Efficient Frontier Research Articles

Determining the equilibrium efficient frontier by proportional frontier shifting for data envelopment analysis with fixed-sum outputs

The equilibrium efficient frontier data envelopment analysis (EEFDEA) has been extensively used to evaluate efficiencies of the decision-making units (DMUs) with fixed-sum outputs. This study develops a new EEFDEA approach based on a proportional frontier-shifting strategy. Our approach applies an iterative procedure to find the equilibrium efficient frontier (EEF). Each iteration uses a proportional frontier-shifting model to improve an inefficient DMU to the efficient frontier by increasing its fixed-sum outputs. Meanwhile, the DMUs on the efficient frontier decrease fixed-sum outputs proportionally to ensure the total fixed-sum outputs are unchanged. Our theoretical developments show that the proportional frontier-shifting strategy is feasible and can finally obtain a unique EEF. The new approach allows DMUs to use their preferred input and output weights when determining the EEF. This generates an EEF that better aligns with real-world practices and avoids the need to construct it as a single hyperplane, as required by conventional EEFDEA methods. It also avoids unfair adjustments in fixed-sum outputs among the DMUs and eliminates the problem of peculiar efficiency evaluation results (i.e., some DMUs obtain extremely high, or infinity, efficiencies). Finally, we apply our approach to a case study of Chinese vehicle industry companies to demonstrate its usefulness and compare it with the previous representative approach.

On the relationship between the value function and the efficient frontier of a mixed integer linear optimization problem

On the relationship between the value function and the efficient frontier of a mixed integer linear optimization problem

Risk tolerance towards research and development investment: the role of firm size and technology intensity

ABSTRACT This research examines how risk tolerance towards research and development (R&D) investment varies by firm size and technology intensity using a case study of four groups of manufacturing firms (i.e. large high-tech firms, small high-tech firms, large low-tech firms, and small low-tech firms) in South Korea. Our research contributes to the literature by offering the first empirical application quantifying different risk tolerances towards R&D investment of firms of varying sizes and technology intensities using total factor productivity and optimal portfolio frontiers. We find that the risk tolerance towards R&D investment is proportional to firm size, and high-tech firms tend to be more risk tolerant than low-tech firms given the same firm size. Furthermore, we find that large low-tech firms have a greater tolerance for risk than small high-tech firms when the present guaranteed return is lower, but risk tolerance is reversed as the current guaranteed return increases. These findings could be used to inform R&D project funding decisions in particular, our finding of higher risk tolerance of small high-tech firms with higher present guaranteed return suggests that government subsidies for R&D investment may function as the present guaranteed return for small high-tech businesses.

Portfolio Optimization Strategies for the Common Investor

Abstract: Financial Analytics is a key field to making investment decisions and has been developed only recently. It involves analytical thinking, computational knowledge and creative thinking about investment strategies. There are many ways to invest money. Some people invest them in Gold, some in real estate, some create a fixed deposit, some in the stock market. Some people diversify their money into different sectors of the market and invest to get an optimal profit by understanding the market. This kind of investment is called portfolio management. Unlike gambling, understanding of the portfolio and its management can actively minimize the risks associated with investment. In the proposed research we tried to study the different strategies of investing in the different sectors and building a portfolio, with the express aim of creating optimal diversified portfolios. Our methods include optimizing the weights of different investment instruments in different sectors, with implementations carried out in Python and using time-series Python libraries. We have focussed on three different investment strategies in particular: (1) Genetic algorithms help us to divide the portfolio (chromosome) into the genes (sectors) and understand it in a better way. Exploiting the existing algorithms for optimizing fitness functions in genetic algorithms, we have implemented one strategy for optimizing portfolios; (2) Efficient frontier analysis from Markowitz theory helps in investing and creating our own portfolio. We developed some of the strategies that help in displaying portfolio allocation and efficient frontier graphs; (3) We have also implemented a new criterion in vogue in the financial markets today, the “Kelly Criterion” preferred by many investors all over the world. We used real time financial stock data to validate and test our functions. All the strategies developed are modular and we also show a proof-of-concept web interface for one of the developed strategies. It is hoped that our work enables investors in making better decisions about where to park their money and converting their wealth into high-yield portfolios.

