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The risk/return trade‐off has been a central tenet of portfolio management since the seminal work of Markowitz [1952]. The basic premise, that higher (expected) returns can only be achieved at the expense of greater risk, leads naturally to the concept of an efficient frontier. The efficient frontier defines the maximum return that can be achieved for a given level of risk or, alternatively, the minimum risk that must be incurred to earn a given return. Traditionally, market risk has been measured by the variance (or standard deviation) of portfolio returns, and this measure is now widely used for credit risk management as well. For example, in the popular Credit‐Metrics methodology (J.P. Morgan [1997]), the standard deviation of credit losses is used to compute the marginal risk and risk contribution of an obligor. Kealhofer [1998] also uses standard deviation to measure the marginal risk and, further, discusses the application of mean‐variance optimization to compute efficient portfolios. While this is reasonable when the distribution of gains and losses is normal, variance is an inappropriate measure of risk for the highly skewed, fat‐tailed distributions characteristic of portfolios that incur credit risk. In this case, quantile‐based measures that focus on the tail of the loss distribution more accurately capture the risk of the portfolio. In this article, we construct credit risk efficient frontiers for a portfolio of bonds issued in emerging markets, using not only the variance but also quantile‐based risk measures such as expected shortfall, maximum (percentile) losses, and unexpected (percentile) losses.

This paper aims to perform an analytical analysis on portfolio allocation when a tracking error volatility (TEV) constraint holds, drawing specific attention to the portfolio efficiency issue. Indeed, it is well known that investors can assign part of their funds to asset managers who are given the task of beating a benchmark portfolio. However, the risk management office often imposes a TEV constraint to the asset managers’ activity to maintain the portfolio risk near to the risk of the benchmark. This situation could lead asset managers to select non efficient portfolios in the total return and absolute risk perspective. However, the risk management office can impose further constraints, such as on maximum variance or maximum value at risk (VaR) to maintain the overall portfolio risk under control.

First the authors define the TEV constrained-efficient frontier (ECTF), a set of TEV constrained portfolios that are mean–variance efficient. Second, they define two new portfolio frontiers analyzing how the imposition of a maximum variance or maximum VaR restriction can reduce the ECTF. Third, they investigate the feasibility of such portfolio frontiers and their relationships.

The authors find that variance or VaR constraint can force asset managers to pursue portfolio efficiency.

This is a practically important issue given that asset managers often receive a constraint on TEV from the risk management office, but the risk management office does not ask them to minimize the TEV as often assumed in the optimizations performed in the literature on this topic.

The optimization of investment portfolios is a topic of major importance in financial decision making, with many relevant models available in the relevant literature. The purpose of this paper is to perform a thorough comparative assessment of different bi-objective models as well as multi-objective one, in terms of the performance and robustness of the whole set of Pareto optimal portfolios.

In this study, three bi-objective models are considered (mean-variance (MV), mean absolute deviation, conditional value-at-risk (CVaR)), as well as a multi-objective model. An extensive comparison is performed using data from the Standard and Poor’s 500 index, over the period 2005–2016, through a rolling-window testing scheme. The results are analyzed using novel performance indicators representing the deviations between historical (estimated) efficient frontiers, actual out-of-sample efficient frontiers and realized out-of-sample portfolio results.

The obtained results indicate that the well-known MV model provides quite robust results compared to other bi-objective optimization models. On the other hand, the CVaR model appears to be the least robust model. The multi-objective approach offers results which are well balanced and quite competitive against simpler bi-objective models, in terms of out-of-sample performance.

This is the first comparative study of portfolio optimization models that examines the performance of the whole set of efficient portfolios, proposing analytical ways to assess their stability and robustness over time. Moreover, an extensive out-of-sample testing of a multi-objective portfolio optimization model is performed, through a rolling-window scheme, in contrast static results in prior works. The insights derived from the obtained results could be used to design improved and more robust portfolio optimization models, focusing on a multi-objective setting.

The purpose of this paper is to argue that simplifications of portfolio selection may no longer be necessary, based on computational advancements of portfolio theory and powerful computers.

