Stochastic Dominance Framework Research Articles

Stochastic dominance algorithms with application to mutual fund performance evaluation

AbstractWhile the possibility for investment A to dominate investment B under the first‐ and second‐order stochastic dominance framework can be tested only at the points of jumps in the probabilities of the distributions, the comparison at interior points is also essential under third‐order, due to the non‐linearity in the difference in the third‐order stochastic dominance integral. Furthermore, it was established that the quantile approach used to test for the first‐ and second‐order dominance does not work under the third‐order. If these points are overlooked, it is possible to conclude that an investment is third‐order inefficient when it is actually efficient. Also, an inefficient investment may not be relegated to the inefficient set. In this work, to test for third‐order efficiency, we derive the expressions for the functions essential for testing the possibility of third‐order stochastic dominance at the interior points and arrive at their restrictions on the common grid of the pairwise investments under consideration. We also develop a program to determine the efficient funds and the funds superior and inferior to the benchmark indices at a fast pace. We find that the size of the efficient set reduces drastically under third‐order. Also, several funds are found to be superior to the indices under second‐ and third‐order.

An interval-based stochastic dominance approach for decision making in forward contracts of electricity market

virtually, all decisions in financial markets are made in the presence of uncertainty. Stochastic dominance is a well-known concept that is broadly implemented for decision making under uncertainty. Thanks to the advantages of this approach, a decision maker is able to exploit available information related to uncertainties with stochastic nature. In this paper, to cope with the uncertainties in the procedure of decision making for forward contracts in an electricity market, a modified stochastic dominance approach is proposed. In the suggested framework, instead of considering a single value for desirable goal in each scenario of benchmark, a profit interval has been allocated to reflect the economic targets of decision maker. In the next step, the allocated profit interval is utilized for decision making problem in the stochastic dominance framework. In order to find the optimal profit profile in such a setting, a two level optimization structure is suggested. To this end, at the lower level of optimization, three different methods namely the prospect stochastic dominance, conditional value at risk (CvaR) and hypothesis testing are applied to find the optimal profit profiles for a number of benchmarks, those are stochastically generated in an interval around a pre-specified profit benchmark. In the upper level, the optimal profit profile is computed by using the Mean-CvaR method. To show the practical aspects and generalizability of our proposed approach, the methods are applied to two different cases, including a retailer and an electricity producer’s decision making problems to determine their involvement in the futures market by maximizing their expected profit over a given planning horizon, while controlling the risk of profit volatility in the electricity market, raised from the uncertainties in the spot market price and the consumer demand. The performance of suggested framework is evaluated through simulation results and relevant conclusions are drawn.

Fuzzy regional inequality measurement: a new stochastic dominance approach with application to Tunisia

Since the economic reforms in 1986, Tunisia's economic growth and urbanisation has occurred a dramatic increases in regional inequality, and a corollary threat to sustainable development and social cohesion. This research clearly demonstrates that the spatial distribution of ethnic minorities reflects not only their spatial segregation, but also the degree of their socio-economic exclusion from the majority. This paper proposes a fuzzy version of dynamic stochastic approach to analyse between-region inequalities. We propose a class of fuzzy index and include them in a stochastic dominance framework to present a dominance criterion enable to class regional distribution. This study contributes to the literatures of inequalities as it takes into consideration the intrinsic nature of poverty.

Stochastic Dominance: An Overall Review and an Empirical Evaluation on the Equity Premium Puzzle

This paper presents all the Stochastic Dominance (SD) rules (including Markowitz and Prospect Stochastic Dominance Rule), situations relating to these rules such as arbitrage, and several classes of preferences consistent to the SD approach. It also contains various algorithms for testing SD relations and necessary and sufficient conditions that may improve the efficiency of each Stochastic Dominance (SD) rule. Finally, it is examined the existence of the well-known equity premium puzzle in several economic environments, under different economic conditions and varying time horizons. The analysis is developed in a Stochastic Dominance framework using original evidence from three markets: US, UK and Germany market. The results show that stocks stochastically dominate bonds at second order (and at any higher order) for any time horizon, under different economic situations and for all international markets (US, UK and Germany market). This implies that stocks outperform bonds in a great percentage and thus the equity premium puzzle is real and quite robust.

