Kendall's tau
The share of pairs of days on which two investments moved in the same order, less the share they moved in opposite order.
Every pair of days is either concordant (both returns ordered the same way) or discordant; tau is the balance between them. It runs smaller in magnitude than Pearson's or Spearman's for the same relationship — about 0.5 where Pearson's reads 0.7 — so a threshold read in tau is a stricter one.
Formula
τb = (Concordant − Discordant) ÷ √((Pairs − A ties)(Pairs − B ties))
How to read it
+1 every pair in the same order, 0 no tendency, −1 every pair opposite.
In Kereon
Charts · Correlation. Tau-b, which corrects for tied returns, by Knight's algorithm; p from the normal approximation with the tie-corrected variance; a 95% interval from Fisher's z with variance 0.437 ÷ (n − 4).
Also called: kendall, kendall's tau, kendall tau.