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Correlation Neglect and Covariance Matrices in Mean-Variance Portfolios

Article Quant Q&A · Author: T123
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Summary

The document explores how behavioral assumptions about perceived correlations affect mean-variance portfolio optimization. It compares a model that modifies the covariance matrix using parameters for correlation neglect with an alternative that represents investors as treating correlations as closer to one. The author reports that some parameter choices can make the adjusted covariance matrix fail to be positive semidefinite, creating numerical problems when calculating portfolio weights.

The author also observes that moving correlations toward zero can generate portfolios outside the efficient frontier, which they describe as super-optimal, and measures inefficiency relative to a no-short-sales frontier using an area integral. These are reported observations from an implementation using daily returns for ten Swiss securities; the document does not provide a resolution or an accepted modeling procedure. Its central practical concern is that behavioral adjustments to covariance estimates may violate mathematical conditions needed for reliable optimization, while different definitions of correlation neglect can produce materially different portfolio outcomes.

Key ideas

  • Behavioral models of correlation neglect can alter the covariance matrix used in mean-variance optimization.
  • Some parameter settings may make an adjusted covariance matrix non-positive-semidefinite.
  • A covariance matrix with invalid properties can create problems when solving for portfolio weights.
  • Treating correlations as moving toward zero can produce portfolios outside the efficient frontier.
  • The document raises modeling questions but does not establish a preferred correction or solution.

Tags

Portfolio constructionRisk managementStatistics
Full text
# How to incorporate "correlation neglect" in a M-V-Framework?


# How to incorporate "correlation neglect" in a M-V-Framework?












at the risk of boring you with another behavioral finance question, i found a bunch of papers on a phenomenon dubbed correlation neglect, where economic agents misperceive the correlation structure of stochastically dependent gambles. Relevant papers in this area are written by Weizsäcker and Ester in 2016 among others. All of these mentioned its relevance for portfolio choice, so i decided to spend a few hours this weekend and took a closer look at those and i'm a bit puzzled:

Weizsäcker and Eyster (2016) model "correlation neglect" using two parameters (k and L) which increase or decrease the covariance matrix. I took the liberty of implementing this approach in a M-V approach. It strikes me that by modifying the covariance matrix according to the form on page 13 (V(k,L)) there seem to be critical areas of the parameter values ​​k and L in which the generated covariance matrix is ​​no longer consistently positive semi-definite. In my case (e.g. 10 Swiss securities, daily returns), this occurs in particular for low values ​​of k. This furthermore frequently creates problems in the numerical determination of the portfolio weights.

I have also contrasted this approach with that of Siebenmorgen and Weber (2003), who model «correlation neglect» as a tendency to perceive/treat correlations=1. In contrast, the Eyster/Weizsäcker (2016) Model captures this effect as a tendency by convergence of the covariance towards zero if k goes to zero. This casues another issue within a M-V framework since combinations of portfolios are now generated that lie outside the efficient boundary ("super-optimal portfolios"). I determined the generated inefficiency compared to portfolios of the efficient frontier using the area integral (here «Inefficiency Measure»): An increase compared to the no-shortsales-efficient frontier (4.33019%) is striking.

Hence my question: In what form (if at all) can the modification of the covariance matrix the iterature proposes be used in an M-V framework, or in what form would it have to be modified? Are there other approaches examining correlation neglect in portfolio choice decisions that could help me model this effect? Thanks a lot for your help, Thomas

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