A theory of misperception in a stochastic dominance framework and its application to structured financial products

We study the mechanism of misperception that leads retail investors to investment choices which are not the most profitable. This mechanism is studied in a stochastic dominance framework from a theoretical perspective and supported by an extensive numerical analysis. Our theoretical contribution is the introduction of a specific definition of stochastic dominance that captures the effects of an asymmetric trend-type misperception. Such a novel conceptualization is consistent with the perspective here adopted, i.e. the misperception is driven by a positive trend affecting the entire set of possible realizations. The financial relevance of the theoretical proposal is highlighted through the paradigmatic case of structured financial products. To this end, we perform a pairwise numerical comparison between investment products to get insights about the inversion of the order of stochastic dominance, leading investors to prefer the less profitable instruments. The critical trend, the value where preferences are reversed, is interpreted as a measure of investors’ misperception and compared with different levels of the volatility. Some behavioural finance-type arguments provide insights on the interpretation of the obtained results. This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Management Mathematics following peer review. The version of record A theory of misperception in a stochastic dominance framework and its application to structured financial products is available online at: https://doi.org/10.1093/imaman/dpw007

Empirical Dynamic Programming

We propose empirical dynamic programming algorithms for Markov decision processes. In these algorithms, the exact expectation in the Bellman operator in classical value iteration is replaced by an empirical estimate to get “empirical value iteration” (EVI). Policy evaluation and policy improvement in classical policy iteration are also replaced by simulation to get “empirical policy iteration” (EPI). Thus, these empirical dynamic programming algorithms involve iteration of a random operator, the empirical Bellman operator. We introduce notions of probabilistic fixed points for such random monotone operators. We develop a stochastic dominance framework for convergence analysis of such operators. We then use this to give sample complexity bounds for both EVI and EPI. We then provide various variations and extensions to asynchronous empirical dynamic programming, the minimax empirical dynamic program, and show how this can also be used to solve the dynamic newsvendor problem. Preliminary experimental results suggest a faster rate of convergence than stochastic approximation algorithms.

The Resale Value of Risk-Parity Equity Portfolios

This article examines the application of risk parity to fully diversify an equity portfolio. It presents wealth accumulation in a stochastic dominance framework, tested over increasing investment horizons. The portfolio construction algorithms consider sector, country, and stocks in achieving an alternative to capitalization-weighted approaches. Risk parity is dominant over 75% of the historical periods for any two-year horizon and is dominant in all cases after six-year horizons. It achieves dominance over capitalization-weighted indices over shorter horizons during periods of higher market volatility, periods of higher inflation, and periods with steep yield curves.

Decision Making Under Uncertainty When Preference Information Is Incomplete

We consider the problem of optimal decision making under uncertainty but assume that the decision maker’s utility function is not completely known. Instead, we consider all the utilities that meet some criteria, such as preferring certain lotteries over other lotteries and being risk averse, S-shaped, or prudent. These criteria extend the ones used in the first- and second-order stochastic dominance framework. We then give tractable formulations for such decision-making problems. We formulate them as robust utility maximization problems, as optimization problems with stochastic dominance constraints, and as robust certainty equivalent maximization problems. We use a portfolio allocation problem to illustrate our results. This paper was accepted by Dimitris Bertsimas, optimization.

A Robust Multi-dimensional Poverty Profile for Uganda

We compute a Multi-dimensional Poverty Index (MPI) for Uganda following the specification by Alkire and Santos and the general approach of Alkire and Forster. Using household survey data we show how the incidence of multi-dimensional poverty has fallen in recent years and we use the decomposability features of the index to explain the reduction in multi-dimensional poverty. The robustness of our results is tested in a stochastic dominance framework and using statistical inference. Notably, we extend the one-dimensional analysis of stochastic dominance to include household size as a second dimension, thus taking into account that MPI indicators are collected at both household and individual levels. Moreover, we extend the standard two-stage application of the MPI to include a third stage, which is important given the high degree of multiple deprivations within the standard of living dimension.

Roots and effects of financial misperception in a stochastic dominance framework

This work deals with the issue of investors’ irrational behavior and financial products’ misperception. The theoretical analysis of the mechanisms driving erroneous assessment of investment performances is explored. The study is supported by the application of Monte Carlo simulations to the remarkable case of structured financial products. Some motivations explaining the popularity of these complex financial instruments among retail investors are also provided. In particular, investors are assumed to compare the performances of different projects through stochastic dominance rules. Unreasonably and in contrast with results obtained by the application of the selected criteria, investors prefer complex securities to standard ones. In this paper, introducing a new definition for stochastic dominance which presents asymmetric property, we provide theoretical and numerical results showing how investors distort stochastic returns and make questionable investment choices. Results are explained in terms of framing and representative effects, which are behavioral finance type arguments showing how decisions may depend on the way the available alternatives are presented to investors.

A Robust Multi-Dimensional Poverty Profile for Uganda

In this paper we compute a multi-dimensional poverty index (MPI) for Uganda following the approach proposed by Alkire and Forster (2007). Using household survey data we show how the incidence of multi-dimensional poverty has fallen in recent years and we use the decomposability features of the index to explain the drivers of reduction in multi-dimensional poverty. We also compare the results from Uganda with other countries for which the MPI has been computed and we note some caveats in such a comparison. The robustness of our estimates is tested in a stochastic dominance framework and using statistical inference. Notably, we extend the one-dimensional analysis of stochastic dominance to take into account household size in a second dimension, which is particularly important as some of the MPI indicators are sensitive to the number of household members. By exploiting a unique sub-sample of the integrated household survey program in Uganda, which has not previously been analyzed, we are also able to match the data-set used for the MPI with data used to compute the conventional estimates of monetary poverty. This enables a more robust assessment of the complementarities of the two types of poverty measures than has been previously possible.