First, the paper reviews the two branches of portfolio optimization and second, presents the results of large‐scale portfolio selection, based on exhaustive sampling in China. Some speedy results support removing the simplification.

The paper finds that for some simplification techniques, the results of simplified models and original models are quite alike, while for other techniques, the results are strikingly distinctive. Moreover, the performance of portfolio optimizers varies from being instantly fast to being unbearably slow, so it pays to be picky.

This paper reports for large‐scale portfolio selection the results of kinds of software and this alone makes the paper unique. Based on the leading software and exhaustive sampling in China, for the first time the difference between the original and simplified models is studied.

Since equity markets have a dynamic nature, the purpose of this paper is to investigate the performance of a revision procedure for domestic and international portfolios, and provides an empirical selection strategy for optimal diversification from an American investor's point of view. This paper considers the impact of estimation errors on the optimization processes in financial portfolios.

This paper introduces the concept of portfolio resampling using Monte Carlo method. Statistical inferences methodology is applied to construct the sample acceptance regions and confidence regions for the resampled portfolios needing revision. Tracking error variance minimization (TEVM) problem is used to define the tracking error efficient frontiers (TEEF) referring to Roll (1992). This paper employs a computation method of the periodical after revision return performance level of the dynamic diversification strategies considering the transaction cost.

The main finding is that the global portfolio diversification benefits exist for the domestic investors, in both the mean-variance and tracking error analysis. Through TEEF, the dynamic analysis indicates that domestic dynamic diversification outperforms international major and emerging diversification strategies. Portfolio revision appears to be of no systematic benefit. Depending on the revision of the weights of the assets in the portfolio and the transaction costs, the revision policy can negatively affect the performance of an investment strategy. Considering the transaction costs of portfolios revision, the results of the return performance computation suggest the dominance of the global and the international emerging markets diversification over all other strategies. Finally, an assessment between the return and the cost of the portfolios revision strategy is necessary.

The innovation of this paper is to introduce a new concept of the dynamic portfolio management by considering the transaction costs. This paper investigates the performance of a revision procedure for domestic and international portfolios and provides an empirical selection strategy for optimal diversification. The originality of the idea consists on the application of a new statistical inferences methodology to define portfolios needing revision and the use of the TEVM algorithm to define the tracking error dynamic efficient frontiers.

This paper seeks to address the question of consistency, regarding the allocation of real estate in the mixed‐asset portfolio.

To address the question of consistency the allocation of real estate in the mixed‐asset portfolio was calculated over different holding periods varying from five to 25 years. For each portfolio and holding period, the percentage of portfolios with real estate was computed, as was the average real estate allocation in the optimum solution. Then, the risk and return differences between the two efficient frontiers, with and without real estate, were calculated to estimate real estate's marginal impact on portfolio performance.

First, the results suggest strongly that real estate has possessed the attribute of consistency in optimised portfolios. Second, the benefits from including real estate in the mixed‐asset portfolio tend to increase as the investment horizon is extended. Third, the position of real estate changes across the efficient frontier from its return enhancing ability to its risk‐reducing facility. Finally, the results show that the gain in return from adding real estate to the mixed‐asset portfolio is typically less compared with the reduction in portfolio risk.

The results highlight a number of issues in relation to the role of direct real estate within a mixed‐asset framework. In particular, the rationale behind the inclusion of real estate in the mixed‐asset portfolio depends on the length of the holding period of the investor and their position on the efficient frontier.

The study examines the attractiveness of direct real estate in the context of mixed‐asset portfolio.

Markowitz showed that assets can be combined to produce an “efficient” portfolio that will give the highest level of portfolio return for any level of portfolio risk, as measured by variance or standard deviation. These portfolios can then be connected to generate what is termed an “efficient frontier” (EF). Discusses the calculation of the efficient frontier for combinations of assets, again using the spreadsheet optimizer. To illustrate the derivation of the efficient frontier, uses the data from the Investment Property Databank Long Term Index of Investment Returns for the period 1971 to 1993. Many investors might require a certain specific level of holding or a restriction on holdings in at least some of the assets. Such additional constraints may be readily incorporated into the model to generate a constrained EF with upper and/or lower bounds. This can then be compared with the unconstrained EF to see whether the reduction in return is acceptable. To see the effect that these additional constraints may have, adopts a fairly typical pension fund profile, with no more than 20 per cent of the total held in property. Shows that it is now relatively easy to use the optimizer available in at least one spreadsheet (EXCEL) to calculate efficient portfolios for various levels of risk and return, both constrained and unconstrained, so as to be able to generate any number of efficient frontiers.

