The two conventions
Lump sum: a single entry, so units = total invested ÷ buy price and the cost is that one price.
DCA: many entries, so units = Σ(amount per period ÷ price at that period) and the cost is the smoothed weighted average.
A fair comparison keeps the total invested identical and uses the same price range.
Formulas
total invested ÷ buy priceunits × final priceΣ(amount per period ÷ price at that period)units × final priceOn a falling path (recompute it yourself)
Total invested 5,200 USDT, price falling linearly from 60,000 to 30,000 USDT:
Lump sum at the start: units = 5,200 ÷ 60,000 = 0.086667, final value = 0.086667 × 30,000 = 2,600 USDT, a return of −50.00%.
52 weekly buys of 100 USDT: about 0.120339 units, average cost about 43,211 USDT, final value about 3,610 USDT, a return of about −30.57%.
On a falling path DCA loses less because more of the money went in at lower prices. That is the opposite of the rising-path result.
On a V-shaped path (recompute it yourself)
Price drops from 50,000 to 25,000 and returns to 50,000, with 4 buys of 1,300 USDT (5,200 USDT in total):
DCA units = 1,300/50,000 + 1,300/25,000 + 1,300/25,000 + 1,300/50,000 = 0.026 + 0.052 + 0.052 + 0.026 = 0.156; average cost = 5,200 ÷ 0.156 ≈ 33,333 USDT.
Final value = 0.156 × 50,000 = 7,800 USDT, a return of +50.00%.
With the same start and end price, the lump sum returns 0% (5,200 → 5,200). The entire gap comes from where the buys landed in between.
Why the conclusion is unstable
The difference comes from the price path, not from one method being inherently better. A lump sum wins when the entry happens to be the low; DCA wins when there is a dip along the way.
So any reported comparison should state the price path it used — without it, the numbers are not comparable.
Notes
All figures exclude fees. DCA makes more buys and therefore pays more cumulative fees, which trims its advantage slightly.
This page compares cost structures mathematically. It does not forecast prices or recommend either approach.
Real-world choices also depend on cash-flow stability and tolerable drawdown, which arithmetic cannot answer.
FAQ
Does a lump sum win in a rising market?
On a linear rising path the lump sum buys at the lowest point and usually does better. Change the path to fall-then-recover or keep-falling and the conclusion reverses.
Why can two plans with the same start and end price differ so much?
Because DCA buys more units at the low points, lifting the weighted position during the dip, while a lump sum keeps all its money locked at the entry price.
Does DCA remove downside risk?
No. It spreads out entry points and reduces dependence on a single one. If the price falls over the long run, DCA loses money too — usually less than a lump sum on the same path.