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

Brian Fleming, Jens Kroeske
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引用次数: 2

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.
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多元化与投资组合方差的分布,第二部分:波动性稳定性作为多元化的衡量标准
我们介绍了一个理解投资组合多样化的新框架,为比较方法提供了一个连贯的基础,并提供了一种新的投资组合构建方法。主要的论点是,仅基于协方差矩阵的多样化措施是模糊的,因为在这样的风险设置中,只有整体投资组合方差是重要的。为了解决这个问题,我们建议将多样化的目的视为减少投资组合方差本身的方差,这反过来只有在考虑过度峰度时才有意义。将多样化和方差的方差联系起来,为普遍存在的均值-方差方法提供了一种自然的延伸。举例说明了通过最小化峰度来最大化多样化的投资组合的直观本质。此外,我们将投资组合维度作为峰度的转换引入,使我们能够根据具有独立和同分布(IID)回报的相等数量的资产来解释多样化。
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