The comparison must fix the total invested
A frequency comparison needs two constants: the same total invested and the same price path. Otherwise a change in the per-period amount or the price range makes the comparison meaningless.
Frequency only changes how many purchases the money is split into — not how much is invested in total.
Formulas
total invested ÷ periodsstart price + (end price − start price) × i ÷ (periods − 1)Σ(amount per period ÷ price at period i)total invested ÷ units accumulatedWorked example (recompute it yourself)
Total invested 5,200 USDT, price rising linearly from 30,000 to 60,000 USDT, changing only the number of periods:
1 period (a single buy at the start): 5,200 USDT in one go, 0.173333 units, average cost 30,000 USDT, final value 10,400 USDT.
52 periods (100 USDT weekly): about 0.120339 units, average cost about 43,211 USDT, final value about 7,220 USDT.
The average costs differ by more than 13,000 USDT, which shows that how the money is split changes the cost structure itself.
Across different period counts
| Periods | Per period | Units | Average cost | Final value | Return |
|---|---|---|---|---|---|
| 1 | 5,200 USDT | 0.173333 | 30,000 USDT | 10,400 USDT | +100.00% |
| 4 | 1,300 USDT | 0.123500 | 42,105.26 USDT | 7,410 USDT | +42.50% |
| 13 | 400 USDT | 0.120973 | 42,984.82 USDT | 7,258.38 USDT | +39.58% |
| 26 | 200 USDT | 0.120541 | 43,138.78 USDT | 7,232.47 USDT | +39.09% |
| 52 | 100 USDT | 0.120339 | 43,211.22 USDT | 7,220.35 USDT | +38.85% |
Total invested 5,200 USDT, price rising linearly from 30,000 to 60,000, fees excluded.
Why the differences converge
On this linear rising path the theoretical average cost of continuous DCA is 30,000 ÷ ln(2) ≈ 43,281 USDT.
The 52-period result of 43,211 USDT is already close to that limit. Moving from 4 to 13 periods changes things noticeably; moving from 26 to 52 leaves only a few dozen USDT of difference.
So the marginal benefit of higher frequency diminishes: it helps most at low frequency, and beyond a point extra periods add almost nothing while adding trades and fees.
Notes
This page uses a linear price model to show how frequency interacts with the bookkeeping. It uses no real historical prices and is not a return forecast.
Return falls as frequency rises here because on a steadily rising path the low-frequency plan bought at a lower starting price. That runs against the intuition that more frequent buying always wins — reverse the path and the conclusion reverses too.
For a real result, use the DCA backtest, which uses historical closes and also reports maximum drawdown.
FAQ
Does higher frequency always lower the average cost?
No. Average cost depends on the prices you buy at, and those are set by the price path. On a linear rising path high frequency is worse; in choppy or falling markets it is usually better.
Why does 52 periods barely differ from 26?
Because by 26 periods the average cost is already close to the continuous-DCA limit of about 43,281 USDT. Extra periods only approach that limit more closely.
Does frequency interact with fees?
Yes. More periods mean more buys and higher cumulative fees, so weigh that cost when raising frequency.