Higher-order Stochastic Dominance Research Articles

Dynamic copula-based expectile portfolios

This study investigates expectile Value-at-Risk (EVaR) as a risk measure in dynamic copula-based portfolio optimization, compared with the common variance and CVaR. To estimate the dependence structure between asset returns, the canonical vine copula augmented with the generalized additive models (GAMC-vine) is used. Applying multivariate conditional distributions from the GAMC-vine model, step-ahead asset return forecasts are obtained and used to construct dynamic copula-based EVaR portfolios. Using ten S&P 500 industry sectors, EVaR leads to a min-risk dynamic GAMC-vine portfolio that achieves higher out-of-sample average return and risk-adjusted ratios. Furthermore, EVaR shows a better portfolio ranking than CVaR. Moreover, the copula-based variance and EVaR portfolios show higher-order stochastic dominance compared to CVaR strategies. Finally, a subsample stochastic dominance analysis reveals that, in overall, the risk minimization does not benefit from the choice of risk modeling. However, the dynamic copula model leads to optimal portfolios that dominate the equally weighted benchmark more often compared to those from historical approach.

Portfolio Optimization with Higher-order Stochastic Dominance Constraints

Optimal portfolio choice is investigated for investors with various types of higher-order risk aversion. Finite systems of convex inequalities are introduced to evaluate the efficiency of a given benchmark, and for constructing enhanced portfolios which dominate the benchmark for all higher-order risk averters. An analysis of equity industry rotation strategies shows that accounting for skewness love and kurtosis aversion increases long positions in recent winner industries which feature more favorable skewness and kurtosis than the market index. An analysis of equity stock index options combinations shows that accounting for higher-order risk aversion leads to buying of underpriced option series in addition to the standard solution of writing of overpriced options. In both applications, optimization with higher-order risk constraints appears leads to superior out-of-sample performance compared with simpler strategies based on heuristic rules, single utility functions and limiting portfolio variance.

Farinelli and Tibiletti ratio and stochastic dominance

Farinelli and Tibiletti (F–T) ratio, a general risk-reward performance measurement ratio, is popular due to its simplicity and yet generality that both Omega ratio and upside potential ratio are its special cases. The F–T ratios are ratios of average gains to average losses with respect to a target, each raised by a power index, p and q. In this paper, we establish the consistency of F–T ratios with any nonnegative values p and q with respect to first-order stochastic dominance. Second-order stochastic dominance does not lead to F–T ratios with any nonnegative values p and q, but can lead to F–T dominance with any $$p<1$$ and $$q\ge 1$$ . Furthermore, higher-order stochastic dominance ( $$n\ge 3$$ ) leads to F–T dominance with any $$p<1$$ and $$q\ge n-1$$ . We also find that when the variables being compared belong to the same location-scale family or the same linear combination of location-scale families, we can get the necessary relationship between the stochastic dominance with the F–T ratio after imposing some conditions on the means. There are many advantages of using the F–T ratio over other measures, and academics and practitioners can benefit by using the theory we developed in this paper. For example, the F–T ratio can be used to detect whether there is any arbitrage opportunity in the market, whether there is any anomaly in the market, whether the market is efficient, whether there is any preference of any higher-order moment in the market, and whether there is any higher-order stochastic dominance in the market. Thus, our findings enable academics and practitioners to draw better decision in their analysis.

The non-integer higher-order Stochastic dominance

We establish a continuum of higher-order stochastic dominance rules. Depending on whether decision makers are risk averse or risk loving, two types of continuum higher-order stochastic dominance rules are established and their properties are illustrated with some examples.

A note on risky targets and effort

This note examines the effort choice problem of a decision maker (DM) who has to meet a target. The more the DM spends on effort, the more likely the target is reached. Besides the risk of missing the target despite his effort, the DM faces additional uncertainty in that both the target and the status quo are subject to exogenous shocks that are beyond the DM’s control. We consider two cases: the additive case in which the DM’s effort affects solely the likelihood of achieving the target, and the multiplicative case in which the DM’s effort also has direct effect on the target and the status quo. Using the theory of monotone comparative statics and risk apportionment, we derive sufficient conditions under which the DM spends more on effort when the target experiences an improvement in risk via higher-order stochastic dominance.

