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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. enter image description here

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. enter image description here

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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    $\begingroup$ Is the raw correlation matrix positive definite, i.e. invertible? $\endgroup$
    – Kermittfrog
    Jun 20, 2022 at 15:24
  • $\begingroup$ @Kermittfrog thanks for this thought. Yes, the original correlation matrix is positive semi definite, however the transformed covariance matrix that stems from it and which has been manipulated by the two parameters isn't. I checked it today and found that it's some bug in the code that caused it. However, the main issue of super optimal portfolios still exists. I built a workaround by fixing the physical variance to an upper level and let the optimizer happily search the weights using this transformed covariance. Until now 226 portfolios are calculated and no hickups yet.. 🤔 $\endgroup$
    – T123
    Jun 21, 2022 at 16:45
  • $\begingroup$ I solved the problem, basically, i made a small mistake in my code :-) $\endgroup$
    – T123
    Oct 5 at 12:59

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