A Fuzzy Approach to the Measurement of Leakages for North American Health System

This paper uses a fuzzy-fuzzy stochastic dominance approach to compare patients’ leakages in the Canadian and the U.S. health care systems. Leakages are defined in terms of individuals who are in bad health and could not have access to health care when needed. To carry his comparison we rely on the assumption that Canada is a strong counter-factual for the U.S. We first develop a class of fuzzy leakages indices and incorporate them in a stochastic dominance framework to derive the dominance criterion. We then use the derived criterion to perform inter-country comparisons on the global level. To provide more insight, we decompose the analysis with respect to gender, ethnicity, income and education. Intra-country comparisons reveal the presence of income based leakage inequalities in both countries yet, gender, ethnic and education based disparities appear to be present in the U.S. only. As for inter-country comparisons, results are in general consistent with the hypothesis that leakages are less important under the Canadian health care system.

Stochastic utility-efficient programming of organic dairy farms

Opportunities to make sequential decisions and adjust activities as a season progresses and more information becomes available characterise the farm management process. In this paper, we present a discrete stochastic two-stage utility-efficient programming model of organic dairy farms, which includes risk aversion in the decision maker’s objective function as well as both embedded risk (stochastic programming with recourse) and non-embedded risk (stochastic programming without recourse). Historical farm accountancy data and subjective judgements were combined to assess the nature of the uncertainty that affects the possible consequences of the decisions. The programming model was used within a stochastic dominance framework to examine optimal strategies in organic dairy systems in Norway.

Poverty-Reducing and Welfare-Improving Marginal Public Price and Price Cap Reforms

This paper extends familiar results on the optimal pricing of publicly provided goods and price cap regulations in a stochastic dominance framework. The key advantage is that the assessment as to whether pricing or price cap reforms are poverty reducing or welfare improving is not contingent on any given social welfare function. Rather, robust assessments of the impact of reforms can be made for wide classes of ethical judgments.

Correlates of Vulnerability in the South African Labour Market

Using the October Household Survey of 1995 (OHS95), this paper seeks to understand the determinants of indigence in the South African labour market. To this end the study presents a description of the labour market, focusing on how covariates such as race, gender, education and location help explain the poverty observed in the labour market. A key innovation of the paper is the application of traditionally household poverty measures to individuals in the labour market. Hence through utilising cumulative distribution functions drawn from the Foster, Greer, Thorbecke (FGT) class of poverty measures, we are able to understand the distribution of earnings within a stochastic dominance framework. Such distribution functions are then derived for a series of labour market categories ranging from employment by race to employment by sector and occupation. In addition, by setting two individual poverty lines, specific measures of poverty are also determined according to the different labour market cohorts. Some of the key results of the study are that farm workers and household domestic workers constitute the most vulnerable individuals amongst the employed. In addition, apart from race, gender and education are crucial determinants of low or zero earnings. Rural labour markets also surface as a key component of poverty in the labour force. Finally, there is sufficient evidence to suggest that a different labour market seems to be operating for Africans and Coloureds on the one hand, and Asians and Whites on the other.

Performance Evaluation of Portfolio Insurance Strategies Using Stochastic Dominance Criteria

The continuing creation of portfolio insurance applications as well as the mixed research evidence suggests that so far no consensus has been reached about the effectiveness of portfolio insurance. Therefore, this paper provides a performance evaluation of the stop-loss, synthetic put and constant proportion portfolio insurance techniques based on a block-bootstrap simulation. Apart from more traditional performance measures, we consider the Value-at-risk and Expected Shortfall of the strategies, which are more appropriate in an insurance context. An additional performance evaluation is given by means of the stochastic dominance framework where we account for sampling error. A sensitivity analysis is performed in order to examine the impact on performance of a change in a specific decision variable (ceteris paribus). The results indicate that a buy-and-hold strategy does not dominate the portfolio insurance strategies at any stochastic dominance order. Moreover, both for the stop-loss and synthetic put strategy a 100% floor value outperforms lower floor values. For the CPPI strategy we find that a higher CPPI multiple enhances the upward potential of the CPPI strategies, but harms the protection level in return. As regards the optimal rebalancing frequency, daily rebalancing should be preferred for the synthetic put and CPPI strategy, despite the higher transaction costs.

