Two formulas for different questions
For equal-length periods, the arithmetic mean is the sum of returns divided by their count. The geometric mean is the nth root of the product of (1 + r), minus one. Convert percentages to decimals first: 30% becomes 0.30 and its growth factor is 1.30.
Each return acts on capital already changed by the previous period. Adding percentages cannot reproduce that compounding. With identical period returns the two means coincide. With varying returns the geometric mean does not exceed the arithmetic mean.
Worked example: +30%, then −20%
Start with 10,000 fictional units. A 30% gain produces 13,000. The following 20% loss applies to 13,000, leaving 10,400. The cumulative gain is 4%, while the arithmetic mean is (30 − 20) / 2 = 5% per period.
The geometric mean is √(1.30 × 0.80) − 1, approximately 1.98% per period. Two consecutive gains of about 1.98% reproduce 10,400. Compounding the arithmetic 5% twice would instead produce 11,025, which is not the observed result.
Period length and external cash flows
If the periods are years, 1.98% is an annual compound rate. If they are months, it is a monthly rate. Any annualization is a separate operation; a short sample does not establish a reliable long-term annual return.
A beginning-to-ending-value calculation assumes no external contributions or withdrawals. Cash flows require linked valuations or another explicitly chosen measurement method. Keep expenses, distributions and currency conventions consistent. Neither historical average guarantees future growth.
A repeatable chart exercise
In Student Wyckoff Pro, choose one available instrument and consecutive equal periods using closed bars. Record each starting and ending value, calculate the returns separately, and multiply their growth factors. Compare that product with the overall price change.
Save the workspace and identify the result as price return unless distributions are accounted for separately. The platform supports observation; this exercise’s average-return arithmetic is performed outside the chart. When results disagree, check dates, currency and cash flows first.
Primary sources
Sources explain the mechanics and limitations; the editorial examples use invented numbers rather than market quotations.
Your next practical step
Use consistent periods on your chart and verify the ending value by compounding the observed changes.
Open the first-chart instructions ↗