Dollar cost averaging: what spreading really does to the price you pay

Regular contributions are probably the most described and the most poorly described practice in stock market investing. The line that appears everywhere, "you buy more when it is low and less when it is high", is correct. The one deduced from it, "you buy the lows and avoid the highs", is not. Between the two there is a calculation, and it fits in a six-row table. This guide works it through, and also shows the two cases where spreading costs you units.

The mechanism fits in one sentence

Everything follows from the amount being fixed while the price is not. With €100 a month, if the unit costs €80 you get 1.25 of them; if it costs €125 you get only 0.80. So you mechanically buy more units at low prices, not because you identified them, but because your budget is constant.

Here is the full calculation over those six months, row by row.

The result is this: €600 bought 6.0702 units, so the price actually paid is €98.84 a unit. The average of the six quoted prices, meanwhile, is €100.83. You paid €1.99 less than the average of the prices, that is 1.97% below it, without having chosen a single one of your dates.

Why the price paid is always below the average price

That is not a coincidence of this example, it is an arithmetic property. The price paid by fixed-amount contributions is the harmonic mean of the prices, not their arithmetic mean. And the harmonic mean of a series of positive numbers is always less than or equal to their arithmetic mean, with equality only when every number is identical.

Put another way: the more scattered the prices, the wider the gap between the two means, and that gap always runs the same way. It is a solid result, and it is also the only arithmetic advantage regular contributions provide. It says nothing about the final return, which depends on the price on the day you sell.

It all comes from the fixed amount, not from the schedule

This point is rarely stated and it is the most illuminating. Take exactly the same schedule, the same six months, the same prices, but buy one fixed unit each month instead of a fixed amount.

Regularity on its own therefore adds nothing: buying one unit a month for six months makes you pay precisely the average of the prices, no more and no less. The €1.99 difference comes entirely from having fixed the amount. That is worth knowing when setting up an automatic contribution with a broker, where both options sometimes exist.

What spreading does not do

Three claims circulate that do not survive the calculation.

"You buy the lows." No: you buy every date in the schedule without exception, including the highest. In the example, month 3 at €125 was duly bought. What varies is the weight of each date in the total, not which dates are selected.

"It returns more than investing all at once." That depends entirely on the path prices take, and the two extreme cases are easy to work out.

In a market that only rises, spreading therefore costs more than 10% of the units, because money that waits is not invested. Since nobody knows the path in advance, the question "which of the two returns more" has no general answer, and any statement to that effect would be a performance claim.

"It protects against losses." No. If the market falls 30% and stays there, a portfolio built by contributions is down, exactly like any other. Spreading changes the average entry price, it does not change the direction of the market.

What spreading really removes: dependence on the date

One effect does remain, and it is measurable. A single lump sum gives an entry price that depends entirely on the day chosen. Over the six months of the example, that price ranges from €80 to €125, a 56% gap between the best and the worst moment. Spread contributions give €98.84, whatever order the prices arrived in.

That is the only rigorous statement: spreading reduces the dispersion of the entry price and removes the timing decision. It does not raise the average of the possible outcomes, it narrows their range. Whether that narrowing is worth giving up the favourable case is a personal trade-off, depending on your horizon and your tolerance for variation. No calculation settles it for you.

The counterweight: fixed costs per order

More contributions means more orders, and many brokers charge a floor amount per transaction. On small sums that floor becomes the largest cost item, well above the annual charges of the fund being bought.

At 4% taken at entry, the 1.97% arithmetic gain obtained above is largely wiped out. It is a simple comparison of magnitudes: the harmonic mean advantage is measured in fractions of a percent, a fixed fee on a small contribution is measured in percent. The guide on compound interest shows what those entry deductions become over several decades.

A practical consequence: keeping track of the holding

Every contribution creates an acquisition at a different price. After three years of monthly contributions, a single portfolio line corresponds to thirty-six purchases. That matters not at all until you sell, and becomes central the day you do, since a capital gain calculation needs a cost basis.

In France, the applicable method is the weighted average cost, recomputed on every acquisition, as the guide on calculating a capital gain sets out. A partial sale therefore does not let you designate which units were sold: it is measured against a single cost basis, that of the whole holding.

What PulseMyPortfolio does with them

The app records each contribution as a separate acquisition, with its date, price and fees, then keeps the weighted average cost up to date with every new line. So you can see at any moment what you actually paid, against the current price, without redoing the calculation. Brokerage fees you enter go into the cost basis, as the tax rule provides.

What it does not do: it does not tell you what amount to contribute, how often, or whether investing all at once would be better. It records and computes. Every calculation runs on your device, as the guide on local-first financial data explains; activating a licence is the only moment a connection is required.

Frequently asked questions

Do regular contributions return more than a lump sum?

There is no general answer, and the table above shows why: in a continuously rising market spreading gets 10.59% fewer units, in a continuously falling one 15.39% more. The outcome depends on a path nobody knows in advance. What is demonstrable is that spreading narrows the range of possible entry prices.

What contribution frequency should be chosen?

The calculation shows frequency pulling in two opposite directions: the more contributions there are, the more the dispersion of the entry price falls, and the more fixed per-order costs pile up. The trade-off depends on your broker's pricing and on your situation, and it is a personal choice PulseMyPortfolio does not make for you.

Should contributions be paused when the market falls?

Pausing or continuing means taking back a timing decision, which is precisely what automatic spreading had set aside. The arithmetic observation is that contributions made at the lowest prices are the ones that buy the most units. That observation is not a recommendation to act either way.

Does it work in a life insurance contract or a PEA too?

The mechanism is arithmetic: it does not depend on the wrapper, only on the amount being fixed and the price varying. What changes from one wrapper to another is how contributions are priced and how the exit is taxed, described in the guide on ETFs and in the glossary.

Why is the price paid not the average of the prices?

Because your contributions do not buy the same number of units. The average price would weight the six months equally; the price you paid weights them by the quantity bought, so more heavily in the cheap months. The result has a name, the harmonic mean, and it is always less than or equal to the ordinary average.

Does an automatic contribution at my broker use a fixed amount or a fixed quantity?

Both exist, depending on the institution and the product. The distinction is not cosmetic: the table above shows that a fixed quantity makes you pay exactly the average price, so without the €1.99 difference the fixed amount produced. It is worth checking in the broker's terms.

What happens to my cost basis if I sell part of my units?

It does not change. Under the weighted average cost method, a partial sale reduces the quantity held and leaves the unit cost basis untouched; it is a new acquisition that changes it. The detail is in the guide on calculating a capital gain.

Can PulseMyPortfolio set up my contributions?

No. The app is not connected to any broker and places no orders. It records the transactions you enter or import from a statement, and derives your cost bases and your position from them.