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This chapter presents the portfolio optimization problem formulated as a multi-criteria mixed integer program. Weighting and lexicographic approach are proposed. The portfolio selection problem considered is based on a single-period model of investment. An extension of the Markowitz portfolio optimization model is considered, in which the variance has been replaced with the Value-at-Risk (VaR). The VaR is a quantile of the return distribution function. In the classical Markowitz approach, future returns are random variables controlled by such parameters as the portfolio efficiency, which is measured by the expectation, whereas risk is calculated by the standard deviation. As a result, the classical problem is formulated as a quadratic program with continuous variables and some side constraints. The objective of the problem considered in this chapter is to allocate wealth on different securities to maximize the weighted difference of the portfolio expected return and the threshold of the probability that the return is less than a required level. The auxiliary objectives are minimization of risk probability of portfolio loss and minimization of the number of security types in portfolio. The four types of decision variables are introduced in the model: a continuous wealth allocation variable that represents the percentage of wealth allocated to each asset, a continuous variable that prevents the probability that return of investment is not less than required level, a binary selection variable that prevents the choice of portfolios whose VaR is below the minimized threshold, and a binary selection variable that represents choice of stocks in which capital should be invested. The results of some computational experiments with the mixed integer programming approach modeled on a real data from the Warsaw Stock Exchange are reported.

Following the traditions of stakeholder salience theory, this paper aims to contend that some institutional investor activists and tactics have more power, legitimacy and urgency than others.

The author undertakes an empirical test of a saliency table looking at the effects of institutional investor heterogeneity on portfolio firm responses using ordinal logistic regression.

This study found heterogeneity for institutional investor type to drive firm responses but not tactic type raising the importance of the attributes of each type of investor activist. The author found a rank ordering of public pension plans, hedge funds and then private multiemployer funds in saliency to portfolio firms. In addition, the use of proxy-based tactics did not help or hurt each investor type. Both findings challenge prior empirical work.

The rank ordering based upon the heterogeneity of institutional investor activists and their tactical interactions are tested providing empirical evidence of the most influential activist investors and tactics in one study, which is rare in the literature.

In addition to the seminal approach of Markowitz (1952) that is based on finding the optimal budget shares for minimizing risk, the authors also make use of the approach developed by Hatemi-J and El-Khatib (2015), which is built on finding the weights as budget shares for maximizing the risk-adjusted return of the underlying portfolio. For testing the stability of the portfolio benefits, the asymmetric interaction between oil, equity and bonds is tested.

Oil is a major investment commodity. The literature shows mixed results regarding oils' ability to provide diversification benefits. This paper re-examines this issue by applying a new portfolio optimization approach.

The authors find that oil still yields portfolio diversification benefits; contrary to the traditional Markowitz portfolio approach, the asymmetric causality test results show that oil does not cause bonds for either positive or negative changes; however, oil does cause stocks but only for stocks' negative changes. Hence, oil can still make the returns of a portfolio of stocks and bonds unstable through oil's effect on stocks.

This is the first attempt to investigate the potential portfolio diversification benefits of stocks, bonds and oil by using the combination of risk and return explicitly in the optimization problem. The new insights provided by this article might be valuable to the investors, financial institutions and policy makers.

The purpose of this article is to help investors build less-concentrated portfolios as well as to construct optimal return-concentration portfolios.

An alternative portfolio objective is proposed where investors care about the level of concentration of their portfolio weights. Minimizing the concentration of portfolio weights leads to the well-known equal-weight portfolio as the optimal choice. Maximizing the trade-off between the portfolio's expected return and the weight concentration produces a novel portfolio with weights proportional to the expected return of each security.

An empirical application with 30 industry portfolios and 1,000 individual stocks finds that both proposed strategies perform well out-of-sample both in terms of the proposed concentration measure but also in terms of more traditional risk-based measures like Sharpe ratios, abnormal returns and market betas.

The optimal risk-concentration portfolio proposed in this paper is a novel result. The portfolio generalizes prior practitioner intuition on focusing on securities with the highest expected returns and the concept of diversification.

This conceptual paper aims to explore portfolio replication to resolve post-COVID pandemic private and public debt. This paper stresses the need to be less dependent on a debt-based system and the emergence Islamic equity market.

This study analyses different types of risks involved in Islamic and conventional portfolios by using risk measures such as relative beta and comparatively examining the systematic and downside risk exposure of Islamic and conventional portfolios. Data was collected monthly from 2016 to 2022.

The findings indicate that the replications of a conventional portfolio into an Islamic portfolio are compatible with the regulatory standard, sharia boundaries and professional practices developed from investment theory. The result shows that Islamic portfolios have lower risk exposure compared with their conventional counterparts in most of the sample years, therefore, become further attractive for debt–equity portfolio swaps and Sharia-compliant investors preferring low-risk preferences. The result confirmed that the Islamic portfolios have a higher return and less risk than conventional portfolios.

The implications of this research are to provide a road map to the regulators, policymakers, governments and the financial industry on how to rearrange some of the public and private debt. A likely remedy is incorporating Islamic financial instrument principles through the equitisation of public and private debt.

This research contributes to investors (particularly those who want to avoid riba [usury] based investment) to make more diversified portfolios by considering Islamic portfolios to reduce risk exposure.

To the best of the authors’ knowledge, this is the first paper to create bivariate debt–equity portfolios swaps composed of Islamic and conventional assets.

