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📜 [專欄新文章] Uniswap v3 Features Explained in Depth
✍️ 田少谷 Shao
📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium
Once again the game-changing DEX 🦄 👑
Image source: https://uniswap.org/blog/uniswap-v3/
Outline
0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion
0. Intro
The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥
While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.
Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅
Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊
If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏
There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!
1. Uniswap & AMM recap
Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.
Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.
Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:
AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.
Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².
Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.
In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP
¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity
² the range is in fact [-∞,∞], while a price in most cases won’t be negative
³ AMM of constant sum does not have price slippage
2. Tick
The whole innovation of Uniswap v3 starts from ticks.
For those unfamiliar with what is a tick:
Source: https://www.investopedia.com/terms/t/tick.asp
By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:
The price range of each tick is predefined by the system instead of being proposed by users.
Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.
Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.
With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯
So, how is the price range of a tick decided?
This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.
The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.
Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.
However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.
This is how price ranges of ticks are decided⁴:
Image source: https://uniswap.org/whitepaper-v3.pdf
With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.
As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.
For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.
p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001
See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?
Image source: https://tenor.com/view/coin-master-cool-gif-19748052
But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?
Price range: max & min
To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.
Image source: https://uniswap.org/whitepaper-v3.pdf
The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.
24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:
1.0001 ^ (2¹⁸) = 242,214,459,604.341
1.0001 ^ -(2¹⁷) = 0.000002031888943
I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌
⁴ For implementation concern, however, a square root is added to both sides of the equation.
How about finding out which tick does a price belong to?
Tick index from price
The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:
Image source: https://www.codecogs.com/latex/eqneditor.php
Let’s try this out, say we wanna find out the tick index of 1000000.
Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm
Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!
⁵ This formula is also slightly modified to fit the real implementation usage.
3. Concentrated liquidity
Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.
Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.
As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!
Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/
Mmm… examples are always helpful for abstract descriptions 😂
Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].
If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.
The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.
However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).
We can observe the following two points from the above example:
Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.
√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.
What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!
Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!
Image source: https://uniswap.org/blog/uniswap-v3/
It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵
⁶ Thanks to Yenwen Feng for the information.
4. Range orders: reversible limit orders
As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:
current price < the targeted price range
current price > the targeted price range
current price belongs to the targeted price range
The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.
The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).
There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!
In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.
Range orders
To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.
The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.
For the price of X to go up, y has to increase and x decrease.
With this pricing mechanism in mind, it’s example time!
Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).
The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.
The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.
If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.
Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.
What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].
This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.
…wut? 🤔
Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!
What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.
The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.
Image source: https://uniswap.org/blog/uniswap-v3/
Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.
To wrap up such an interesting feature, we know that:
Only one token is required for range orders.
Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯
I will be discussing more the impacts of v3 in 5. Impacts of v3.
⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.
Reversible limit orders
As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.
We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].
Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.
The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.
As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:
When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸
When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸
A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!
⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.
5. Impacts of v3
Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:
Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.
The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.
LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏
In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.
After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔
Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!
6. Conclusion
That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂
There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅
If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!
Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟
Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.
👏 歡迎轉載分享鼓掌
Part 2 of our Yeosu Trip! For DAY 2, we hopped on the Yeosu city bus 🚌 to take as around the famous tour spots of the city including the fun cable car ride to dolsan park and Odongdo Island. And also got to see the Yin Sun Sin Square with lots of good food too!
麗水自由行第二天！😝 跟著我們一起坐麗水的觀光巴士 🚌 遊玩麗水著名的各各景點吧～從高空纜車坐到突山公園，到梧桐島到李舜臣廣場和各種好吃的美食！而且我們還發現了特大號24cm大的珍珠奶茶店～
Connect with Me!
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Music by Disco Shrine - Wanna Get Away - https://thmatc.co/?l=5D41374
Music by Carter Vail - Milk Carton - https://thmatc.co/?l=4E7EFB00
Music by Carter Vail - Love-15 - https://thmatc.co/?l=C1197F9A
Music by HubbaBubbas - Address - https://thmatc.co/?l=25DC162B
Music by MYSM - Honeymoon At The Holiday Inn - https://thmatc.co/?l=A2912F93
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What I use:
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#wheninSingapore #Gardensbythebay
hi cả nhà ~
Trong chuyến đi trao đổi sinh viên tại Singapore 3 tuần vừa rồi, mình có tranh thủ chút cuối tuần để đi Gardens by the bay và Night Festival. Hy vọng mọi người sẽ thích video này nha !!~
THANKS FOR WATCHING !!
