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Dollar-cost averaging vs lump sum
You have a sum to invest. Put it all in now, or spread it over months? Model both against the same market path and see the gap.
Given a known market path, this is simple arithmetic and the answer is exact. But you do not know the path. Historically, lump-sum investing has beaten averaging roughly two thirds of the time, for the plain reason that markets rise more often than they fall — and averaging wins in the third of cases where they do not. The value of spreading purchases is that it caps the regret if you happen to buy the top, which is a behavioural benefit, not a mathematical one. That can still be the right reason to choose it.
How this is calculated
- The lump sum is invested at month zero and compounds at the "during the spread" rate for the spread period, then at the "afterwards" rate for the remainder.
- The averaged path holds the uninvested balance at the cash yield, moving one instalment into the market at the end of each month.
- The break-even figure is the return during the spread at which the two strategies finish level, solved numerically.
- Both paths use the same rates after the spread ends, so the horizon length affects the absolute figures but not which strategy wins.
- Taxes, transaction costs and bid-ask spreads are not modelled.
Common questions
Is lump sum or dollar-cost averaging better?
On average, investing a lump sum immediately has historically produced higher ending balances roughly two thirds of the time, because markets rise more often than they fall and time in the market compounds. Dollar-cost averaging wins in the minority of periods where the market falls after you would have invested, and it reduces the worst-case outcome.
Why would anyone choose to average in, then?
Because the expected-value argument assumes you will hold through a decline without selling. If spreading purchases is what lets you actually invest the money and stay invested, the behavioural benefit can outweigh the arithmetic cost. A plan you follow beats a better plan you abandon.
Does the cash yield change the answer?
It narrows the gap. When cash pays 4% or 5%, the uninvested portion is not idle, so averaging costs less than it did in a zero-rate environment. Set the cash yield to zero to see the difference.
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