My probability that a Kolmogorov-Smirnov (KS) test directly reflects statistical similarity was 60%, but I update it to 35% due to hypothesis sensitivity.
These tests are useful for measuring distributional distance, but their interpretation critically depends on the relevance of reference distributions.
If the benchmark does not capture heavy tails or typical asymmetry, for example, venture capital returns, the test may indicate a misleading similarity.
A KS test concluding similarity between a VC portfolio and a standard Gaussian distribution would mask the true extreme risks inherent to this type of asset.