Chaos and the compass rose

We show that the recently discovered compass pattern in stock returns that results from discrete jumps of stocks seriously distorts the null distribution of the Brock-Dechert-Scheinkmann (BDS) chaos test: Under the null hypothesis of i.i.d. returns, the true rejection probability exceeds the nominal size by wide margins, which suggests that much of the evidence for chaos that has so far been found in stock returns might well be due to the fact that prices change only in discrete ticks.