copyright © 2013 John Wiley & Sons, Ltd.     

The relationship between portfolio diversification and firm value: The evidence from corporate venture capital activity

Corporate venture capital (CVC) activity exposes firms to new technologies and markets. An important but as yet unexplored question is the relationship of the industry diversification profile of the portfolio of venture companies to corporate value creation. Insights from options and diversification perspectives support our hypothesis that diversification of a corporate investor's portfolio of venture companies is related to corporate wealth creation in a U‐shaped relationship. We also propose that a corporate investor's financial constraints moderate the relationship between the diversification profile of its CVC portfolio and value creation. When we tested our hypotheses using a sample of CVC investments across multiple industries, we found support for them, and these findings may inform the CVC activities of corporate investors. Copyright © 2013 John Wiley & Sons, Ltd.     

Strategies for managing a portfolio of alliances

Interorganizational relationships are recognized as an increasingly important source of competitive advantage. Hence, goal‐oriented management of the alliance portfolio—all the alliances of the focal firm—plays a decisive role in company performance. Consequently, the configuration and development of the alliance portfolio become important strategic issues. In light of that, this article develops theoretical propositions that seek to clarify what determines the configuration and evolution of an alliance portfolio, and then presents the results of a longitudinal study to illustrate the developed theoretical framework. Building on contingency theory and a coevolutionary framework, we were able to identify three distinctive types of portfolio strategies at business level and to illustrate how they interact with the development of the business strategy and the business environment. Encompassing all this, the study illustrates and explains developmental paths and patterns in the evolution of an alliance portfolio. The developmental course typically evolves from adapting to shaping and to exploiting (stabilizing), according to the state of strategic uncertainty and the firm's resource endowment. A sudden increase in exogenous strategic uncertainty, however, can lead to a strategic shift back to an exploration or hybrid strategy. Copyright © 2007 John Wiley & Sons, Ltd.     

Product variety arising from hedging in the fashion supply chains

Consider a well-defined fashion apparel category, where the variants are distinguished by style and colour, and are subject to two equally likely states of the world: State1 when some variants become popular and others unpopular, and State2 when the reverse takes place. We analyse the optimal portfolio and variety arising from hedging against uncertainty triggered by the states, by integrating the Markowitz and the Newsboy models, while carefully considering demand correlations. We show that due to the complex structure of the uncertainty, building hedging portfolios with competing items is necessary for optimality. We also show how mis-specifying the distributions can lead to very bad trade-offs between risk and expected profit, caused by a lack of proper hedging.     

Technological capabilities and firm performance: The case of small manufacturing firms in Japan

The purpose of this study is to investigate the relationship between technological capabilities and firm performance. We divide technological capabilities into two types—refinement capability, which involves the improvement of the existing asset portfolio, and reconfiguration capability, which involves the restructuring of the asset portfolio through the integration of new assets. The results of an analysis of a sample of 302 small and medium-sized manufacturing firms in Japan suggest that refinement capability relates more positively to operational efficiency than does reconfiguration capability, and that reconfiguration capability relates more positively to strategic performance than does refinement capability. The results also suggest that firms with superior refinement capability tend to possess superior reconfiguration capability. Our findings show that both external and internal factors, such as technological volatility, inter-firm collaboration, and firm age and size, are significantly associated with the level of refinement and reconfiguration capabilities possessed by a firm.

Pawn to Save a Chariot,or Drawbridge Into the Fort? Firms' Disclosure During Standard Setting and Complementary Technologies Within Ecosystems

Research summary: W ithin an ecosystem, standard setting coordinates development of complementary technologies across firms. But each firm can itself own multiple of these complementary technologies. We study how a firm's own complementary technologies influence its disclosure inclination during standard setting. We identify a tradeoff: disclosure increases value‐creation of the firm's non‐disclosed complementary technologies, but also heightens expropriation risk. Using data on the U.S. communications equipment industry 1991–2008, we show that the firm's complementary technologies increase its disclosure inclination when its technological areas are less crowded, but decrease such inclination when there are SSO members with strong expropriation abilities. Findings stress that disclosure involves but a piece of the firm's portfolio; a systemic perspective of the entire portfolio provides a more comprehensive picture of value‐creation during standard setting . Managerial summary: W hy should a firm disclose its key technology to participate in standard setting within an ecosystem? We urge managers to think beyond “disclosing to ensure compatibility with other firms' complementary technologies within the ecosystem” as a motivation, to also consider how disclosure affects the firm's own complementary technologies within its portfolio. Disclosure in one technological area makes the firm's nondisclosed complementary technologies in other areas more valuable to itself, especially with fewer rivals competing in these other areas. But disclosure also renders the firm susceptible to losing these complementary technologies to rivals, especially when rivals have strong expropriation abilities. Analyzing disclosure decisions by communication equipment firms, we show that this tradeoff is indeed a relevant consideration in managers' strategic calculations when participating in standard setting . Copyright © 2017 John Wiley & Sons, Ltd.     

Beyond institutional voids: Business groups,incomplete markets,and organizational form

We extend the “institutional voids” perspective on business groups by examining the value‐adding potential of two of the characteristic features of business groups: their diverse portfolio and multi‐entity organizational form. We maintain that portfolio diversity affords affiliates privileged access to opportunities hidden by incomplete strategic factor markets. We hypothesize that the multi‐entity organizational form enables superior sensing and seizing of these growth opportunities by affiliate firms. We further suggest that, in the context of institutional reforms, these characteristics strengthen business group affiliates' ability to capitalize on the expanded set of opportunities made available by the reform program. Empirical analyses on a sample of Indian firms over the period 1994–2010 support our hypotheses. Implications for theory and future directions are discussed. Copyright © 2013 John Wiley & Sons, Ltd.