Compounding reality check for monthly return claims
“Steady 5% a month” sounds modest. It is phrased to sound modest — a single digit, a short period, nothing like the triple-digit figures that trip alarm bells. Run it through compounding and it becomes a claim of close to 80% a year, every year, indefinitely. That gap between how a monthly claim sounds and what it asserts is the most useful filter a non-specialist has.
This page is about the arithmetic of claims. None of the rates below are presented as achievable, and nothing here suggests any return is. They are what the claims themselves say, once multiplied out.
A monthly rate is an annual claim in disguise
Compounding a monthly rate r for n months gives (1 + r)ⁿ. The
compounding calculator does this for any
inputs; here is what common claims assert, as multiples of the starting balance:
| Claimed rate | Implied per year | After 3 years | After 5 years | After 10 years |
|---|---|---|---|---|
| 2% a month | +26.8% | 2.0× | 3.3× | 11× |
| 5% a month | +79.6% | 5.8× | 18.7× | 349× |
| 10% a month | +213.8% | 30.9× | 304.5× | about 92,700× |
| 20% a month | +791.6% | 709× | about 56,000× | over 3 billion× |
Daily claims are worse. “1% a day” compounds to about 12× over 252 trading days and about 38× over 365 calendar days.
The last column is the reductio. For any account large enough to matter, a strategy that really compounded at 10% a month for a decade would end up needing to be a material fraction of the market it trades. The rate cannot be both constant and real, because the strategy would run out of market before it ran out of months.
So the first check costs nothing: convert the claim to an annual figure and a multi-year multiple, and ask whether anyone with that record would be selling it.
Returns do not scale with size
Compounding assumes the same rate applies to a balance of any size. Trading does not work that way.
- Market impact grows with size. Orders that fill cleanly at a small size walk the book at a larger one, and the cost comes straight out of the rate — see spread, depth and what liquidity actually costs you.
- Opportunities are finite. An edge that exists in a thin instrument or a short window has a capacity. Beyond it, extra capital earns nothing extra.
- Slippage concentrates where it hurts. On stop-outs, in fast markets, in exactly the conditions a larger position struggles to exit — slippage explained.
A small account showing a high monthly rate is not evidence that the rate survives a hundredfold increase in size. The compounding table silently assumes that it does.
Smooth numbers imply no volatility, and volatility drags
A claim of “5% every month” is also a claim that the monthly returns barely vary. Real returns vary, and variation lowers what compounds.
The same arithmetic average produces very different results depending on the swings around it. Five illustrative sequences, each alternating two monthly returns that average +5%:
| Alternating monthly returns | Arithmetic average | Compounded per month | After 12 months |
|---|---|---|---|
| +5%, +5% | +5% | +5.00% | 1.80× |
| +15%, −5% | +5% | +4.52% | 1.70× |
| +25%, −15% | +5% | +3.08% | 1.44× |
| +35%, −25% | +5% | +0.62% | 1.08× |
| +45%, −35% | +5% | −2.92% | 0.70× |
The last row averages +5% a month and loses 30% over the year. A loss of 35% needs a gain of about 54% to recover, and +45% is not enough — the drawdown recovery table shows the asymmetry in full.
A rough rule: compounded return ≈ arithmetic average − variance ÷ 2. The bigger the swings, the more the average overstates what you keep. This is volatility drag, and it is why an arithmetic average is the flattering way to report a volatile record.
When a claim gives an “average monthly return”, ask whether it is arithmetic or compounded. If they will not say, assume arithmetic, and assume the true compounded figure is lower by an amount that depends on swings you have not been shown.
Costs compound too
Fees, funding and slippage are charged per trade, so for an active strategy they are a steady per-period drag — and a drag compounds exactly as a return does, in the other direction.
As an example, a strategy whose costs come to 1% of the balance each month loses about 11.4% of the balance to costs over a year before any return is counted. At 0.5% a month it is about 5.8%; at 2% a month, about 21.5%. The trading fee calculator gives the per-trade figure for your own rates, and fee drag over a year works through turnover.
A claim quoted gross of costs is a claim about something no account experiences. A claim quoted “net of fees” frequently still excludes funding and slippage.
Short records compound noise
A few good months, annualised, produce spectacular numbers. That is arithmetic, not evidence. Three months at a high rate is consistent with luck, a single favourable market regime, or a strategy selected after the fact from several that were tried.
The longer the claim’s implied compounding horizon, the more months of record it needs to be taken seriously — and the less likely it is to have them. The evaluation problem is the same one covered in how many trades before you can judge a strategy: a small sample cannot distinguish a genuine edge from a run of luck, and compounding the sample’s average amplifies whichever one it happened to be.
Using the arithmetic as a filter
Every one of these questions can be answered without evaluating the strategy itself:
- What does the rate imply per year and over five years? If the multiple is implausible, the claim is too.
- Arithmetic or compounded average? And what was the worst month?
- What was the maximum drawdown, and what recovery did it require?
- How long is the record, and was it live? Backtests of language models are especially weak — see how to evaluate an AI trading claim.
- At what account size? Does the claimed rate plausibly survive more capital?
- Net of which costs? Fees, funding and slippage, or fees alone?
A claim that cannot answer these is not information. A claim that answers them honestly will rarely look like a smooth monthly percentage.
What this means in practice
- Treat a constant-rate projection as a picture of the curve’s shape, never as a forecast. The calculator’s own notes say the same.
- Read your own results compounded, not averaged. If you report your trading to yourself as an average monthly return, you are flattering it by the variance.
- Guard the downside first. Because losses compound as surely as gains, a cap on the size of bad periods can do more for the compounded outcome than an improvement in the average — the reasoning behind a daily loss limit and behind sequence of returns risk.
FAQ
What does 5% a month compound to in a year?
About 79.6%, because each month’s return is earned on the balance including previous gains: 1.05 multiplied by itself twelve times is roughly 1.796. Over ten years the same rate implies a multiple of about 349 times the starting balance, which is why steady monthly claims deserve scrutiny rather than acceptance.
Why are monthly return claims often misleading?
A monthly figure sounds small but compounds into very large annual and multi-year multiples. Such claims usually also imply low volatility, ignore costs that compound against the account, and rest on short records. An arithmetic average monthly return also overstates what the account actually compounded, by an amount that grows with the size of the swings.
What is the difference between arithmetic and compounded average return?
The arithmetic average adds the period returns and divides by the number of periods; the compounded average is the constant rate that would produce the same ending balance. They are equal only when returns never vary. With alternating months of +45% and −35%, the arithmetic average is +5% a month while the account loses about 30% over a year.
Can a trading account compound at a constant rate?
No real account does. Returns vary from period to period, costs are charged on activity, and market impact grows as the balance grows, so both the rate and its consistency degrade with size. A constant-rate projection is useful for seeing the shape of compounding, not for forecasting an account.