Difference between White's reality check and Monte Carlo permutation In finance, two procedures are sometimes used to help evaluate the likelihood that positive results were obtained strictly due to data mining:


*

*White's Reality Check (WRC), described in White's (2000) Econometrica paper titled "A  Reality  Check  for  Data  Snooping",

*Monte Carlo Permutation (pair matching of historical data with signals without replacement).


These procedures apply when a researcher compares, for example, numerous trading rules, and selects the one that performs best on the historical data. The question is whether the best performing rule is much better than what one would expect from the best rule selected from among useless, uninformative rules.
I read the following passage in a textbook explaining the difference between WRC and MCP:

Both WRC and MC test the null hypothesis that all rules in a
  data-mined universe are useless. In the context of WRC, a useless rule
  has an expected return equal to zero. In the context of MCP, useless
  refers to a rule whose output values are randomly paired with the
  market's future change.

Aren't these two null hypotheses equivalent?
 A: I assume you are referring to Aronson's book "Evidence-Based Technical Analysis", p. 329. 
The two procedures, WRC (which is basically bootstrapping) and MC, both test "whether a specific trading rule (TR) performs no better than a specific benchmark" (H0). In this sense, they are equivalent. 
However, as they involve different methods to come to the conclusion whether H0 can be rejected, unsurprisingly they are not equivalent in a sense that WRC would reject H0 iff MC rejects it. 
Thus, there may be TRs such that WRC passes them whereas MC blocks them and vice versa.
A: WRC is specific. It uses the stationary bootstrap method of Politis and Romano, which does block bootstrap of random blocksize to ensure staionarity of the test statistic. Consequently, it isn't just any old bootstrap but constrains the end density to some extent.
I don't know the MC method you mention. If it is not a bootstrap then it sounds like it isn't particularly well justified. If it turns out to be just IID bootstrap, it may result in overly broad densities, failing to reject the null more often. 
