This requires proof. I downloaded the longest timeseries of Bitcoin trading activity available (Mt.Gox USD), and set the following:
A person wants to invest $1,000 in Bitcoin, and has the following options:
- Invest it all now, at an average price this week.
- Invest it in 4 equal lots in 4 subsequent weeks, starting this week.
- Invest it similarly over 8 weeks
- Over 12 weeks.
- Over 26 weeks (6 months)
- Over 52 weeks (12 months).
Then I calculated, how many bitcoins can be gained/lost by spreading the purchases. Result:
On average, by buying all instantly, the following advantage over other options was gained:
4 weeks = +8%
8 weeks = +20%
12 weeks = +33%
26 weeks = +79%
52 weeks = +161%.
In some cases DCA does come out ahead. In the 10% cases that most favored DCA, their advantage was (negative sign=DCA advantage):
4 weeks = -13%
8 weeks = -22%
12 weeks = -31%
26 weeks = -30%
52 weeks = -46%.
On the other hand the 10% most favorable cases for instant buying yield the following:
4 weeks = +33%
8 weeks = +77%
12 weeks = +101%
26 weeks = +214%
52 weeks = +416%.
By dollar cost averaging, the most would have been gained by having a 52-week plan instead of an instant lock-in in the week of 6.6.2011. (-77% less coins for instant).
By buying instantly, the largest advantage over DCA would have been by buying in the week of 27.9.2010 instead of during the following year (+629% more coins).