This paper aims to investigate the dynamic portfolio optimisation performance of numerous samples of Shariah-compliant firms in the USA vis-à-vis the overall conventional sample.

This paper constructs efficient frontiers and subsequently the capital market line using the ovport set of commands in STATA. From the capital market line, the tangent portfolio is found, and the Sharpe ratio of the tangent portfolio is the primary measurement of the dynamic portfolio optimisation performance of the samples of Shariah-compliant samples in this study.

This paper finds that the overall conventional sample will outperform the Shariah-compliant samples in most cases. However, there exists a consistent trend whereby the performance of the overall conventional sample will converge towards the performance of the Shariah-compliant samples (and even be lower at times), as the market approaches a looming crisis suggesting that the Shariah-compliant samples do not experience significant deteriorations in their performance as compared to the conventional sample and that they provide stability during such times.

This paper assumes no transaction costs, illiquidity, bid-ask spread and non-compliant revenue purification all of which may negatively affect portfolio performance.

The findings of this paper suggest that Shariah-compliant samples should be included in portfolios during times of crisis because they are less affected by market-wide volatility.

The stability of Shariah-compliant samples reflects the conservativity of the contemporary Shariah stock screening methodologies and the Shariah itself.

Portfolio optimisation studies on Shariah-compliant samples are usually static in nature and are conducted in selected Muslim countries. This paper studies the dynamic portfolio optimisation in the USA where a liquid Islamic capital market is non-existent.

The purpose of this paper is to contribute to the existing stock return predictability and idiosyncratic risk literature by examining the relationship between stock returns and components derived from the decomposition of stock returns variance at the portfolio and firm levels.

A theoretical model is used to decompose the variance of stock returns into two volatility and two covariance terms by using a conditional Fama-French three-factor model. This study adopts portfolio analysis and Fama-MacBeth cross-sectional regression to examine the relationship between components of idiosyncratic risk and expected stock returns.

The portfolio analysis results show that volatility terms are negatively related to expected stock returns, and alpha risk has the most significant relationship with stock returns. On the contrary, covariance terms have positive relationships with expected stock returns at the portfolio level. Furthermore, the results of the Fama-MacBeth cross-sectional regression show that only alpha risk can explain variations in stock returns at the firm level. Another finding is that when volatility and covariance terms are excluded from idiosyncratic volatility, the relation between idiosyncratic volatility and stock returns becomes weak at the portfolio level and disappears at the firm level.

This is the first study that examines the relations between all the components of idiosyncratic risk and expected stock returns in equal-weighted and value-weighted portfolios. This research also suggests covariance terms of idiosyncratic volatility as new predictors of stock returns at the portfolio level. Moreover, this paper contributes to the idiosyncratic risk literature by examining whether all the four additional components explain all the systematic patterns included in the unconditional idiosyncratic risk.

This study aims to introduce a tree-structured linear and quantile regression framework to the analysis and modeling of equity returns, within the context of asset pricing.

The approach is based on the idea of a binary tree, where every terminal node parameterizes a local regression model for a specific partition of the data. A Bayesian stochastic method is developed including model selection and estimation of the tree structure parameters. The framework is applied on numerous U.S. asset pricing models, using alternative mimicking factor portfolios, frequency of data, market indices, and equity portfolios.

The findings reveal strong evidence that asset returns exhibit asymmetric effects and non- linear patterns to different common factors, but, more importantly, that there are multiple thresholds that create several partitions in the common factor space.

To the best of the authors' knowledge, this paper is the first to explore and apply a tree-structured and quantile regression framework in an asset pricing context.

Though of fairly recent origin, the capital‐asset pricing model (CAPM) is becoming a dominant influence in the analysis of financial and investment decisions. While continuing to undergo stringent theoretical and empirical examination, the demonstrable explanatory and predictive ability of the CAPM have led to its widespread recognition as the foundation of modern financial management. Though usually attributed to Sharpe, Lintner and Mossin, the origins of the CAPM can be traced back to the celebrated work of Harry Markowitz on portfolio selection.

The purpose of this paper is to investigate relative portfolio performance between sin stock returns and faith‐based returns.

Similar to Hong and Kacperczyk, Jensen's alpha was utilized to conduct tests along with three asset‐pricing models and rolling regression technique to reveal that faith‐based and sin betas move in opposite directions during most of the sample period.

Norm‐neglect was found, in that Jensen's alpha is positive and significant for the sin portfolio. Further, evidence in favor of norm‐conforming investor behavior was found, where Jensen's alpha is negative and significant for the faith‐based portfolio. These findings provide evidence that the sin portfolio outperforms the faith‐based portfolio relative to the market. A rolling regression technique reveals that faith‐based and sin betas tend to move in opposite directions during most of the sample period. The evidence suggests that faith‐based beta has an average estimated beta of one, mimicking the market. The sin portfolio, however, has an average estimated beta of one‐half. Finally, the reward‐to‐risk measure, Sharpe ratio, is statistically higher for the sin portfolio relative to the faith‐based portfolio.

This paper contributes to the literature in the following distinct ways. First, three asset‐pricing models are estimated to examine Jensen's alpha for sin and faith‐based portfolios. Second, a rolling regression procedure is used to examine the dynamic behavior relative to the market of the sin and faith‐based portfolios. Third, use is made of the Jobson and Korkie test, which allows for statistical comparisons of Sharpe ratios. Lastly, daily instead of monthly data and a different sample period are used to examine the research questions posed in this study.