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This paper addresses two most important problems of mean-lower partial moment (MLPM) portfolio selection theory, the convexity of efficient frontier and the availability of target returns that permit two-fund separation (TFS). The convexity of the efficient frontier is a very crucial property as it guarantees the existence of various important results. However, in the MLPM framework, the convexity has not been analytically proved yet. In this paper, we provide an analytical proof for this convexity. On the other hand, in the MLPM framework, the separation is guaranteed for two specific targets—risk-free rate and mean return. The question of which other targets admit the separation has not been solved for the last three decades. As a result, non-separation occurs with the use of arbitrary targets and thereby several pitfalls arise in the MLPM portfolio optimization and asset ranking (Brogan and Stidham, Eur J Oper Res 184(2):701–710, 2008; Hoechner et al., Int Rev Finance 17(4):597–610, 2017). We solve this problem by showing the existence and uniqueness of a generalized family of target returns that guarantees the MLPM separation. The discovery of generalized target provides a sound theoretical foundation to use a modified version of Kappa ratio which, unlike the usual Kappa ratio, always satisfies the maximum principle and the invariance property (Pedersen and Satchell, Quant Finance 2(3):217–223, 2002; Zakamouline, Quant Finance 14(4):699–710, 2014). Finally, we conduct empirical experiments that illustrate our theoretical results and unfold some interesting facts.

In this paper, we investigate the optimal investment-reinsurance strategy for an insurer with two dependent classes of insurance business, where the claim number processes are correlated through a common shock. It is assumed that the insurer can invest her wealth into one risk-free asset and multiple risky assets, and meanwhile, the instantaneous rates of investment return are stochastic and follow mean-reverting processes. Based on the theory of linear-quadratic control, we adopt a backward stochastic differential equation (BSDE) approach to solve the mean-variance optimization problem. Explicit expressions for both the efficient strategy and efficient frontier are derived. Finally, numerical examples are presented to illustrate our results.

The Markowitz frontier of optimal portfolios is valid in both mean–variance space and in mean–standard deviation space. There are, however, some curious differences because lines in one space become curves in the other. This article explores and explains the curiosity. Key Findings ▪ The capital allocation line is a curve in mean–variance space. ▪ There is a line in mean–variance space that connects the riskless rate with the tangency portfolio, but it is not a capital allocation line. ▪ Volatility can be either standard deviation or variance, but their efficient frontier geometry is curiously different.

Investment fund investment strategies and asset allocations typically are based on a multiplicity of complex (possibly competing) goals that often are incorporated in a simple return target. The challenge is to develop a portfolio whose expected return at least equals the target but has a volatility less than a disaster-avoidance risk limit. However, such a goal-matching return only provides a 50/50 chance of success. Truly important goals may require a higher probability of success, such as 60%. This article focuses on efficient portfolios and the return they can provide with a specified probability of assurance. The key step is to map the efficient frontier into an assurance frontier that plots risk-adjusted returns with a 60% success probability. This frontier typically has a peak return that is the highest available risk-adjusted return. In some cases, this peak portfolio is at the risk limit. In other cases, even with a monotonically rising efficient frontier, the peak may fall well below the maximum volatility limit. Key Findings ▪ Portfolios with expected returns that just match a goal-based target may have only a 50/50 assurance of success (even after those targets have been properly revised to account for, e.g., inflation, fund expenses, and geometric effects). ▪ Portfolios that have the best risk-adjusted return can sometimes be found at a volatility that is well short of a fund’s maximum risk limit. ▪ Longer horizons generally lead to higher peak returns that can enhance prospects of success.

