Stochastic Dominance Efficiency Research Articles

A non-parametric approach to determine an efficient premium for drought insurance

Insurance to deal with prolonged drought periods in rural Africa requires a practical method to estimate accurate premium values that minimize economic losses. We use non-parametric methods to determine the risk non-neutral insurer’s premium for drought insurance on rain-fed crops. Premium values are estimated on the basis of percentage of the expected yield losses over the potential yields. Expected yield losses are estimated based on data on the levels of rainfall, potential evapotranspiration and water-holding capacity of the soil, and water requirement of the crop. Maize crop in West Kenya, and rice crop in the Central High Plains of Madagascar are taken as case studies. To check if farmer’s choice of starting seasons affects the expected yields and the values of premium, we employ forecasted yields for two different sowing dates (October vs. November) for maize, and two different transplantation dates (November vs. December) for rice. The mean-variance (E-V), the First-Degree Stochastic Dominance (FSD), and the Second-Degree Stochastic Dominance (SSD) efficiency criteria are used to rank each pair of distributions. Results show that an insurer for maize production in Western Kenya would require a premium value between 43 and 55% of the potential yields to fully cover the loss caused by lack of rainfall. Under E-V and FSD, the two yield distributions cannot be ranked, but under SSD the yield distribution of the October-sown maize dominates that of November. For lowland rice in the Central High Plains of Madagascar, all three efficiency criteria indicate that the yield distribution of the December-transplanted rice dominates that of November and the premium values are less than 4 % of the potential yields.

Sensitivity of environmental performance index based on stochastic dominance

The Environmental Performance Index (EPI) is a popular sustainability index. It is a composite index which ranks 180 countries based on their environmental performance in 32 indicators. Using the EPI data and stochastic dominance efficiency methodology, this paper examines the sensitivity to the subjective weights assigned to the indicators and categories of environmental performance. The findings show a remarkable variation in environmental performance based on alternative weights which are selected using Stochastic Dominance criteria. Except for 2020, the environmental health category in EPI gets relatively higher importance in the optimal scenario, and ecosystem vitality gets relatively higher weights in the inferior scenario, suggesting that the environmental health category achievements have been relatively higher for most countries over time. The ranking analysis also shows major variations in country rankings with alternative weights. Two countries, Maldives and Gabon, would have experienced more than 100 position changes in their rankings with alternative weights. Furthermore, 67 countries would have experienced 30 or more position changes in their rankings and 37 countries experienced an EPI score change of more than 50 (out of 100) with alternative weights. Overall, the results illustrate the importance of sensitivity analysis of composite indices to increase reliability and transparency.

Is the index efficient? A worldwide tour with stochastic dominance

We conduct a broad study of stochastic dominance efficiency on financial markets. We show that in the long run the vast majority of 17 equity market indices across the globe are inefficient at order two relative to their industry components. In the short run, the past stochastic dominance relation between the index and sub-indices predicts future dominance. Trading rules accounting for the predictability of stochastic dominance improve the out-of-sample certainty equivalents of risk-averse investors. The gains are especially pronounced for European and developing markets, while no consistent outperformance of alternative strategies is found for the S&P 100 and Nikkei 225 indices.

Diversification benefits of cat bonds: An in‐depth examination

AbstractWe investigate whether the inclusion of Cat Bonds in portfolios composed of traditional assets and common factors is beneficial to investors. Various mean‐variance spanning tests performed for the period of 2002 to 2017 show that under different market conditions, the addition of Cat Bonds gives rise to previously unattainable portfolios. Using the Engle (2002) Dynamic Conditional Correlation (DCC) model, we find that including Cat bonds increases significantly the time‐varying Sharpe ratio and the Choueifaty and Coignard (2008) maximum diversification ratio. Cat Bonds provide needed diversification during critical times particularly during episodes of crisis and of high volatility. Under the second‐order stochastic dominance efficiency (SDE) tests, the null hypothesis that portfolios without Cat Bonds are efficient cannot be rejected. Out‐of‐sample analyses indicate that the performance of portfolios with Cat Bonds included varies depending on the performance measures employed, the portfolio construction techniques used and the assets or factors considered.

