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Interesting…. Under what assumptions precisely is it optimal to dollar cost average over a short time interval, if short time fluctuations have a large magnitude relative to long term drift? Like eg if you assume geometric brownian motion it doesn’t seem to help?

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Yes, you're correct about geometric brownian motion. The model must include some mean-reverting component (implied by "short time fluctuations") for DCA to come out ahead, and such a component would violate standard no-arbitrage assumptions.

This is a reason I haven't made active use of DCA. But DCA doesn't give up much, either, so I'm fine with "passively" engaging in DCA-like behavior by haphazardly dumping spare money into index funds after min("significant" drop, time limit) instead of purely maximizing time in market.

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