PARTIAL · sizing
Hypothesis
The Shannon entropy of the binned return distribution measures disorder; low-entropy windows (concentrated returns) carry more exploitable structure.
Math — Shannon entropy
$$ H = -\sum_{i} p_i \log_2 p_i $$
Method
Entropy of binned rolling returns; correlate with subsequent strategy hit-rate and with volatility-of-volatility.
Results
| Low-entropy → higher hit-rate | weak but present |
| Mostly a vol-of-vol proxy | partially |
| Best use | sizing modifier |
A weak, partly-independent regime measure — low-entropy windows do show modestly higher signal hit-rates, but much of it overlaps vol-of-vol. Kept as a minor sizing modifier, not a trigger.
Information-theoretic measures sometimes add a sliver beyond variance — but always net out the variance overlap before crediting the entropy.