Second order of stochastic dominance efficiency vs mean variance efficiency

In this paper, we compare two of the main paradigms of portfolio theory: mean variance analysis and expected utility. In particular, we show empirically that mean variance efficient portfolios are typically sub-optimal for non satiable and risk averse investors. We illustrate that the second order stochastic dominance (SSD) efficient set is the solution of a multi-objective optimization problem. We further show that the market portfolio is not necessarily a solution to this optimization problem. We also conduct an empirical analysis, examining the ex ante and ex post performance of SSD and mean variance efficient portfolios, using a bootstrap approach. In an ex ante analysis, we compare empirical moments, the level of diversification and set distances of mean variance and SSD efficient sets. We also show that the global minimum variance (GMV) portfolio and the part of the mean variance efficient frontier (MVEF) composed of highly diversified portfolios is second order stochastically dominated. This result also provides a possible alternative explanation for the diversification puzzle. Conducting an ex post analysis, we construct second order stochastic dominating strategies that outperform the GMV portfolio in terms of wealth and various other performance measures, producing a positive ex post opportunity cost.

Production efficiency in agriculture in Nigeria: Do migrant remittances matter?

This paper investigates how remittances flow to Nigeria from household migrants affect farm production efficiency of the left behind in rural areas. We used the Living Standard Measurement Survey data set and applied production frontier models to generate production efficiency scores for migrant and non-migrant farm households. Using simple ANOVA and stochastic dominance analysis we test the hypothesis of a negative migrant remittances effect on production efficiency. The mean production efficiency for migrants was higher and statistically significant at p<0.05. We also find a higher technical efficiency across all percentiles for migrant households. Though access to remittances played an important role in the improvement of farmer’s production efficiency, it may not be sufficient as there were observed crosses at some points of the stochastic dominance efficiency curves for migrant and non-migrant households that suggests some possible trade-offs.

Upper-contour strategy-proofness in the probabilistic assignment problem

Bogomolnaia and Moulin (J Econ Theory 100:295–328, 2001) show that there is no rule satisfying stochastic dominance efficiency,equal treatment of equals and stochastic dominance strategy-proofness for a probabilistic assignment problem of indivisible objects. Recently, Mennle and Seuken (Partial strategyproofness: relaxing strategy-proofness for the random assignment problem. Mimeo, 2017) show that stochastic dominance strategy-proofness is equivalent to the combination of three axioms, swap monotonicity,upper invariance, and lower invariance. In this paper, we introduce a weakening of stochastic dominance strategy-proofness, called upper-contour strategy-proofness, which requires that if the upper-contour sets of some objects are the same in two preference relations, then the sum of probabilities assigned to the objects in the two upper-contour sets should be the same. First, we show that upper-contour strategy-proofness is equivalent to the combination of two axioms, upper invariance and lower invariance. Next, we show that the impossibility result still holds even though stochastic dominance strategy-proofness is weakened to upper-contour strategy-proofness.

Diversification Benefits of Cat Bonds: An In-Depth Examination

We investigate whether the inclusion of Cat Bonds in portfolios composed of traditional assets and common factors is beneficial to investors. Various mean‐variance spanning tests performed for the period of 2002 to 2017 show that under different market conditions, the addition of Cat Bonds gives rise to previously unattainable portfolios. Using the Engle (2002) Dynamic Conditional Correlation (DCC) model, we find that including Cat bonds increases significantly the time‐varying Sharpe ratio and the Choueifaty and Coignard (2008) maximum diversification ratio. Cat Bonds provide needed diversification during critical times particularly during episodes of crisis and of high volatility. Under the second‐order stochastic dominance efficiency (SDE) tests, the null hypothesis that portfolios without Cat Bonds are efficient cannot be rejected. Out‐of‐sample analyses indicate that the performance of portfolios with Cat Bonds included varies depending on the performance measures employed, the portfolio construction techniques used and the assets or factors considered.

Advancements in stochastic dominance efficiency tests

We present new results for fourth and fifth order stochastic dominance (FOSD and FISD, respectively) circumventing shortcomings in Post and Kopa (2013) and Fang and Post (2017).

