Industry Problems

Liquidity Openness
In 2020, Uniswap introduced its version 2, which mentioned the concept of programmable liquidity. At one point, it is similar to the concept of an open liquidity. They opened and conducted a method to implement on-chain price oracles, which can be considered open data. Uniswap also utilizes the atomic property of Ethereum to leverage flash swaps. In short, you can ask for tokens before paying them with some conditions. If the conditions aren’t met, the transaction will be rolled back. The flash swaps are a superpower for arbitrageurs to explore the price differential.[1]
It’s clear that the liquidity openness on Uniswap is still limited when Liquidity Provider Token (LPT) cannot be consumed by other financial services. In the last half of 2020, the term “Yield Farming” was gathering notice as it accepted LPT to earn other tokens. However, these services are dependent on third parties without native support from Uniswap.[2]
SushiSwap is a younger but more innovative AMM than existing platforms before. It provides a comprehensive DeFi market with many services including swap, yield farming, lending & borrowing, staking, and so on. All these services are built up by themselves, which means they fully control the liquidity and circulate it in their platform. On Solana, Raydium is the current top DEX. Currently, they have services such as swapping, staking, and farming. However, Raydium seems to share the same vision as SushiSwap when they maintain the private permission in DeFi services development.[3]
Symmetric Deposit
It’s worth mentioning about the constant product function (CPF) which expresses the pricing curve in the aforementioned protocols. The main idea behind seems very simple, but it has strongly proved functionality and possibility in both experimentally[4] and practically. The CPF formulates the quoted price via the pair of token reserves. Giving token AAA
, and BBB
 with corresponding reserves RAR_ARA​
, RBR_BRB​
, the algorithm will maintain the following equation,
(1) RA∗RB=kR_A*R_B=kRA​∗RB​=k
​
where k>0k>0k>0
 is a constant defined at the initial state[5]. In other words, let’s call αααα
 the “changing rate” of RAR_ARA​
 after an exchange (sell AAA
, buy BBB
 for example). Then RA′=1αRAR'_A=\frac{1}{α} R_ARA′​=α1​RA​
 induces RB′=αRBR'_B = αR_BRB′​=αRB​
, where 0<α<10<α<10<α<1
, to maintain the constant product,
(2) RA×RB=RA′×RB′=kR_A× R_B = R'_A×R'_B= kRA​×RB​=RA′​×RB′​=k
​
At an arbitrary timestamp ttt
, the quoted price p(t)=RB(t)/RA(t)p^{(t)}=R^{(t)}_B/R^{(t)}_Ap(t)=RB(t)​/RA(t)​
. Therefore, the first liquidity provider (LP) must deposit both tokens, A and B, with reserves that satisfy the reference market price at the initial state, p(0)=RB(0)/RA(0)p^{(0)}=R^{(0)}_B/R^{(0)}_Ap(0)=RB(0)​/RA(0)​
. After the pool’s setup, subsequent LPs must follow the quoted price by depositing both tokens accordingly. But what if users only have one type of token? We call this problem Symmetric Deposit.
Swap Possibilities
Definition 1. Let ppp
 be the current quoted price, p′p'p′
 be the next quoted price, then a slippage rate,
(3) s=p′ps=\frac{p'}{p}s=pp′​
.
Applying to the CPF,
(4) s=RB′/RA′RB/RA=α2.s=\frac{R'_B/R'_A}{R_B/R_A}=α^2.s=RB​/RA​RB′​/RA′​​=α2.
​
The slippage rate is amplified when routing. When there are no direct pools for the desired pair of tokens, traders need to swap through other middle tokens before reaching the destination, and even then, there might be no route for said desired pair at all. This problem, called Swap Possibilities, reduces the liquidity effectiveness and affects user experience.
Impermanent Loss
Lastly, one of the biggest risks of liquidity provision is impermanent loss[6]. Due to price deviation or reserves deviation, from the initial state, the value of assets is no longer greater than or equal to a HODL strategy[7].
______________________________
[1] H. Adams, N. Zinsmeister, and D. Robinson, “Uniswap v2 core,” 2 2020. [Online].
[2] K. Rapoza, “DeFi ‘Yield Farming’: How To Get DeFi Yield, And Why Invest In It,” 06 2021. [Online].
[3] Raydium Team, “Raydium Protocol Litepaper,” 03 2021. [Online].
[4] G.Angeris, H.-T.Kao, R.Chiang, C.Noyes, and T.Chitra, “An Analysis of Uniswap Markets,” Cryptoeconomic Systems Journal, 2019.
[5] H. Adams, “Uniswap Whitepaper,” 11 2018. [Online].
[6] N. Hindman, “Beginner’s Guide to (Getting Rekt by) Impermanent Loss,” 11 2020. [Online].
[7] HODL: Hold On for Dear Life, a slang among the cryptocurrency community, meaning you should hold a cryptocurrency instead of selling it.

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Liquidity Openness

Symmetric Deposit

Swap Possibilities

Impermanent Loss