# Opening up Markets to price the Risk/Payoffs of LPing

## Context

One of the core primites and innovations of decentralized finance are Automated Market Makers. Decentralized exchanges in which people trade against a pool of capital instead of against counterparties. [WIP ]

Being a liquidity provider for a pair on a AMM, generally has the following risk profile:

1. Long the two tokens provided;
2. Short the path-independent volatility *in the relative price between the two tokens LPed*".

The second point is due to what has been called Impermanent Loss: the potential loss that liquidity providers incur by LPing, without taking into account fees accrued, versus their outcome if holding the two assets idly in the same initial proportion.

This happens because, to keep the ratio of the two assets provided about constant, as asset A goes up in value relative to B, the LP position is in effect progressively selling A as it appreciates and accumulating B, or vice-versa in the opposite direction.

$$IL(k) = \frac{2\sqrt{k}}{1+k} - 1$$

Or, conceptually:

$$IL = \frac{\Delta PoolValue_{USD}}{ \Delta HoldValue_{USD}} - 1$$

And for taking this position, LPs get paid the fees generated by trades, proportionally to their ownership of the total liquidity.

## Problem

Increasingly, a lot of people in the space have been bearish on LPing volatile assets as a strategy. For many positions and time periods, the impermanent loss taken has in fact outpaced the fees made, meaning that a 50/50 holding position on the same two assets would have been more profitable.

However, at least for the current state of DeFi, it really is essential that incentives to provide liquidity in AMM designs can be made profitable.

## Possibilities

### Lending and Borrowing LP shares

Opening up lending and borrowing is probably the quintessential way of generating longing and shorting possibilities on spot markets.

With sufficiently liquid markets for overcollateralized lending and borrowing of LP shares, the risks and strategies around providing liquidity in AMMs would be much better priced.

If someone thought that the impermanent loss of a specific volatile LP position would exceed fees accrued, they could borrow the LP share, sell it for the underlying tokens, and close the trade by doing the reverse at some point in the future.
This position would have the exact opposite payoff of LPing (modulo borrowing interest):

$$+Impermanent Loss - FeesAccrued$$

Essentially hoping for high volatility in the relative price between the two assets and not sufficient trading activity to cover IL.

However, to enter this position, this side would be paying an interest to the lenders of the LP shares. As such, not taking into account the extra layer of smart contract risk, LPs would have access to an aditional source of payoff: lending interest, received for allowing other participants to take the inverse bet to them.

These interest rates should, under somewhat efficient markets, tend towards the point at which the EV of LPing or going short LP is thought to be the same.

They would also allow much greater sophistication around liquidity provision in AMM designs, as new hedging and speculation strategies would be opened up.

### Funding rate based products for LP shares

Perpetual futures have been a widly successful and adopted product in crypto markets, for simple tokens and coins, with current volumes far outstriping their spot counterparts.

They're also a good mechanism to price the relative demand in the market to go long or short a specific asset, as the more popular of the two sides will end up paying a funding rate to the less popular.
As in any supply and demand market, we would expect this funding rate to, at any time, be close to the amount that makes the two sides (long and short) equally in demand.

If we had funding rate-based products for LP shares, anyone claiming that LPing on a specific pair over some timeframe had negative EV could express that view by entering a short position on it's equivalent perp.

## Considerations and Future work

1. The first big elephant in the room here are the case of non-fungible LP shares, such as Uniswap v3.
This piece is always assuming fungible, full-range shares such as uniswap v2, curve and balancer's, as it is much harder to have any sort of liquid market for the non-fungible/unique LP shares case.

2. The second is the long tailness of LP pairs since 1. there are tens of thousands of tokens and 2. LP pairs theoretically scale up to quadratically to the number of tokens out there.
Realistically it wouln'd ever be possible to have liquid markets (either borrow/lend or perps) for even a small percentage of all possible pairs.
However, I do think that for the largest ones we could, and that the benefit of such markets would come disproportionally from having the few top ones (think ETH-USDC, BTC-ETH, etc)

3. Third, the fragmentation in the DEX market. BPTs, crvXYZ, UNI-LPXs, etc. The fragmentation between DEXes would cap the liquidity of these markets as even for a specific pair (say, ETH-USDC), the LP shares for that pair are not fungible between different DEXes.
Again, the only sensible solution is to focus on the very top pairs/DEX combos where some liquidity could be formed.