Stochastic Dominance Research Articles

Enhancing Portfolio Decarbonization Through SensitivityVaR and Distorted Stochastic Dominance

Recent trends in portfolio management emphasize the importance of reducing carbon footprints and aligning investments with sustainable practices. This paper introduces SensitivityVaR (SensitivityVaR), an advanced distortion risk measure that combines Value-at-Risk (VaR) and Expected Shortfall (ES) with the Cornish–Fisher expansion. SensitivityVaR provides a more robust framework for managing risk, particularly under extreme market conditions. By incorporating first- and second-order distorted stochastic dominance criteria, we enhance portfolio decarbonization strategies, aligning financial objectives with environmental targets such as the Paris Agreement’s goal of a 7% annual reduction in carbon intensity from 2019 to 2050. Our empirical analysis evaluates the impact of integrating carbon intensity data—including Scope 1, Scope 2, and Scope 3 emissions—on portfolio optimization, focusing on key sectors like technology, energy, and consumer goods. The results demonstrate the effectiveness of SensitivityVaR in managing both risk and environmental impact. The methodology led to significant reductions in carbon intensity across different portfolio configurations, while preserving competitive risk-adjusted returns. By optimizing tail risks and limiting exposure to carbon-intensive assets, this approach produced more balanced and efficient portfolios that aligned with both financial and sustainability goals. These findings offer valuable insights for institutional investors and asset managers aiming to integrate climate considerations into their investment strategies without compromising financial performance.

Choices under uncertainty and the investment horizon

AbstractMean–Variance (M–V) is the most popular investment rule employed by both practitioners and researches. For a short-planned investment horizon, this rule generally conforms with expected utility paradigm. However, for a relatively long horizon, generally more than one year, the distributions of returns become positively skewed, hence the M–V rule loses ground. As the horizon increases, by the M–V rule one needs (mistakenly) to increase the weight of bonds in the stock–bond portfolio, e.g., almost 100% in bonds for a 30-year horizon. Expected utility maximization recommending almost 100% in stocks for long horizons. This, gap is of crucial importance, because life expectancy is increasing, implying longer investment horizons. For long horizons the mean–coefficient-of-variance rule conforms with expected utility, as the distributions are close to log-normal. For intermediate horizons one should employ stochastic dominance or direct expected utility maximization.

PENGUKURAN RISIKO PORTOFOLIO SAHAM JAKARTA ISLAMIC INDEX DENGAN STOCHASTIC DOMINANCE

Stocks is one of the assets which has a high level of liquidity. Optimizing stock investment can be done by diversifying the portfolio. Stochastic Dominance is a portfolio formation method that looks at the amount of dominance of each stock pair. This study’s purpose is to apply the Stochastic Dominance method to create an optimal portfolio on sharia index called JII from April 2018 to March 2022. This study indicate that out of the 5 selected stocks, there are 4 stocks that dominate each stock pair, including ADRO, ICBP, PTBA, UNTR. ADRO proportion are 57,14% while ADRO, PTBA, and UNTR’s proportion are each 14,28%. The level of risk on this research is measured by a VaR with historical simulation method. Using this method, the maximum potential loss of the formed portfolio for the next month is 8.5% at a 95% confidence level.

Minimum adjustment cost consensus model with bounded risk preference attitudes: A perspective based on fractional stochastic dominance

Linguistic multi-attribute group decision making with linguistic distribution assessment (LMAGDM-LDA) problems have been widely investigated. However, in the existing studies, the risk attitudes of decision maker are seldom considered. Inspired by this, in this paper, we employ the idea of fractional stochastic dominance to develop a consensus reaching framework for LMAGDM-LDA with bounded risk preference attitudes. Then, we design an interactive learning algorithm for obtaining the bounded risk preference threshold. Next, we analyze the deception behaviors and average behaviors of experts, and develop the minimum adjustment cost consensus model with bounded risk preference attitude (MACC-BRP). And we justify the connection between the MACC-BRP and the minimum adjustment cost consensus model with other risk attitudes. Furthermore, we provide a distance-based method to obtain the rankings of alternatives. Furthermore, a numerical analysis is provided to show the computation process of the proposed method, and a comparison analysis and a simulation analysis are further conducted to show the advantages and features of the proposal. The simulation results show the effects of the risk preference threshold, the intrinsic individual weight and the average threshold. The comparison results show that the proposed minimum adjustment cost consensus models have clear advantages.

