The Lab

Where it comes from

• Dollar-cost averaging (DCA) means buying a fixed amount of money's worth on a schedule, say every week, instead of all at once.
• The practice is older than any one book. Benjamin Graham described it for ordinary investors in The Intelligent Investor (1949), as a way to keep buying through good markets and bad.
• In 1979 George Constantinides showed that, in theory, DCA can't be the best plan: some other plan always does at least as well.
• In 1995 Meir Statman asked why so many people use it anyway. His answer was regret: a plan that spreads out the buying spares you the feeling of having put everything in on the worst day.

The maths, step by step

1. When the price falls. Put in 1,000. The price is 100, then 50.

• All at once: 1,000 ÷ 100 = 10 coins, worth 10 × 50 = 500.
• Half each day: 500 ÷ 100 + 500 ÷ 50 = 5 + 10 = 15 coins, worth 750.

2. When it rises. The price is 100, then 200.

• All at once: 10 coins, worth 2,000.
• Half each day: 5 + 2.5 = 7.5 coins, worth 1,500.

3. The "averaging". In step 1, the two buys cost 1,000 for 15 coins: 1,000 ÷ 15 = 66.67 a coin. The average of the two prices was 75.

• Equal amounts buy more coins when the price is low. So the average cost per coin is never above the average price, and is equal only when the price never changes. (Mathematicians know this as the harmonic mean being no larger than the plain one.)
• This is real, but it is not an edge. All at once bought everything at the first price, and in a rising market that is lower still.

4. Why all at once wins on average. Say a coin grows a steady 20% a year. All at once, the money grows the whole year: ×1.200. In 12 monthly buys, the first month's money grows the whole year but the last month's grows only one month. The pot ends at ×1.105.

• If something tends to rise, money put in later spends less time rising.
• That cost is the price of the calmer ride.

5. How much DCA keeps in the coin. With 12 equal buys, the share of the money in the coin climbs from 1/12 to 12/12. Its average is 13 ÷ 24 = 54%.

• So DCA is, on average, about half in and half out.
• That is why its swings are smaller, and why the fair way to judge it is against simply putting half in.

What we tested and found

This section is ours. It repeats the known result on crypto, with coins that died as well as coins that lasted.

We spread the same money over 1, 2 or 4 years, with a new start every Monday, on Bitcoin, Ether and Solana, and on the top-20 coins picked at the start of 2018, 2020 and 2022.

• On the coins that rose, all at once usually ended higher. On Bitcoin, weekly DCA ended at ×1.23 against ×1.40 over 1 year, and ×2.19 against ×3.41 over 4 years. DCA was ahead in only 24% to 43% of starts.
• DCA was calmer. Bitcoin over 1 year: the typical worst fall was 29% with DCA, against 52% all at once.
• The calm was the cash it held back. DCA kept 51% to 60% of its money in the coin on average, close to step 5. Putting half in on day one did about as well: DCA beat it in only 31% to 46% of starts.
• Who won depended on the path. DCA won when the price fell during the buying, and lost when it rose.
• It didn't save dying coins. On the 2022 top-20, most lost money over 4 years whichever way they were bought. DCA lost less: on seven coins that kept falling, it ended with 18% to 29% of the money, against 3% to 9% all at once.