Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy

Carmichæl, Benoı̂t; Koumou, Gilles Boevi; Moran, Kevin

doi:10.2139/ssrn.2610814

Cited by 15 publications

(15 citation statements)

References 90 publications

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“…The monotonicity in portfolio size axiom was also used by Rudin and Mor-gan (2006) to support the portfolio diversification index and by Vermorken, Medda, and Schroder (2012) to support the diversification delta. In addition to the axioms of duplication invariance and monotonicity in portfolio size, Carmichael, Koumou, and Moran (2015) discuss the axioms of degeneracy in portfolio size and degeneracy relative to dissimilarity to support Rao's Quadratic Entropy. Meucci, Santangelo, and Deguest (2015, Example 1) discuss the axiom of market homogeneity to support the effective number of bets.…”

Section: Related Literaturementioning

confidence: 99%

Determination of Quebec's Quarterly Real GDP and Analysis of the Business Cycle, 1948–1980

Fortin

Joanis²,

Kabore³

et al. 2022

J Bus Cycle Res

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We provide an axiomatic foundation for the measurement of correlation diversification measures in a one-period portfolio model. We propose a set of nine desirable axioms for this class of diversification measures. We name the measures satisfying these axioms coherent correlation diversification measures which we distinguish from coherent risk measures. We provide the decision theoretic foundations of our axioms by studying their compatibility with investors' preference for diversification in rank-dependent expected utility theory. We examine some of the most frequently used methods for measuring correlation diversification in terms of our axioms. Lastly, we explore whether our axioms have a representation function.

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Section: Related Literaturementioning

confidence: 99%

Determination of Quebec's Quarterly Real GDP and Analysis of the Business Cycle, 1948–1980

Fortin

Joanis²,

Kabore³

et al. 2022

J Bus Cycle Res

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show abstract

“…Diversification using different entropy measures were explored by Yu (2014) [ 23 ]. Lastly, approaches using Rao’s quadratic entropy and diversity measures (Rao, 1982, 1985, 2004, 2010) [ 24 , 25 , 26 , 27 , 28 ] are discussed in detail by Carmichael (2015) [ 29 ].…”

Section: Modern Portfolio Theorymentioning

confidence: 99%

An Entropy-Based Approach to Portfolio Optimization

Mercurio

Xie

2020

Entropy

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This paper presents an improved method of applying entropy as a risk in portfolio optimization. A new family of portfolio optimization problems called the return-entropy portfolio optimization (REPO) is introduced that simplifies the computation of portfolio entropy using a combinatorial approach. REPO addresses five main practical concerns with the mean-variance portfolio optimization (MVPO). Pioneered by Harry Markowitz, MVPO revolutionized the financial industry as the first formal mathematical approach to risk-averse investing. REPO uses a mean-entropy objective function instead of the mean-variance objective function used in MVPO. REPO also simplifies the portfolio entropy calculation by utilizing combinatorial generating functions in the optimization objective function. REPO and MVPO were compared by emulating competing portfolios over historical data and REPO significantly outperformed MVPO in a strong majority of cases.

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“…Mainly it was used in statistics and in ecology. However, Carmicheal et al [2015] presented this entropy as a measure of portfolio diversification. The Rao's Quadratic Entropy for portfolio is defined as:…”

Section: Definitions Of Selected Diversification Measuresmentioning

confidence: 99%

“…In the presented research the function D was defined for the covariance matrix. The values of d ij were calculated according to the following formula [Carmicheal et al 2015…”

Section: Definitions Of Selected Diversification Measuresmentioning

confidence: 99%

See 1 more Smart Citation

International Diversification in the Periods of Major Economic Changes

Gluzicka¹

2018

PRACE NAUKOWE UNIWERSYTETU EKONOMICZNEGO WE WROCŁAWIU

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Diversification is one of the most important elements considered in the process of the construction of investment portfolios. A special role is attributed to the diversification in periods of rapid changes in the financial markets. In the article, the problem of international diversification was analysed on the example of selected European, American and Asian markets. The level of diversification was assessed by various measures: Portfolio Diversification Index, Rao's Quadratic Entropy and Diversification Ratio. In the study diversified portfolios were compared. These portfolios were constructed for the data from the periods before, during and after the last economic crisis. The conducted research showed that European markets were most diversified, regardless of the nature of the analysed period. The study also showed that strongly interrelated countries did not necessarily have strong influence on diversification.

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Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy

Cited by 15 publications

References 90 publications

Determination of Quebec's Quarterly Real GDP and Analysis of the Business Cycle, 1948–1980

Determination of Quebec's Quarterly Real GDP and Analysis of the Business Cycle, 1948–1980

An Entropy-Based Approach to Portfolio Optimization

International Diversification in the Periods of Major Economic Changes

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