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I've seen this advice all over too, but it's never accompanied by anything approximating a mathematical proof. IMO, the burden of proof is on showing DCA works, not the other way around. In any case, the problem with your analogy is that if you have no information about that sin wave, you're equally likely to be investing at a local minimum.

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> you're equally likely to be investing at a local minimum.

If you invest at a few different times, whether fixed interval or random, is this not increasing the probability of approach an average value over the period you're investing?

I'm not asserting it's a good idea, I'm not using it as a strategy myself (or in fact making investment choices myself at all really), I'm just interested from the technical perspective.

> If you invest at a few different times, whether fixed interval or random, is this not increasing the probability of approach an average value over the period you're investing?

It does indeed increase the probability that you will approach the average value over that period.

But there's no reason to believe that average will be lower than the current value.

> But there's no reason to believe that average will be lower than the current value.

100%, not disagreeing. But it does reduce the risk that you're buying at an outlier price.

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