What is dollar-cost averaging?

Dollar-cost averaging — in Europe often simply called a savings plan — means investing a fixed amount of money at regular intervals, for example €200 every month, whatever the price. When prices are high, the fixed amount buys fewer shares; when prices are low, it buys more. It is the way most people build a portfolio from their income, and many brokers run it automatically.

How the average price works out

With a fixed amount $A$ invested in each of $n$ periods at prices $P_1, \dots, P_n$ , the average cost per share is the total invested divided by the total number of shares bought:

\bar{P} = \frac{n \, A}{\sum_{k=1}^{n} A / P_k} = \frac{n}{\sum_{k=1}^{n} 1/P_k}

This is the harmonic mean of the prices, which is never higher than their ordinary average: investing a fixed amount automatically buys more at low prices.

A simple illustration

€300 is invested every month for four months, while the price moves as follows:

Month	Price	Shares bought
1	€30	10.0
2	€20	15.0
3	€25	12.0
4	€30	10.0
Total		47.0

The same €300 every month. The cheapest month buys half as many shares again as the dearest.

\bar{P} = \frac{1{,}200}{47} \approx 25.53

The average of the four prices is €26.25, but the average cost per share is €25.53. At the final price of €30, the €1,200 invested is worth €1,410, although the price ended where it started.

What it does and does not do

It spreads the entry over time, so no single bad moment determines the purchase price.
It builds discipline: investing automatically every month removes the temptation to wait for a "better moment".
It does not guarantee a gain. If prices fall steadily, every purchase loses value.
It does not beat a lump sum on average. When a large amount is already available, investing it at once has usually produced higher returns, because markets rise more often than they fall. Spreading it out then mainly reduces the risk of regret.

Things to keep in mind

Costs per purchase: with small monthly amounts, fixed order fees can take a large share; free or low-cost savings plans solve this.
The interval matters little. Monthly or quarterly investing gives very similar long-term results.
Keep going in downturns. The method works best when purchases continue while prices are low — which is exactly when stopping is most tempting.

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