FRM Part I · FRM Exam Part I · Hypothesis Testing
A researcher tests 20 independent, uncorrelated trading strategies, each at a 5% significance level, and every null hypothesis (no excess return) is actually true. What is the approximate probability that at least one strategy is falsely found significant?
About 64.2%. With 20 independent true nulls each tested at 5%, the chance of no false rejection is 0.95^20, roughly 0.358, so the chance of at least one false positive is about 0.642. This illustrates the data-snooping problem.
- A5.0%
- B64.2%Correct
- C100.0%
- D36.0%
Explanation
P(at least one false rejection) = 1 − 0.95^20 = 1 − 0.3585 = 0.6415, about 64%. Using 5% ignores multiple testing. 36% is the probability of no false rejection, the complement.
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