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Why Zero Correlation Can Be Preferable for Diversification

Article Quant Q&A · Author: abu
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Summary

The document considers how to score portfolio diversification using correlation with a reference portfolio. It asks whether a negative correlation should receive a higher diversification score than correlation near zero. The response argues that, when the aim is diversification, correlation closer to zero is the appropriate target.

The brief rationale is that an exposure positively correlated with a reference portfolio can be reversed by shorting that reference, producing the corresponding negative correlation. This suggests negative correlation alone need not represent a uniquely superior diversification property. The exchange gives no formal scoring rule, portfolio constraints, empirical evidence, or discussion of other risk measures, so the claim is a limited intuition rather than a full portfolio construction framework.

Key ideas

  • For diversification relative to a reference portfolio, the response favors correlation nearer zero.
  • A negative correlation is not automatically more valuable than a low positive correlation.
  • Shorting the reference portfolio can reverse the sign of an exposure's correlation.

Tags

Portfolio constructionStatistics
Full text
# Preference between low (zero) and negative correlation


# Preference between low (zero) and negative correlation












I am trying to create an artificial score grading user's portfolio correlation. In terms of diversification, lower correlation is obviously better. However, should negative correlation get a higher score than correlation close to zero?

## Answer by delsim (score 1, accepted)

https://quant.stackexchange.com/a/40811

If you want diversification, then closer to zero is what you want.

Trivially, a positive correlation (+ x) with respect to some reference portfolio can be reversed (- x) by just shorting the reference portfolio.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.