Assessing stochastic dominance of downside and upside financial risk profiles using the block maxima method in extreme value theory

This paper aims to assess the stochastic dominance of the extreme downside (negative return) and upside (positive return) risk profiles of three US stock market indices, namely NASDAQ Composite, S&P 500 and Dow Jones Industrial Average (DJIA) based on the block maxima method in extreme value theory. The extreme downside and upside risk profiles were developed using two datasets of 360 monthly minimum and maximum daily log returns respectively (from January 1992 to December 2021). Extreme losses beyond the 80th percentile (corresponding to a tail probability of less than 0.2) of the theoretical extreme risk profiles were adopted to investigate stochastic dominance. Pairwise comparisons show that the DJIA stochastically dominates the other two indices in both extreme negative and positive returns. Moreover, the extreme upside risk profile of the DJIA stochastically dominates its extreme downside risk profile. The paper finds that investment in short positions (encountering upside risk) provides the least extreme risk compared with long positions (encountering downside risk) for the DJIA, as well as both short and long positions for the S&P 500 and NASDAQ Composite.

A nonparametric test of [formula omitted]th-degree inverse stochastic dominance

This paper proposes a nonparametric test for mth-degree inverse stochastic dominance which is a powerful tool for ranking distribution functions according to social welfare. We construct the test based on empirical process theory. The test is shown to be asymptotically size controlled and consistent. The good finite sample properties of the test are illustrated via Monte Carlo simulations. We apply our test to the inequality growth in the United Kingdom from 1995 to 2010, and obtain a more complete ranking of the income distributions.

Probability of Causation with Sample Selection: A Reanalysis of the Impacts of Jóvenes en Acción on Formality

This article identifies the probability of causation when there is sample selection. We show that the probability of causation is partially identified for individuals who are always observed regardless of treatment status and derive sharp bounds under three increasingly restrictive sets of assumptions. The first set imposes an exogenous treatment and a monotone sample selection mechanism. To tighten these bounds, the second set also imposes the monotone treatment response assumption, while the third set additionally imposes a stochastic dominance assumption. Finally, we use experimental data from the Colombian job training program Jóvenes en Acción to empirically illustrate our approach’s usefulness. We find that, among always-employed women, at least 10.2% and at most 13.4% transitioned to the formal labor market because of the program. However, our 90%-confidence region does not reject the null hypothesis that the lower bound is equal to zero.

Connection between higher order measures of risk and stochastic dominance

Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been observed by the intriguing concept of the risk quadrangles, for example. Stochastic dominance is a binary relation for random variables to compare random outcomes. It is demonstrated that the concepts of higher order risk measures and stochastic dominance are equivalent, they can be employed to characterize the other. The paper explores these relations and connects stochastic orders, higher order risk measures and the risk quadrangle. Expectiles are employed to exemplify the relations obtained.

Measures of stochastic non-dominance in portfolio optimization

Stochastic dominance rules are well-characterized and widely used. This work aims to describe and better understand the situations when they do not hold by developing measures of stochastic non-dominance. They quantify the error caused by assuming that one random variable dominates another one when it does not. To calculate them, we search for a hypothetical random variable that satisfies the stochastic dominance relationship and is as close to the original one as possible. The Wasserstein distance between the optimal hypothetical random variable and the original one is considered as the measure of stochastic non-dominance. Depending on the conditions imposed on the probability distribution of the hypothetical random variable, we distinguish between general and specific measures of stochastic non-dominance. We derive their exact values for random variables with uniform, normal, and exponential distributions. We present relations to almost first-order stochastic dominance and to tractable almost stochastic dominance. Using monthly returns of twelve assets captured by the German stock index DAX, we solve portfolio optimization problems with the first-order and second-order stochastic dominance constraints. The measures of stochastic non-dominance allow us to compare the optimal portfolios with respect to different orders of stochastic dominance from a new angle. We also defined the closest dominating and closest approximately dominating portfolios. They brought a better understanding of the relationship between the two types of optimal portfolios. Using moving window analysis, the relationship of the in-sample measure of stochastic non-dominance to out-of-sample performance was studied, too.

To revise or not to revise? This is the question

AbstractBuy and hold and periodical revisions are two competing investment strategies. Revising to the optimal one-period investment weights seemingly dominates the buy-and-hold strategy with random and uncontrolled investment weights determined by asset price changes. This intuition is misleading as both investment strategies are theoretically included in the risk aversion efficient set. Considering only economically relevant preferences, with stocks-bonds portfolios, both strategies are empirically included in the risk aversion efficient set as long as the investment horizon is shorter than 20 years. However, for an investment horizon longer than twenty years, the buy and hold strategy empirically dominates the revision strategy by Almost First-degree Stochastic Dominance ($$AFSD$$ AFSD ) rule, namely by all economically relevant utility functions. When the horizon is indefinitely long, holding only stocks dominates the stock–bond portfolios of both the B&H(S) and the RV(S). However, this theoretical result may be practically irrelevant for most investors with a horizon shorter than 20 years.

