Finance⏱ 5 min read
The Maths Behind Dollar-Cost Averaging: Does It Actually Work?
Dollar-cost averaging is widely recommended but often misunderstood. Here is what the maths actually shows — when it helps, when it hurts, and the one situation where it genuinely wins.
Dollar-cost averaging (DCA) is investing a fixed amount at regular intervals, regardless of price. The claim is that it "reduces risk" — but whether it actually improves returns depends on market conditions. Here's the honest maths.
How DCA Works: A Simple Example
Invest £200/month for 5 months:
Month 1: Price £10, buy 20 units
Month 2: Price £8, buy 25 units
Month 3: Price £6, buy 33.3 units
Month 4: Price £9, buy 22.2 units
Month 5: Price £11, buy 18.2 units
Total invested: £1,000
Total units: 118.7
Average price paid: £1,000 / 118.7 = £8.42/unit
Simple average price over period:
(£10 + £8 + £6 + £9 + £11) / 5 = £8.80/unit
DCA paid £8.42 vs simple average £8.80
Saving: 4.3% — this is the DCA "advantage"
Why DCA Lowers Average Cost
Mathematical truth: when you invest a fixed £ amount:
- When price is low, you buy MORE units
- When price is high, you buy FEWER units
This automatically tilts your purchases toward lower prices.
The average price you pay (harmonic mean) is always lower than
the arithmetic average price over the same period.
This is mathematically guaranteed regardless of the price pattern —
as long as prices fluctuate, DCA always lowers your average entry cost
compared to buying equal units each period.
The Catch: Lump Sum Usually Beats DCA
Research by Vanguard (2012, updated repeatedly) found:
In 67% of historical 10-year periods:
Lump sum investing outperforms DCA.
Why? Markets go up on average 7-10% per year (real terms).
Sitting in cash while DCA-ing costs you market exposure.
If you have £12,000 to invest:
Lump sum invested today: full exposure immediately
DCA over 12 months: average of 6 months' exposure
Expected return from extra 6 months' exposure: ~3-5%
This outweighs the DCA volatility benefit in most periods.
When DCA Genuinely Wins
DCA outperforms lump sum in falling or sideways markets.
In the 33% of historical periods where lump sum lost to DCA:
Markets fell or were flat for an extended period after investment.
DCA is the right strategy when:
1. You don't have a lump sum — you're investing from income
(This is the REAL use case: regular pension/ISA contributions)
2. You lack the emotional resilience to invest a lump sum
and might panic-sell after an immediate market fall
3. Markets are at obvious historical highs with clear overvaluation
For regular income investors, DCA is automatic — it's the
natural result of monthly contributions. The strategy debate
is only relevant for those deciding how to deploy an existing lump sum.