Empirical Analysis of Portfolio Allocation During Market Turbulence Based on Efficient Frontier

The global financial markets have experienced considerable turmoil due to the COVID-19 pandemic, in this context, portfolio management becomes critically important. This paper employs Monte Carlo Simulation to determine Efficient Frontier of a portfolio comprising fourteen US technology stocks in the period of COVID-19 pandemic by python, which also allocates portfolios for Minimum Volatility and Maximum Sharpe Ratio, along with their key parameters. According to this study, Maximum Sharpe Ratio portfolio outperforms Minimum Volatility portfolio in terms of cumulative return. However, its important to note that Maximum Sharpe Ratio portfolio also experiences a greater maximum drawdown. Additionally, this paper visually depicts the optimal allocation of asset weights across different levels of risk aversion using a chart. Furthermore, it identifies NVDA as the optimal choice for investors who have low degree of risk-aversion due to its high volatility and expected return. Conversely, IBM and CSCO emerge as the preferred choices for risk-averse investors, as they effectively mitigate the portfolios entire risk.

Impact of a regulatory target and external factors on the waste efficiency of Italian municipalities.

Due to increasing consumption and urbanisation, urban waste management and recycling are a primary concern in Italy. Italian waste collection underwent significant reform with the introduction of a sorted collection target of 65% of total collected waste in Legislative Decree No. 152/2006. In this article, we analyse the effect of this regulatory target on the efficiency of waste collection in 275 Italian municipalities in the years 2016-2019. We estimate the coefficients of the cost efficiencies of the sorted and unsorted waste without assuming functional forms for the efficient frontier or the distribution of efficiency. Our findings suggest that municipalities that met the 65% sorted waste target demonstrated higher efficiency as costs increased, whereas those that failed to meet the target demonstrated higher inefficiency as costs increased. Strong effects emerged for population and urban economic development on the success of waste collection, whereas only marginal effects were observed for population density and city size. To improve the situation of municipalities that are not meeting the 65% target, we propose several policy measures, including 'neighbourhood solidarity'.

ESG integration strategy with a multivariate normal distribution

Purpose: The paper aims to present a new framework for ESG integration strategies in portfolio optimization problems. The optimization in the new structure focuses on the portfolio level, and the procedure is not focused on utility functions or on preliminary weights applied to the asset level. It applies the resampling technique, and all the portfolios are optimal portfolios in the mean-variance space. It uses a filtering process where only optimal portfolios with lower ESG risks are considered. Therefore, this technique works only with optimized portfolios, avoids concentration bias, and considers estimation errors in the expected returns and in the covariance matrix. Design/methodology/approach: The sample mean returns and covariance matrices generated by a multivariate normal distribution are applied in mean-variance optimization to generate several portfolios in the efficient frontiers. An ESG filtering process is used to select portfolios with lower ESG risks from a sample of 42 companies listed on the Brazilian stock exchange with returns from the period of 2018/01/01 to 2024/04/22.Findings: Integration strategy costs may be lower than the best-in-class strategy costs and may be similar to the costs of a negative screening strategy. Social implications: The paper presents a framework that considers social, environmental, and governance factors in the portfolio optimization process.Originality: The main contribution of this paper is to present a new framework that combines resampling of returns’ mean and covariance based on a multivariate normal distribution with an ESG portfolio filtering process.

Investment Portfolio with Convex Optimization and Risk Adjustment Using Multi-Factor Model and Multi-Armed Bandit Algorithm

This paper examines the creation of investment portfolios through convex optimization, multifactor models, and the multi-armed bandit (MAB) algorithms, focusing on the KL-UCB strategy to optimize decisions in uncertain settings. It explores the impact of systematic risk factors using the Fama-French three-factor model, estimating the influence of market, size, and value premiums via linear regression. The use of Monte Carlo simulation is detailed for generating potential asset allocations and calculating their expected returns, volatility, and Sharpe ratios. The optimize minimize function from the SciPy library is employed to construct an efficient frontier and determine optimal asset allocation, aiming to maximize returns or minimize volatility across various risk levels. The findings suggest that the strategy of dynamic weight adjustments combined with the KL-UCB algorithm enhances portfolio returns, particularly during market volatility. The research also reveals a portfolio inclination towards large-cap growth stocks due to the negative impacts of size and value premiums. It concludes that dynamic weight adjustment strategies offer significant potential in optimizing portfolio performance in complex market conditions, though leveraging increases risk and should be carefully managed according to investor risk tolerance.