A stochastic-demographic model to explain success and dominance in international sports

We model a stochastic, demographic-based framework to examine how an empirically proven, so-called first mover advantage affects the long-term sporting success of states by considering, among other things, demographic developments and the accumulation of sport-related human capital. In order to clarify and formalize this advantage in a sports economics framework, we draw on the concept of the stochastic dominance. Since our model is dynamic, it allows us to show how the probability of success of a nation evolves and under which conditions the stochastic dominance reduces.

Risk sharing under heterogeneous beliefs without convexity

We consider the problem of finding (Pareto-)optimal allocations of risk among finitely many agents. The associated individual risk measures are law-invariant, but with respect to agent-dependent and potentially heterogeneous reference probability measures. Moreover, we assume that the individual risk assessments are consistent with the respective second-order stochastic dominance relations, but remain agnostic about their convexity. A simple sufficient condition for the existence of Pareto optima is provided. The proof combines local comonotonic improvement with a Dieudonné-type argument, which also establishes a link of the optimal allocation problem to the realm of “collapse to the mean” results.

θ-Weighted mixture distribution: the Weibull-Lomax case

IntroductionThis article introduces a new family of weighted mixture distributions, referred to as θ-WM. The θ-WM family is generated by combining two distributions weighted by a parameter θ, offering notable flexibility to model a wide range of complex phenomena. A special case study of the θ-weighted mixture distribution of Weibull-Lomax (θ-WMWLx) is included, resulting from the combination of Weibull and Lomax distributions.MethodsThe research thoroughly examines the reliability and statistical properties of the θ-WMWLx distribution. Key aspects such as stochastic dominance, survival and hazard functions, mean residual life, and moments are addressed. The maximum likelihood method is used to estimate unknown parameters.ResultsThe research findings show that the θ-WMWLx distribution provides a superior fit compared to competing distributions. The analyses are validated using three real datasets, demonstrating the effectiveness of the proposed distribution.DiscussionThe θ-WMWLx distribution stands out for its ability to model complex phenomena with high precision. Validation with real data confirms that the proposed distribution offers a better fit than existing distributions, highlighting its utility and applicability in various statistical analysis contexts.

Distributionally Robust Newsvendor Under Stochastic Dominance with a Feature-Based Application

Problem definition: In this paper, we study the newsvendor problem under some distributional ambiguity sets and explore their relations. Additionally, we explore the benefits of implementing this robust solution in the feature-based newsvendor problem. Methodology and results: We propose a new type of discrepancy-based ambiguity set, the JW ambiguity set, and analyze it within the framework of first-order stochastic dominance. We show that the distributionally robust optimization (DRO) problem with this ambiguity set admits a closed-form solution for the newsvendor loss. This result also implies that the newsvendor problem under the well-known infinity-Wasserstein ambiguity set and Lévy ball ambiguity set admit closed-form inventory levels as a by-product. In the application of feature-based newsvendor, we adopt general kernel methods to estimate the conditional demand distribution and apply our proposed DRO solutions to account for the estimation error. Managerial implications: The closed-form solutions enable an efficient computation of optimal inventory levels. In addition, we explore the property of optimal robust inventory levels with respect to the nonrobust version via concepts of perceived critical ratio and mean repulsion. The results of numerical experiments and the case study indicate that the proposed model outperforms other state-of-the-art approaches, particularly in environments where demand is influenced by covariates and difficult to estimate. Funding: X. Li is supported by the Singapore Ministry of Education [Tier 1 Grant 23-0619-P0001, 24-0500-A0001] and National Natural Science Foundation of China [Grant 72331004]. L. Zhang is partially supported by the National Natural Science Foundation of China [Grants 72171156 and 72231002] and the Hong Kong Research Grants Council [Grant 16212419]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0159 .

A note on convex stochastic dominance and diversification with applications

. In this note, we present an overlooked result derived from Fishburn’s Convex Stochastic Dominance (CSD) (Fishburn (1974a; 1974b). We demonstrate that CSD is a sufficient condition for establishing second-order stochastic dominance in the context of linear combinations of random variables. While this result may appear straightforward, to the best of our knowledge, it has not been explicitly presented as we have done in this work. Furthermore, the implications of this finding are extensive, as it can be applied to various areas of research, as we illustrate in this study.

Stochastic dominance testing of poverty in Mozambique

AbstractNational assessments produced regularly from 1996/97 to 2019/20 provide standard estimates of the evolution of poverty in Mozambique. Stylised facts point to significant reduction in monetary and multidimensional poverty until 2014/15, even though characterised by persistent urban–rural and regional inequalities in several dimensions, followed by worsening deprivation during 2014/15–2019/20. In this paper, we rely on first-order dominance (FOD) methodology to check the robustness of standard poverty estimates while providing deeper insights into what happened in this poverty-stricken country. Our main findings include that the capital city, Maputo, and surrounding areas progressively came to dominate all other provinces in terms of well-being, and the provincial rankings from spatial FOD analysis are very stable over time. Rural areas, mainly those in the northern and central regions, are, with a few exceptions, always at the bottom of the ranking. Moreover, our FOD temporal analysis reveals that 2019/20 dominates, with a high degree of confidence, the results from earlier years, pointing to positive development over time, but with one important exception. The comparison between 2019/20 and 2014/15 is indeterminate, indicating that no significant advancement took place during this period. What stands out is the compelling need for concerted policy action to address the strong and persistent spatial gaps in welfare and poverty, including the capacity to respond effectively to external and internal shocks.

