What is Impermanent Loss & How it Actually Happens
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Transcript:
Let’s say that one day you decided to invest your crypto to earn some passive income. So you went to Uniswap and invested your tokens in a liquidity pool, and soon after that, you started earning some returns on your tokens, but after a while, you needed the money you invested and you cashed out your tokens from the pool.
But when you tried to calculate the profits you made, you found out that it would have been better if you didn’t invest in this pool, and you actually have missed on some profits you could have made if you simply held your tokens and didn’t invest them. This is what is known as impermanent loss in the crypto space. Welcome to Crypto Bee where we explain cryptocurrencies and DeFi topics in the most simple and beginner-friendly way.
In this video, you will know what is impermanent loss and how it actually happens, and finally, we will talk about different scenarios for impermanent loss, so grab a snack and let’s get started. So, what is impermanent loss? Impermanent loss is simply the loss of profits you could have made if you held your tokens and didn’t invest them in a liquidity pool.
To help you understand what that means, let’s go over an example. Let’s say that you invested 2 Ethereum and 4000 Tether tokens. The price of Ethereum was 2000 dollars, meaning that the total worth of your tokens equal 8000 dollars. Let’s say that you left the tokens in the pool for six months and when you decided to cash out your tokens, the pool gave you 1.
5 Ethereum and 4700 Tether tokens, we will explain why you got less ethereum and more tether in a minute but for now let’s say the price of ethereum has jumped to two thousand five hundred dollars so now your 1.5 ethereum is worth three thousand seven hundred fifty dollars and you have another four thousand seven hundred fifty dollars in tether tokens making the total value of your tokens equal eight thousand five hundred, which means that you made a profit of $500 from your initial $8,000 investment. But let’s see what could have happened if you held
your tokens and didn’t invest them. The two Ethereum coins will be worth $5,000 at the new price, and add to them the 4,000 tether tokens, and we get a total of 9000 dollars which means that you could have made 1000 dollars in profit so as you can see in this case you make an additional 500 dollars this 500 dollars you could have made is the impermanent loss during these six months you may have earned returns on your tokens let’s say that you earned $320. If you subtract them from the impermanent loss,
you will get $180. Which means that you actually lost $180 by investing your tokens in this pool. To be able to understand why impermanent loss happens and why the pool gave you less Ethereum and more Tether tokens, there are three very important points you need to understand about liquidity pools. We actually have a detailed video about them, but for now let’s go over these points very quickly.
So as you may know, a liquidity pool is a pool containing two tokens, and people come to it to swap their tokens. The tokens in this pool come from investors like you who want to earn some returns on their crypto, so for every swap made with your tokens, you get 0.
3% of the swap amount as profit the first point you need to understand here is that the price of a token in a liquidity pool depends on the supply and demand of this token for example if we have a pool containing link tokens and tether tokens and a lot of people want to buy link tokens the pool will continuously raise its price so it may sell the first token for $10, the second one for $11, and the third for $12.
This is done to never run out of linked tokens in the pool. What ZAP means for us here is that a liquidity pool can have prices different from the prices of centralized exchanges like Coinbase and Binance. Just keep that in your mind. The next point we have here is that if you want to invest some tokens in a pool you need to put in the two tokens you can’t deposit just one token and you also need the ratio between the two tokens to be 50 50.
for example if you have ten thousand dollars to invest into this link tether pool you need to put in five thousand dollars in tether tokens and five thousand dollars in tokens, which may equal 500 Link tokens. The third point and the most important one is that when you want to cash out your money, you cash out your portion or your percentage of the pool, not the same amounts of tokens you initially deposited.
For example, if a pool has 9,000 Link tokens and 90 ninety thousand tether tokens and then you deposited one thousand link tokens and ten thousand tether tokens making a total of ten thousand link tokens and one hundred thousand tether tokens then you now own ten percent of the pool if at the time you want to cash out your money a lot of people had bought link tokens from the pool and now there are only eight thousand link tokens and one and 120 thousand tether tokens.
