Portfolio Rho-Presentativity
Portfolio Rho-Presentativity
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DOI：
10.2139/ssrn.2971867
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发表时间：
2019-10
期刊：
影响因子：
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通讯作者：
Tristan Froidure;Khalid Jalalzai;Yves Choueifaty
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文献类型：
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作者：
Tristan Froidure;Khalid Jalalzai;Yves Choueifaty
给定一个投资领域，我们考虑所有资产与权重组合的相关性向量[公式：见文本]。这个向量提供了一个等价于[公式：参见文本]的表示，并导致了[公式：参见文本]的概念-代表投资组合，它与所有资产具有正相关或暴露。这个类别包含了众所周知的投资组合，并补充了代表性投资组合的概念，即投资于所有资产（例如市值指数）的正数。然后我们引入最大化的概念[公式：见文本]-代表性投资组合，在没有特定约束的情况下最大化所有资产的总敞口[公式：见文本]，通过一些对称的，增加的和凹的实值函数[公式：见文本]来衡量。建立了一个基本特征，并证明了这些投资组合是多头的、多样化的，并且形成了一个满足资产协方差矩阵变化的局部正则性条件的多面体的有限联合。尽管它的规模很小，但它包含了许多知名的、可能受到限制的只做多的投资组合，将它们汇集在一个共同的框架中。这也允许我们明确地描述最大权重约束对最小方差投资组合的影响。最后，几个理论和数值应用说明了我们的结果。
Given an investment universe, we consider the vector [Formula: see text] of correlations of all assets to a portfolio with weights [Formula: see text]. This vector offers a representation equivalent to [Formula: see text] and leads to the notion of [Formula: see text]-presentative portfolio, that has a positive correlation, or exposure, to all assets. This class encompasses well-known portfolios, and complements the notion of representative portfolio, that has positive amounts invested in all assets (e.g. the market-cap index). We then introduce the concept of maximally [Formula: see text]-presentative portfolios, that maximize under no particular constraint an aggregate exposure [Formula: see text] to all assets, as measured by some symmetric, increasing and concave real-valued function [Formula: see text]. A basic characterization is established and it is shown that these portfolios are long-only, diversified and form a finite union of polytopes that satisfies a local regularity condition with respect to changes of the covariance matrix of the assets. Despite its small size, this set encompasses many well-known and possibly constrained long-only portfolios, bringing them together in a common framework. This also allowed us characterizing explicitly the impact of maximum weight constraints on the minimum variance portfolio. Finally, several theoretical and numerical applications illustrate our results.