The ESG-efficient frontier under ESG rating uncertainty

The impact of ESG score uncertainty on the risk-return profile of socially responsible optimal portfolios is analyzed. Focusing on the 109 largest French company stock prices between 2021 and 2024, uncertainty about ESG score is measured through the lens of investors’ assessment rather than from ESG rating agencies. The efficient frontier is generalized by introducing the degree of investors’ social responsibility to the classic Markowitz approach. Our results show that taking into account ESG uncertainty substantially degrades the trade-off between portfolio return and volatility for highly responsible and low-risk portfolios.

Planning improvements through data envelopment analysis (DEA) benchmarking based on a selection of peers

Incorporating preferences on suitable peers into benchmarking analyses may ensure the setting of appropriate targets, which enable designing plans for improving performance that are aligned with management. This paper deals with target setting in situations where decision makers (DMs) have previously made a selection of peer candidates for the benchmarking of a given organization. A first approach is developed within the framework of conventional Data Envelopment Analysis (DEA), which is the technology mostly used in non-parametric frontier analysis. It provides targets from reference sets consisting of peer candidates that span a face of the strong efficient frontier of the production possibility set (PPS). These targets result from solving a DEA-like model, thus preventing from the need to identify all of the maximal efficient faces (MEFs) of the DEA frontier. We also propose a second approach where the convexity in DEA is somehow relaxed to allow additionally for reference sets consisting of candidates that are Pareto-efficient, provided that their convex hull is not dominated by other units. In that sense, the targets found can be seen as representing best practices. This approach broadens the range of alternatives when planning improvements, and may eventually provide closer targets.

Modeling mispricing risk of defined contribution pension plan with a mean–variance criteria

This manuscript addresses modeling mispricing risk of defined contribution pension plan (DCPP) with a mean–variance criterion to obtain the optimal investment strategy. Provides a way for the sustainability of pensions by investing in the financial market. The pension manager’s objective is to maximize the expected terminal wealth while simultaneously minimizing the associated risk. We employ the stochastic dynamic programming principle (SDPP) and the Lagrange dual theorem to derive the efficient frontier and strategy, then two special cases are examined. Last, we conduct a numerical analysis to show how different parameters influence the efficient frontier and strategy. This analysis sheds light on the economic implications of our findings.

Approximations and inference for envelopment estimators of production frontiers

Nonparametric methods have been commonly used to assess the performance of both private and public organizations. Among them, the most popular ones are envelopment estimators such as Free Disposal Hull (FDH) or Data Envelopment Analysis (DEA), which estimate the attainable sets and their efficient boundaries by enveloping the cloud of observed units in the appropriate input-output space. However, these nonparametric envelopment techniques do not provide estimates of marginal products and other coefficients of economic interest. This paper presents a new approach that provides local estimates of all the desired partial derivatives and economic coefficients, which complement and complete the analysis based on nonparametric envelopment estimators. We improve nonparametric estimators by estimating nonparametrically smoothed efficient boundaries and providing derivatives and other coefficients without having to assume any parametric structure for the frontier and the inefficiency distribution. Our approach offers several advantages, such as a flexible nonparametric adjustment of the efficient frontier based on local linear models; a general multivariate efficiency model based on directional distances where one can choose the desired benchmark direction; the possibility of assessing the impact of external-environmental variables; a bootstrap-based statistical inference for deriving confidence intervals on the estimated coefficients for nonparametric and robust frontier approximations; the possibility of including factors aggregating inputs or outputs and recovering the estimated coefficients in the original units. To demonstrate the usefulness of the proposed approach, we provide an illustration in the field of education, where economic coefficients are important but the parametric assumptions have been questioned.

Cost-effectiveness Analysis of Colorectal Cancer Screening Strategies Using Active Learning and Monte Carlo Simulation.

