On a Stochastic Model of Diversification

TL;DR

This paper introduces a stochastic model of diversification, defining a new partial ordering of portfolios that aligns with second order stochastic dominance, offering a novel perspective on risk comparison.

Contribution

It proposes a new definition of diversification as a binary relationship between portfolios that coincides with second order stochastic dominance.

Findings

The new diversification definition aligns with second order stochastic dominance.

Provides a different perspective on risk comparison between portfolios.

Abstract

We propose a definition of diversification as a binary relationship between financial portfolios. According to it, a convex linear combination of several risk positions with some weights is considered to be less risky than the probabilistic mixture of the same risk positions with the same weights. It turns out to be that the proposed partial ordering coincides with the well-known second order stochastic dominance, but allows to take a look at it from another perspective.