Vé Flower dome + Cloud Forest mình mua tại Klook : 23SGD/người
==============================
MUSIC:
Dabin - Parttime Lover
Lucas Estrada - Blinding Lights
習近平帶著心腹胡春華、劉鶴，到重慶扶貧的玄機。貿易戰令既得利益者不滿，若大陸有反習勢力，地點會是西南霸王薄熙來的根據地重慶。六四屠城三十周年，華為和Leica這對拍檔，為這個特殊日子做了工作。習滅佛為要人人發錢寒。最不想香港人忘記六四的是習近平。既濟、未濟兩卦，人生修行的終極解脫。(完整文字版將會在節目後上載至易經講堂網頁）
#貿易戰 #坦克人 #重慶扶貧 #六四30週年
==========
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==========
Wong Wai Man 2019年4月23日 星期二下午5：00
北京近日逼害宗教信仰的行動全面升級，大陸多地各類型的佛教造像接連被拆毀。這是繼各地天主教堂、基督教堂、回教寺被破壞後的相繼行動。
在中華文化中，佛教有別於其他宗教。
自東漢後期傳入中土，佛教在魏晉南北朝時期發展蓬勃，在唐太宗時大盛。
佛教的哲學思想，和中國傳統的儒家思想和道家思想，天然揉合，成了我們今天的中華文化。
不需要是佛教行人，都會深信形而上的世界，有位神祇，像觀音菩薩，關注世間苦難的聲音。
習近平滅佛，想滅的，不是世界宗教的一宗一派，是貫徹中共1921在上海創黨後的舉動，要斬斷中華文化的血脈，大陸人民不能有高層次的道德追求，不能有個人的千秋理想，人人發錢寒，只能靠動物本能生存，便於中共統治。
所以，毛澤東批孔子，今日習近平也要禁老子，儒家道家都是罪。
他們一脈相承，其實，目標是徹底斬斷中華文化的根。
中美貿易談判，已經一年了。
美國完全沒有結束的意願，特朗普將習近平當猴子的耍弄。
他在等反習勢力在大陸集結，待兩派力量差不多時，美國才出手。他目標似乎不只習垮台，他要完結共產主義。
所以，特朗普說起習這個對手時，是輕佻的：
「不需要有貿易協議，美國也是贏家。」
「我對習說他是皇帝，習稱自己是主席；我說，沒有任期的主席就是皇帝了。習聽後很開心，打哈哈……」
這個時候，習近平帶著他兩個心腹，兩位副總理，胡春華和劉鶴，到重慶扶貧。
扶貧到重慶？
薄熙來出事前，重慶一直被視為上海後的奇蹟城市，有所謂的「重慶模式」。
貿易戰已令到改革開放得益者不滿，如果大陸有反習勢力，地點會是重慶，那是西南霸王的根據地。
這個時候，香港的中聯辦，竟然倒掛五星紅旗。
九七前，新華社香港分社門前的五星旗，可曾試過倒掛一天？
習近平定於秦王一尊之後，對外政策，令到周邊關係緊張。
但中共的敵人，始終在體制之內，這是他們的宿命。
習近平是老毛的好學生，不喜歡走資的鄧小平，改革開放派也不喜歡習近平。
今年是六四屠城三十周年，其實，大陸的政治山頭，和香港人，都沒有忘記這個日子。
華為和Leica這對拍檔，分別為這個特殊日子，做了工作。
華為出了最新手機型號P30 Pro, Leica出了微電影，鏡頭上反映了坦克人王維林。
似乎大家都不想忘記這個日子，香港人更不會忘記，因為六四改變了中共的國策，改變了對港政策，也改變了香港人的命運。
不想我們忘記六四的，還有習近平。
《周易》六十四卦，最後兩卦是六十三卦的水火既濟和六十四卦的火水未濟卦。
最後的既濟和未濟卦，都有一個「濟」字。「濟」是齊水而過，是渡河的意思，普濟眾生，知周萬物，道濟天下，是《易經》的聖人救世主張。
大乘佛教也重視「濟」，渡河，渡過輪迴苦海的方法，就是波羅蜜多。佛教行人用六種方法，是謂六波羅蜜多，渡過彼岸。
渡彼岸，即是過大川，《易經》很多爻辭，都說到「利涉大川」。
六十四卦最後兩卦，是對人生成敗的總檢討。人生修行的終極解脫，就是在既濟和未濟兩卦。
既濟，是搞掂了；未濟，是未解決。
成功只是一個階段，這個階段既濟，但下個階段還未搞掂，未解決。
生命如果以既濟為止，那人生便只是一個封閉的死局；但血肉人生其實是逆水行舟，永無止境。
既濟之後是未濟，即是說，即使你成佛，只是成佛之路既濟，但你為什麼成佛呢？目的是普渡眾生，這個工作永遠不完，永遠未濟。
所以，既濟未濟，根本就是一個卦，因為兩卦，既相綜，又相錯，又相互，又相交。六十四卦，只有這一組的關係是如此。
人生以「濟」為目的，就是要過江。濟是齊水而過，普渡眾生，苦海慈航，端看你本領夠不夠。
既濟未濟兩卦相綜，即相反角度看，完全不一樣。
如果既濟代表成功，未濟代表失敗，原來成功失敗，端視你從那個角度看。這邊看既濟，那邊看原來是未濟，人生成敗，要靈活一點看，不能只從一個固定角度看問題。
成功有時是下一階段大挫敗的開始。所以，成敗為一體兩面，互為因果。很多時候，看似未濟，但不要放棄，原來另一邊看，正是既濟。
2019年4月23日星期二下午5:00
你的收看、訂閱、讚好便是對「易經講堂」的支持，謝謝。
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