Diversification and the Distribution of Portfolio Variance, Part 1: Sums of IID Variables and Higher-Order Moments

5 Pages Posted: 3 Jan 2018 Last revised: 8 Jul 2020

See all articles by Brian Fleming

Brian Fleming

Dimensionless Ltd

Jens Kroeske

Aberdeen Standard Investments

Date Written: July 17, 2017

Abstract

For a weighted sum of asset returns that are independent and identically distributed (IID) up to variance, we derive expressions linking the distribution of variance across assets with higher-order portfolio moments, assuming these quantities are finite. In particular, we show concise relationships for portfolio skewness and kurtosis and, within a general framework, review related metrics in the literature for measuring diversification.

Keywords: Portfolio diversification, Entropy, Effective support size, Higher-order moments, Skewness, Kurtosis

JEL Classification: C10, C40, C49, G11

Suggested Citation

Fleming, Brian and Kroeske, Jens, Diversification and the Distribution of Portfolio Variance, Part 1: Sums of IID Variables and Higher-Order Moments (July 17, 2017). Available at SSRN: https://ssrn.com/abstract=3094243 or http://dx.doi.org/10.2139/ssrn.3094243

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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