What Are AHPR and GHPR? Formulas and the Gap

AHPR and GHPR are the average return of a single trade, expressed as a percentage of the capital standing before that trade: AHPR takes the arithmetic mean of those returns, GHPR the geometric one. They measure the same trades, answer different questions, and the distance between them reads how volatile the results were.

How it works

Each closed trade gets a holding period return, its net result over the capital behind it:

HPRᵢ = (profit + swap + commission)ᵢ / Capital before trade i

AHPR = ( Σ HPRᵢ / N ) × 100
GHPR = ( [ Π (1 + HPRᵢ) ] ^ (1/N) − 1 ) × 100

Costs sit inside the numerator: commission and swap are folded into every trade before it becomes an HPR, so both figures are net.

One detail about the base matters. Our implementation seeds the running capital with the account's total lifetime deposits, then rolls it forward by each trade's net result. On an account funded in instalments, early trades are measured against money that had not arrived yet, which drags both figures toward zero; on a single-deposit account the base behaves exactly as the formula reads.

GHPR is never above AHPR. That is arithmetic, not a property of trading: the geometric mean of positive numbers is at most the arithmetic mean, equal only when every number is identical. The shortfall is approximately half the variance of the returns:

GHPR ≈ AHPR − σ² / 2

Two trades make the point. A +50% followed by a −50% gives an AHPR of exactly 0%, while the account sits at 0.75 of where it started. GHPR is √(1.50 × 0.50) − 1 = −13.4%, which compounded twice lands precisely on that 0.75. The arithmetic mean describes a result nobody received; the geometric one reproduces the balance.

Why it matters

You cannot spend an arithmetic mean. Only the geometric figure, raised to the number of trades, returns what the account actually did, which makes GHPR the number to quote and AHPR its yardstick. A wide gap between them is the volatility tax: what variance removes from compounding before it reaches the balance.

The asymmetry gets brutal at the tail. A single trade that removes the entire capital sets one factor in the product to zero, and a product with a zero in it is zero: GHPR reads −100% however good the preceding thousand trades were. That is the argument for position sizing over win rate, restated as multiplication: a method with a healthy AHPR and enough standard deviation to occasionally risk everything still has a negative geometric expectation.

AHPR is not decoration: it is per-trade expectancy restated as a percentage of capital rather than in pips or currency, which makes it comparable across account sizes. Read as a pair, the two say what the average trade earned and what was left of it after variance.

What the data shows

The figures below describe accounts published on ShowMyTrades, not traders in general. The median published account has 171 closed trades and a median time-weighted return of +3.2%. Spread that return evenly across that many trades and the geometric return per trade comes to about +0.018%, which the panel would round to +0.02%. That is an illustration, not a measured median, but it is the honest scale of these numbers and why they look underwhelming on almost every real account.

The same population has a median profit factor of 1.28, net of swap and commission, and a median win rate of 68.8%. A page can therefore carry a strong-looking win rate beside a GHPR barely off zero without contradiction. What matters is the sign, the gap to AHPR, and how many trades produced them.

Where you see it on ShowMyTrades

Both sit in the Advanced Statistics module on every published account page, labelled AHPR and GHPR, at the foot of the Performance Metrics column below Profit Factor, Standard Deviation, Sharpe Ratio, Z-Score (Probability) and Expectancy. Each prints as a signed percentage to two decimals, green at or above zero, red below.

The module has four views — Table, Weekday, Hourly and Duration. AHPR and GHPR live on the Table view; the other three show which trades produced the variance separating them. Both values are computed by our statistics service when the account syncs, not in your browser.

Common misunderstandings

• "AHPR is the average, so it is the honest one." It is an average nobody earns. Whenever results vary it overstates compounded growth, by roughly half the variance.
• "They are monthly or annual returns." They are per trade. The same +0.02% means very different things at 20 trades and at 2,000, so read them next to Total Trades in the Trades column of the same module.
• "A GHPR near zero means the system does not work." At normal per-trade risk both numbers are small and the panel rounds to two decimals. An account showing +0.02% per trade over several hundred trades is up double digits.
• "A positive AHPR with a negative GHPR is a bug." It is the signature of large swings: returns can average above zero and still compound downward, which is the most useful thing this pair tells you.

For how per-trade figures fit into a record you intend to show other people, see tracking trading performance.

Related terms