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.     

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.     

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 inexact l2-norm penalty method for cardinality constrained portfolio optimization

Abstract

We analyze and solve a single-period portfolio optimization problem with non-convex constraints, which address practical concerns of investment such as the active share weights of sectors and the number of stocks held in a portfolio. We reformulate the problem to simplify the computation and propose an inexact l₂-norm penalty method to solve the problem.     

Real Estate Investment Funds: Performance and Portfolio Considerations

This paper presents the results of a study dealing with a number of issues regarding real estate investment. Utilizing a data set consisting of returns from two of the oldest, continuously operating commingled real estate funds (CREFs), questions relative to investment performance, inflation hedging attributes and diversification benefits are addressed. The methodology used in exploring these issues are variants of the traditional capital asset pricing model (CAPM), extended to consider uncertain inflation (CAPMUI) and an arbitrage pricing model in which real estate performance is judged relative to a more inclusive market index representing larger numbers of substitute investments. Finally, issues relative to portfolio performance are considered by constructing portfolios containing all possible combinations of real estate, stocks and bonds to assess the potential for diversification benefits and portfolio performance.     

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.     

Real Estate Returns: A Comparison with Other Investments

Real estate returns, measured unleveraged, have been between those of stocks and bonds over 1960–1982. Due to appraisal smoothing and imperfect marketability, one must be careful about directly comparing measured real estate returns with those on other assets. It is likely, however, that low correlations with stocks and bonds make real estate a diversification opportunity for traditional portfolio managers. In addition, the issue of how various assets are priced is addressed. While stocks are priced primarily on market or beta risk, and bonds are priced primarily on interest rate and default risk, the real estate pricing mechanism includes residual risk and non-risk factors such as taxes, marketability costs and information costs.     

The evolution of coopetitive and collaborative alliances in an alliance portfolio: The Air France case

This research studies the evolution of the composition of an alliance portfolio from a coopetition perspective. Building on resource dependence theory, market uncertainty appears to be a driver of alliance portfolio formation and evolution. Scholars have previously neglected key dimensions in analyzing the composition of firms' alliance portfolios: the partner type (pure partner or competitor) and partner interactions (horizontal, vertical or mixed). We build on the coopetition and alliance portfolio literature to explore (1) the composition of an alliance portfolio and (2) its evolution over time. We illustrate our theoretical framework with a longitudinal single-case study of Air France's alliance portfolio. First, we show that when market uncertainty is high, firms do not increase their reliance on collective strategies, but they do modify the composition of their portfolio. Second, to address high levels of market uncertainty, firms rely more on coopetitive alliances than on collaborative alliances. Third, firms use more horizontal than vertical interactions when market uncertainty is high.     

Industrial tail exposure risk and asset price: Evidence from US REITs

In this study, we investigate the impact of industry-based tail dependence risk on the cross-section of stock returns. To this end, we propose a novel tail risk dependence measure (industrial tail exposure risk [ITER]), which captures the tail risk exposure of individual stocks to multiple industries. Using US equity real estate investment trusts (REITs) data from 1993 to 2020, we document that stocks in the highest ITER portfolio outperform stocks in the lowest ITER portfolio by 8.40% per annum. This positive return spread is significant even after controlling for well-known firm characteristics. The return premium of ITER is stronger for small, value, and highly levered stocks and is substantially high during recession periods. Finally, the effects of ITER are cross-sectionally more associated with REITs that have greater degrees of the following factors: bivariate tail exposure risks of major industries, exposure to local industry tail risk, geographical concentration, and ownership of home-biased investors. Overall, our results suggest that REIT investors are indeed averse to tail risks that are associated with various sectors.     

Two-step multi-criteria model for selecting optimal portfolio

In spite of a large number of multi-criteria models applied to solve the problem of optimal portfolio selection and a large number of market criteria and accounting criteria proposed for these models, the problem of portfolio containing securities from different industries has not yet been adequately solved. Namely, neither can stocks of companies from different industries be compared using the same criteria nor can the weight of a particular criteria be equal for them all. Therefore this paper develops a new two-step model that will overcome the shortcomings of the previously used models. The model is divided into two different but related pillars: the choice of different industries to form the overall portfolio and the choice of portfolio for each industry. The multi-criteria model used in this paper is a modified multi-criteria programming model based on the PROMETHEE II approach. The selected model has been applied at the Zagreb Stock Exchange (ZSE) as a real case.     

How Does the Federal Reserve's Large‐Scale Asset Purchases (LSAPs) Influence Mortgage‐Backed Securities (MBS) Yields and U.S. Mortgage Rates?

