I Think it Valuable, from Victor Niederhoffer
I think it valuable to test the hypothesis that on certain days there are more crosses of the round number 50 as in 3250 in emini futures than is random.
Theo Athanasiadasis writes:
This needs to be tested on intraday basis. On daily basis there is no statistical evidence. There is a small tendency to have more crossings than expected but in line with randomness. Happy to share the testing process/code. The idea is to compare the historical ES crossings of 50 (based on settlement prices) with random index moves that could have happened (bootstrapped delta estimated from adjusted prices).
Since emini inception (10k simulations):
Historical Number of Crossings=1260
Expected Num Crossings (average of random bootstraps)=1246
Confidence Interval=[1196,1296]
Pval = .32
Similarly for the last 10years
Historical Number of Crossings=654
Expected Num Crossings (average of random bootstraps)=642
Confidence Interval=[608,677]
Pval = .29
What is perhaps more interesting from daily data is the 100point rounds. There is close to non-random tendency for ES to avoid crossing those levels frequently.
Since emini inception (10k simulations):
Historical Number of Crossings=620
Expected Num Crossings (average of random bootstraps)=649
Confidence Interval( 5,95) =[614,686]
Pval = .92
Similarly for the last 10years
Historical Number of Crossings=314
Expected Num Crossings (average of random bootstraps)=334
Confidence Interval( 5,95)=[308,361]
Pval = .91