"Average return is positive but the account loses money" is not a glitch in your account. It happens because the "average" you see and the "compounding" your account actually experiences are two different calculation methods. The arithmetic mean simply adds up each period's return and divides by the number of periods. It assumes that each period starts with the same principal and that returns do not carry over to the next period. But your account balance rolls forward continuously: money earned this period becomes principal for the next period, and money lost this period shrinks the base for the next period. Once returns have volatility, the geometric mean (compound return) will be lower than the arithmetic mean, and the gap depends on how large the volatility is. If the "positive average" you see is an arithmetic mean, it describes a parallel world that your account never actually lived through.
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A reproducible example: up 50%, down 50%, arithmetic says 0, account loses 25%
Suppose you invest 100. In the first year it rises 50%, so the account becomes 150. In the second year it falls 50%, so the account becomes 75. The arithmetic mean of the two periods is (50% − 50%) ÷ 2 = 0%, which looks like "no gain, no loss." But your account went from 100 to 75, an actual loss of 25%.
The geometric mean works differently: you need to find the fixed annual growth rate r such that 100 × (1+r) × (1+r) = 75. Solving gives r ≈ −13.4%. This negative compound return is the annualized growth rate your account truly experienced.
In this example, the arithmetic mean of 0% is right at the boundary of "positive," yet the account clearly loses money. If the two-period returns are +60% and −50%, the arithmetic mean becomes +5%, which looks profitable, but the account goes from 100 to 80, still losing 20%. The more "attractive" the arithmetic mean looks, the more it often indicates large volatility, and volatility erodes compounding more heavily.
Where the gap comes from: volatility drag
The difference between the arithmetic mean and the geometric mean is called "volatility drag" in quantitative finance. A commonly used approximation is: geometric mean ≈ arithmetic mean − variance ÷ 2.
This approximation shows three things. First, as long as returns have volatility (variance greater than 0), the geometric mean must be lower than the arithmetic mean. Second, the larger the volatility, the larger the gap. Third, the arithmetic mean itself is not "wrong" — it has its own uses in some mathematical modeling scenarios — but it cannot be used to predict the final value of your account. Your account's final value is determined by the geometric mean, not the arithmetic mean.
Crypto assets typically have annualized volatility of 50%–80% or even higher. Using 60% volatility as a rough estimate, the volatility drag is about (0.6)² ÷ 2 = 18%. That means a strategy showing +10% in arithmetic mean terms could be around −8% in compounding terms. Of course, this is only a hypothetical example, and the actual number depends on the specific return sequence, but it explains why a strategy with a "positive average return" can still lose money in a real account.
Fees and slippage widen the gap further
The examples above have not yet included trading costs. Every buy and sell generates fees, and market orders may also incur slippage. These costs occur on every trade, and they also erode returns in a multiplicative way rather than an additive way.
For example (the following is a hypothetical calculation), suppose your total cost per trade is 0.2% (0.1% to buy + 0.1% to sell), and you trade 50 times. If each trade uses roughly the same principal, the total cost is about 50 × 0.2% = 10% of principal. But this 10% is not simply subtracted from the "average return." It is deducted from the principal of each period, then amplified by compounding, so the erosion of final value can exceed 10%. High-frequency traders especially need to pay attention to this: a strategy whose arithmetic mean looks good may turn negative in geometric terms once round-trip costs are included.
Which number should you look at
If you want to know whether your account actually made or lost money, looking only at the "average return" shown by a broker or data platform is not enough. You need to confirm which calculation method is being used, and prioritize the geometric mean (annualized compound return).
A practical verification method is: open your account's equity curve, record the starting net value and current net value, and calculate (current net value ÷ starting net value)^(1/number of years) − 1. That result is your geometric annualized return, which already includes the actual impact of all volatility and costs. If this number is negative, then no matter how good some "average return" indicator looks, your account is losing money.
For strategy evaluation, the arithmetic mean still has reference value, but it answers a different question: "If you invest the same amount of new money each period and do not roll over the returns, how much can you earn on average per period?" If your actual approach is to hold and compound, the answer to that question has nothing to do with your account's fate. Mixing up the two measures is exactly what creates the confusion of "positive average, negative account."
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References
- Rongtong Fund · Annualized Return, 2026-11-01
- Ivo Welch · Corporate Finance (4th ed.) - Chapter on Performance Measures, 2026-11-01
- Graham Capital · Terminal Wealth Under Leverage, 2026-11-01
- Blockcircle · Shannon's Demon and the Rebalancing Bonus in Crypto Portfolios, 2026-11-01
- BingX · How to Decode Trading Fees and Slippage on BingX Spot Market, 2026-11-01
- Aptus Capital Advisors · Leveraged ETFs: The Hidden Costs of Volatility Drag, 2026-11-01
- Sohu · How Portfolio Rebalancing Creates Returns "Out of Thin Air", 2026-11-01
