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.     

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.     

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.     

Another Take on Real Estate's Role in Mixed‐Asset Portfolio Allocations

This article examines real estate's role in institutional mixed‐asset portfolios using both private‐ and public‐real estate indices, as a means of examining varying real estate‐related risk/return opportunities. In so doing, this article also examines the effects of: (1) increasing the investment horizon, (2) placing constraints on the maximum allocation to any one asset class, and (3) varying the risk preferences of investors. The empirical results suggest—using infinite‐horizon returns and all of the caveats that accompany such a perspective—that real estate allocations of approximately 10–15% of the mixed‐asset portfolio represent an upper bound for most investors. For those investors preferring low‐risk portfolios, (unlevered) private real estate is the vehicle serving this allocation preference; for those investors preferring high‐risk portfolios, public real estate (with its embedded leverage of 40–50%) is the vehicle serving this allocation preference—with such vehicles serving as substitutes for a variety of noncore real estate strategies. In some sense, the distinction between private and public real estate is more about the use of leverage. For those investors preferring moderate‐risk portfolios, an intermediate‐leverage approach seems optimal.     

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.     

The origins and underpinning principles of e-scape

In this article I describe the context within which we developed project e-scape and the early work that laid the foundations of the project. E-scape (e-solutions for creative assessment in portfolio environments) is centred on two innovations. The first concerns a web-based approach to portfolio building; allowing learners to build their portfolios in real-time, directly from hand-held peripheral technologies in studios, workshops, laboratories, and from off-site settings. The second concerns the development of a radical web-based approach to the assessment of performance as captured in these portfolios. In many parts of the world, portfolios feature as part of school-based assessments—including those undertaken for school-leaving and certification purposes. In this setting assessment reliability is critical and (judged by practice in England & Wales) is typically far from satisfactory. The approach developed within e-scape has radically improved assessment reliability. Whilst these two innovations represent the most dramatic outcomes of the project, they arose from a set if principles held by the team of researchers in the Technology Education Research Unit (TERU) at Goldsmiths University of London. And central to these principles is that both the portfolio and the assessment approaches should be embedded in a view of active learning, such that engagement with them has a positive impact on classroom practice. As the title suggests, this paper outlines the origins, underlying principles and early development of project e-scape.     

New Product Portfolio Management: Practices and Performance

Effective portfolio management is vital to successful product innovation. Portfolio management is about making strategic choices—which markets, products, and technologies our business will invest in. It is about resource allocation—how you will spend your scarce engineering, R&D, and marketing resources. It focuses on project selection—on which new product or development projects you choose from the many opportunities you face. And it deals with balance—having the right balance between numbers of projects you do and the resources or capabilities you have available. In this article, the authors reveal the findings of their extensive study of portfolio management in industry. This study, the first of its kind, reports the portfolio management practices and performance of 205 U.S. companies. Its overall objective was to gain insights into what portfolio methods companies use, whether they are satisfied with them, the performance results they achieve with the different approaches, and suggestions for others who are considering implementing portfolio management. The research first assesses management's satisfaction with portfolio methods they employ and notes that some firms face major problems in portfolio management. Next, businesses are grouped or clustered into four groups according to management's view of portfolio management: Cowboys, Crossroads, Duds, and Benchmark businesses. The research first assesses management's satisfaction with portfolio methods they employ and notes that some firms face major problems in portfolio management. Next, businesses are grouped or clustered into four groups according to management's view of portfolio management: Cowboys, Crossroads, Duds, and Benchmark businesses. Various performance metrics are used to gauge the performance of the business's portfolio. The results reveal major differences between the best and the worst. Benchmark businesses are the top performers. Their new product portfolios consistently score the best in terms of performance—high-value projects, aligned with the business's strategy, the right balance of projects, and the right number of projects. The authors take a closer look at these benchmark businesses to determine what distinguishes their projects from the rest. Benchmark businesses employ a much more formal, explicit method to managing their portfolio of projects. They rely on clear, well-defined portfolio procedures, they consistently apply their portfolio method to all projects, and management buys into the approach. The relative popularity of various portfolio methods—from financial methods to strategic approaches, bubble diagrams, and scoring approaches—are investigated. Not surprisingly, financial approaches are the most popular and dominate the portfolio decision. But what is surprising is the dubious results achieved via financial approaches. Again, benchmark businesses stand out from the rest: they place less emphasis on financial approaches and more on strategic methods, and they tend to use multiple methods more so than the rest. Strategic methods, along with scoring approaches, yield the best portfolios; financial methods yield poorer portfolio results. The authors provide a number of recommendations and suggestions for anyone setting out to implement portfolio management in their business.     

A portfolio–evaluation framework for selecting R&D projects

This study aims to form the basis for constructing a framework for evaluating alternative portfolios of R&D projects. This study provides an extensive literature review on portfolio selection. Most of the existing studies deal with the portfolio selection problem by evaluating individual projects and then seeking ways to combine them for an R&D portfolio. However, the combination of individually good projects unnecessarily constitutes the optimal portfolio. In particular, this study discusses three portfolio effects: (1) the difference between the preference for the portfolio as a whole and the preference for the projects, (2) the interrelation among projects, (3) the size of portfolio selection problems. This study develops a three–phase framework for evaluating R&D portfolios and proposes a new taxonomy of the portfolio attributes (i.e. independent, interrelated, and synergistic). This study concludes with a discussion of future research, directed toward increasing the applicability of portfolio–selection approaches for managing R&D portfolios.     