Detection of colorectal cancer (CRC) in the early stages through available screening tests increases the patient's survival chances. Multimodal screening policies can benefit patients by providing more diverse screening options and balancing the risks and benefits of screening tests. We investigate the cost-effectiveness of a wide variety of multimodal CRC screening policies. We developed a Monte Carlo simulation framework to model CRC dynamics. We proposed an innovative calibration process using machine learning models to estimate age- and size-specific adenomatous polyps' progression and regression rates. The proposed approach significantly expedites the model parameter space search. Two multimodal proposed policies (i.e., 1] colonoscopy at 50 y and fecal occult blood test annually between 60 and 75 y and 2] colonoscopy at 50 and 60 y and fecal immunochemical test annually between 70 and 75 y) are identified as efficient frontier policies. Both policies are cost-effective at a willingness to pay of $50,000. Sensitivity analyses were performed to assess the sensitivity of results to a change in screening test costs as well as adherence behavior. The sensitivity analysis results suggest that the proposed policies are mostly robust to the considered changes in screening test costs, as there is a significant overlap between the efficient frontier policies of the baseline and the sensitivity analysis cases. However, the efficient frontier policies were more sensitive to changes in adherence behavior. Generally, combining stool-based tests with visual tests will benefit patients with higher life expectancy and a lower expected cost compared with unimodal screening policies. Colonoscopy at younger ages (when the colonoscopy complication risk is lower) and stool-based tests at older ages are shown to be more effective. We propose a detailed Markov model to capture the colorectal cancer (CRC) dynamics. The proposed Markov model presents the detailed dynamics of adenomas progression to CRC.We use more than 44,000 colonoscopy reports and available data in the literature to calibrate the proposed Markov model using an innovative approach that leverages machine learning models to expedite the calibration process.We investigate the cost-effectiveness of a wide variety of multimodal CRC screening policies and compare their performances with the current in-practice policies.

Optimal Reinsurance and Derivative-Based Investment Decisions for Insurers with Mean-Variance Preference

In our study, we investigate reinsurance issues and optimal investment related to derivatives trading for a mean-variance insurer, employing game theory. Our primary objective is to identify strategies that are time-consistent. In particular, the insurer has the flexibility to purchase insurance in proportion to its needs, explore new business, and engage in capital market investments. This is under the assumption that insurance companies’surplus capital adheres to the classical Cramér-Lundberg model. The capital market is made up of risk-free bonds, equities, and derivatives, with pricing dependent on the underlying stock’s basic price and volatility. To obtain the most profitable expressions and functions for the associated investment strategies and time guarantees, we solve a system of expanded Hamilton–Jacobi–Bellman equations. In addition, we delve into scenarios involving optimal investment and reinsurance issues with no derivatives trading. In the end, we present a few numerical instances to display our findings, demonstrating that the efficient frontier in the case of derivative trading surpasses that in scenarios where derivative trading is absent.

Numeraire choice, shadow profit, and inefficiency measurement

We study a programming approach to inducing inefficiency measures for convex technologies. It takes the technology and the numeraire as given and uses variational arguments to isolate shadow prices that make a decision maker’s observed behavior as efficient as possible. The focus is on how the numeraire determines the element of the efficient frontier to which a decision maker’s performance is compared, the resulting technical inefficiency measure, and whether that measure offers a cardinal representation of the technology. We use the results to study an inefficiency measure, the polyhedral measure, that generalizes an array of existing measures.

Production scale expansion and congestion in two-stage network systems

In managerial practice, decision-makers usually confront the problem of whether an organization (or decision-making unit, DMU) could expand its production to increase output. This paper develops new approaches for production scale expansion analysis and target setting of two-stage network systems based on data envelopment analysis. First, the technique of fixing the strongly efficient frontier is adopted to ensure that the analysis proceeds on the efficient frontier. Second, a model is proposed to obtain the maximum aggregated output for each DMU. A two-step procedure is then developed for production scale expansion analysis to check if expanding a DMU’s production scale (i.e., increasing the inputs and intermediate measures) would increase, maintain, or decrease its outputs (due to congestion). Further, we build a model to set appropriate production scale expansion targets for DMUs capable of increasing outputs through production scale expansion, considering their limited ability to increase inputs. Our approach always proceeds with production scale expansion analysis on the production efficient frontier. It also provides a simple sufficient and necessary condition to judge the congestion situation of a DMU in production scale expansion. Finally, we illustrate the proposed approach using a simple numerical example and a case study of China’s agricultural industry.

