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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.

Standard multivariate tests of mean variance efficiency (MVE) have been criticised on the grounds that they require regression residuals to have a multivariate normal distribution. Generally, the existing evidence suggests that the normality assumption is questionable, even for monthly returns. MacKinlay and Richardson (1991) developed a generalised method of moments (GMM) framework which provides tests which are valid under much weaker distributional assumptions. They examined monthly US data formed into size based portfolios, for mean‐variance efficiency relative to the Sharpe‐Lintner CAPM. They found that inferences regarding mean‐variance efficiency can be sensitive to the test considered. In this paper we further investigate their GMM tests using monthly Australian data over the period 1974 to 1994. We extend upon their analysis to consider an alternative version of their GMM test and also to examine a zero‐beta version of the CAPM. Similar to the US case, our results also indicate sensitivity of inferences to the tests used. Finally, while we find that the GMM tests generally provide rejection of mean‐variance efficiency, tests involving the zero‐beta CAPM, particularly when a value‐weighted market index is used, prove less prone to rejection.

The primary objective of this study is to propose a robust multiobjective solution search approach for a mean-variance multiple correlated quality characteristics optimisation problem, so-called “multiple response optimisation (MRO) problem”. The solution approach needs to consider response surface (RS) model parameter uncertainties, response uncertainties, process setting sensitivity and response correlation strength to derive the robust solutions iteratively.

This study adopts a new multiobjective solution search approach to determine robust solutions for a typical mean-variance MRO formulation. A fine-tuned, non-dominated sorting genetic algorithm-II (NSGA-II) is used to derive efficient multiobjective solutions for varied mean-variance MRO problems. The iterative search considers RS model uncertainties, process setting uncertainties and response correlation structure to derive efficient fronts. The final solutions are ranked based on two different multi-criteria decision-making (MCDM) techniques.

Five different mean-variance MRO cases are selected from the literature to verify the efficacy of the proposed solution approach. Results derived from the proposed solution approach are compared and contrasted with the best solution(s) derived from other approaches suggested in the literature. Comparative results indicate significant superiorities of the top-ranked predicted robust solutions in nondominated frequency, closeness-to-target and response variabilities.

The solution approach depends on RS modelling and considers continuous search space.

In this study, promising robust solutions are expected to be more suitable for implementation than point estimate-based MOO solutions for a real-life MRO problem.

No evidence of earlier research demonstrates the superiority of a MOO-based iterative solution search approach for mean-variance MRO problems by simultaneously considering model uncertainties, response correlation and process setting sensitivity.

This study investigates the impact of uncertainty on the mean-variance relationship. We find that the stock market's expected excess return is positively related to the market's conditional variances and implied variance during low uncertainty periods but unrelated or negatively related to conditional variances and implied variance during high uncertainty periods. Our empirical evidence is consistent with investors' attitudes toward uncertainty and risk, firms' fundamentals and leverage effects varying with uncertainty. Additionally, we discover that the negative relationship between returns and contemporaneous innovations of conditional variance and the positive relationship between returns and contemporaneous innovations of implied variance are significant during low uncertainty periods. Furthermore, our results are robust to changing the base assets to mimic the uncertainty factor and removing the effect of investor sentiment.

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 response to common criticisms on the appropriateness of mean-variance in asset allocation decisions involving hedge funds, we offer a mean-Gini framework as an alternative. The mean-Gini framework does not require the usual normality assumption concerning return distributions. We also evaluate empirically the differences in allocation outcomes between the two frameworks using historical data. The differences turn out to be significant. The evidence thus confirms the inappropriateness of the mean-variance framework and enhances the attractiveness of mean-Gini for this asset class.

The purpose of this paper is to analyze the mean-variance capital asset pricing model (CAPM) and downside risk-based CAPM (DR-CAPM) developed by Bawa and Lindenberg (1977), Harlow and Rao (1989), and Estrada (2002) to assess which downside beta better explains expected stock returns. The paper also explores whether investors respond differently to stocks that co-vary with declining market than to those of co-vary with rising market.

The paper uses monthly data of closing prices of stocks listed at the Karachi Stock Exchange (KSE). The data cover the period from January 2000 to December 2012. The standard, downside, and upside betas are estimated for different sub-periods,and then,their validity to quantify the risk premium is tested for subsequent sub-periods in a cross sectional regression framework. Though our empirical methodology is similar to that of Fama and MacBeth (1973) for testing the CAPM and the DR-CAPM, our approach to estimate the downside beta is different from earlier studies. In particular, we follow Estrada ' s (2002) suggestions and obtain the correct and unbiased estimation of the downside beta by running the time series regression through origin. The authors carry out the two-pass regression analysis using the generalized method of moment (GMM) in the first pass and the generalized least squares (GLS) estimation method in the second pass.

