scholarly journals The concept of stochastic dominance in ranking investment alternatives

2005 ◽  
Vol 50 (164) ◽  
pp. 135-149
Author(s):  
Dejan Trifunovic
Keyword(s):  
Stochastic Dominance ◽  
Distribution Functions ◽  
Third Order ◽  
Ranking Problem ◽  
First Order ◽  
Order Stochastic Dominance ◽  
Arbitrage Opportunities ◽  
Second Order Stochastic Dominance ◽  
Mean Variance ◽  
Almost Stochastic Dominance

In order to rank investments under uncertainty, the most widely used method is mean variance analysis. Stochastic dominance is an alternative concept which ranks investments by using the whole distribution function. There exist three models: first-order stochastic dominance is used when the distribution functions do not intersect, second-order stochastic dominance is applied to situations where the distribution functions intersect only once, while third-order stochastic dominance solves the ranking problem in the case of double intersection. Almost stochastic dominance is a special model. Finally we show that the existence of arbitrage opportunities implies the existence of stochastic dominance, while the reverse does not hold.

scholarly journals Second-Order Stochastic Dominance, Reward-Risk Portfolio Selection, and the CAPM

2008 ◽  
Vol 43 (2) ◽  
pp. 525-546 ◽  
Author(s):  
Enrico De Giorgi ◽  
Thierry Post
Keyword(s):  
Stock Returns ◽  
Portfolio Selection ◽  
Stochastic Dominance ◽  
Risk Model ◽  
Second Order ◽  
Order Stochastic Dominance ◽  
Market Portfolio ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Mean Variance

AbstractStarting from the reward-risk model for portfolio selection introduced in De Giorgi (2005), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. In contrast to the mean-variance model, reward-risk portfolio selection arises from an axiomatic definition of reward and risk measures based on a few basic principles, including consistency with second-order stochastic dominance. With complete markets, we show that at any financial market equilibrium, reward-risk investors' optimal allocations are comonotonic and, therefore, our model reduces to a representative investor model. Moreover, the pricing kernel is an explicitly given, non-increasing function of the market portfolio return, reflecting the representative investor's risk attitude. Finally, an empirical application shows that the reward-risk CAPM captures the cross section of U.S. stock returns better than the mean-variance CAPM does.

scholarly journals Beyond Mean–Variance: The Mean–Gini Approach to Optimization Under Uncertainty

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Mengyu Wang ◽  
Hanumanthrao Kannan ◽  
Christina Bloebaum
Keyword(s):  
Decision Analysis ◽  
Stochastic Dominance ◽  
Pareto Frontier ◽  
Optimization Under Uncertainty ◽  
Cumulative Distribution ◽  
Order Stochastic Dominance ◽  
Wide Range ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Mean Variance

In probabilistic approaches to engineering design, including robust design, mean and variance are commonly used as the optimization objectives. This method, however, has significant limitations. For one, some mean–variance Pareto efficient designs may be stochastically dominated and should not be considered. Stochastic dominance is a mathematically rigorous concept commonly used in risk and decision analysis, based on the cumulative distribution function (CDFs), which establishes that one uncertain prospect is superior to another, while requiring minimal assumptions about the utility function of the outcome. This property makes it applicable to a wide range of engineering problems that ordinarily do not utilize techniques from normative decision analysis. In this work, we present a method to perform optimizations consistent with stochastic dominance: the Mean–Gini method. In macroeconomics, the Gini Index is the de facto metric for economic inequality, but statisticians have also proven a variant of it can be used to establish two conditions that are necessary and sufficient for both first and second-order stochastic dominance . These conditions can be used to reduce the Pareto frontier, eliminating stochastically dominated options. Remarkably, one of the conditions combines both mean and Gini, allowing for both expected outcome and uncertainty to be expressed in a single objective which, when maximized, produces a result that is not stochastically dominated given the Pareto front meets a convexity condition. We also find that, in a multi-objective optimization, the Mean–Gini optimization converges slightly faster than the mean–variance optimization.