Precautionary self-insurance-cum-protection

Precautionary self-insurance-cum-protection (SICP) arises when an individual spends more on SICP when background risk is introduced. We develop a two-period model wherein additive/multiplicative background risk prevails in the second period. Using the theory of monotone comparative statics and risk apportionment, we derive necessary and sufficient conditions under which the individual spends more on SICP when the background risk deteriorates via higher-order stochastic dominance. Prudence is called for to create a precautionary motive that induces the individual to shift his wealth in a way to reduce the loss of expected utility caused by the addition of background risk, thereby giving rise to the precautionary SICP.

Higher Order Stochastic Dominance and Aggregate Investor Preferences

This paper finds necessary and sufficient conditions of Nth-order stochastic dominance (SD) for risk aversion and develops linear tests for Nth-order SD. We introduce a linear FDSD (fourth-order SD and decreasing absolute risk aversion SD) test for standard risk aversion. A positive research shows that higher order risk attitude cannot explain pricing errors of the small size and high value benchmark portfolios. The empirical results also suggests that any Nth-order SD criterion might not be superior to MV rule when the MV kernel does not violate non-satiation. FDSD has the best discriminate power and substantially improves the pricing kernel.

Comparing the Homogeneity of Income Distributions Using Polarization Indices

In the context of polarized societies, income homogeneity is linked to the frequency and the intensity of social unrest. Most homogenous countries exhibit a lower frequency of intense social conflicts and less homogeneous countries show a higher frequency of moderate social conflicts. This paper develops a methodology to compare the degree of homogeneity of two income distributions. We use for that purpose and index of polarization that does not account for alienation. This index is the identification component of polarization that measures the degree to which individuals feel alike in an income distribution. This development leads to identification dominance curves and derives first-order and higher-order stochastic dominance conditions. First-order stochastic dominance is performed through identification dominance curves drawn on a support of identification thresholds. These curves are used to determine whether identification, homogeneity, or similarity of individuals is greater in one distribution than in another for general classes of polarization indices and ranges of possible identification thresholds. We also derive the asymptotic sampling distribution of identification dominance curves and test dominance between two distributions using Intersection Union tests and bootstrapped p-values. Our methodology is illustrated by comparing pairs of distributions of eleven countries drawn from the Luxembourg Income Study database.

Allocation of risk capital based on iso-entropic coherent risk measure

Purpose : The potential of diversified portfolio leads to the risk capital allocation problem. There are many kinds of methods or rules to allocate risk capital. However, they have flaws, such as non-continuity, unfairness. In order to get a better method, we propose a new risk measure to be the base of risk capital allocation rule. Design/methodology/approach : We proposed two kinds of allocation methods: one is marginal risk contribution based on iso-entropic coherent risk measure(IE), the other one is to combine the minimal excess allocation(EBA) principle and IE into risk capital allocation. The iso-entropic coherent risk measure has many advantages over others; it is continuous and more powerful in distinguishing risks, consistent with higher-order stochastic dominances than other risk measures. And EBA is consistent with the amount of risk, which means fairness for risk capital allocation. Findings : Through cases, simulations and empirical application, it shows that these two allocation rules satisfy some good properties, can be more efficient, more precise and fairer. And the EBA based on IE may be the better one. Research limitations/implications : However, there are some problems still open. One is how to treat the negative value of allocation. Second is that the consistence between the allocated risk capital and the amount of the risk needs to be studied further. Originality/value: A good risk measure is very important for risk capital allocation. We proposed two methods to deal with risk capital allocation based on a new coherent risk measure called iso-entropic risk measure, which is smooth and consistent with higher-order stochastic dominance and has higher resolution of risk. It shows that the risk capital allocation rules based on iso-entropic risk measure are better than the other rules.

Almost Higher Order Stochastic Dominance

In this paper, we develop the concept of almost stochastic dominance for higher order preferences and investigate the related properties of this concept.

