Multivariate Tests for Stochastic Dominance Efficiency of a Given Portfolio

2007 ◽  
Vol 42 (2) ◽  
pp. 489-515 ◽  
Author(s):  
Thierry Post ◽  
Philippe Versijp
Keyword(s):  
Multivariate Statistics ◽  
Stochastic Dominance ◽  
Statistical Power ◽  
Investment Portfolio ◽  
Tail Risk ◽  
Multivariate Tests ◽  
The Mean ◽  
Empirical Tests ◽  
Mean Variance ◽  
Power Properties

AbstractWe develop empirical tests for stochastic dominance efficiency of a given investment portfolio relative to all possible portfolios formed from a given set of assets. Our tests use multivariate statistics, which result in superior statistical power properties compared to existing stochastic dominance efficiency tests and increase the comparability with existing mean-variance efficiency tests. Using our tests, we demonstrate that the mean-variance inefficiency of the CRSP all-share index relative to beta-sorted portfolios can be explained by tail risk not captured by variance.

scholarly journals Abnormal Portfolio Asset Allocation Model: Review

2020 ◽  
Vol 1 (1) ◽  
pp. 46-54
Author(s):  
Nurfadhlina Bt Abdul Halima ◽  
Dwi Susanti ◽  
Alit Kartiwa ◽  
Endang Soeryana Hasbullah
Keyword(s):  
Asset Allocation ◽  
Asset Returns ◽  
Higher Moments ◽  
Investment Portfolio ◽  
Allocation Model ◽  
Model Review ◽  
The Mean ◽  
Mean Variance ◽  
Skewness And Kurtosis ◽  
Normally Distributed

It has been widely studied how investors will allocate their assets to an investment when the return of assets is normally distributed. In this context usually, the problem of portfolio optimization is analyzed using mean-variance. When asset returns are not normally distributed, the mean-variance analysis may not be appropriate for selecting the optimum portfolio. This paper will examine the consequences of abnormalities in the process of allocating investment portfolio assets. Here will be shown how to adjust the mean-variance standard as a basic framework for asset allocation in cases where asset returns are not normally distributed. We will also discuss the application of the optimum strategies for this problem. Based on the results of literature studies, it can be concluded that the expected utility approximation involves averages, variances, skewness, and kurtosis, and can be extended to even higher moments.

PORTFOLIO MODEL UNDER FRACTAL MARKET BASED ON MEAN-DCCA

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050142
Author(s):  
WEIDE CHUN ◽  
HESEN LI ◽  
XU WU
Keyword(s):  
Analytical Solution ◽  
Correlation Analysis ◽  
Capital Market ◽  
Cross Correlation ◽  
Investment Portfolio ◽  
Cross Correlation Analysis ◽  
Risk Criterion ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

Under the realistic background that the capital market nowadays is a fractal market, this paper embeds the detrended cross-correlation analysis (DCCA) into the return-risk criterion to construct a Mean-DCCA portfolio model, and gives an analytical solution. Based on this, the validity of Mean-DCCA portfolio model is verified by empirical analysis. Compared to the mean-variance portfolio model, the Mean-DCCA portfolio model is more conducive for investors to build a sophisticated investment portfolio under multi-time-scale, improve the performance of portfolios, and overcome the defect that the mean-variance portfolio model has not considered the existence of fractal correlation characteristics between assets.

Optimal selection of financial risk investment portfolio based on random matrix method

2020 ◽  
Vol 20 (3) ◽  
pp. 859-868
Author(s):  
Jie Tian ◽  
Kun Zhao
Keyword(s):  
Covariance Matrix ◽  
Random Matrix ◽  
Financial Risk ◽  
Good Effect ◽  
Investment Portfolio ◽  
Variance Model ◽  
Minimum Risk ◽  
The Mean ◽  
Risk Investment ◽  
Mean Variance

The optimization of investment portfolio is the key to financial risk investment. In this study, the investment portfolio was optimized by removing the noise of covariance matrix in the mean-variance model. Firstly, the mean-variance model and noise in covariance matrix were briefly introduced. Then, the correlation matrix was denoised by KR method (Sharifi S, Grane M, Shamaie A) from random matrix theory (RMT). Then, an example was given to analyze the application of the method in financial stock investment portfolio. It was found that the stability of the matrix was improved and the minimum risk was reduced after denoising. The study of minimum risk under different M values and stock number suggested that calculating the optimal value of M and stock number based on RMT could achieve optimal financial risk investment portfolio result. It shows that RMT has a good effect on portfolio optimization and is worth promoting widely.

scholarly journals Stochastic dominance theory for location-scale family

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Wing-Keung Wong
Keyword(s):  
Stochastic Dominance ◽  
Indifference Curve ◽  
Efficient Set ◽  
Alternative Proof ◽  
Efficient Sets ◽  
Scale Parameters ◽  
General Utility ◽  
The Mean ◽  
Mean Variance ◽  
Variance Criterion

Meyer (1987) extended the theory of mean-variance criterion to include the comparison among distributions that differ only by location and scale parameters and to include general utility functions with only convexity or concavity restrictions. In this paper, we make some comments on Meyer's paper and extend the results from Tobin (1958) that the indifference curve is convex upwards for risk averters, concave downwards for risk lovers, and horizontal for risk neutral investors to include the general conditions stated by Meyer (1987). We also provide an alternative proof for the theorem. Levy (1989) extended Meyer's results by introducing some inequality relationships between the stochastic-dominance and the mean-variance efficient sets. In this paper, we comment on Levy's findings and show that these relationships do not hold in certain situations. We further develop some properties among the first- and second-degree stochastic dominance efficient sets and the mean-variance efficient set.

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.

Cryptocurrencies and portfolio diversification in an emerging market

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Lehlohonolo Letho ◽  
Grieve Chelwa ◽  
Abdul Latif Alhassan
Keyword(s):  
Market Economy ◽  
Value At Risk ◽  
Emerging Market ◽  
Efficient Frontier ◽  
Conditional Value At Risk ◽  
Portfolio Risk ◽  
Investment Portfolio ◽  
Content Type ◽  
The Mean ◽  
Mean Variance

PurposeThis paper examines the effect of cryptocurrencies on the portfolio risk-adjusted returns of traditional and alternative investments within an emerging market economy.Design/methodology/approachThe paper employs daily arithmetic returns from August 2015 to October 2018 of traditional assets (stocks, bonds, currencies), alternative assets (commodities, real estate) and cryptocurrencies. Using the mean-variance analysis, the Sharpe ratio, the conditional value-at-risk and the mean-variance spanning tests.FindingsThe paper documents evidence to support the diversification benefits of cryptocurrencies by utilising the mean-variance tests, improving the efficient frontier and the risk-adjusted returns of the emerging market economy portfolio of investments.Practical implicationsThis paper firmly broadens the Modern Portfolio Theory by authenticating cryptocurrencies as assets with diversification benefits in an emerging market economy investment portfolio.Originality/valueAs far as the authors are concerned, this paper presents the first evidence of the effect of diversification benefits of cryptocurrencies on emerging market asset portfolios constructed using traditional and alternative assets.

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