Staking Tokens

Penumbra’s staking token, denoted PEN, represents units of unbonded stake.

Rather than treat bonded and unbonded stake as being two states of the same token, Penumbra records stake bonded with a particular validator with a delegation token, denoted dPEN. Conversion between PEN and dPEN occurs with an epoch-varying exchange rate that prices in what would be a staking reward in other systems. This ensures that all delegations to a particular validator are fungible, and can be represented by a single token representing an ownership share of that validator’s delegation pool.

Stake bonded with different validators is not fungible, as different validators may have different commission rates and different risk of misbehavior. Hence dPEN is a shorthand for a class of assets (one per validator), rather than a single asset. dPEN bonded to a specific validator $v$ can be denoted dPEN(v) when it is necessary to be precise.

Each flavor of dPEN is its own first-class token, and like any other token can be transferred between addresses, traded, sent over IBC, etc. Penumbra itself does not attempt to pool risk across validators, but nothing prevents third parties from building stake pools composed of these assets.

The base reward rate for bonded stake is a parameter $r_e$ indexed by epoch. This parameter can be thought of as a “Layer 1 Base Operating Rate”, or “L1BOR”, in that it serves as a reference rate for the entire chain. Its value is set on a per-epoch basis by a formula involving the ratio of bonded and unbonded stake, increasing when there is relatively less bonded stake and decreasing when there is relatively more. This formula should be decided and adjusted by governance.

Each validator declares a set of funding streams, which comprise both the destinations of their commission and the total commission rate $c_{v,e}\in [0,1]$. $c_{v,e}$ is subtracted from the base reward rate to get a validator-specific reward rate $$r_{v,e}=(1-c_{v,e})r_e.$$.

The base exchange rate between PEN and dPEN is given by the function $$\psi (e)=\prod _{0\le i<e}(1+r_i),$$ which measures the cumulative depreciation of stake PEN relative to the delegation token dPEN from genesis up to epoch $e$. However, because dPEN is not a single asset but a family of per-validator assets, this is only a base rate.

The actual exchange rate between stake PEN and validator $v$’s delegation token dPEN(v) accounts for commissions by substituting the validator-specific rate $r_{v,e}$ in place of the base rate $r$ to get $${\psi }_v(e)=\prod _{0\le i<e}(1+r_{v,i}).$$

Delegating $x$ PEN to validator $v$ at epoch $e_1$ results in $x/{\psi }_v(e_1)$ dPEN. Undelegating $y$ dPEN(v) from validator $v$ at epoch $e_2$ results in $y{\psi }_v(e_2)$ PEN. Thus, delegating at epoch $e_1$ and undelegating at epoch $e_2$ results in a return of $${\psi }_v(e_2)/{\psi }_v(e_1)=\prod _{e_1\le e<e_2}(1+r_{v,e}),$$ i.e., the staking reward compounded only over the period during which the stake was bonded.

Discounting newly bonded stake by the cumulative depreciation of unbonded stake since genesis means that all bonded stake can be treated as if it had been bonded since genesis, which allows newly unbonded stake to always be inflated by the cumulative appreciation since genesis. This mechanism avoids the need to track the age of any particular delegation to compute its rewards, and makes all shares of each validator’s delegation pool fungible.