An investor is expected to analyze the market risk while investing in equity stocks. This is because the investor has to choose a portfolio which maximizes the return with a minimum risk. The mean-variance approach by Markowitz (1952) is a dominant method of portfolio optimization, which uses variance as a risk measure. The purpose of this paper is to replace this risk measure with modified expected shortfall, defined by Jadhav et al. (2013).

Modified expected shortfall introduced by Jadhav et al. (2013) is found to be a coherent risk measure under univariate and multivariate elliptical distributions. This paper presents an approach of portfolio optimization based on mean-modified expected shortfall for the elliptical family of distributions.

It is proved that the modified expected shortfall of a portfolio can be represented in the form of expected return and standard deviation of the portfolio return and modified expected shortfall of standard elliptical distribution. The authors also establish that the optimum portfolio through mean-modified expected shortfall approach exists and is located within the efficient frontier of the mean-variance portfolio. The results have been empirically illustrated using returns from stocks listed in National Stock Exchange of India, Shanghai Stock Exchange of China, London Stock Exchange of the UK and New York Stock Exchange of the USA for the period February 2005-June 2018. The results are found to be consistent across all the four stock markets.

The mean-modified expected shortfall portfolio approach presented in this paper is new and is a natural extension of the Markowitz’s mean-variance and mean-expected shortfall portfolio optimization discussed by Deng et al. (2009).

In real estate industry, managers' choices in portfolio construction impact directly on the performance of real estate fund. Looking at the literature, real estate diversification criteria are related to tenants' characteristics, to endogenous and exogenous risk and to financial choices. The aim of the paper is to study the role of different risk profiles in the investment selection and in the construction of an efficient real estate portfolio.

The first step is to find out an investment selection model based on the main risk factors. The aim was to check the ability of qualitative criteria (tenant, exogenous, endogenous and financial risks) to identify ex ante the best investment opportunities. The observation of the portfolios' composition on the efficient frontier and the proximity of individual property to the efficient frontier point out which risk factors are more important. The second step is to define a model to construct a portfolio, with non correlated investments, based on the main risk factors. This ability was tested by comparing the classifications made according to quality criteria, which can potentially be used ex ante to construct a diversified portfolio, with the results of cluster analysis. The results from the cluster analysis, free from quality profiles, are therefore considered as the best diversification strategy.

The results stemming from the use of a real estate database supplied by Fimit SGR (Unicredit banking group) showed that an ex ante study of risk profiles can help to identify those investment opportunities which are more or less near to the efficient frontier, although there is no prevailing criterion to identify a portfolio able to maximise investment diversification benefits. To identify more efficient portfolio is necessary to define an evaluation approach that considers simultaneously different risk profiles of real estate investments.

The paper considers the Italian market, a young market for institutional real estate investments characterised by high growing opportunities. The value added of the paper is to study the relationship of different real estate specific risks considered in literature (tenant risk, endogenous and exogenous risk) and financing choices in order to define a more complete model to evaluate real estate portfolios.

Uses modern portfolio theory and a spreadsheet optimizer to make an ex‐post examination of the strategic diversification effects of including property in a multi‐asset portfolio, using UK appraisal‐based (smoothed) data and several derived desmoothed series. Includes an additional low‐risk asset (cash) to investigate whether property′s place in the portfolio is maintained. In particular, considers the significance of constraining assets to match typical institutional portfolio levels. Concludes that previously supposed benefits of including property are overstated. Property still has a place in an institutional portfolio, but the analyses should not be based simply on the use of appraisal or desmoothed data in a portfolio optimizer without applying appropriate constraints.