Diversification and the Distribution of Portfolio Variance, Part 2: Volatility Stability as a Measure of Diversification

10 Pages Posted: 30 Jul 2020 Last revised: 10 Aug 2021

See all articles by Brian Fleming

Brian Fleming

Dimensionless Ltd

Jens Kroeske

Aberdeen Standard Investments

Date Written: July 18, 2021

Abstract

We introduce a new framework for understanding portfolio diversification that provides a coherent basis for comparing methodologies and offers a new approach to portfolio construction. The primary argument is that measures of diversification based only on a covariance matrix are ambiguous because in such a risk setting only the overall portfolio variance is of any import. To resolve this we propose that the purpose of diversification is most helpfully viewed as reducing the variance of portfolio variance itself, which in turn is only meaningful when one accounts for excess kurtosis. Connecting diversification and the variance of variance provides a natural extension to the ubiquitous mean-variance approach. Examples are provided to demonstrate the intuitive nature of portfolios that maximize diversification through minimizing kurtosis. Furthermore, we introduce portfolio dimensionality as a transformation of kurtosis that allows us to interpret diversification in terms of an equivalent number of assets with independent and identically distributed (IID) returns.

Keywords: Portfolio Diversification, Higher-Order Moments, Variance of Variance, Kurtosis, Dimensionality, Minimum Variance, Diversification Ratio, Risk Parity

JEL Classification: C10, C40, C49, C61, G11

Suggested Citation

Fleming, Brian and Kroeske, Jens, Diversification and the Distribution of Portfolio Variance, Part 2: Volatility Stability as a Measure of Diversification (July 18, 2021). Available at SSRN: https://ssrn.com/abstract=3646432 or http://dx.doi.org/10.2139/ssrn.3646432

Brian Fleming (Contact Author)

Dimensionless Ltd ( email )

Edinburgh
United Kingdom

Jens Kroeske

Aberdeen Standard Investments ( email )

1 George Street
Edinburgh, EH2 2LL
United Kingdom

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