A Primer on Power Tokens

Robert Leifke
Numo
Published in
4 min readJan 13, 2023

At the root of it, the Numoen Core protocol is a replicating market maker (RMM). A term that describes an automated market maker (AMM) who’s portfolio of assets are constantly rebalanced by arbitrageurs to guarantee an arbitrary payoff. This payoff can also correspond to a continuously leveraged portfolio. Using this knowledge, we’ve created a fully autonomous and permissionless protocol for minting Power Tokens! A type of leveraged token that gives traders squared leverage on any token.

So what are leveraged tokens?

They are a crypto-native invention initially introduced by centralized exchanges to allow for easy perpetual leverage exposure, “perps” on a few high volume assets like BTC and ETH. They were then popularized on-chain by Index Coop with the ETHFIL-2x token. One of the many benefits included constant 2x leverage exposure on ETH without needing margining or risk a liquidation. Under the hood, leveraged tokens worked by wrapping a perpetual futures position and minting a synthetic token on this where each token holder is still obligated to pay funding to shorts.

Some of the drawbacks in the (Index Coop/Squeeth) design:

  • Super-permissioned (centralized)
  • Needs shorts
  • Slippage on redemptions

So we came up with a model that allows for:

  • Fully autonomy
  • Permissionless markets
  • No slippage on redemptions

Numoen’s Power Tokens work a bit different from centralized counterparts.

Overview

For starters, the protocol enables for the first time, the permissionless creation of Power Tokens for any desired market. These option-like derivatives have a unique attribute — squared leverage. This means that for any market (token), a Power Token holder has upside to the power of 2 on their gains.

If the price of ETH goes up by 2, then a trader’s gains will go up by 4x. If the price goes up by 4, then a trader’s gains will go up by 16x and so on.

  • Payoff Graph from Power Perptuals by David White (Paradigm)

Why squared leverage? In a space where the demand for leverage is insatiable, squared leverage allows traders to earn more on large price swings. Another unique attribute to squared leverage is the convexity. In layman terms, Power Tokens provide traders option-like exposure through the curvature present in the payoff as opposed to a straight line. The convexity can also be useful for hedging and pricing volatility. Because Power Tokens rebalance at every price to the power of two, the payoff is quadratic. As proven in spanning power perpetuals by Joe Clark, the quadratic payoff can hedge any constant product market maker (CPMM) position including the LP shares of Uniswap.

To achieve the properties of a Power Token, the automated market maker (AMM) pools liquidity to a “capped power” invariant.

In this system, lenders provide liquidity like they would in a traditional AMMs, but with Numoen Core the fees associated with the LP position is instead a funding rate earned when a user lends out their liquidity position.

Providing liquidity to Numoen Core pool is the same experience as providing it to a Uniswap V2 pool. But you earn funding from people going long or short.

To buy a Power Token that is long on ETH, you simply swap into ETH+ which gives you squared exposure on ETH. In minting a Power Token, a trader provides collateral in the token they are speculating. Under-collateralization is not possible in this system and nor are liquidations. That is becuase Power Tokens are NOT synthetic. They represent claim to the underlying assets at all times just as a LP share of an AMM would. Because their is no liquidations, the payoff is capped to four times the price. Meaning the maximum leverage a user takes on by holding a Power Token is 16x leverage.

Ultimately with a Numoen Power Tokens, you can get leverage on any market in decentralized finance (DeFi). All without the risks of external oracle dependencies, custody, liquidations, or privileged permissions. Truly DeFi!

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