In this paper we propose a hybrid quantum-classical algorithm for dynamic portfolio optimization with minimal holding period. Our algorithm is based on sampling the near-optimal portfolios at each trading step using a quantum processor, and efficiently post-selecting to meet the minimal holding constraint. We found the optimal investment trajectory in a dataset of 50 assets spanning a one year trading period using the D-Wave 2000Q processor. Our method is remarkably efficient, and produces results much closer to the efficient frontier than typical portfolios. Moreover, we also show how our approach can easily produce trajectories adapted to different risk profiles, as typically offered in financial products. Our results are a clear example of how the combination of quantum and classical techniques can offer novel valuable tools to deal with real-life problems, beyond simple toy models, in current NISQ quantum processors., 6 pages, 4 figures, revised version

The recent growth in economic and financial markets has brought the focus on energy derivatives as an alternative investment class for investors, financial analysts, and portfolio managers. The financial modeling and risk management of portfolios using the energy derivatives instrument is a requirement and challenge for researchers in the field. The energy and other commodity futures force the expert investors to investigate the broader investment spectrum and consequently diversify their portfolios using the futures instruments. Going beyond the conventional portfolios and developing out-of-the-box strategies that comply with the changing financial and economic advancements are the keys to long-term sustainability in the financial world. This study investigates the impact of diversification with five energy futures from January 2011 to July 2020 on three traditional commodity futures portfolios. The results show that diversification increased the returns while simultaneously reducing the portfolio volatility in all portfolios. The diversified portfolios provided higher returns than the traditional portfolios for the same level of risk. This study also revealed that the results might improve when a short position in the futures contracts is allowed. Moreover, we conclude that adding multiple energy futures in a portfolio provides enhanced diversification results, whereas the WTI crude oil futures fail to diversify any portfolio considered in the study.

Scientists are increasingly considering quality in nonparametric frontier efficiency studies in health care. There are many ways to include quality in efficiency analyses. These approaches differ, among other things, in the underlying assumptions about the influence of quality on the attainable efficiency frontier and the distribution of inefficiency scores. The aim is to provide an overview of how scholars have taken quality into account in nonparametric frontier efficiency studies and, at the same time, to address the underlying assumptions on the relationship between efficiency and quality. To this end, we categorized empirical efficiency studies according to the methodological approaches and quality dimensions and collected the quality indicators used. We performed a Web of Science search for studies published in journals covered by the Science Citation Index Expanded, the Social Sciences Citation Index, and the Emerging Sources Citation Index between 1980 and 2020. Of the 126 studies covered in this review, 78 are one-stage studies that incorporate quality directly into the efficiency model and thus assume that quality impacts the attainable efficiency frontier. Forty-four articles are two-stage studies that consider quality in the first and the second stage or the second stage only. Four studies do not assume a priori a specific association between efficiency and quality. Instead, they test for this relationship empirically. Outcome quality is by far the most frequently incorporated quality dimension. While most studies consider structural quality as an environmental variable in the second stage, they include outcome quality predominantly directly in the efficiency model. Process quality is less common.

In general portfolio, optimization is a technique for selecting the proportion of assets to make a better portfolio by maximizing the expected return while also minimizing the risk. In this research, the k-means clustering method is used to classify stocks are listed on the LQ45 Index and select stocks whose has prices tend to be increased. Then the Markowitz approach is used to analyze the performance of optimization portfolio models that have a minimum variance in expected return and risk. After understanding the performance of this portfolio optimization, future works will be able to apply this model in cloud computing or artificial intelligence. In addition, investors will develop a better view of the latest performance of the stocks are listed in the LQ45 index and support them decide which stocks should be included in their portfolios, thus prevent wrong decisions.

This paper investigates a time-consistent investment strategy under the mean-variance criterion for an investor who accumulates retirement savings through a defined contribution (DC) pension plan with stock and bond investment opportunities. The expected return rate on the stock is modulated by an unobservable predictor which follows a mean-reverting stochastic process. The evolution of the instantaneous interest rate is described by the Vasicek model. In addition, the contribution rate of the DC pension plan is stochastic and correlated with financial risks coming from the stochastic interest rate and stock price. In a game theoretic framework, we derive a closed-form equilibrium investment strategy and corresponding equilibrium value function for the mean-variance criterion by adopting the filtering technique and the stochastic control method. Furthermore, we provide an equilibrium investment strategy and equilibrium value function when the expected return rate of the stock is completely observable. Finally, some numerical examples are presented to demonstrate the sensitivity analysis of the equilibrium investment strategy and equilibrium efficient frontier. Numerical analysis confirms that there is non-negligible information loss on the equilibrium investment strategy and equilibrium value function due to partial observation in the stock price dynamics.