A statistical similarity with minor deviations is simply not enough for the risks we manage; where is the maximum expression of rigor?
Executing Kolmogorov-Smirnov tests can show resemblance, but they do not reveal the full tail asymmetry of risks we need to anticipate for system stability.
For example, a KS test might conclude a general similarity between our reserves and an index, but it could miss extreme movements in the foreign exchange market that would directly threaten the credibility of our interventions.
We must go beyond adequate conclusions and seek tools that precisely identify points of rupture.