Stochastic Dominance Approach to OECD’s Better Life Index

Ever since the inception of OECD’s Better Life Index in 2011, a string of literature have emerged offering different aggregation procedures for the 11 dimensions of the index encompassing the broad categories of material living standards and quality of life. What is the most optimistic weighting scheme that allows more countries to achieve better measured well-being outcomes? What is the most pessimistic weighting scheme that worsens outcomes for more countries? Stochastic dominance efficiency is a data driven aggregation method that allows us to answer such questions which may be beneficial to policy makers and researchers. We offer rankings of countries across dimensions as well as rankings based on a single composite index aggregating all dimensional indicators. This type of analysis not only presents an opportunity to examine the sensitivity associated with re-weighting indicators, but this approach also reveals which indicators are driving overall improvement in measured well-being and which ones are hindering it. We find that the worst-case scenario rankings are generally more correlated with the equal-weighting scheme. And the best-case scenario weights offer a far more equal distribution of achievements across countries.

Sensitivity of university rankings: implications of stochastic dominance efficiency analysis

ABSTRACTTo create their rankings, university-ranking agencies usually combine multiple performance measures into a composite index. However, both rankings and index scores are sensitive to the weights assigned to performance measures. This paper uses a stochastic dominance efficiency methodology to obtain two extreme, case-weighting vectors using the Academic Ranking of Worldwide Universities (ARWU) and Times Higher Education (THE) data, both of which lead to the highest and lowest index outcomes for the majority of universities. We find that both composite scores and rankings are very sensitive to weight variations, especially for middle- and low-ranked universities.

Stochastic Dominance Approach to Measuring Child Development

We measure global performance when it comes to child development outcomes based on Save the Children UK’s Child Development Index, a composite measure comprising health, education, and nutrition. We rely on consistent tests of stochastic dominance efficiency to derive the most optimistic scenario for measured child development where more countries achieve better measured outcomes based on the least variable combination of components of the index. Using the same approach, we also derive the most pessimistic scenario where more countries achieve worse measured outcomes. This approach presents an opportunity to study the sensitivity of the Child Development Index and allows us to better understand the aspects of child development by offering a glimpse into the index components most responsible for driving or hindering improvements in measured child development across countries. To gain a sense of the evolution of the dimensions, we consider four time periods: 1995 - 1999, 2000 - 2004, 2005 - 2010, and 2011 - 2016. We find that in the most optimistic scenario for measured child development, increasing the weight attached to the education dimension over time allows more countries to achieve better measured outcomes. On the other hand, shifting majority of the weight towards health results in the most pessimistic scenario. These results indicate that improvements in children’s education outcomes have outpaced health and nutrition. That is, relative to health and nutrition, more countries find it easier to achieve better education outcomes.

Extensions on Stochastic Dominance Efficiency Tests

We consider second, third, fourth and fifth order stochastic dominance (SSD, TSD, FOSD and FISD, respectively) as well as decreasing absolute risk aversion (DARA) stochastic dominance (DSD). For comparison with DSD we also consider stochastic dominance (ESD) based on CARA utility functions. Their relevance in practice arises from empirical evidence on individual preferences fitting to preference models underlying such stochastic dominance relations. Assuming a known, discrete and finite probability distribution we derive necessary and sufficient efficiency tests under the six types of stochastic dominance. Simple arguments yield well-known SSD and TSD efficiency tests which are subsequently used to develop new FOSD, FISD, DSD and ESD efficiency tests. We provide numerical demonstration using stock market data of the US.

Sensitivity of University Rankings: Implications of Stochastic Dominance Efficiency Analysis

To create their rankings, university-ranking agencies usually combine multiple performance measures into a composite index. However, both rankings and index scores are sensitive to the weights assigned to performance measures. This paper uses a stochastic dominance efficiency methodology to obtain two extreme, case-weighting vectors using the Academic Ranking of Worldwide Universities (ARWU) and Times Higher Education (THE) data, both of which lead to the highest and lowest index outcomes for the majority of universities. We find that both composite scores and rankings are very sensitive to weight variations, especially for middle- and low-ranked universities.

Is it Efficient to Buy the Index? A Worldwide Tour with Stochastic Dominance.

