Answer and evidence
Why do fixed-capital returns and drawdowns differ from compounded results?
Short answer. Compounded and fixed-capital drawdowns use different denominators: a fall from 1.50 to 1.05 of starting capital is a −45.0% fixed-capital drawdown but a −30.0% compounded drawdown from peak equity. Supporting analysis →
- Evidence type
- Evidence review; a review or worked illustration, not a new causal experiment.
- Sample and scope
- 2024-11-01 – 2026-10-31. Bitcoin monthly benchmark (November 2024 – October 2026, N = 24 months) under fixed-capital addition vs compounded buy-and-hold. Published measurements and sample counts.
- Limits of this answer
- Methodological comparison using the 24-month month-end Bitcoin benchmark. Month-end series omit intra-month drawdowns, funding payments, taxes and account-level margin constraints.
Key findings
- Over the 24-month Bitcoin benchmark sample (November 2024–October 2026), arithmetic fixed-capital monthly returns summed to +29.97%, whereas compounded buy-and-hold returned +10.24% due to volatility drag. Evidence →
- Fixed-capital accounting measures each month’s closed-trade profit or loss against constant starting capital (profits withdrawn, losses topped up), preventing a single early rally from inflating the weight of later months. Evidence →
Research reviewed 2026-11-04; page presentation updated 2026-11-04. These findings describe the studied market or measurement method, not any individual strategy’s rules.
Published evidence
| Accounting method | Period return formula | 24M BTC return (%) | Max month-end drawdown (%) | Drawdown denominator |
|---|---|---|---|---|
| Fixed capital (non-compounded) | Sum of monthly returns: Σ r_t | +29.97 | −60.84 | Initial fixed capital (1.00) |
| Compounded (buy and hold) | Product of monthly links: Π (1 + r_t) − 1 | +10.24 | −49.35 | Running peak equity |
Why fixed-capital and compounded numbers diverge
A strategy that trades a fixed dollar notional each month and withdraws profits (or tops up losses) earns the arithmetic sum of its monthly percentage returns. A buy-and-hold position that leaves all gains and losses invested earns the geometric product. Whenever returns fluctuate, the compounded return is lower than the arithmetic sum by approximately half the variance per period (volatility drag).
Across the 24-month Bitcoin benchmark from November 2024 through October 2026, the 24 monthly returns sum to +29.97%, while compounding those exact same 24 monthly returns yields +10.24%. Alternating +20% and −20% months sum to 0.0% on fixed capital, but lose 4.0% per two-month pair when compounded.
Why capacity-constrained strategies report on fixed capital
Compounding assumes a strategy can scale its position size proportionally as equity grows without moving market prices or exhausting order-book depth. Many systematic crypto strategies operate in thin liquidity where position sizes must remain capped.
Reporting on fixed capital treats every month with equal weight. Under compounding, a large gain in year one multiplies the dollar size of year two, making recent performance dominate the dollar curve and obscuring whether the underlying edge remained stable across time.
How drawdown definitions differ between the two methods
On fixed capital, cumulative equity is 1 + Σ r_t, and drawdown is the fall from the highest prior cumulative peak measured in units of initial capital. Under compounding, drawdown is (equity / running peak) − 1, measured as a percentage of the higher peak.
When cumulative equity has risen above starting capital, a fixed-capital drawdown expressed in initial-capital units can appear larger in percentage points than the relative compounded drawdown, as shown in the 24-month Bitcoin comparison (−60.84% of starting capital versus −49.35% of peak equity).
Why shouldn’t fixed-capital returns be compounded by readers?
Compounding a published fixed-capital series after the fact assumes that larger orders would have received identical execution prices and that no intra-month margin limits would have been breached. If a strategy’s live sizing is fixed, arithmetic addition reflects how it is actually run.
What is volatility drag in crypto returns?
Volatility drag is the gap between arithmetic average returns and compounded geometric returns caused by variance. A 50% loss requires a 100% gain to break even when compounded, but only a +50% gain on constant starting capital.
Limitations
Methodological comparison using the 24-month month-end Bitcoin benchmark. Month-end series omit intra-month drawdowns, funding payments, taxes and account-level margin constraints.