Buying in instalments or all at once: what the arithmetic actually says
Averaging in genuinely lowers your average cost below the average price — that part is provable. It still loses to buying at once in a rising market, and both facts are true simultaneously. Here are the worked numbers.
Not financial advice. This article is for informational purposes only.
The short version
Buying fixed amounts at intervals gives you an average cost below the average of the prices you paid. That is not a claim, it is arithmetic, and it always holds. It does not follow that averaging in beats buying at once — in a rising market, buying at once wins clearly, because more of your capital was exposed for longer. Two worked examples below, one in each direction, with the same numbers.
The argument about averaging in versus buying at once is usually conducted with confident claims and no numbers. It is a question with an arithmetic core, and once you do the arithmetic the disagreement mostly dissolves — because the two sides are each right about a different thing.
The provable part
Spending a fixed amount at each interval buys more units when the price is low and fewer when it is high, automatically. Your average cost per unit is therefore not the average of the prices — it is the harmonic mean of them, which is always lower whenever prices vary at all.
Four purchases of 100 each, at prices of 100, 50, 25 and 50:
| Purchase | Price | Amount spent | Units bought |
|---|---|---|---|
| 1 | 100 | 100 | 1.00 |
| 2 | 50 | 100 | 2.00 |
| 3 | 25 | 100 | 4.00 |
| 4 | 50 | 100 | 2.00 |
| Total | — | 400 | 9.00 |
Average cost is 400 divided by 9, which is 44.44. The simple average of the four prices is 56.25. You paid 21% less per unit than the average price, without predicting anything.
This is a mathematical identity, not a market observation. The harmonic mean of a set of positive numbers is always less than or equal to their arithmetic mean, with equality only when every number is identical. So the effect never fails — it just gets smaller as prices get steadier.
Why that does not settle the question
The comparison people actually care about is not “average cost versus average price”. It is “instalments versus buying the whole amount at the start”. Those are different questions, and the second has a different answer.
Same 400, same four periods. Buying at once means 4 units at 100. Ending price 50:
| Approach | Units held | Value at 50 |
|---|---|---|
| Instalments | 9.00 | 450.00 |
| All at once | 4.00 | 200.00 |
Instalments win decisively — a falling-then-recovering path is the best case for them. Now the same method on a rising path, prices 100, 125, 150, 175:
| Approach | Units held | Average cost | Value at 175 |
|---|---|---|---|
| Instalments | 3.04 | 131.66 | 531.67 |
| All at once | 4.00 | 100.00 | 700.00 |
Buying at once wins by a wide margin. Note that instalments still delivered on their promise — the average cost of 131.66 is below the 137.50 average of the prices paid. The mechanism worked perfectly and the outcome was still worse, because three quarters of the capital arrived after the asset had already risen.
That is the whole resolution. Averaging in reliably improves your entry price relative to the prices available. Buying at once maximises time exposed. When an asset rises over the period, exposure dominates. When it falls and recovers, entry price dominates. Neither approach is better in general, because the question is really about which of those two you are trying to optimise.
What actually decides it for a real person
Since the arithmetic does not produce a winner, the decision rests on circumstances — and here the considerations are more practical than mathematical.
Do you have a lump sum at all? Most people investing from income never face this choice. Money arrives monthly, so it is invested monthly. The comparison is academic, and the honest framing is that instalments are not a strategy but a description of the cashflow.
What happens if you are immediately down 40%? This is the question the arithmetic cannot reach, and it decides more outcomes than any calculation. A plan abandoned at the worst moment performs far worse than either approach followed consistently. If buying at once would mean watching a large loss on a single decision you made on one day, and that would make you sell, then instalments are better for you — not because the expected value is higher, but because you will still be there.
How volatile is the asset? The benefit of averaging scales with dispersion. In a market that routinely halves and doubles, the gap between harmonic and arithmetic mean is large. In a stable one it is negligible, and the fixed costs of many small purchases can exceed the benefit.
What do the transactions cost? Twelve purchases incur twelve sets of fees and twelve crossings of the spread. On the numbers in the real cost of a trade, at roughly 0.23% per purchase that is about 2.8% of the total — which can wipe out the averaging benefit entirely on a low-volatility asset. Fewer, larger instalments are usually better than many tiny ones.
Two things this does not do
It is not risk reduction. Once fully invested you hold exactly the same position either way, with exactly the same exposure. Averaging in changes the path to the position, not the position. Describing it as “reducing risk” conflates the transition with the destination.
It does not protect against a permanent decline. If an asset falls and never recovers, averaging in means buying more of it on the way down. The lower average cost is worthless if the price never returns. Averaging is a method for handling volatility, not for handling being wrong about the asset.
Our instalment calculator will run these numbers on whatever schedule and prices you want to test, including the unfavourable paths. Test both directions, because a tool run only on a chart that went up is a machine for producing confidence. Nothing here is advice about which to use, or about whether to buy anything at all — see our disclaimer.
Key takeaways
- Fixed-amount buying gives an average cost equal to the harmonic mean of prices, always at or below their average.
- In the worked falling-then-recovering example: 44.44 average cost against a 56.25 average price, 21% better.
- On a rising path, buying at once won 700 to 531.67 — the averaging mechanism worked and the outcome was still worse.
- Averaging optimises entry price; buying at once optimises time exposed. Which wins depends on the path.
- Most people investing from income are not making this choice at all — monthly cashflow decides it for them.
- At roughly 0.23% per purchase, twelve instalments cost about 2.8% and can erase the averaging benefit.
- Averaging in changes the path, not the destination. It is not risk reduction, and it does not help if you are wrong about the asset.