The paper develops a necessary condition for stochastic dominance efficiency at any order. We find that equity market indices of seventeen developed and developing countries across the globe are inefficient, nearly always at order three and very often at order two, making them not a suitable investment for a risk-averse and prudent investors. The indices are often dominated by individual industry sub-indices, with consumer goods, services, and utilities performing especially well. Macro factors such as the GDP growth rate, inflation, unemployment, and the current account balance predict future efficiency of the equity market indices, but exhibit the opposite signs for developed and developing markets. Strong values of aggregate economic indicators point to a higher likelihood of the equity market index efficiency for well-balanced economies; but they signal a lower likelihood of efficiency for less balanced economies, which heavily rely on only several key industries.

Quantile forecast combination using stochastic dominance

This paper derives optimal forecast combinations based on stochastic dominance efficiency (SDE) analysis with differential forecast weights for different quantiles of forecast error distribution. For the optimal forecast combination, SDE will minimize the cumulative density functions of the levels of loss at different quantiles of the forecast error distribution by combining different time-series model-based forecasts. Using two exchange rate series on weekly data for the Japanese yen/US dollar and US dollar/Great Britain pound, we find that the optimal forecast combinations with SDE weights perform better than different forecast selection and combination methods for the majority of the cases at different quantiles of the error distribution. However, there are also some very few cases where some other forecast selection and combination model performs equally well at some quantiles of the forecast error distribution. Different forecasting period and quadratic loss function are used to obtain optimal forecast combinations, and results are robust to these choices. The out-of-sample performance of the SDE forecast combinations is also better than that of the other forecast selection and combination models we considered.

Optimal privatization portfolios in the presence of arbitrary risk aversion

We consider the global portfolio of privatized state assets from 1985 to 2012 in the non-parametric decision-making context of Stochastic Dominance Efficiency for broad classes of investor preferences. We estimate all possible portfolios in the context of Strategic vs. non-Strategic and Cyclical vs. non-Cyclical asset allocations that dominate the market benchmark and provide a complete efficiency ranking. The optimal solutions are computed using linear and mixed integer programming formulations. Dominant portfolios tend to overweight non-Cyclical and non-Strategic assets, while rotation may take place across business cycles. Bayesian investment style return attribution analysis, based on Monte Carlo Integration, suggests that Growth drives returns during the first business cycle, rotating to a balanced mix of styles with Size and Debt Leverage during the second business cycle and finally to Size during the last business cycle. Value is found to be the least influential style in all periods.

Testing for the implicit weights of the dimensions of the Human Development Index using stochastic dominance

In 2010, United Nations’ Development Programme changed the indicators used to obtain education and income indices in the Human Development Index (HDI). In this paper, we use the Stochastic Dominance Efficiency methodology to evaluate the implicit weights of the dimensions used in the new measurement of the HDI. We find, contrary to the earlier literature, that the implicit weight attached to the education dimension is relatively low suggesting that it is relatively harder to achieve high scores in this dimension compared to other dimensions.

Probabilistic assignment of indivisible objects when agents have the same preferences except the ordinal ranking of one object

Bogomolnaia and Moulin (2001) show that there is no rule satisfying equal treatment of equals, stochastic dominance efficiency, and stochastic dominance strategyproofness for a probabilistic assignment problem of indivisible objects. Kasajima (2013) shows that the incompatibility result still holds when agents are restricted to have single-peaked preferences. In this paper, we further restrict the domain and investigate the existence of rules satisfying the three properties. As it turns out, the three properties are still incompatible even if all agents have the same preferences except the ordinal ranking of one object.

Diversification benefits of commodities: A stochastic dominance efficiency approach

Abstract We revisit the question whether commodities should be included in investors’ portfolios. We employ for the first time a stochastic dominance efficiency (SDE) approach to construct optimal portfolios with and without commodities and we evaluate their comparative performance. SDE circumvents the necessity to posit a specific utility function to describe investor’s preferences and it does not impose distributional assumptions on asset returns. We find that commodities provide diversification benefits both in- and out-of-sample. This evidence is stronger when commodity indices which mimic dynamic commodity trading strategies are used. We explain our results by documenting that commodity markets are segmented from the equity and bond markets.