Discounting TVL by how long it lasts
One formula turns a horizon into a number anyone can read on a chart: $500M at nine days is $35M of durable liquidity.
The attestation is a primitive. Several quantities of independent interest follow from it directly, and the most legible one needs no integration at all — you can put it on a chart next to TVL and the argument makes itself.
dTVL
Discount liquidity by its expected persistence relative to a reference duration:
dTVL_P = L_P · min( 1, H_P / H_ref )^ψ · c_PWith H_ref = 90 and ψ = 1, a pool holding $500M with a nine-day horizon at confidence 0.7 reports $35M. The same pool with a ninety-day horizon reports $350M.
$500M
headline TVL, either way
$35M
dTVL at a nine-day horizon, 0.7 confidence
$350M
dTVL at a ninety-day horizon
Aggregated across a chain, the sum behaves very differently from headline TVL during an incentive programme: rising with organic deposits, flat or falling as subsidised deposits accumulate against a fixed expiry date. Two lines on one chart, diverging, is an argument that needs no explanation.
Emission efficiency
Protocols running incentive programmes currently evaluate them on TVL acquired per dollar spent. That measures the wrong thing — it rewards buying liquidity that leaves the moment payment stops.
The durability-aware version measures durable liquidity-days purchased:
η_c = ∫ ( dTVL_P(t) − dTVL_P(t₀) ) dt / Σ R_P(t)This is a genuinely uncomfortable metric for programme operators, which is precisely its value. A campaign that triples TVL while dTVL stays flat has bought nothing except a number on a dashboard.
What a protocol actually learns
A protocol with $2M to spend on liquidity acquisition evaluates three schedules through the counterfactual endpoint:
| Schedule | Peak TVL | Post-campaign horizon | η |
|---|---|---|---|
| $2M over 30 days | Highest | Under a week | Near zero |
| $1M over 90 days | Middle | Moderate | Middle |
| $500K over 90 days + 30-day lock | ~40% lower | Several times longer | Highest |
The protocol is buying liquidity-days, not liquidity. Without η it has no way to compare these except by peak TVL, which ranks them in exactly the wrong order.
Durability-adjusted yield
An advertised APY assumes the position can be held. For a strategy requiring duration d:
APY_dur(d) = APY_P · S_P(d) − ( 1 − S_P(d) ) · χ_PThe second term is the one that gets left out of every yield comparison. A breach is not merely the absence of yield — it is a realised loss taken at the worst possible moment, when everyone is exiting the same door.
Run the numbers and a 40% APY pool with a four-day horizon, evaluated for a thirty-day hold, frequently prices below a 6% APY pool with a two-year horizon. That calculation is currently done by nobody, because S_P has not existed.
Portfolio horizon, and the diversification that is not there
An allocator holding eleven positions wants one statement, not eleven. The minimum horizon across positions is too conservative — a small position breaching is survivable. The weighted mean is too permissive, because breaches correlate.
Cleaton computes the joint survival directly, with a Gaussian copula over the marginals and correlation from the cross-pool feature, then reports the effective number of independent exposures alongside it:
n_eff = 1 / Σᵢ w̃ᵢ²In the worked case from the paper, an agent allocating $50M across eleven candidate pools discovers that four of them draw incentives from the same treasury with expiries inside a nine-day band — an effective exposure count of 4.2 against a nominal eleven. It had constructed what it believed was a diversified book. What it held was a concentrated bet on one treasury’s emission policy.
No single-pool query would have surfaced that. It is only visible in the correlation structure — and correlation is the feature most likely to be underestimated in a young system. Nineteen campaigns funded by the same treasury and expiring within a fortnight of one another are, for practical purposes, one campaign.