Break-Even
Break-Even primitives answer “when am I made whole?” — find the price at which fees offset IL, or the holding period at which fee income compensates current IL drag.
V2/V3 only in v2.0. The closed-form upside/downside α framing maps cleanly to constant-product math but requires fresh derivation for weighted and amplified pools.
Primitives in this category
Section titled “Primitives in this category”FindBreakEvenPrice— closed-form upside and downside α at which accumulated fees exactly offset IL.FindBreakEvenTime— linear projection of how long until current fees catch up to current IL drag.
Protocol coverage
Section titled “Protocol coverage”| Protocol | Coverage | Notes |
|---|---|---|
| Uniswap V2 | Full | FindBreakEvenPrice, FindBreakEvenTime. |
| Uniswap V3 | Full | Both primitives, full-range and concentrated-range (range-scale factor k = √r/(√r-1)). |
| Balancer | Deferred (v2.1) | Weighted-pool IL α^w + (1-w)·α^(w-1) - 1 doesn’t have a general closed-form inverse; Newton iteration converges cleanly but the symmetric upside/downside-α framing needs work. |
| Stableswap | Deferred (v2.1) | Fresh derivation needed over the invariant; mirrors AssessDepegRisk’s ε ↔ δ fixed-point but inverted. |
MCP tool exposure
Section titled “MCP tool exposure”Neither primitive is in the curated v2.0 set. Break-even questions are downstream of position-analysis — agents typically derive thresholds LLM-side after running AnalyzePosition. The category exists for the explicit request “give me the break-even price” without requiring the LLM to derive it.