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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).

This study investigates the diversification benefits of multiple cryptocurrencies and their usefulness as investment assets, individually or combined, in enhancing the performance of a well-diversified portfolio of traditional assets before and during the pandemic COVID-19.

This paper uses two optimization techniques, namely the mean-variance and the maximum Sharpe ratio. The naïve diversification rules are used for comparison. Besides, the Sharpe and the Sortino ratios are used as performance measures.

The results show that cryptocurrencies diversification benefits occur more during the COVID-19 pandemic rather than before it, with the maximum Sharpe ratio portfolio presenting its highest performance. Furthermore, the results suggest that, during COVID-19, the diversification benefits are slightly better when using a combination of cryptocurrencies to an already well-diversified portfolio of traditional assets rather than individual ones. This serves to improve the performance of the maximum Sharpe ratio portfolio, and to some extent, the naïve portfolio. Yet, cryptocurrencies, whether added individually or combined to a well-diversified portfolio of traditional assets, don't fit in the minimum variance portfolio. Besides, the efficient frontier during COVID-19 pandemic dominates the one before COVID-19 pandemic, giving the investor a better risk-return trade-off.

To the best of the author's knowledge, this is the first study that examines the diversification benefits of multiple cryptocurrencies both as individual investments and as additional asset classes, before and during COVID-19 pandemic. The paper covers all analyses performed separately in previous studies, which brings new evidence regarding the potential for cryptocurrencies in portfolio diversification under different portfolio strategies.

The purpose of this paper is to present a procedure for finding the efficient frontier, i.e. a non‐decreasing curve representing the set of Pareto‐optimal or non‐dominated portfolios, when the standard Markowitz' classical mean‐variance model is enriched with additional constraints.

The mean‐variance portfolio optimization model is extended to include integer constraints that limit a portfolio to have a specified number of assets, and to impose limits on the proportion of the portfolio held in a given asset. Optimization‐based procedures run into difficulties in this framework and this motivates the investigation of heuristic algorithms to find acceptable solutions.

The problem is solved by a greedy randomized adaptive search procedure (GRASP), enhanced by a learning mechanism and a bias function for determining the next element to be introduced in the solution.

This is believed to be the first time, a GRASP for finding the efficient frontier for this class of portfolio selection problems is used.

The purpose of this paper is to conceptualise a workable strategic asset allocation (SAA) model, given the data paucity problem, and involve an ex ante framework that is distributional free.

The SAA model is developed within a semi‐quantitative and expert‐based framework – the analytic hierarchy process (AHP) – and not a purely time‐series one. It is developed on the basis of consensus by a group of real estate investment experts, who agree on a fixed investment time horizon so that the time factor is disregarded as a variant. The SAA becomes the interface around which a set of tactical bands is imposed, subject to the Markowitz mean‐variance optimisation, and utilizing the total‐return data set of the Jones Lang LaSalle Real Estate Intelligence Service‐Asia. The lower and upper limits of the tactical bands represent the cyclical attractiveness of the various Asian office markets as growth and value‐added markets

The SAA‐AHP model robustly reflects expert judgement among a cohesive group of real estate investment experts, with regard to a Pan‐Asia office market portfolio of eight major Asian cities. Through pair‐wise comparisons and subject to consistency checks in terms of the consistency ratio of <0.10, then the comparative expert assessment of the macro‐economic and the real estate specific factors driving individual Asian real estate markets, would be consistent (i.e. non conflicting). Then the total weighted evaluations of individual markets are derived and deployed as the SAA portfolio mix. This portfolio mix thus becomes the appropriate interface, around which the tactical asset allocation (TAA) is developed within defined tactical bands. These bands must be in line with the underlying Asian real estate market analysis and their cyclical positions. The TAA is obtained through the Markowitz mean‐variance portfolio optimisation, with the objective of locating the optimally efficient TAA on the Markowitz efficient frontier, under a maximising risk‐adjusted‐return Sharpe ratio.