The results indicate that the mean-variance CAPM shows a negative risk premium for monthly returns of selected stocks. However, the results for the DR-CAPM of Bawa and Lindenberg (1977) and Harlow and Rao (1989) provide evidence of a positive risk premium for the downside beta. In contrast, the DR-CAPM of Estrada (2002) shows a negative risk premium in some sub-periods while the positive premium in the others. By comparing the risk premium for both downside and upside risks in a single-equation framework, the authors show that the stocks that co-vary with a declining market are compensated with a positive premium for bearing the downside risk. Yet, the risk premium for stocks that are negatively correlated with declining market returns is negative for all the three-downside betas in all the examined sub-periods.

The empirical findings of the paper are of great significance for investors for designing effective investment strategies. Specifically, the results help investors to identify an appropriate measure of risk and to construct well-diversified portfolio. The results are also useful for firm managers in capital budgeting decision-making process as they enable them to cost equities appropriately. The results also suggest that the risk-return relationship implied by mean-variance CAPM is negative and therefore this model is not suitable for gauging the risk associated with stocks traded in KSE. Yet, the authors show that DR-CAPM out performs in quantifying the risk premium.

Unlike prior empirical studies, the authors follow Estrada’s (2002) suggestions where downside beta is calculated using regression through origin to find correct and unbiased beta. Departing from the existing literature the authors estimate three different versions of DR-CAPM along with the standard CAPM for comparison purpose. Finally, the authors apply sophisticated econometrics methods that help in lessening the problem of non-synchronous trading and the issue of non-normality of returns distribution.

The author proposes an update to the mean variance (MV) framework that replaces a constant risk aversion parameter using a dynamic risk aversion indicator. The contribution to the literature is made through making the static risk aversion parameter operational using an indicator of market sentiment. Results suggest that Sharpe ratios improve when the author replaces the traditional risk aversion parameter with a dynamic sentiment indicator from the behavioral finance literature when allocating between a risky portfolio and a risk-free asset. However, results are mixed when using the behavioral framework to allocate between two risky assets.

The author includes a dynamic risk aversion parameter in the mean variance framework and back test using the traditional and updated behavioral mean variance (BMV) framework to see which framework leads to better performance.

The author finds that the behavioral framework provides superior performance when allocating between a risky and risk-free asset; however, it under performs when allocating between risky assets.

The research is based on back testing; therefore, it cannot be concluded that this strategy will perform well in real-time circumstances.

Portfolio managers may use this strategy to optimize the allocation between a risky portfolio and a risk-free asset.

An improved allocation between risk-free and risky assets that could lead to less leverage in the market.

The study is the first to use such a sentiment indicator in the traditional MV framework and show the math.

The purpose of this paper is to address three key objectives. The first is the proposal of an enhanced multiobjective optimisation (MOO) solution approach for the mean and mean-variance optimisation of multiple “quality characteristics” (or “responses”), considering predictive uncertainties. The second objective is comparing the solution qualities of the proposed approach with those of existing approaches. The third objective is the proposal of a modified non-dominated sorting genetic algorithm-II (NSGA-II), which improves the solution quality for multiple response optimisation (MRO) problems.

The proposed solution approach integrates empirical response surface (RS) models, a simultaneous prediction interval-based MOO iterative search, and the multi-criteria decision-making (MCDM) technique to select the best implementable efficient solutions.

Implementation of the proposed approach in varied MRO problems demonstrates a significant improvement in the solution quality in worst-case scenarios. Moreover, the results indicate that the solution quality of the modified NSGA-II largely outperforms those of two existing MOO solution strategies.

The enhanced MOO solution approach is limited to parametric RS prediction models and continuous search spaces.

The best-ranked solutions according to the proposed approach are derived considering the model predictive uncertainties and MCDM technique. These solutions (or process setting conditions) are expected to be more reliable for satisfying customer specification compared to point estimate-based MOO solutions in real-life implementation.

No evidence exists of earlier research that has demonstrated the suitability and superiority of an MOO solution approach for both mean and mean-variance MRO problems, considering RS uncertainties. Furthermore, this work illustrates the step-by-step implementation results of the proposed approach for the six selected MRO problems.

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.