Cardano Research: A Big Reserve Alone Won't Secure Proof-of-Stake

A peer-reviewed paper by Cardano Foundation researcher Manvir Schneider and Paolo Penna of Input Output Global (IOG) was published on October 2 in the official AFT 2026 proceedings, in Schloss Dagstuhl's LIPIcs series. The Foundation presented it in a post on October 13. The paper cites Cardano as the canonical example of a network that funds rewards from fees and a gradually spent reserve. The authors conclude that a reserve spending policy should not be judged only by the date the reserve would nominally run out.

Economic Security and the Reserve Threshold in the AFT 2026 Paper

The study, "Reserve Depletion and Security Runway in Proof-of-Stake Systems," was presented at the 8th Conference on Advances in Financial Technologies in London. It focuses on economic security, using an economic model to examine how much secure capacity validators provide when their rewards come from fees and the reserve while token price and demand change. The Cardano Foundation is a Swiss nonprofit supporting Cardano's development and adoption, and IOG is the engineering and research company behind the Ouroboros protocol.

The model describes the shift from reserve funding to fee funding. While a network is young, fees do not cover the cost of the target security level, so a token reserve pays the difference until growing usage lets fees take over. The security runway is the period during which the reserve, at current token price and demand, can still sustain that target. According to the paper, that period does not end when the reserve is empty, but when it first becomes too small to cover the shortfall.

The authors call the line between a sufficient and an insufficient reserve the reserve threshold: the smallest amount that still funds the target under given market conditions. The threshold divides the possible states of a network into three zones. When demand is too weak, no amount can sustain the target. In the middle zone, security depends on a subsidy from the reserve, while in the third zone the threshold is zero because fees alone fund security.

Cardano's Reserve, the ρ Parameter and Stake Pool Rewards

According to Cardano's monetary policy documentation, fees from all blocks in an epoch go into a reward pot, which also receives a fixed percentage of the remaining ADA reserve. That percentage, the ρ parameter, is set at 0.3 percent per epoch. At that rate, the documentation says, half of the remaining amount is spent within four to five years. Of the reward pot, 20 percent (the τ parameter) goes to the treasury, and the rest is distributed as rewards in ADA.

The study models not Cardano's rules but a general case with two parameters: the share of fees returned to the reserve and the share of the reserve paid out each period. Validators in the model pay their costs in an external currency, such as dollars, while the reserve is held in the native token. The authors therefore note that the level of security a reserve can fund depends on the number of tokens multiplied by their price, not on the token count alone.

Reaching the zone in which fees alone fund security follows a different logic. According to the paper, it depends on demand rather than token price, because the fees users pay are already measured in the external currency.

A Stress Test for Protocol Governance and the Model's Limits

Theorem 15, which the authors say is intended for protocol governance, translates pessimistic assumptions about price and demand into a minimum reserve size for a given time horizon. According to the theorem, if the reserve meets that condition, security is maintained on every price and demand path that stays above the chosen floors. It is a conservative estimate because the test ignores future fee inflows into the reserve, and the guarantee holds within the theorem's assumptions.

The authors also set out the model's limits. Price and demand are taken as given, so the paper does not explain token valuation or adoption. Validators are symmetric in the baseline version, which is why the threshold should be read as a benchmark. The numerical examples use illustrative parameters, including five validators, and are not a calculation for Cardano. Community members asked for exactly such a calculation for Cardano's current state in replies to the Foundation's post.

As a next step, the authors propose an adaptive policy in which payouts and fee retention would follow the state of the network, for example by cutting payouts after a price drop or retaining more fees when the reserve is low. Protocol governance would then choose a rule that adjusts to reserve size, price and demand, subject to incentive and credibility constraints. The authors describe this as a move from evaluating an existing policy to designing a new one and name it as a topic for their future research.