Position & Risk

In the V2 DEX, liquidity providers all provide liquidity to the same price range (0 to infinity). However, in Pangea(V3 DEX), each liquidity provider provides liquidity to his own price range.

Therefore, a liquidity provider's liquidity position basically consists of a price range($P_l$, $P_u$) and liquidity($L$). And, as discussed in the previous chapter, based on the price at the time of liquidity provision, liquidity will be provided with Y tokens for lower price ranges and X tokens for higher price ranges.

When the market price ($P_c$) of the pool that is supplying liquidity changes, the proportion of assets in the liquidity position changes as shown below. If it goes outside a given price range, that liquidity is no longer available for trading, just like lazy liquidity, and yields no more swap fee income.

In addition, if the price range is set too narrow, the proportion of the asset in the position will change significantly even with a small price change. So liquidity providers should set the price range in consideration of the volatility of the asset they are providing.

Liquidity Provider’s Risk : IL(Impermanent Loss)

The liquidity provider of the CPAMM(Constant Product Automated Market Maker) DEX carries the risk of Impermanent Loss(IL). IL stands for “a decrease in the assets’ value that occurred because liquidity was provided to DEX compared to when they were just held without being provided to”. This occurs because, as the price changes from the pool price at the time of supplying liquidity, the proportion of tokens that have lost value in the liquidity position increases and the proportion of tokens that have risen in value decreases. IL can be calculated by the formula below.

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

$k$ = change in price relative to price at the time of liquidity supply($P = \frac{y}{x}$). ($P' = P*k$. where $k>0$)

IL increases as the price at the time of calculation($P' = P*k$) moves away from the price at the time of liquidity supply($P$), and becomes 0 when it returns to the price at the time of liquidity supply.

Using the above formula, when different price ranges are set, the amount of IL that can occur as the price changes is as follows.

Position Price Range	price = +10% (k = 1.1)	price = +20% (k = 1.2)	price = +50% (k = 1.5)	price = +100% (k = 2)
Full Range	-0.113%	-0.414%	-2.02%	-5.719%
10% ~1,000%	-0.166%	-0.606%	-2.955%	-8.364%
25% ~ 400%	-0.227%	-0.828%	-4.041%	-11.438%
50% ~ 200%	-0.387%	-1.414%	-6.898%	-19.526%
90% ~ 111%	-2.211%	-6.632%	-17.836%	-31.530%
95% ~ 105%	-3.525%	-7.910%	-18.961%	-32.467%

As above, as the Concentration Ratio increases by concentrating liquidity more, the amount of IL that can occur when the price changes also increases. In other words, the higher the rate of return by raising the Concentration Ratio, the more IL you have to risk.

Therefore, liquidity providers should set up different strategies depending on the nature of the token pairs they supply. The optimal strategy for stable coin pairs with little price fluctuation might be aiming for high returns by raising the Concentration Ratio as much as possible, whereas the one for recently listed coin pairs might be with low Concentration Ratio to cope with the expected high price volatility.