Why average returns differ from actual capital growth

If an account gains 20 percent in one period and loses 20 percent in the next, the arithmetic average of the two returns is zero. That does not mean capital returns to its starting point. The second percentage applies to a different amount. Reading a managed-account record requires separating an average of percentages from the actual capital path.

Two periods without external cash flows

Start with 100, assume no deposits or withdrawals and temporarily exclude costs. A 20 percent gain raises capital to 120. The next period’s 20 percent loss removes 24, leaving 96. The total return is therefore negative 4 percent rather than zero.

This is a hypothetical calculation, not an account result or forecast. Reversing those same two returns does not change the ending value in this no-cash-flow, no-cost model, although the intermediate path differs. Deposits, withdrawals or path-dependent charges can change that conclusion.

Reading chained growth

For consecutive periods, multiply the factors of one plus each return. In the example, 1.2 multiplied by 0.8 equals 0.96. The geometric average for the two equal-length periods is the square root of 0.96 minus one, approximately negative 2.02 percent per period. It answers a different question from the zero arithmetic average.

Do not overlook period length

Comparing monthly, quarterly and yearly figures without specifying duration can mislead. Annualizing a short result introduces a rate-conversion or repetition assumption and must not be presented as an actual full-year outcome. State the start and end dates and the conversion formula beside the reported number.

What changes when money enters or leaves?

With external cash flows during the record, a balance change is not itself trading performance. A measure intended to evaluate a method may differ from a measure of an investor’s actual experience. Ask the report to show cash movements, timing and calculation method separately. One average cannot answer all of these questions.

Consider costs and variability alongside the average

Fees, currency conversion and the timing of deductions can affect net growth. In variable paths, losses change the capital base. Recovering from a 20 percent decline requires a 25 percent gain on the remaining amount. That arithmetic relationship is not a promise that recovery will occur or a prediction of its timing.

A return-claim checklist

• Is the number an arithmetic average, compounded growth rate or total return?
• Are the periods equally long and their dates specified?
• How are costs and external cash flows treated?
• Can the reader see drawdowns and intermediate equity alongside the final value?
• Are annualized figures labeled separately from realized results over a full year?

Enter explicit assumptions in the capital-growth and scenario tools and do not treat the output as an actual account record. When reviewing trading-account histories, ask for return definitions and information limitations.

This is calculation education, not a recommended investment rate. A higher average alone establishes neither liquidity, tolerable risk nor a better outcome for every investor.