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.     

Differentiating CREF Performance

We examine factors underlying the differences in commingled real estate fund (CREF) performance using a sample of 65 CREFs during 1985–2002. More than half of the individual CREFs underperformed the employed benchmark. However, portfolios of CREFs performed well in both up and down markets, smaller CREFs outperformed larger CREFs, and top performing CREFs continued to outperform. Differential CREF performance appears to be attributable to property selection, rather than allocation across real estate sectors. Liquidity-constrained CREFs exhibited lower risk. CREFs with large benchmark tracking error experienced inferior performance. These findings indicate important cross-sectional differences among CREFs and diversification opportunities for pensions employing multiple CREF investment strategies.     

Using mean-Gini and stochastic dominance to choose project portfolios with parameter uncertainty

Although a variety of models have been studied for project portfolio selection, many organizations still struggle to choose a potentially diverse range of projects while ensuring the most beneficial results. The use of the mean-Gini framework and stochastic dominance to select portfolios of research and development (R&D) projects has been gaining attention in the literature despite the fact that such approaches do not consider uncertainty regarding the projects’ parameters. This article discusses, with relation to project portfolio selection through a mean-Gini approach and stochastic dominance, the impact of uncertainty on project parameters. In the process, Monte Carlo simulation is considered in evaluating the impact of parametric uncertainty on project selection. The results show that the influence of uncertainty is significant enough to mislead managers. A more robust selection policy using the mean-Gini approach and Monte Carlo simulation is proposed.     

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.     

Analyzing the impact of user-generated content on B2B Firms' stock performance: Big data analysis with machine learning methods

Marketing scholars are interested in the big data of user-generated content (UGC) from social media platforms. However, the majority of current UGC studies have been conducted in the business-to-consumer (B2C) context. To fill the knowledge gap in business-to-business (B2B) research, we investigate whether UGC has differential impacts on stock performance for B2B and B2C firms by using big data. We collect a large dataset of 84 million tweets from 20.3 million Twitter accounts and 8 years of stock data for 407 companies from the S&P500 index. The results from machine learning methods are transformed into a monthly panel data. We conduct fixed effects model on the panel data. We find that UGC has a significant impact on firms' stock performance and that its impact on stock performance is much stronger among B2C firms than among B2B firms. While consumers' positive sentiment does not play a significant role in stock performance, consumers' negative sentiment and WOM significantly impact stock prices.     

Can Fund Managers Select Outperforming REITs? Examining Fund Holdings and Trades

Despite at least six empirical studies published since 2000 designed to assess fund managers’ Real Estate Investment Trust (REIT)‐selection ability, their skill remains in question. Unlike previous studies, we examine fund holdings and trades of REITs to answer this question. This approach allows us to explicitly account for portfolio rebalancing that alters REIT‐characteristic weights of fund portfolios. Results show that fund managers, after controlling for property type, size and momentum, generated significant positive alpha with their securities‐selection ability. To understand the sources of such ability, we examine whether fund managers who followed certain trading strategies outperformed relative to other managers. The potential trading strategies are based on public information related to geographic concentration, net‐asset‐value‐to‐price ratios, income and appreciation styles and leverage of the underlying REITs. Comparative and regression analyses show that none of the strategies fully explains why fund managers were able to select REITs that outperformed. We surmise that the outperformance mainly derives from the endemic abilities of managers to uniquely process REIT‐specific information and generate private valuation beliefs that lead to profitable investment decisions.     

Corporate technology portfolios and R&D performance measures: a study of technology intensive firms

This paper examines the relations between technology portfolio strategies and five commonly used research and development (R&D) performance measures. Patent and financial data of 78 US-based technology companies from 1976 to 1995 were gathered and analysed to investigate how a well-managed technology portfolio can create synergy and affect R&D performance. A technology portfolio can be characterized by its composition and technology concentration. A valuable technology portfolio that consists of patents with higher average citation made and self-citation ratio can have a positive effect on firm value. Our findings suggest that large firms may enjoy advantages for technological innovation because they can exploit synergy effects of their technology portfolios. Technology concentration strategy does not work well because firms focusing on few technology fields can experience diseconomy to patents received since high-quality patents are increasingly difficult to obtain. This paper lays the groundwork for future empirical research on technology portfolio and R&D performance.     