Testing for risk aversion: a stochastic dominance approach

We conduct an experiment based on the Stochastic Dominance framework in order to investigate risk-aversion in isolation of other effects such as subjective probability distortion, the ‘certainty effect’, and ‘framing’ effects. The result is striking: most individuals are not risk-averse.

Incentive Conflicts and Portfolio Choice in the Insurance Industry

Introduction This article analyzes the financial incentives of employees and policyholders versus financiers of insurance firms within a stochastic dominance framework. It examines the risk-taking incentives of the insurer with respect to asset portfolio choice, and how the payoffs to each of the firm's claimants depend on the final value of the portfolio. Mayers and Smith (1981), Doherty and Garven (1986), and Cummins (1988) have examined these incentives using an option pricing model paradigm. In this article, we adopt the discrete time, risk-neutral valuation approach previously used by Doherty and Garven (1986). The development of a generalized option valuation model in the discrete time framework, under costly contracting,(1) requires the adoption of one of two sets of assumptions. The first set requires that the return on the insurer's asset portfolio and the claims made on its policies are normally distributed and that individuals have constant absolute risk aversion (Rubinstein, 1976). The second set requires that the return on assets and the cost of claims are lognormally distributed and that either there is no friction to continuous trading or that investors have constant relative risk aversion (Brennan, 1979; Stapleton and Subrahmanyam, 1984). The advantage of stochastic dominance in analyzing the effects of these conflicts is that it avoids the necessity of imposing restrictions on individual preferences (Levy and Sarnat, 1972; Bawa, 1975). In many cases, conclusions are obtainable without any extensive knowledge about return distributions and/or utility functions. Moreover, this framework has pedagogical value in that many of the incentive conflicts can be demonstrated simply. This article begins by developing the notion of risky investment portfolios in a stochastic dominance context, followed by an analysis of the incentives of insurer stakeholders. Incentive conflicts between owners and employees and between owners and customers are shown to vary with organizational form. Two Risky Investment Portfolios Assume that the insurer has two mutually exclusive investment portfolios from which to choose. One portfolio is riskier than the other in that it is a simple mean-preserving spread of the less risky one. The expected returns from both portfolios are the same, although the actual returns vary by state of nature. (The figure portrays total end-of-period returns and not rates of return.) In states with returns below the expected return, the riskier portfolio provides lower returns, whereas in states where returns exceed the expected return, the riskier portfolio outperforms the less risky one. Because the two asset return lines intersect at the point that equates their expected returns, we can be sure that, by way of second-degree stochastic dominance, any risk-averse individual faced with only these two mutually exclusive choices will prefer the less risky portfolio. This is true by construction, regardless of the precise shape of his or her utility function and irrespective of the exact probability distribution of states. Conflict Between Employees, Policyholders, and Owners The incentive conflicts among the claimants to a stock insurance firm can be explored using the stochastic dominance paradigm. The simplest case--a single period model--is presented, and employees, policyholders, and financiers are considered.(2) Labor costs (and other fixed costs) are assumed to be set at levels that reflect the conflicting incentives of owners versus employees. In other words, employees are able to ascertain the firm's incentives to choose an asset portfolio that would be adverse to their interests, and they negotiate for compensating wage levels accordingly. Similarly, policyholders are aware of the incentives for the insurer to choose an asset portfolio that would be adverse to their interests, and they demonstrate this awareness by lowering the premiums that they are willing to pay for insurance policies. …

Excess Asset Reversions and Shareholder Wealth

ABSTRACTThe ownership of pension assets in a defined benefit pension plan is an unresolved issue in corporate finance. The issue is important because it defines the appropriate investment policy for a pension fund. In this paper, we summarize the ownership debate in the form of two mutually exclusive theories. We then focus on a recently popular event in pension finance, excess asset reversions. Our paper demonstrates the valuation effects associated with this event in a stochastic dominance framework. Under certain conditions, a reversion constitutes an expropriation of wealth from the participants and beneficiaries of the plan to the firm. Using data provided by the Pension Benefit Guaranty Corporation and the Center for Research in Security Prices tape, we examine the returns to the shareholders of 58 companies which conducted excess asset reversions between 1980 and 1984. Our results show that large abnormal returns accrued to these shareholders around the time of the reversion. These findings have implications both for the appropriate investment policy of pension funds and for public policy with respect to plan terminations.

Time Dominance Efficiency Analysis

ABSTRACTBuilding on the stochastic dominance framework, time dominance efficiency analysis provides similar rules for a partial ordering of temporal prospects. Time dominance does not require any quantitative information about temporal preferences for screening decision alternatives according to their net present values. A binary time dominance proposition extends recent sufficient conditions and adds necessity. The paper's main contribution is the development of set time dominance. By eliminating binary undominated projects which no one would choose, set time dominance minimizes time efficient sets without imposing further preference assumptions.