The Diversification Delta: <i>A Higher-Moment</i><i>Measure for Portfolio Diversification</i>

Vermorken, Maximilian A.; Medda, Francesca; Schröder, Thomas

doi:10.3905/jpm.2012.39.1.067

Cited by 25 publications

(25 citation statements)

References 13 publications

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“…On the other hand, a portfolio that distributes the investment uniformly across all the available assets is considered highly diversified. The weight‐based measures are generally based on the Herfindahl index (Hamza, Kortas, L'Her, & Roberge, ; Kacperczyk, Sialm, & Zheng, ; King, ; Kumar, ; Woerheide & Persson, ) or the Shannon entropy measure (Bera & Park, ; Vermorken, Medda, & Schroder, ). The limitation of weight‐based measures is obvious; they rely solely on the distribution of portfolio weights and ignore the risk characteristics of the portfolio constituents.…”

Section: Measuring Portfolio Diversificationmentioning

confidence: 99%

Improving portfolio diversification: Identifying the right baskets for putting your eggs

Sharma

Vipul

2018

Manage Decis Econ

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We measure the economic value of diversification for international multiasset investment strategies. This study implements five existing diversification measures and proposes a novel measure of diversification, the unsystematic risk ratio (URR). Only the URR and the effective number of bets measures predict the future risk-adjusted performance. These relations are robust to the choice of investment horizon and degree of relative risk aversion. The diversification benefits are larger for the frontier and emerging markets than for the developed markets, for multiasset strategies than for single asset class strategies, and for the pre-crisis and post-crisis periods than for the financial crisis period.

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Section: Measuring Portfolio Diversificationmentioning

confidence: 99%

Improving portfolio diversification: Identifying the right baskets for putting your eggs

Sharma

Vipul

2018

Manage Decis Econ

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“…Finally, Vermorken et al (2012) have developed the diversification delta, a higher-moment measure for portfolio diversification using Shannon entropy. 2 However, none of the above measures have proven totally satisfactory.…”

Section: Portfolio Diversification Measuresmentioning

confidence: 99%

Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy

2015

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Abstract:This paper extends the use of Rao(1982b)'s Quadratic Entropy (RQE) to modern portfolio theory. It argues that the RQE of a portfolio is a valid, flexible and unifying approach to measuring portfolio diversification. The paper demonstrates that portfolio's RQE can encompass most existing measures, such as the portfolio variance, the diversification ratio, the normalized portfolio variance, the diversification return or excess growth rates, the Gini-Simpson indices, the return gaps, Markowitz's utility function and Bouchaud's general free utility. The paper also shows that assets selected under RQE can protect portfolios from mass destruction (systemic risk) and an empirical illustration suggests that this protection is substantial.

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“…However, the construction of the DD measure based on the exponential of the weighted mean of the entropies of the individual assets leads to some issues that will be examined in this study. For example, it is easy to illustrate that the proposed measure does not provide a range of 0 ≤ DD ≤ 1 as suggested by Vermorken et al (2012). This is true, in particular, when assets with a different level of risk or variance are combined, which makes an accurate interpretation of the measure quite difficult.…”

mentioning

confidence: 96%

“…As stated in Vermorken et al (2012), different diversification measures have been proposed in the finance literature. Various researchers consider the use of the correlation matrix, as well as alternative measures such as clustering based methods, the portfolio diversification index, and the return gaps.…”

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confidence: 99%

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The Diversification Delta: A Different Perspective

Flores¹,

Bianchi²,

Drew³

et al. 2017

JPM

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In a 2012 article published in this Journal, Vermorken, Medda, and Schröder introduce a new measure of diversification, the Diversification Delta (DD), based on the entropy of the portfolio return distribution. Entropy as a measure of uncertainty has been used successfully in several frameworks and takes into account the entire statistical distribution rather than just the first two moments. In this article, the authors highlight some drawbacks of the DD measure and go on to propose an alternative measure based on exponential entropy which overcomes the identified shortcomings. The authors present the properties of this new measure and propose it as an alternative for portfolio optimization that incorporates higher moments of asset returns such as skewness and excess kurtosis.

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The Diversification Delta: A Higher-MomentMeasure for Portfolio Diversification

Cited by 25 publications

References 13 publications

Improving portfolio diversification: Identifying the right baskets for putting your eggs

Improving portfolio diversification: Identifying the right baskets for putting your eggs

Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy

The Diversification Delta: A Different Perspective

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