Portfolio construction is fundamentally based on the correlation between assets. The lack of correlation creates diversification, yet limited work has been conducted in testing alternative forms of correlation. Most construction work is based on Pearson correlation, which looks at linear dependence across assets. There are limitations with Pearson correlation, so sometimes an alternative is used, Spearman's rho correlation, which is based on rank ordering. Spearman's correlation can adjust for non-normality and outliers, but there is a problem with the assumption of monotonicity. The third alternative, Kendall's Tau is based on measuring the concordance between asset pairs through counting the sign of movements across assets.
A relatively simple paper looks at the portfolio construction of daily foreign exchange pairs using all of the same parameters except for the correlation matrix. See "Beyond Correlation: Enhancing currency portfolio construction through Kendall's Tau and Correspondence Analysis". I was surprised by the results. Yes, volatility is higher, but the overall portfolio performs better. There are clear benefits from using Kendall's Tau. The numbers are compelling enough to ask a simple question: "Why not try this alternative?"
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