Average return versus compound growth: reconcile the equity curve

Use returns on a consistent capital base

For n equally defined periods, arithmetic mean return is Σr_i / n. With no external cash flows, compounded growth is Π(1 + r_i) − 1. The geometric average per period is the product raised to 1/n, minus one, when the positive wealth factors make that expression meaningful.

Trade-level R multiples are not automatically account returns. A +2R trade with a 0.5% account-risk allocation differs from +2R with a 2% allocation. Concurrent positions and unused cash also change the mapping. Build the account curve from the actual capital and P&L convention before interpreting its average.

Separate final wealth from path risk

For fixed percentage returns applied to the full account with no cash flows, rearranging the same factors leaves their final product unchanged. It can still change drawdown and the experience of holding the strategy. If sizing, cash flows or stop policies depend on the path, changing order can also change the realized returns themselves.

Volatility drag describes the difference between arithmetic and compound growth under a specified return process. It is not an extra brokerage fee to subtract again. Costs should already be included in each net return; adding a separate drag deduction to the exact compounded product would double-count the effect.

Worked example: two zero-average sequences, different wealth

Start with a hypothetical 10,000-USDT account. Sequence A earns +20% and then −20%, so its arithmetic mean is 0%. Equity goes to 12,000 and then 9,600, producing −4% total growth. Sequence B earns +5% and then −5%, also averaging 0%, but ends at 9,975, or −0.25%.

The geometric period averages are √0.96 − 1 ≈ −2.0204% and √0.9975 − 1 ≈ −0.1251%. The different final balances arise directly from multiplying the factors. These are constructed net-return sequences; no inference about a particular strategy’s future volatility follows.

Do not multiply the average into a return promise

An observed 1% mean trade return multiplied by 100 trades is not a guaranteed 100% account gain. Returns may overlap, use different capital, incur changing costs or be selected from a favorable period. Even a correctly compounded historical curve remains a sample rather than a forecast.