Savings Plans and the Cost-Average Effect: What the Maths Really Shows

What you will learn

• How an ETF savings plan works and which costs matter for small monthly amounts.
• How to calculate the average cost per unit and why it is below the average price.
• Why the cost-average effect does not guarantee a better result than investing all at once.
• How to decide between a lump sum and spreading an amount over time.

Explanation

What a savings plan is

An ETF savings plan (German: Sparplan) is a standing order at your broker: on a fixed date, a fixed euro amount is used to buy units of a fund. Most brokers allow fractional units, so €100 buys exactly €100 worth, for example 2.5 units at €40.

The cost-average effect

The cost-average effect (German: Durchschnittskosteneffekt; in English also "pound-cost" or "dollar-cost averaging") describes a simple fact: a fixed euro amount buys more units when the price is low and fewer units when it is high. So your average cost per unit is always equal to or lower than the simple average of the purchase prices.

Average cost per unit = total euros invested ÷ total units bought

Mathematically, this average cost is the harmonic mean of the prices, which is never higher than the ordinary (arithmetic) mean. That part is guaranteed.

What it does not show

The effect compares your average cost with the average price. It does not compare your result with investing the whole amount on day one. If prices rise over time, a lump sum invested earlier buys more units at lower prices and usually ends higher. If prices fall first, spreading the purchase ends higher. Because nobody knows the path in advance, neither method is "better" in every case.

The honest reasons for a savings plan are practical:

• For most people, monthly income is the source of investment money, so investing monthly is simply investing as soon as the money exists.
• It creates a habit and removes the question "is now a good time?".
• Spreading a large inheritance over, say, 6–12 months can reduce regret if prices fall right after you invest. This lowers timing risk, but it also keeps money uninvested for longer.

Costs for small amounts

Fixed order fees hurt small purchases. A €1.50 fee on €100 is 1.5% of each payment; on €25 it would be 6%. Many brokers offer savings plans without order fees for selected ETFs, but conditions change, so check the current price list. The ongoing fund costs (TER) and spreads were covered in lesson 5.

Worked example

Hypothetical example: €400 to invest in an ETF, either as €100 per month for four months or all at once in month 1. Fractional units are allowed. We ignore order fees, spreads and taxes.

Case A: prices fall and recover partly

Prices in months 1–4: €50, €40, €50, €25. Price at the end: €40.

1. Units bought: 100 ÷ 50 = 2; 100 ÷ 40 = 2.5; 100 ÷ 50 = 2; 100 ÷ 25 = 4. Total = 10.5 units.
2. Average cost: €400 ÷ 10.5 = €38.10. Simple average price: (50 + 40 + 50 + 25) ÷ 4 = €41.25.
3. Savings plan value: 10.5 × €40 = €420 (+€20).
4. Lump sum: €400 ÷ €50 = 8 units → 8 × €40 = €320 (−€80).

Case B: prices rise steadily

Prices in months 1–4: €40, €45, €50, €55. Price at the end: €60.

1. Units: 2.5 + 2.222 + 2 + 1.818 = 8.540 units.
2. Average cost: €400 ÷ 8.540 = €46.84, below the simple average of €47.50.
3. Savings plan value: 8.540 × €60 = €512.42.
4. Lump sum: €400 ÷ €40 = 10 units → 10 × €60 = €600.

In both cases the average cost is below the average price, yet the savings plan wins in Case A and loses in Case B. The path of prices decides, not the method.

Common mistake

Practice activity

A savings plan invests €200 per month. Prices in months 1–4 are €20, €25, €16 and €20. The price at the end is €20. Ignore all costs.

1. How many units do you own?
2. What is your average cost per unit, and what is the simple average price?
3. What is your portfolio worth, and what would a lump sum of €800 in month 1 be worth?

Key takeaways

• A savings plan buys a fixed euro amount at regular dates; fractional units make this exact.
• Average cost per unit = euros invested ÷ units bought, and it is never above the simple average price.
• Whether a savings plan beats a lump sum depends on the price path, which nobody knows in advance.
• For small monthly amounts, fixed order fees can be the largest cost; check current broker conditions.

Next step

In the next lesson you will learn how to rebalance a portfolio back to its target mix, with clear rules for when and how.