Abstract
Linearity can be used to introduce qualitative analysis in portfolio optimization using very specific heuristics which in some cases carries enough information to anticipate the entire (qualitative) rank of solutions. This result is shown in the first part of our study. In the second part we show that correct analysis of optimal portfolios, and in particular those minimizing portfolio variance, requires complementary quantitative analysis with qualitative analysis as not all efficient portfolio have the same return-to-risk quality, and those minimizing variance may not minimize risk. In this section, we also introduce some notes of caution on the application of heuristics when applied to portfolios calculated in non-standard ways. The third and last section extends the literature by critically reviewing different ways in which qualitative heuristics can complement portfolio selection methods while also reviewing existing, full-fledged qualitative portfolio optimization methodologies.
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