Finding Reliable Shortest Paths in Dynamic Stochastic Networks

A reliable a priori shortest path (RASP) offers the least time budget and ensures that a traveler can arrive at the destination on time with the desired probability. A RASP is equivalent to enumerating all nondominated paths under the first-order stochastic dominance rule. Compared with the problem in static networks, the RASP problem becomes more complex in dynamic networks because it is more difficult to compute path travel time distributions. Two modules of process are the keys to solving the RASP problem. One module is the convolution scheme (how to compute a path travel time distribution from its member links' travel time distributions), and the other module is the stochastic dominance scheme (how to determine nondominated paths). This study aims to find an efficient solution algorithm for this problem. An alternative convolution method is developed on the basis of the adaptive discretization approach, which was originally proposed to solve the RASP problem in static networks. In contrast, the higher-order stochastic dominance rule can be shown to reduce the number of nondominated paths; this rule promises to improve computational efficiency. Numerical experiments show that the second-order stochastic dominance rule offers good approximations, and the central processing unit time is reduced by at least 50%.

Testing for Restricted Stochastic Dominance: Some Further Results

Extensions are presented to the results of Davidson and Duclos (2007), whereby the null&#x0D; hypothesis of restricted stochastic non dominance can be tested by both asymptotic and&#x0D; bootstrap tests, the latter having considerably better properties as regards both size and&#x0D; power. In this paper, the methodology is extended to tests of higher-order stochastic dominance.&#x0D; It is seen that, unlike the first-order case, a numerical nonlinear optimisation problem&#x0D; has to be solved in order to construct the bootstrap DGP. Conditions are provided for a&#x0D; solution to exist for this problem, and efficient numerical algorithms are laid out. The empirically&#x0D; important case in which the samples to be compared are correlated is also treated,&#x0D; both for first-order and for higher-order dominance. For all of these extensions, the bootstrap&#x0D; algorithm is presented. Simulation experiments show that the bootstrap tests perform&#x0D; considerably better than asymptotic tests, and yield reliable inference in moderately sized&#x0D; samples.

Stochastic dominance analysis of Asian hedge funds

We employ the stochastic dominance approach that utilizes the entire return distribution to rank the performance of Asian hedge funds as traditional mean-variance and CAPM approaches could be inappropriate given the nature of non-normal returns. We find both first-order and higher-order stochastic dominance relationships amongst the funds and conclude that investors would be better off by investing in the first-order dominant funds to maximize their expected wealth. By investing in higher-order dominant funds, risk-averse investors can maximize their expected utilities but not their wealth. In addition, we find the common characteristic for most pairs of funds is that one fund is preferred to another in the negative domain whereas the preference reverses in the positive domain. We conclude that the stochastic dominance approach is more appropriate compared with traditional approaches as a filter in hedge fund selection. Compared with traditional approaches, the SD approach, not only is assumption free, but also provides greater insights to the performance and risk inherent in a hedge fund's track record.

Convex orders for linear combinations of random variables

Abstract Linear combinations ∑i=1kbiXi and ∑i=1kaiXi of random variables X1,…,Xk are ordered in the sense of the decreasing convex order and the Laplace order, where (b1,…,bk) is majorized by (a1,…,ak), when the underlying random variables are independent but possibly nonidentically distributed, and the joint density is arrangement increasing, respectively. Finite mixture distributions ∑i=1kaiFXi(x) and ∑i=1kbiFXi(x) are compared in the sense of the usual stochastic order, the convex order and higher-order stochastic dominance. The comparison between ∑i=1kIbiXi and ∑i=1kIaiXi is also studied for binary random variables I a i ,I b i (i=1,…,k) . Some applications in economics and reliability are described.

Stochastic dominance of higher orders and its implications

Higher order stochastic dominance has been considered from a reliability theoretic point of view and related to moment inequalities among life distributions. A generalization of HNBUE/ HNWUE class of distributions has been conceived and its relationship with higher order stochastic dominance has been studied.