We conduct an empirical analysis of the Federal Reserve's large‐scale asset purchases (LSAPs) on mortgage‐backed securities (MBS) yields and mortgage rates. We estimate a cointergrated, error‐correction model that links Federal Reserve securities purchases and stocks of Treasury and MBS securities to equilibrium MBS yields and mortgage rates. The Federal Reserve's accumulation of MBS and Treasury securities lowered MBS yields and mortgage rates by more than what would have been suggested by changes in market expectations alone, suggesting that portfolio rebalancing effects of LSAPs are an important consideration for monetary policy transmission. Our estimates also suggest that the Federal Reserve must hold a substantial market share of agency MBS or of Treasury securities to significantly lower MBS yields and in turn significantly lower mortgage rates.     

An Intertemporal Capital Asset Pricing Model with Owner‐Occupied Housing

This article studies portfolio choice and asset pricing in the presence of owner‐occupied housing in a continuous time framework. The unique feature of the model is that housing is a consumption good as well as a risky asset. Under general conditions, that is, when the utility function is not Cobb–Douglas and the covariance matrix is not block‐diagonal, the model shows that the market portfolio is not mean‐variance efficient, and the traditional capital asset pricing model fails. Nonetheless, a conditional linear factor pricing model holds with housing return and market portfolio return as two risk factors. The model also predicts that the nondurable consumption‐to‐housing ratio (ch) can forecast financial asset returns. The two factor pricing model conditioning on ch yields a good cross‐sectional fit for Fama–French 25 portfolios.     

Institutional Investors' Preferences for REIT Stocks

This article investigates the determinants of real estate investment trusts (REIT) portfolio investment and institutional REIT ownership using multivariate Tobit regressions. We contend that many institutional investors take larger positions in more liquid assets like REIT stocks, as compared with private real estate equities, because of liquidity considerations. Consistent with this contention, we find that liquidity constraints are significantly related to REIT portfolio investment by institutional investors. We also find that institutional investors have different preferences for REIT stocks than do other investors; they generally prefer larger, more liquid REIT stocks.     

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?     

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.     

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.     

An Empirical Investigation of the Antecedents and Outcomes of NPD Portfolio Success

Managing new product development (NPD) portfolios is difficult and little is known about how successful NPD portfolio management can improve overall firm performance. Despite regular calls in the literature for more research on NPD portfolio management, what successful NPD portfolio management means and how firms can achieve it remains unclear. For this reason, this paper combines theory and previous empirical findings to build a model of the antecedents and outcomes of NPD portfolio success. We generate and test 12 hypotheses with empirical data from 189 paired dyads in Dutch firms. Our results show that all three dimensions of NPD portfolio decision‐making effectiveness (i.e., portfolio mindset, focus, and agility) are associated with achieving the three dimensions of NPD portfolio success (i.e., strategic alignment, maximal NPD portfolio value, and portfolio balance), which in turn influences market performance. While a portfolio mindset and agility are related to all three dimensions of NPD portfolio success, focus is related only to strategic alignment and maximal value. No one dimension of NPD portfolio decision‐making effectiveness or portfolio success is sufficient to achieve overall market performance. We also found several unexpected findings with important implications. For example, portfolio balance, one recommended measure of portfolio success, has no direct link to market performance, but operates through the other two dimensions of NPD portfolio success, i.e., strategic alignment and maximal portfolio value. We conclude our paper with implications for further theory development and testing on successful NPD portfolio decision‐making, and with implications for managerial practice.     

Likely gains from market timing in Japan

This paper explores the potential gains and required predictive ability of market timing in Japan and then compares the results to previously reported findings from another developed financial market — the United States — and a developing Asia Pacific financial market — Singapore. Shifts between cash equivalents and common stocks are evaluated. The results demonstrate that the potential gains from market timing in Japan are quite attractive and that the minimum predictive accuracy required for successful market timing may be attainable by some portfolio managers. However, for the period examined, the results also indicate that larger incremental gains result from market timing Singapore stocks and cash equivalents.An earlier version of this paper was presented at the Second Annual Pacific Basin Finance Conference in Seoul, Korea in 1991. The author appreciates the helpful comments of Lim Kian Guan and two anonymous referees.     

Real Estate Investment Trusts, Small Stocks and Bid-ask Spreads

This study examines the liquidity of Real Estate Investment Trusts (REITs), as measured by their bid-ask spread. We find that REIT spreads have increased over the period 1986–1990, are inversely related to market capitalization, and are similar in magnitude to spreads on other stocks of comparable size. Analysis of variance tests indicate that REIT spreads are similar across equity, mortgage and hybrid asset types. Multivariate regression results indicate that market capitalization is the primary determinant of REIT bid-ask spreads, and spreads are larger for National Association of Securities Dealers Automated Quotations (NASDAQ) REITs than for New York Stock Exchange (NYSE) REITs. The regression results also indicate that spreads are lower for equity REITs than for mortgage or hybrid REITs, and are inversely related to the fraction of the REIT's shares held by institutional investors. The similarity between REIT spreads and those of other common stocks holds in both bull and bear real estate markets and suggests that, from a liquidity perspective, REITs are similar to other common stocks.