Some evidence on the gains from international diversification for Canadian investors

It is easily demonstrated ex post that international portfolio diversification results in increased returns and reduced risk. However, to determine the value of international diversification as an effective portfolio management strategy, it is necessary to form portfolios based on information available at the time of their composition, and then evaluate the performance of the portfolio in the following months. This is the main focus of our study, which adds several innovations to past research. First, we use daily rates of return on 23 national indices to evaluate the value of international diversification for a Canadian investor. Second, we evaluate the predictive value of the historical variance-covariance matrix vis-à-vis alternative models. Third, we use the Bayes-Stein correction to reduce errors in the historical return vector. Finally, we use a quadratic programming model in order to introduce the effects of constraints on the optimisation process. The results, obtained over the 1986–1989 period, are not in favour of international diversification. Returns on diversified portfolios were often lower than returns on the low-risk Canada market during the low-performance portfolio test periods. In other cases, higher returns on diversified portfolios could not be justified by their higher volatility. It is possible that these results may be partially due to the effects of the market crash in October 1987. Nevertheless, our study brings up many directions for future research. Is international diversification in fact profitable? Is portfolio optimisation appropriate in an international context? Finally, what is the best way to estimate the expected return vector in various markets?     

Algorithm portfolios for logistics optimization considering stochastic demands and mobility allowance

The vehicle routing problem with stochastic demand (VRPSD) is a well known NP-hard problem. The uncharacteristic behaviour associated with the problem enhances the computational efforts required to obtain a feasible and near-optimal solution. This paper proposes an algorithm portfolio methodology based on evolutionary algorithms, which takes into account the stochastic nature of customer demand to solve this computationally complex problem. These problems are well known to have computationally complex objective functions, which make their solutions hard to find, particularly when problem instances of large dimensions are considered. Of particular importance in such situations is the timeliness of the solution. For example, Apple was forced to delay their shipments of iPads internationally due to unprecedented demand and issues with their delivery systems in Samsung Electronics and Seiko Epson. Such examples illustrate the importance of stochastic customer demands and the timing of delivery. Moreover, most of the evolutionary algorithms, known for providing computationally efficient solutions, are unable to always provide optimal or near optimal solutions to all the VRPSD instances within allocated time interval. This is due to the characteristic variations in the computational time taken by evolutionary algorithms for same or varying size of the VRPSD instances. Therefore, this paper presents portfolios of different evolutionary algorithms to reduce the computational time taken to resolve the VRPSD. Moreover, an innovative concept of the mobility allowance (MA) in landmoves based on the levy’s distribution function has been introduced to cope with real situations existing in vehicle routing problems. The proposed portfolio approach has been evaluated for the varying instances of the VRPSD. Four of the existing metaheuristics including Genetic Algorithm (GA), Simulated Annealing (SA), Artificial Immune System (AIS), TABU Search (TS) along with new neighbourhood search, are incorporated in the portfolios. Experiments have been performed on varying dimensions of the VRPSD instances to validate the different properties of the algorithm portfolio. An illustrative example is presented to show that the set of metaheuristics allocated to certain number of processors (i.e. algorithm portfolio) performed better than their individual metaheuristics.     

A Comparison of the Recent Performance of Publicly Traded Real Property Portfolios and Common Stock

In this study we compare the returns earned by investments in publicly traded limited partnerships (PTLPs), finite life equity REITs, and traditional equity REITs with those resulting from investing in common stocks (proxied by closed-end mutual funds). Performance comparisons are made using generalized stochastic dominance (GSD). This tool avoids the joint hypothesis problem that arises when an asset pricing model is used as a performance benchmark. The results of the analysis indicate that the performance of the closed-end mutual funds was preferred to that of the individual equity REITs (both traditional and finite life) and PTLP securities by a wide array of risk-averse investors. This result was most pronounced following the passage of the Tax Reform Act of 1986 which severely restricted the tax deductibility of real estate losses. When the equity REITs were combined into portfolios, their performance dominated the mutual funds during the 1980–85 period. Further, the PTLP portfolio returns were preferred to several of the mutual funds even in the post-1985 period. These findings reflect the fact that the securitized real property portfolios studied are not as well diversified as mutual funds. However, the mutual funds remained the dominant investment alternative in the post-1986 period.     

Robust future‐oriented technology portfolios: Black–Litterman approach

We propose a new way of constructing more robust technology portfolios to overcome the weaknesses of previous technology portfolios based either on the judgments of experts or on quantitative data such as patents. Instead of using historical data, the method of nonlinear forecasting enables us to forecast the future number of patent citations and accordingly, to use the forecast as a quantitative proxy for future returns and risks of technologies. Using the Black–Litterman portfolio model, we improve the accuracy of inputs by combining the future views of experts with the future returns and risks of technologies. As a consequence of this, the portfolio becomes strongly future‐oriented. With our approach, corporate managers use both experts and data more effectively to build robust technology portfolios. In particular, our method is of great help for companies launching new businesses because the method avoids heavy dependency on internal experts with little knowledge about emerging technologies. A company entering the molecular amplification instrument market is exemplified herein.     

Do Common Risk Factors in the Returns on Stocks and Bonds Explain Returns on REITs?

The monthly returns on equity and mortgage real estate investment trusts (REITs) are analyzed over the period July 1976 to December 1992. The results indicate that risk premiums on equity REITs are significantly related to risk premiums on a market portfolio of stocks as well as to the returns on mimicking portfolios for size and book-to-market equity factors in common stock returns. Mortgage REIT risk premiums are significantly related to the three stock market factors and two bond market factors in returns. Also, mortgage REIT shares underperform by an average of 6.8% per year.