Law of Iterated Expectations
The law of iterated expectations says E[E[X | finer info]] = E[X | coarser info] — you cannot improve an expectation by forgetting information, and towers of forecasts must nest.
Definition
Law of Iterated Expectations refers to you cannot improve an expectation by forgetting information, and towers of forecasts must nest. Keep that definition fixed when comparing series, managers, or regimes — renaming the same tape does not create a new signal.
Why it matters
It is a named object desks use to frame risk, positioning, or process. When you cannot improve an expectation by forgetting information, and towers of forecasts must nest shifts, related hedges, limits, and narratives usually need an explicit update rather than a quiet assumption.
Case
Suppose a desk is positioned for the opposite of what law of iterated expectations is saying. If you cannot improve an expectation by forgetting information, and towers of forecasts must nest moves against that book, the first question is not “is the story clever?” but whether size, hedges, and stop logic still match the observation.
How to read it
Keep the definition fixed, then challenge it with cross-checks before sizing. Prefer a short written null hypothesis for Law of Iterated Expectations: what would falsify the current reading in the next window?