Lump sum vs dollar-cost averaging: the real gap

Lump sum vs dollar-cost averaging is the question of what to do with money you already have: put it all in today, or feed it in over several months. The argument about it is loud. The arithmetic is quieter, and it is worth knowing first. Run your own amount through the lump sum vs monthly calculator as you read.

One thing to separate before starting. Investing part of every paycheck is also called dollar-cost averaging, but that is not a choice between two options — the money did not exist yet. This page is about a sum you are holding now.

What spreading it in costs, if returns are steady

Take $50,000, held for 20 years. Option one invests it all today. Option two invests $4,167 a month for 12 months, with the waiting money earning nothing. Here is what each ends with, if returns average:

• 4% a year: $109,556 all at once, $107,260 spread. A gap of $2,296, or 2.1%.
• 7% a year: $193,484 against $186,557. A gap of $6,927, or 3.7%.
• 10% a year: $336,375 against $319,570. A gap of $16,805, or 5.3%.

Under a steady positive return the lump sum has to win, because more of the money is invested for longer. That result is close to a tautology. What it tells you is the size of the cost, not whether it is worth paying.

The gap is set in the first year, then it just scales

At 7%, the lump sum is 3.7% ahead at the end of year one. After 20 years it is still exactly 3.7% ahead. Once the last instalment goes in, both pots hold the same thing and grow at the same rate, so the percentage gap is frozen. Only the dollar figure grows, because it is a share of a bigger pot.

That means the one lever that matters is how long the money waits. At 7%, over the same 20 years:

• Spread over 3 months: 1.1% behind the lump sum.
• Over 6 months: 2.0% behind.
• Over 12 months: 3.7% behind.
• Over 24 months: 7.2% behind.
• Over 36 months: 10.8% behind.

A longer spread is not a safer version of the same thing. It is a bigger bet that prices will fall while you wait.

What happened in real markets

A steady return cannot show the case where averaging wins, so historical data is the only real test. Vanguard's 2023 paper compared investing at once with splitting the money into three equal monthly parts, using global stock returns (the MSCI World index) from 1976 to 2022 and measuring wealth one year later:

• Investing at once came out ahead 68% of the time, with no interest paid on the waiting cash.
• When the waiting cash earned the three-month Treasury bill rate, investing at once was still ahead 65% of the time.
• Averaging beat leaving the money in cash for the year 69% of the time.
• In the worst outcomes averaging did better. At the 5th percentile, $100,000 in all-stock portfolios became $85,906 with averaging and $82,947 invested at once.

The same paper notes that a longer averaging period costs more, which matches the arithmetic above. History is a record of what happened, not a forecast of what will.

“You buy more when prices are low” — true, but not the point

The case usually made for averaging is that a fixed amount buys more shares when prices are low, so the average cost per share ends up below the average price. That is true. It is also true whichever way the market goes, which is why it cannot be the reason averaging wins. Three hypothetical paths, $3,000 either invested at $100 a share on day one or as $1,000 in each of three months:

• Price dips and recovers ($100, $80, $100): averaging buys 32.5 shares at an average cost of $92.31, worth $3,250. The lump sum's 30 shares are worth $3,000. Averaging wins.
• Price rises ($100, $110, $120): averaging buys 27.4 shares at an average cost of $109.39, below the $110 average price — and they are worth $3,291. The lump sum is worth $3,600. Averaging loses.
• Price keeps falling ($100, $80, $60): averaging is worth $2,350, the lump sum $1,800. Averaging loses less.

In every path the average cost came in below the average price. What decided the result was simply whether prices were higher or lower at the end of the buying period than at the start.

So what does averaging actually buy?

A smaller worst case, and a smaller chance of watching a large sum fall the week after you invest it. Vanguard's paper frames it the same way: lower expected wealth in exchange for less exposure to a bad start. That is insurance, and like most insurance it has an expected cost, which is the gap above. Whether it is worth paying depends on how you would react to a fall, and a plan you stick with can matter more than either figure. That is your call, not a sum.

If the money would otherwise sit in cash for a while, it is also worth seeing what cash itself costs over time — the inflation calculator shows that side.

Not financial advice. Steady-return examples assume uninvested cash earns nothing, no fees, no tax and no dealing costs. The return scenarios and price paths are illustrations, not forecasts. Historical figures are from the Vanguard paper linked above; past performance does not predict future results.