Conditions of Equivalence Among E-V, SSD, and E-H Portfolio Selection Criteria: The Case for Uniform, Normal and Lognormal Distributions

Philippatos, George C.; Gressis, Nicolas

doi:10.1287/mnsc.21.6.617

Cited by 38 publications

(16 citation statements)

References 13 publications

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“…Philippatos and Gressis [10] first established a mean entropy criteria for portfolios. Nawrocki and Harding [11] discussed how to use entropy to measure investment performance and introduced the state-value weighted entropy method.…”

Section: Introductionmentioning

confidence: 99%

Properties of Risk Measures of Generalized Entropy in Portfolio Selection

Zhou

Liu

et al. 2017

Entropy

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This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the following properties, which various scholars have associated with effective risk measures: Monotonicity, Translation Invariance, Sub-additivity, Positive Homogeneity, Consistency and Convexity. Measures based on Fuzzy Entropy, Credibility Entropy, and Sine Entropy all exhibit the same properties: Sub-additivity, Positive Homogeneity, Consistency, and Convexity. These measures based on Information Entropy and Hybrid Entropy, meanwhile, only exhibit Sub-additivity and Consistency. Cumulative Residual Entropy satisfies just Sub-additivity, Positive Homogeneity, and Convexity. After identifying these properties, we develop seven portfolio models based on different risk measures and made empirical comparisons using samples from both the Shenzhen Stock Exchange of China and the New York Stock Exchange of America. The comparisons show that the Mean Fuzzy Entropy Model performs the best among the seven models with respect to both daily returns and relative cumulative returns. Overall, these results could provide an important reference for both constructing effective risk measures and rationally selecting the appropriate risk measure under different portfolio selection conditions.

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Section: Introductionmentioning

confidence: 99%

Properties of Risk Measures of Generalized Entropy in Portfolio Selection

Zhou

Liu

et al. 2017

Entropy

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“…From previous studies, the mean-entropy portfolios are consistent with the Markowitz full-covariance model under three different return distributions [13]. Furthermore, entropy has a higher explanatory power for the expected return than the capital asset pricing model [17]. Entropy, as a measure of uncertainty of returns, can be an important factor to select an appropriate set of stocks in which to invest.…”

Section: Introductionmentioning

confidence: 59%

Stock Selection for Portfolios Using Expected Utility-Entropy Decision Model

Yang

Feng

Wan-hua

2017

Entropy

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Yang and Qiu proposed and then recently improved an expected utility-entropy (EU-E) measure of risk and decision model. When segregation holds, Luce et al. derived an expected utility term, plus a constant multiplies the Shannon entropy as the representation of risky choices, further demonstrating the reasonability of the EU-E decision model. In this paper, we apply the EU-E decision model to selecting the set of stocks to be included in the portfolios. We first select 7 and 10 stocks from the 30 component stocks of Dow Jones Industrial Average index, and then derive and compare the efficient portfolios in the mean-variance framework. The conclusions imply that efficient portfolios composed of 7(10) stocks selected using the EU-E model with intermediate intervals of the tradeoff coefficients are more efficient than that composed of the sets of stocks selected using the expected utility model. Furthermore, the efficient portfolio of 7(10) stocks selected by the EU-E decision model have almost the same efficient frontier as that of the sample of all stocks. This suggests the necessity of incorporating both the expected utility and Shannon entropy together when taking risky decisions, further demonstrating the importance of Shannon entropy as the measure of uncertainty, as well as the applicability of the EU-E model as a decision-making model.

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“…Still on this line, Philippatos and Gressis (1975) conduct a comparative study between the mean-variance model and the mean-entropy model, where he observes that the models are equivalent for normal and uniform distributions.…”

Section: The Caldeira Indexmentioning

confidence: 99%

Performance Indexes: Similarities and Differences

Caldeira

Gassenferth

Pacheco

et al. 2013

Ind. Jour. Man. & Prod.

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The investor of today is more rigorous on monitoring a financial assets portfolio. He no longer thinks only in terms of the expected return (one dimension), but in terms of risk-return (two dimensions). Thus new perception is more complex, since the risk measurement can vary according to anyone's perception; some use the standard deviation for that, others disagree with this measure by proposing others. In addition to this difficulty, there is the problem of how to consider these two dimensions. The objective of this essay is to study the main performance indexes through an empirical study in order to verify the differences and similarities for some of the selected assets. One performance index proposed in Caldeira (2005) shall be included in this analysis.

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Conditions of Equivalence Among E-V, SSD, and E-H Portfolio Selection Criteria: The Case for Uniform, Normal and Lognormal Distributions

Cited by 38 publications

References 13 publications

Properties of Risk Measures of Generalized Entropy in Portfolio Selection

Properties of Risk Measures of Generalized Entropy in Portfolio Selection

Stock Selection for Portfolios Using Expected Utility-Entropy Decision Model

Performance Indexes: Similarities and Differences

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