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Why Long-Short Portfolio Correlation Can Differ from Leg Correlations

Article Quant Q&A · Author: kamal kumawat
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Summary

The document raises a portfolio-construction question about how correlations among long-only and short-only factor portfolios relate to the correlation of their combined long-short portfolio. The example concerns quality and value portfolios: the long-only portfolios are reported as strongly correlated with one another, as are the short-only portfolios, while the combined long-short portfolios have a correlation close to zero.

The central lesson sought is that correlations among portfolio legs do not by themselves determine the correlation between combined portfolios. The combined correlation also depends on cross-correlations between long and short components and on the relative volatility or weighting of each leg. The post asks how to decompose the combined correlation, but supplies no answer, derivation, or data beyond its reported example. It is therefore useful as a prompt to examine covariance aggregation, but it does not establish why the observed relationship arose or provide a complete decomposition method.

Key ideas

  • The correlation between combined long-short portfolios can differ substantially from correlations between their individual long or short legs.
  • A combined portfolio’s covariance depends on cross-correlations between all component legs.
  • The relative volatility and weighting of each component affect the resulting portfolio correlation.
  • The document poses the decomposition problem but does not provide a derivation or explanation of its example.

Tags

Factor investingPortfolio constructionStatistics
Full text
# Relationship between correlations of long only and short only portfolio with long-short portfolio?


# Relationship between correlations of long only and short only portfolio with long-short portfolio?












I am working on one quality and value factor, the correlation between a long-only or short only portfolio of these two factors is respectively 0.7 and 0.8, and the correlation between combined long-short portfolio is approx 0.02. I wanted to understand why did it happen and also it would be helpful if someone can explain how to break Corr(L1+L2, S1+S2) into the correlation of Corr(L1, L2) and Corr(S1, S2) and other terms. Thanks a lot for reading this in advance.

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