compoundsimLump Sum vs Dollar-Cost Averaging: Which Ends Higher?
The same sum invested at once or spread over 1 to 20 years, across 1,000 simulated futures: which ended higher and how deep the paper losses went.
Published
The same sum invested at once or spread over 1 to 20 years, across 1,000 simulated futures: which ended higher and how deep the paper losses went.
Published
In the simulation, if you already have a sum to invest, putting it all in at once ended higher in more futures than spreading it in. When the same amount went into the S&P 500 all at once or in parts over 12, 36 or 60 months, across 1,000 simulated 20-year futures, the lump sum ended ahead in 72%, 79% and 84% of them. Spreading it in, though, kept the paper losses shallower when a crash came soon after the start. It is a trade between growth and how big a fall you can sit through, and each side has its reasons.
Dollar-cost averaging here means taking a sum you already have and investing it in equal parts over a number of months. The setup:
The model moves between a calm regime, where prices move gently, and a wild regime, where they swing hard and fall more often. How it works is explained in how Monte Carlo simulation works for investing.
Here is the money after 20 years, as a multiple of the starting sum. The 10th percentile is the level one path in ten ended below.
10th to 90th percentileMedian
| Money after 20 years (×) | 10th percentile | Median | 90th percentile | Lump sum ended higher |
|---|---|---|---|---|
| All at once | 2.93 | 8.16 | 24.74 | - |
| Over 12 months | 2.90 | 7.87 | 23.70 | 72% |
| Over 36 months | 2.77 | 7.31 | 20.56 | 79% |
| Over 60 months | 2.68 | 6.79 | 18.38 | 84% |
| Monthly for 20 years | 2.04 | 3.98 | 8.66 | 96% |
The lump sum had the highest median and 90th percentile, and the longer the money was spread, the lower they were. The reason is simple: money that goes in earlier spends longer in stocks. The waiting Treasuries grow too, but they grew less than stocks: over the 20 years from 2006, 1.9% a year against 11.1% for the S&P 500.
Who ends ahead is settled while the money is going in. Once the last part is in, both hold the same stocks and rise and fall by the same share. That is why the share of futures where the lump sum ended higher was the same after 5 or 10 years as after 20.
The lump sum was ahead at the 10th percentile too: about level with spreading over 12 months, and further ahead the longer the money was spread. That compares the tenth-worst result of each plan, though, not the same futures. Among the futures where the lump sum ended in its worst tenth, spreading over 60 months ended higher in 44% of them, far more often than across all futures, where the lump sum was ahead in 84% and spreading won in the rest. A lump sum falls behind mainly when stocks grow less than the waiting Treasuries during the years the money is going in, and in futures that start badly, spreading it in tends to pay off more.
Even the lump sum's bad outcomes ended well above the starting sum after 20 years. The S&P 500's own history, by how long it was held, shows the background. The chart shows how widely the annualized total return varied depending on the month you started in, for every start since 1993.
Worst to best10th to 90th percentileMedian
Held for one year, the annualized return ranged from -43.4% to 56.2%, and 18% of the windows lost money. Even over 10 years, 8% of the windows lost money (the worst was -3.4% a year). No window of 12 years or more lost money in this data, and the worst 20 years returned 4.7% a year.
A lump sum spends almost all of the 20 years in stocks. In the past, every window that long ended above where it started. The model shows the same pattern: the lump sum's 10th percentile was 1.06× after 5 years and 2.93× after 20. A few caveats:
In the model, a lump sum held 20 years still ended below the starting sum in 0.7% of the futures. Something that never happened in the data can still happen, rarely, in a model that is not bound to the one order history took. Over a shorter span the picture changes: after 5 years, the lump sum ended below the starting sum in 7% of the futures, and its 10th percentile was about level with the sum spread over 60 months (1.07×), the spread sum slightly ahead.
The same holding-period figures are in the table on the S&P 500 page of the index data.
What spreading buys shows up along the way. We compared how far the whole sum, including the money still waiting, fell below its starting value at any point (the paper loss).
| Deepest paper loss over 20 years | Median | 10th percentile |
|---|---|---|
| All at once | -4.1% | -24% |
| Over 12 months | -2.2% | -21% |
| Over 36 months | -0.9% | -16% |
| Over 60 months | -0.5% | -12% |
| Monthly for 20 years | -0.1% | -1% |
With a lump sum, one path in ten had a paper loss of -24% or deeper at some point. Spread over 60 months, the same level was -12%.
The lump sum is easiest to regret in the futures where a crash comes right after the money goes in. With nothing added or taken out afterwards, a lump sum ends on the same amount whether the crash comes in year 1 or year 10. But selling in fear after a big fall locks the loss in. When the money is spread in, each part buys at a different price, so the timing of a crash matters too: a fall while the money is going in lets the later parts buy cheaper. It is the mechanism described in sequence of returns risk, where the timing of a crash matters while money is taken out, seen from the side of putting money in.
Dollar-cost averaging is often praised for lowering your average cost. Buying the same amount each month buys more units when the price is low and fewer when it is high, so the average cost per unit ends up below the average price over the period. That is true. It does not mean you end up with more than a lump sum.
Take $3,000, invested as $1,000 a month for three months or all at once at the start (made-up prices, to show the arithmetic):
| Price path | Average cost (spread) | Average price | Value in month 3 (spread) | Value in month 3 (lump sum) |
|---|---|---|---|---|
| $100 → $50 → $100 | $75 | about $83.33 | $4,000 | $3,000 |
| $100 → $150 → $200 | about $138.46 | $150 | about $4,333 | $6,000 |
Both times, the average cost is below the average price. Yet when the price rose, the lump sum ended higher. A lower average cost happens either way; which one ends higher depends on whether the price fell or rose while the money was going in. In the period this data covers, stocks rose over the long run, so in the model too the lump sum ended higher in more futures.
This comparison is for money you already have. If you invest from your salary each month, there is no lump sum to put in. Investing each paycheck as it arrives is, in effect, investing each month's money all at once.
In the Monte Carlo simulator you can compare a lump sum ($120,000 in, $0 a month) with $500 a month for 20 years (also $120,000 in total). It cannot spread a sum over the first few years as this article does, and it adds each monthly contribution at the end of the month, so its figures do not match these.
Many tax-advantaged accounts cap how much you can put in each year. With such a cap, a sum larger than the yearly limit cannot go into the account at once and is spread over years whether you choose to or not. The rules differ by country, so check them for the account you use. If the cap lets you put the sum in over about five years, the gap between the 60-month and 240-month rows roughly shows the gap between filling the allowance early and drip-feeding it over 20 years. Which suits you depends on whether you weigh growth or paper losses more. Taxes are covered in what rate of return to assume.