The SAA‐AHP model is reliant on an ex ante assessment of alternative asset allocation strategies on the basis of expert judgement of the macroeconomic environment and the Asian office markets. It is an appropriate SAA alternative to one based on the typical economic‐sized indicators, for example, the urban GDP.

In September‐October 2008 the Russian stock markets came under severe strain amidst the global financial crisis. During this time the Russian government intervened several times to halt the trade to impede the continuous slide. The government justified its actions owing to the argument that the crisis was due to a trickledown effect from the financial crisis in the USA and the other developed markets. The purpose of this paper is to put to test the government's claim by exploring the level of integration between Russia and the USA and European equity markets.

The study employs Markov Regime Switching Model for tracking structural breaks in the time series. This method divides the data into three periods, i.e. pre crisis, during crisis and post crisis. Next the Multivariate GARCH‐DCC model technique is used to establish the time varying linkages in order to verify the contagion effect. In the final step the Markowitz mean‐variance framework is used to position each individual index portfolio with respect to the efficient frontier to analyze the impact of crisis as well as Russian government intervention.

The findings suggest that the Russian equity market is weakly integrated with US and strongly integrated with European markets. The results correspond to the underlying financial and economic linkages between Russia, the US and Europe. When examined in a portfolio setup, the results show sudden fall in correlation among the Russian, US and European equity markets suggesting weak linkages among these markets. Finally, the Markowitz Efficient frontier indicates dramatic rise in volatility on the day intervention began and ended which signifies the increased uncertainty among the investors owing to Russian government ad hoc interventions.

The paper attempts to examine the Russian government intervention in the backdrop of financial crisis 2008 and concludes that the government intervention essentially increased the uncertainty in the local as well as international markets. Therefore, it is essential that the government should avoid direct intervention in its stock market.

In the real world, the variance of portfolio returns provides only a limited quantification of incurred risks, as the distributions of returns have “fat tails” and the dependence between assets are only imperfectly accounted for by the correlation matrix. Value‐at‐risk and other measures of risks have been developed to account for the larger moves allowed by non‐Gaussian distributions. In this article, the authors distinguish “small” risks from “large” risks, in order to suggest an alternative approach to portfolio optimization that simultaneously increases portfolio returns while minimizing the risk of low frequency, high severity events. This approach treats the variance or second‐order cumulant as a measure of “small” risks. In contrast, higher even‐order cumulants, starting with the fourth‐order cumulant, quantify the “large” risks. The authors employ these estimates of portfolio cumulants based on fat‐tailed distributions to rebalance portfolio exposures to mitigate large risks.

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.

Markowitz’s mean‐variance approach is used to identify the returns to vertical investment in the pork industry. In addition to previous efforts, this paper considers not only returns to stock ownership, but uses operating return on investment in pork slaughter and hog production to evaluate the impacts of vertical investment within the industry segment. Results suggest there are indeed diversification incentives for vertical investment in the pork industry. However, results do differ for vertical direct investment versus investment through stock ownership.

This paper examines the effect of cryptocurrencies on the portfolio risk-adjusted returns of traditional and alternative investments within an emerging market economy.

The paper employs daily arithmetic returns from August 2015 to October 2018 of traditional assets (stocks, bonds, currencies), alternative assets (commodities, real estate) and cryptocurrencies. Using the mean-variance analysis, the Sharpe ratio, the conditional value-at-risk and the mean-variance spanning tests.

The paper documents evidence to support the diversification benefits of cryptocurrencies by utilising the mean-variance tests, improving the efficient frontier and the risk-adjusted returns of the emerging market economy portfolio of investments.

This paper firmly broadens the Modern Portfolio Theory by authenticating cryptocurrencies as assets with diversification benefits in an emerging market economy investment portfolio.

As far as the authors are concerned, this paper presents the first evidence of the effect of diversification benefits of cryptocurrencies on emerging market asset portfolios constructed using traditional and alternative assets.

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.