scholarly journals CAPM, Dominancias Estocásticas & Diversificación

UDA AKADEM ◽  
2020 ◽  
pp. 120-154
Author(s):  
Freddy Benjamín Naula-Sigua ◽  
Diana Jackeline Arévalo-Quishpi ◽  
Diego Mauricio Loyola-Ochoa
Keyword(s):  
Asset Pricing ◽  
Stochastic Dominance ◽  
Second Order ◽  
Capital Asset Pricing ◽  
Pricing Model ◽  
Capital Asset ◽  
Asset Pricing Model ◽  
First Order ◽  
Order Stochastic Dominance ◽  
Second Order Stochastic Dominance

El artículo expone de forma aplicativa a la teoría de diversificación del portafolio, cuyos cimientos se trasladan a Markowitz (1952). Acorde a esto, inicialmente se expusieron a grandes rasgos las bases de Capital Asset Pricing Model (CAPM), así como de la diversificación.  Además, se explican ideas como las de dominancia estocástica, de primer orden; y, dominancia estocástica, de segundo orden, que plantean una forma alternativa y previa de evaluación de las opciones de inversión. Se utilizan cuatro acciones en el presente estudio, las cuales, pertenecen a: Banco de Chile (BCH), Banco Santander (BSANTANDER), Parque Arauco (PARAUCO) y Falabella (FALABELLA); estas acciones pertenecen a la Bolsa de Comercio de Santiago, Chile. Los resultados, respecto a CAPM, muestran que la mayoría se comporta en forma similar a como lo hace el mercado; es decir, tienen un beta cercana a 1. El análisis de Dominancias no permitió establecer Dominancia Estocástica de Primer Orden, no obstante, sí Dominancia Estocástica de Segundo Orden; FALABELLA domina estocásticamente en segundo a tanto a PARAUCO como BSANTANDER. Finalmente, se encontró un portafolio óptimo compuesto por las cuatro acciones; a pesar de que se permiten ventas cortas, la composición del portafolio óptimo no muestra acciones con proporciones negativas. Esta técnica serviría muy bien para valoración de diferentes proyectos, reemplazando los rendimientos de las acciones por los de los proyectos.Palabras clave: CAPM, Diversificación, Finanzas, Markowitz, Portafolio Óptimo. ABSTRACThe article introduces the reader in applicative way to the theory of portfolio diversification, the foundations of which were transferred to Markowitz in 1952. According to this, initially they were exposed to great features the CAPM (Capital Asset Pricing Model) and diversification foundations. In addition, ideas such as the first-order stochastic dominance and the second-order stochastic dominance were explained, as one previous and alternative way of evaluating investment options. Four actions were used in this study, they all belong to: Banco de Chile (BCH), Banco Santander (BSANTANDER), Parque Arauco (PARAUCO) and Falabella (FALABELLA); These shares belong to the Santiago Stock Exchange, Chile. The results, with respect to CAPM, showed that the majority behave similarly to how does the market; that is to say, they have a beta around 1. Dominance analysis does not allow you to establish the First-Order Stochastic Dominance, however yes second-Order Stochastic Dominance; FALABELLA dominates stochastically in second order, to both PARAUCO and BSANTANDER. Finally, an optimal portfolio was found, consisting of the four stocks; Although short sales are allowed, the optimal portfolio composition does not show stocks with negative proportions. This technique would be very useful for evaluating different projects, replacing the returns of the shares for those of the projects.

Visualizing the Variance of a Random Variable

2011 ◽  
Vol 18 (01) ◽  
pp. 71-85
Author(s):  
Fabrizio Cacciafesta
Keyword(s):  
Stochastic Dominance ◽  
Mean Absolute Error ◽  
Random Variable ◽  
Absolute Error ◽  
Second Order ◽  
Taylor Formula ◽  
Order Stochastic Dominance ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Options Theory

We provide a simple way to visualize the variance and the mean absolute error of a random variable with finite mean. Some application to options theory and to second order stochastic dominance is given: we show, among other, that the "call-put parity" may be seen as a Taylor formula.

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