An improved equilibrium efficient frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs

In recent years, significant development has been made in efficiency evaluation for Decision-Making Units (DMUs) with fixed-sum outputs. The Generalized Equilibrium Efficient Frontier Data Envelopment Analysis (GEEFDEA) approach introduced by Yang et al. (2015) is one of the most representative methods. In the GEEFDEA approach, all DMUs are adjusted to become efficient under the same set of weights, indicating that the Equilibrium Efficient Frontier (EEF) constructed consists of only one hyperplane. However, in practical scenarios under the Variable Return to Scale (VRS) assumption, the production frontier always consists of multiple hyperplanes, presenting a more complex shape. To fill this research gap, we propose an improved Equilibrium Efficient Frontier Data Envelopment Analysis approach. Our approach allows DMUs to have different weights for inputs, variable-sum outputs, and fixed-sum outputs, resulting in an EEF with multiple hyperplanes. It is noted that our new approach uses a non-linear model to obtain the EEF. We show that the model can be linearized in the case of a single fixed-sum output. In situations involving multiple fixed-sum outputs, we propose an algorithm based on the Expectation Maximization (EM) mechanism to solve the model to obtain an EEF. Finally, we illustrate the advantages of our new approach through a numerical example and a case study in the global motor vehicle industry.

Deep learning the efficient frontier of convex vector optimization problems

In this paper, we design a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater’s condition. The proposed machine learning methodology provides both an inner and outer approximation of the weakly efficient frontier, as well as an upper bound to the error at each approximated efficient point. In numerical case studies we demonstrate that the proposed algorithm is effectively able to approximate the true weakly efficient frontier of CVOPs. This remains true even for large problems (i.e., many objectives, variables, and constraints) and thus overcoming the curse of dimensionality.

Evaluating the performance of intercity road freight transport: Double-frontier parallel network cross-efficiency model

Performance assessment of Intercity Road Freight Transport (IRFT) involve a complex set of considerations to ensure the efficient transportation of goods between their origins and destinations. Notably, Data Envelopment Analysis (DEA) models are often the preferred approach for conducting assessment studies that involve multiple inputs and outputs. Even though the conventional Cross-Efficiency (CE) technique addresses the limitations of DEA in producing comparable results, it still fails to consider the evaluation of internal system operations. The use of Network CE leads to more realistic results in assessing problems. It addresses not only the limitations of the DEA model in producing comparable results but also considers the performance of internal operations and system efficiency. Incorporating CE into a Parallel Network System (PNS), which is known as CE-PNS, has also a significant drawback as it neglects both the optimistic and pessimistic viewpoints based on the efficient and anti-efficient frontiers simultaneously, and may therefore fail to provide a comprehensive analysis. The primary objective of this study is to propose a new double-frontier network CE that takes into account two perspectives simultaneously. Indeed, this study is the first to incorporate the concepts of CE and double-frontier DEA into a PNS to provide an effective tool for assessing Iranian IRFT. For this purpose, the Cross-Inefficiency (CIE) technique is first incorporated into the PNS, called CIE-PNS, which explores the relationship between system inefficiency and internal divisions. The CE-PNS and CIE-PNS may yield different results. Therefore, Double-Frontier CE for a PNS (DFCE-PNS) is derived by combining the efficiency results obtained from CE-PNS and CIE-PNS. This study also examines different inputs and outputs to assess the performance of Iranian IRFT. The results demonstrate that DFCE-PNS yields more comprehensive and reliable results.

Portfolio Analysis of Five Stocks Under Different Constraints Based on Markowitz Model & Index Model

Since the dawn of the 21st century, while there has been an abundance of talented fund managers, truly exceptional asset portfolios have been rare. Addressing this phenomenon, the study delves into the current state of asset management, employing two renowned financial models: the Markowitz model and the Index model. These models are utilized to analyze the returns and risks of five high-performing assets. Additionally, acknowledging the diversity of investor preferences, this paper incorporates five different constraints to cater to a wider spectrum of client needs. The crux of the research is the optimization of the asset portfolio, grounded in these models and constraints. The paper findings indicate that the integration of the Markowitz and Index models with the capital market line and the efficient frontier proves highly effective in the management of risk asset portfolios. In this paper, the Markowitz model consistently excels over the index model in both minvariance and maxsharpe scenarios. This study has important reference value for investors in related fields.