Capital Efficiency
This is the sales pitch for Orbital AMM, formalized. We'll derive the efficiency multiplier and show why concentrated liquidity is essential for stablecoin trading.
The Efficiency Formula
Capital efficiency is defined as:
where:
- q = r(1 − 1/√n) is the equal-price point reserve
- x_min is the virtual reserve at the depeg threshold
Intuitively: efficiency measures how much more capital is deployed at the current price compared to a uniform liquidity pool.
Derivation
In a uniform pool (like Curve), liquidity is spread across all possible prices. Most of this liquidity is never used — it's "out of the money" at the current price.
In Orbital, LPs can concentrate liquidity within a specific price range. The capital that would have been "wasted" on unused price ranges is now deployed where trades actually happen.
The ratio q / (q − x_min) captures this:
- q represents the "active" capital at the current price
- x_min represents the capital at the edge of the price range
- The denominator is the "wasted" capital in a uniform pool
Numerical Example
For n = 5 tokens at a 0.99 depeg threshold:
x_min ≈ 0.549r (computed from the virtual reserve formula)
efficiency = 0.553r / (0.553r − 0.549r) ≈ 150×
This means Orbital provides 150× more liquidity at the current price than Curve would with the same capital.
Efficiency at Different Depeg Thresholds
| Depeg Threshold | Efficiency (n=5) |
|---|---|
| 0.90 | ~15× |
| 0.95 | ~30× |
| 0.99 | ~150× |
| 0.995 | ~300× |
| 0.999 | ~1500× |
Tighter ticks (higher depeg thresholds) mean more efficiency but narrower price coverage. The choice depends on how stable you expect the tokens to be.
The Tradeoff
Concentrated liquidity is a bet on price stability. If a token depegs beyond your tick range, your liquidity becomes inactive — you're no longer earning fees, and you're holding only the depegged token.
This is the same tradeoff as Uniswap V3: higher returns in exchange for active management. Orbital just generalizes it to n tokens.
Comparison to Curve
Curve's stableswap invariant provides about 1-2× capital efficiency for stablecoins (depending on the specific implementation). Orbital's 150× is two orders of magnitude better.
The difference: Curve's liquidity is uniform across all price ratios. Orbital's is concentrated where stablecoins actually trade.
Real-world impact: For a $10M liquidity pool, Orbital provides the same effective liquidity as a $1.5B Curve pool. This is why concentrated liquidity is essential for efficient stablecoin trading.