YT

Yield Token

YT represents the right to the yield of staked yield-bearing tokens, obtained by staking yield-bearing tokens and specifying a lock-up period. YT separates the yields from the yield-bearing tokens, allowing it to be traded on secondary markets and used to build other DeFi Lego components.

A true universal fungible YieldToken

Unlike YieldTokens from other protocols in the market, which are either NFTs or special FTs (e.g., Pendle), these are non-fungible. This characteristic leads to a lack of liquidity for YieldTokens and reduces the composability of the protocol.

OutStake's YT is a genuinely fungible token (FT), offering excellent liquidity and strong composability. For every 1 yield-bearing token staked for 1 day, 1 YT is minted. If 𝑥 yield-bearing tokens is staked for 𝑦 days, 𝑥𝑦 YT will be minted. Therefore, theoretically, 1 YT is anchored to the yields generated by staking 1 yield-bearing token for 1 day.

YT can be freely traded and can be redeemed at any time to claim the accumulated yields in the yield pool. When burning YT, the redemption of yields is proportional to the amount of YT burned relative to the total YT supply.

The Stability Mechanism of YT

YT is an yield rate token entirely tied to yield rates. Theoretically, 1 YT represents the yields generated by 1 yield-bearing token over 1 day. Initially, the redeemable value of YT (the yields redeemed by burning YT) starts at zero after the first YT is minted and grows slowly over time. Burning YT redeems yields proportionally, so it does not affect its redeemable value. The redeemable value of YT only decreases when new YT is minted, and the amount by which it decreases will be fully re-accumulated in the future (due to the staking of new yield-bearing tokens).

Theoretically, the pegged yield rate corresponding to its redeemable value will stop growing when it reaches the actual yield rate of the yield-bearing asset. However, in actual operation, some users may prematurely burn their YT before the lock-up period of their staked yield-bearing tokens expires (it has been verified that not burning YT after expiration does not take away profits from others), resulting in a decrease in the circulating supply of YT. Meanwhile, the profit pool continues to accumulate yields, ultimately causing the pegged yield rate corresponding to YT's redeemable value to exceed the actual yield rate ceiling. This subsequently leads to two possible scenarios:

1. In the future, burning YT will enable users to redeem greater yields, increasing the returns for long-term stakers. Meanwhile, the number of PT minted from subsequent new stakes will slightly decrease, resulting in an increase in the fixed interest rate corresponding to SP.

2. Users can stake more yield-bearing tokens to mint new YT and immediately burn them to redeem yields for arbitrage, while locking in a higher yield rate. However, this will provide more fuel for the next interest rate breakthrough, and the growth of its pegged interest rate is permanent.

Broader prospects

YT is not only a tool for helping long-term stakers earn more yield but also a truly fungible, universal yield token. Additionally, it represents Web3's first decentralized algorithmic stablecoin anchored to yield rate(inflation rate). In the competitive market, YT remains connected to these yield rates. Looking ahead, Outrun will utilize YT’s unique features and community to develop even more innovative products.

The mathematical model of YT

While YT may appear simple on the surface, the ability for YT to be freely traded and for any YT holder to redeem yields at any time introduces a highly complex game-theoretic process and mathematical model.

The following, we construct a minimal model to calculate impermanent profit and losses.

Assuming that the accumulated yields in the YieldPool is 0, and 1 YT is pegged to the yield produced by 1 yield-bearing token over 1 day, which we denote as 𝑦.

User A stakes 𝑎 yield-bearing tokens and locks them for 𝑚 days, which will mint 𝑎𝑚 YTs. We will consider other users as a collective entity, referred to as User B, who stakes 𝑏 yield-bearing tokens and locks them for 𝑛 days, which will mint 𝑏𝑛 YTs.

After 𝑡 days:

The Impermanent Profit and Loss Ratio (IPnLR) can be obtained by dividing the actual earnings by the expected earnings and then subtracting 1. IPnLR = (Actual Earnings / Expected Earnings) - 1

The impermanent profit and loss (IPnL) can be obtained by multiplying each user's impermanent profit and loss ratio (IPnLR) by their respective expected earnings. IPnLa = IPnLRa * Expected Profit_A IPnLb = IPnLRb * Expected Profit_B

From the above figure, we can deduce that there is an impermanent profit and loss conservation between User A and User B. If User A and User B lock up their assets for the same duration, both parties would experience no impermanent profit or loss. In other words, an individual user's impermanent profit and loss are correlated with the weighted average duration of other users in the staking pool.

Of course, the above is just a minimal model. The actual situation will be more complex due to the influence of multiple players in the game. Therefore, we will set a maximum lock-up time limit -- MaxLockInterval. The closer the user's lock-up time is to MaxLockInterval, the smaller the IL and the larger the IP. Additionally, users can reduce IL and obtain more IP by redeeming their principal immediately upon the expiration of the lock-up period and then staking to mint REY again. When the user's lock-up time is MaxLockInterval, there will definitely be no IL.

Based on the model presented above, Outrun can help long-term stakers earn more income. We believe that ETH staking itself aims to make Ethereum more decentralized and secure. Therefore, users who contribute to the long-term protection of Ethereum should be rewarded more generously.