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GuySrinivasan comments on Why you should consider buying Bitcoin right now (Jan 2015) if you have high risk tolerance - Less Wrong
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When I see the concept of dollar cost averaging my math intuition module throws up a big red "This Is Clearly Wrong" sign. I never seem to have that thought when I have the time and inclination to tease out what's wrong and write a clear explanation of why it's BS (or find out that it's not).
Today is no exception. But here are some pointers my math intuition module is producing which say "investigate this, it will show you what's wrong":
If you flip a coin and invest the lump sum $3000 at either $40, $50, or $60 with equal probability, your expected value is 61.66 shares, not 60.
The "average price" should be the harmonic mean, not the arithmetic mean, and buying at the harmonic mean gets you 61.66 shares.
If you have the option of buying $3000 worth at $50, that doesn't mean you could switch to instead buying at a non-zero-variance-distribution with arithmetic mean $50 over time.
DCA lowers risk, while keeping the same EV. And the most common alternative, trying to time the market, has a long history of miserable failure by virtually all investors.
It's canonical investment advice for a reason.
Ander's claim, which I see repeated a lot, seems to be that it is positive EV rather than neutral. That's the bit that raises my hackles.
For a normal person who's saving money off their paycheque, DCA is superior to saving up a lump sum and investing that. This is true for exactly the same reason that DCA is inferior to a lump sum in the case where you're investing a lump sum - it gets you into the market faster, and stocks outperform cash.