Archive / Crypto & DeFi / E836
Hedged full-range DEX liquidity earns no carry after convexity cost
Hedging the price risk of full-range constant-product DEX liquidity leaves -0.23 bp per day over 21,682 pool-days: swap fees of +3.47 bp are cancelled by a convexity cost of -3.61 bp.
Anyone can deposit two tokens into a decentralised exchange pool and earn a fee on every swap. The known cost is that the pool's price curve loses value when prices move. The belief: with the price exposure hedged on a perpetual-futures venue, heavy retail trading pays fees above that cost. We tested 63 pools over 365 days, 21,682 pool-days, rebalancing the hedge daily. The hedged result was -0.23 bp per day (1 bp = 0.01%): fees of +3.47 bp were matched by a curve cost of -3.61 bp.
A passive liquidity provider, with price risk hedged away, collects swap fees that exceed the cost of providing the liquidity.
Why people believe it
A full-range constant-product pool earns a fee on every swap, and retail flow in small tokens is heavy and does not shop around for the best price. The pool pays for this through convexity: when the price ratio moves by a factor r, the hedged position loses about (r - 1)^2 / 8 per dollar. If daily turnover times the fee rate is larger than that variance term, the hedged position should earn a steady daily carry.
Why it would persist The argument, as stated before testing
Liquidity providers should compete until the marginal one breaks even, but retail flow is heavy and price-insensitive, so fees could stay above the variance cost.
We took a fixed list of the simplest pools: two-token, full-range, at least $500k deposited, with each token either a dollar stablecoin or an asset that has a perpetual future. For each pool and each day we added up four things per dollar of liquidity: the fee earned, the loss from the curve as the price moved, the funding earned on the short hedge, and the cost of rebalancing the hedge. We averaged over all pool-days and tested whether the average was clearly above zero.
Pooled mean at least +2 bp per day (about 7% per year), week-clustered interval lower bound above 0, at least 60% of pools positive, holdout mean above 0.
Pooled mean at or below 0, or week-clustered interval lower bound at or below 0.
5 bp x 0.5 x |sqrt(r) - 1| rebalancing cost per hedged token; realised funding. Hedge margin and pool entry or exit costs not modelled.
Fee versus convexity decomposition; a cut excluding 13 pools with suspected ticker clashes (declared in advance); a secondary rule holding a pool only when its trailing 7-day mean of h is positive, reported and not a pass condition.
The pooled mean is -0.23 bp per day with an interval from -1.06 to +0.56 bp; the kill rule (mean at or below 0) is met.
- Pooled over 21,682 pool-days in 63 pools, the hedged result was -0.23 bp per day, 95% interval -1.06 to +0.56 bp, against a pass bar of +2 bp.
- Fees contributed +3.47 bp per day and the curve's convexity cost -3.61 bp; funding on the hedges was -0.01 bp and rebalancing cost -0.07 bp per day, which sums to about -0.23 bp.
- The median pool-day earned +1.35 bp while the mean was -0.23 bp; the worst single pool-day lost 2,197 bp.
- Excluding the 13 pools with suspected ticker clashes, the result was +0.11 bp per day, interval -0.80 to +0.93 bp.
- 65% of pools were positive and the last 90 days alone earned +2.09 bp per day, interval +1.23 to +2.88 bp, so those two conditions were met and only the mean and interval criteria failed. The last 90 days is a slice of the same year and was not the verdict test.
- The secondary rule (hold a pool only after a positive trailing 7-day mean) earned +1.55 bp per day, interval +0.97 to +2.08 bp, about 5.8% per year on liquidity before hedge margin. It is below the +2 bp bar and was not a pass condition.
- Chosen after seeing results: two standard Solana pools paired with SOL and a stablecoin earned +6.9 and +5.8 bp per day (fee 8.4 vs convexity 1.4 bp per day for those standard pools), while one small-token pool lost 24 bp per day, of which -21 bp was funding on its short hedge, and another lost 10 bp. A few pools picked after the fact do not change the pooled result, which is the test.
Fees and curve cost cancel
Average daily fee income and convexity cost per $ of liquidity over all pool-days, next to the hedged result. The two components are almost equal and opposite; the pass bar was +2 bp.
Chart data (bp per day)
| bp per day | |
|---|---|
| Swap fees | 3.47 |
| Convexity cost | -3.61 |
| Hedged LP result | -0.23 |
The primary result and the cuts around it
Mean hedged result per pool-day with week-clustered 95% intervals. The pre-registered pooled cut includes 0; the last 90 days and the trailing-filter rule are positive, but neither was the verdict test and the filter is T-bill-sized.
Chart data (bp per day)
| Mean | 95% low | 95% high | |
|---|---|---|---|
| All pool-days (verdict) | -0.23 | -1.06 | 0.56 |
| Without 13 ticker-clash pools | 0.11 | -0.8 | 0.93 |
| Last 90 days | 2.09 | 1.23 | 2.88 |
| Trailing 7-day filter | 1.55 | 0.97 | 2.08 |
Selected pools differ widely (picked after the fact)
Selected pools picked after the results were known, so they illustrate dispersion and do not test anything. Funding on a short hedge can erase more than the fee.
Chart data (bp per day)
| bp per day | |
|---|---|
| Solana standard SOL-stablecoin pool A | 6.9 |
| Solana standard SOL-stablecoin pool B | 5.8 |
| Small-token pool B | -10 |
| Small-token pool A (hedge funding -21) | -24 |
Why it failed Interpretation · not established
On average across the 63 pools, fees and the curve's variance cost are nearly equal, which is what the loss-versus-rebalancing literature predicts when liquidity competes until the marginal provider breaks even. Some pools did earn a carry, but they were few and picked after the fact, and the pooled average did not.
Lesson
Full-range pools are priced close to break-even: fees of +3.47 bp per day roughly equal a convexity cost of -3.61 bp, as the loss-versus-rebalancing equilibrium predicts. The positive recent (+2.09 bp) and filtered (+1.55 bp) cuts are not a trading edge; the filtered result is about 5.8% per year on liquidity before hedge margin, T-bill-like.
Scope of this result
Covers 63 full-range constant-product pools from one day's inventory (so only pools alive at that time), daily rebalancing, a 5 bp rebalancing cost, and October 2025 to October 2026. Base APY may include a protocol fee share, which would overstate fees. It does not cover concentrated-liquidity or just-in-time liquidity, other fee tiers, hedge margin costs, or pools that were closed before the inventory date.
A rejected experiment applies to the tested conditions and does not prove an idea can never work. bp = basis point, 0.01%.
1. Test design
Pre-registeredDataUniverseSignalExecutionCostsControlsSample splitPass criterionKill criterionPower2. Result
ObservationsInstrumentsNet mean95% intervalMedianWorstFinding 1Finding 2Finding 3Finding 4Finding 5Finding 6Finding 73. Interpretation
Why it failedLessonScope4. Reproducibility
StepsGrade