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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.

Without short-sales constraints, mean-variance (MV) and power-utility portfolios generated from historical data are often characterized by extreme expected returns, standard deviations, and weights. The result is usually attributed to estimation error. I argue that modeling error, that is, modeling the portfolio problem with just a budget constraint, plays a more fundamental role in determining the extreme solutions and that a more complete analysis of MV problems should include realistic constraints, estimates of the means based on predictive variables, and specific values of investors’ risk tolerances. Empirical evidence shows that investors who utilize MV analysis without imposing short-sales constraints, without employing estimates of the means based on predictive variables, and without specifying their risk tolerance miss out on remarkably remunerative investment opportunities.

The capital asset pricing model (CAPM) is the most widely used asset pricing model that measures risk–return relationship. The CAPM is based on Markowitz’s mean variance analysis. The advancement of Islamic finance leads to the question whether or not the practice of modern investment theories and analyses such as the Markowitz’s mean variance analysis and CAPM are in accordance to shariah and could be used in pricing Islamic financial assets. Therefore, this paper aims to present a review of the CAPM and to discourse the set of assumptions underlying the model in terms of shariah compliance.

Although most of the assumptions are not contradictory to shariah principles, there are Islamic variables such as prohibition of short selling, purification and zakat that should be taken into consideration when pricing Islamic financial assets. We then develop a mathematical model which is a modification of the traditional CAPM that incorporates principles of Islamic finance and integrating zakat, purification of return and exclusion of short sales.

As a proof-of-concept, this paper presents the results of an empirical study on the proposed shariah-compliant CAPM in comparison to the traditional CAPM. The results show that the proposed Islamic CAPM is appropriate and applicable in examining the relationship between risk and return in the Islamic stock market.

This study contributes to existing body of knowledge by presenting an algorithm and mathematical derivation of the shariah-compliant CAPM which has been lacking in the literature of Islamic finance. The paper offers a novel approach in pricing Islamic financial assets in accordance to shariah, advocated by modern investment theories of Markowitz’s mean variance analysis and CAPM.

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.

The paper uses 101 years of Chilean and international financial assets returns to investigate mean-variance optimal portfolio allocations. The key conclusion is that the share of international unhedged investments is substantial even in minimum risk portfolios (20%), unless the period 1980–2002 is assumed to be drawn from a different distribution and previous history is disregarded. In addition to that, the paper finds that mean-variance optimal investors would have generated substantial demand for an asset replicating the return profile of an efficient pay-as-you-go pension scheme. Labour income and departures from log-normality of returns might, however, affect the latter conclusion.

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.

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).

Aims to test to determine whether the selection of the historical return time interval (monthly, quarterly, semiannual, or annual) used for calculating real estate investment trust (REIT) returns has a significant effect on optimal portfolio allocations.

Using a mean‐variance utility function, optimal allocations to portfolios of stocks, bonds, bills, and REITs across different levels of assumed investor risk aversion are calculated. The average historical returns, standard deviations, and correlations (assuming different time intervals) of the various asset classes are used as mean‐variance inputs. Results are also compared using more recent data, since 1988, with, data from the full REIT history, which goes back to 1972.

Using the more recent REIT datarather than the full dataset results in optimal allocations to REITs that are considerably higher. Likewise, using monthly and quarterly returns tends to understate the variability of REITs and leads to higher portfolio allocations.

The results of this study are based on the limited historical return data that are currently available for REITs. The results of future time periods may not prove to be consistent with the findings.

Numerous research papers arbitrarily decide to employ monthly or quarterly returns in their analyses to increase the number of REIT observations they have available. These shorter interval returns are generally annualized. This paper addresses the consequences of those decisions.

It has been shown that the decision to use return estimation intervals shorter than a year does have dramatic consequences on the results obtained and, therefore, must be carefully considered and justified.

Purpose – This chapter gives an overview of meta-analytic methods and illustrates the use of these methods for synthesising research findings. The advantages of performing a meta-analysis are described. Pitfalls in meta-analyses are also discussed. The chapter is intended to present the main elements of a meta-analysis and guide readers to literature presenting meta-analytic methods in greater detail.

Methodology – Key references in the meta-analysis literature are quoted and examples of meta-analyses are presented.

Findings – A meta-analysis is a useful tool for summarising knowledge in fields where a large number of studies have been reported. In addition to providing summary estimates of results, a meta-analysis can be applied to identify factors that produce systematic variation in study findings.

Research implications – Methods of meta-analyses keep developing to deal with complex data structures, thus extending the type of research findings that are amenable to meta-analyses.

Practical implications – Performing a meta-analysis saves labour by eliminating the need to read and digest a large number of studies in order to get an overview of the current state-of-knowledge in a field. Moreover, a meta-analysis establishes a system for easily and quickly updating knowledge as new studies become available.