Precautionary risk-reduction and saving decisions: Two sides of the same coin?

We provide new results about the comparative static effects of income risk and interest rate risk on optimal risk-reduction and saving decisions. We combine arguments from the risk apportionment literature with monotone comparative statics. Risk reduction and saving are Edgeworth-Pareto substitutes for (mixed) risk averters and Edgeworth-Pareto complements for (mixed) risk lovers. For changes in income risk, risk reduction and saving are Nth-degree risk complements for risk lovers. For changes in interest rate risk, risk reduction and saving are Nth-degree risk substitutes for risk averters. The individual's risk attitude and the source of risk thus co-determine the effects of risk changes on optimal. We also discuss several extensions including multiple loss states, higher-order risk reduction, stochastic dominance, non-separable utility, and inflation risk.

The k-th order mean-deviation model for route choice under uncertainty

This study introduces the k-th order mean-deviation model for optimizing route choice within large, stochastic, and time-variant networks. This model addresses the limitations of the traditional mean-standard deviation approach by better handling extreme outcomes in travel times. It features an objective function called the “travel time budget”, which combines the average path travel time with a safety margin. This margin is defined by a trade-off coefficient and a selected deviation measure (total or semi) of the travel time. The model is divided into three variations: 1) The mean-total deviation (MTD) model for symmetric travel time distributions, 2) The mean-upper-semi-deviation (MUSD) model for asymmetric distributions prioritizing upper semi-deviations, suitable for risk-averse travelers, and 3) The mean-lower-semi-deviation (MLSD) model for asymmetric distributions focusing on lower semi-deviations, preferred by risk-prone individuals. We explore these models’ alignment with the stochastic dominance (SD) rule and develop a solution methodology based on SD principles. Numerical experiments in two real-world transportation networks demonstrate the models’ effectiveness and show how the choice of deviation affects route selection decisions.

Economics of herbicide‐free crop production

AbstractAmbitious pesticide policies aiming to reduce pesticide applications and risks have been introduced across Europe. Herbicides represent a major part of pesticide use, but the uptake of mechanical or agronomic alternatives remains low. We here explore underlying reasons and provide policy insights for supporting a transformation to herbicide‐free production, accounting for both economic and agronomic drivers. We develop detailed extensions to an existing bio‐economic modeling approach and use stochastic dominance analysis to assess the performance of non‐chemical alternatives to herbicides under different production and market conditions exante. We apply our approach to Swiss wheat production and find that herbicide‐free production is not viable without financial support, and thus requires additional per‐hectare agri‐environmental payments and price markups to be economically viable. We find that currently available support payments in Switzerland are sufficient in achieving economic viability of herbicide‐free production. Moreover, we confirm the relevance of risk and risk preferences and identify a risk‐reducing character of herbicide‐free production systems with support payments. Our analysis provides insights on potential drivers, trade‐offs, decision‐making factors, and policies for a transition to non‐chemical weed control.

Enhancing climate resilience in northern Ghana: A stochastic dominance analysis of risk-efficient climate-smart technologies for smallholder farmers

Northern Ghana is a semi-arid region characterised by a unimodal rainfall pattern, and hot and dry weather conditions. Heavy reliance on rain-fed agriculture and the lack of resources for irrigation, makes smallholder farmers in the region increasingly vulnerable to climate-related crop failures. In recent years, climate-smart technologies (CSTs) such as changing planting dates (PD), compartmental bunding (CB), mulching (M), and transplanting (TP) have been recommended to minimise yield losses. However, there is limited information on the most risk-efficient CSTs for crops cultivated in the region. This study used a stochastic dominance approach to identify the most risk-efficient CSTs for maize, rice, and sorghum. The stochastic modelling process employed the Aqua-crop model to simulate climate-related yield variability using Ghana climate data, and gross margin variability with crop budgets from literature sources. From the study's findings, changing planting date from April to May was the most risk-efficient choice for maize and sorghum under farmers' and recommended practices. In contrast, transplanting was the most risk-efficient technology for rice farming in the study area. The study also highlights the importance of considering the risk-averse nature of smallholder farmers when selecting CSTs. By identifying the most risk-efficient CSTs, the study can help improve the resilience of smallholder farmers. These findings have important implications for the development and adoption of CSTs in northern Ghana.