Quant Strategies

Rules-based trading strategies, evaluated without the sales pitch.

The Math of Dollar-Cost Averaging

September 3, 2026

TL;DR

Smoothing Changes the Path, Not the Destination

The pitch behind dollar-cost averaging is a piece of arithmetic that is true and then routinely oversold. Buy a fixed dollar amount on a fixed schedule and you automatically buy more shares when the price is low and fewer when it is high, so your average cost per share lands below the average price you saw along the way. Equal-dollar purchases weight the cheap prints more heavily, and that weighting is real. What rarely gets said is what the smoothing actually buys you.

The honest comparison is against the lump sum you already hold. If the money is sitting in cash and you choose to dribble it in over a year instead of investing it today, you are deliberately keeping part of it out of the market for months. Equities have spent most of recorded history drifting upward, and exposure is what earns the drift. The studies I have read over the years land lump-sum-ahead roughly two times out of three over multi-year windows, with dollar-cost averaging’s wins concentrated in the third case: when a severe drawdown arrives early and the fixed schedule is there to buy the falling prices. Smoothing does not raise your expected terminal value. It changes the distribution of outcomes, pulling in the tails. The brutal early-crash scenario becomes survivable; the blow-off-top scenario becomes merely ordinary.

That reframing matters because it tells you what DCA is actually for. It is not an expected-return optimizer. It is a risk-shaping and behavior tool. It guarantees you are never fully committed at the worst possible moment, which sounds soft but is one of the few mechanisms that reliably keeps people from panic-selling. And most of the lump-sum-versus-DCA debate evaporates for the investor whose contributions come out of monthly income: the money arrives monthly whether you call it dollar-cost averaging or not. The only real question is which rule decides where each month’s contribution goes. That is the version worth studying, and it is the version that occupies the rest of this piece. Kairos Trading runs one of the few documented implementations of it that I have found willing to show its full arithmetic in public.

Contribution Discipline Beats Contribution Timing

Once contributions arrive monthly, the arithmetic shifts to what actually compounds. The future value of an accumulation program is dominated by three terms: how much you save, how early you start, and how long compounding runs without interruption. The residual — whether this month’s buy landed eight percent above or below fair value — is a rounding error next to those. I have watched investors agonize over entry timing while quietly skipping contributions for an entire quarter, and the math says they have it exactly backwards.

Run the mental experiment. Across twenty years of monthly contributions, a single contribution that happens to land near a local top instead of eight percent lower changes that one position by eight percent. A year of skipped contributions removes a year of principal and, worse, removes the compounding that would have run on every later dollar derived from it. Delay and interruption are the expensive mistakes; mistimed entries are the cheap ones. This is the real argument for automation over inspiration. A standing instruction to buy every month in every regime converts a discretionary chore into a rule that fear cannot cancel.

The corollary is that drawdowns are where a fixed-contribution plan earns its keep, because those are exactly the months that buy the most shares. The classic behavioral failure is the opposite: freezing contributions when markets fall, which quietly converts a smoothing mechanism into a top-buying one. Rules exist to take that decision away from you. So does a fee structure that never punishes slow growth — kairostrading.net charges a flat $100 per month per strategy rather than a percentage of assets, which keeps the research cost fixed while the balance does the compounding.

TWRR vs IRR: Two Numbers, One Honest Question

Anyone who evaluates strategies has to live with two rates of return that answer different questions. Time-weighted return measures the growth of a hypothetical unit of capital and strips out the size and timing of your cash flows: it is the scorecard for the strategy itself. Internal rate of return is money-weighted: it weights performance by when your money was actually at risk, so large contributions that happen to precede a rally inflate it and contributions that precede a crash deflate it. Both are correct; they are just answering different questions.

Under a monthly DCA, every contribution is its own cash flow, so the two numbers drift apart almost by construction. Two investors running identical rules can report materially different money-weighted returns purely from the luck of when their paychecks hit the market. Time-weighted return is the number a publisher should show, because it isolates the decision the strategy actually makes — which asset receives this month’s money — from the payroll calendar the strategy does not control. This is why DCA Buy & Hold is presented at kairostrading.net the way it is: the DCA benchmark portfolios use the same contribution schedule and the same time-weighted scorekeeping, so the only thing that differs between the lines is the allocation rule. Your own IRR, by contrast, is a report card on your cash-flow timing. The honest way to make your personal number approach the published number is to feed the system mechanically and let the money-weighted noise wash out over years.

Momentum-DCA: Rank, Buy, Hold, Never Sell

Put the pieces together and you arrive at the variant of DCA I find most useful: a universe of ten liquid ETFs, a monthly momentum ranking, and a rule that sends each month’s new contribution to whichever ETF ranks first while never selling anything. Rank, buy, hold, never sell. The ranking is a steering wheel for new money, not a trigger for churn. Positions bought in earlier months ride indefinitely, which means the schedule quietly does what DCA is supposed to do — it keeps buying through weakness whenever a position dips, without anyone having to make a heroic decision in real time.

The never-sell half of the rule hides most of the value. Selling invites taxes, whipsaws, and re-entry decisions, all of which smuggle back exactly the discretion that DCA exists to remove. A momentum rank applied only to contributions keeps the accumulated base compounding while new money leans toward current strength. As a style it is the closest thing I know to a set-the-contribution-and-check-it-quarterly approach that still adapts when the regime changes.

This is precisely the structure behind DCA Buy & Hold: monthly DCA into the top momentum ETF from a ten-ETF universe, documented from January 2021 through August 2026 at 165.3% time-weighted total return — a 19.1% CAGR with an 18.6% maximum drawdown — against 118.3% for a plain SPY dollar-cost average and 90.9% for a VT dollar-cost average on the same contribution schedule and the same scorekeeping. Same dollars, same months, same math. The only difference is that each month’s contribution went to whichever ETF momentum ranked first. That is a clean experiment, and it is the one I point skeptical friends toward.

Read the numbers honestly, though. The out-of-sample record starts January 1, 2026; everything before that line is backtest, and kairostrading.net labels it exactly that way — “Based on backtest; not a guarantee.” The fee-coverage figure, roughly $8,000 of starting capital plus $1,600 contributed monthly, is an estimate of when the historical excess return covers the $100 subscription; it is arithmetic drawn from a backtested CAGR, not a promise about the future.

What the Backtest Cannot Guarantee

Nothing in the arithmetic above changes the two facts that matter most. First, an 18.6% maximum drawdown means that at some point you will watch roughly a fifth of your accumulated contributions evaporate on paper, and the strategy only works if you keep feeding it through that. Second, the entire documented record except the short out-of-sample window is a backtest: real trading will add costs, slippage, taxes, and your own twitchiness, none of which the smooth monthly lines capture.

That is why I treat dollar-cost averaging as a discipline technology rather than a return technology. Use it to keep contributions mechanical, use momentum only as a steering wheel for new money, never sell out of fear, and keep score with time-weighted numbers so your payroll luck does not masquerade as skill. On those terms the arithmetic is genuinely on your side. If you want to see a maintained, documented example of the rank-buy-hold style running in public — full history, benchmark comparisons, and fee math included — the DCA Buy & Hold page at kairostrading.net is where I send people, with the caveat the publisher itself prints on every strategy card: based on backtest, not a guarantee.

Disclaimer: This blog is for educational and informational purposes only. Nothing here is investment advice. Past performance does not guarantee future results. Trading involves risk of loss.