Then you will get 10% of these tokens which equals 800 link tokens and 12 thousand tether tokens, just like what happened in the example we explained at the beginning. If you have been enjoying the video so far, give us a like as a new channel, it really helps us. Now that you know these important points points let’s now get to how impermanent loss happens and how to calculate it so impermanent loss happens only when the price of one or the two tokens in the pool change the greater the change the larger the impermanent loss
so let’s take an example let’s say that you want to invest two thousand dollars in an ethereum tether pool. Currently, this pool has eighteen ethereum coins and nine thousand tether tokens. Let’s say the price of ethereum is currently at five hundred dollars, so, you put in one thousand tether tokens and two ethereum, making the total in the pool twenty ethereum and ten thousand tether tokens, which means that now, you own 10% of the pool.
Let’s say that after 6 months the price of Ethereum jumps to $650, as we have said before, the pool will still sell 1 Ethereum for $500. So, traders can see now that they can make an easy profit by buying the cheap Ethereum from your pool at $500, and then sell it to other exchanges at $650. Traders who do this are called arbitrage traders as we have said before the pool will begin to raise the price of ethereum as this trader continues buying it until the price reaches 650 dollars and that is when no more
profits can be made by doing some calculations we find out that the maximum amount of Ethereum this trader can buy before the price reaches 650 was 2.45 Ethereum, and by doing more calculations, we find out that this trader paid for them 1,402 Tether tokens. We will actually explain how to do these calculations at the end of the video, as they are a little complicated.
But for now, this arbitrage trader can make a profit by selling this Ethereum at the current price the video as they are a little complicated. But for now, this arbitrage trader can make a profit by selling this Ethereum at the current price of $650, making an easy profit of $190. Now, the pool has 17.
55 Ethereum and 11,402 Tether tokens, we get those numbers by subtracting the 2.45 Ethereum from the initial 20 we had, and adding the 1,402 Tether tokens subtracting the 2.45 ethereum from the initial 20 we had and adding the 1 402 tether tokens paid by the trader let’s say that you want to cash out your money now you own 10 of the pool which means that the pool will give you 10 of the two available tokens so you will get 1140 tether tokens and 1.75 ethereum let’s now see the value of these tokens the 1.
755 ethereum multiplied by the new price of 650 dollars will give us 1140 dollars add them to the other 1140 dollars we have in tether tokens and the result will be a total of 2280 dollars so you made a profit of 280 dollars we will talk about the fees you earned in a minute but let’s now see what could have happened if you held your tokens and didn’t invest them first you would still have the one thousand tether tokens which are equal to one thousand dollars and also you would have the two ethereum which at the new prices are worth one thousand three hundred dollars adding the two together, we get a total of 2 thousand 300 dollars.
so you could have had 2 thousand 300 dollars if you didn’t invest your tokens in the pool. to calculate impermanent loss, we subtract 2 thousand 280 from 2 thousand 300 to get 20 dollars. which means that you could have had 20 dollars more if you held your tokens.
But still, this doesn’t tell us the whole story, at the end of the day, you are investing to make profits. So, let’s consider the returns you earned during these 6 months. You should know that all pools are different and each pool offers a different APY on your invested tokens. But let’s say that the pool you invested in gives you a 12% APY, which is pretty achievable in many liquidity pools.
You left your tokens for 6 months, which means that you earned 6% only on your tokens. So, 6% on the $2,000 you invested equals $120, which as you can see in this example, completely covers your impermanent loss and leaves you with an additional $100 in profit profit compared to holding your tokens you should also know that it is called impermanent loss because you don’t actually take the loss until you actually cash out your tokens from the pool that is when it becomes a permanent loss but for example if you didn’t withdraw your tokens and
waited until the price of ethereum falls again close to the price you deposited at, the impermanent loss will be much lower, or it can disappear completely if you cash out when the price of ethereum is at exactly 500 dollars. Now let’s go see another example in which the price of ethereum falls. Let’s say that you invested the same 2000 dollars in the same pool with the same number of tokens.
The current price of ethereum is 500 and you own 10 of the pool let’s say that after a while the price of ethereum dropped to 350 as we have said before the pool will still have the old price of 500 so an arbitrage trader can buy ethereum at 350 from other exchanges and then sell it to the pool at 500 in this case the pool will continuously lower the price it pays for each ethereum coin and by doing some calculations we find that the maximum amount of ethereum the trader can sell to the pool at high prices is 3.9 ethereum any more than that the pool will pay less than 350
ethereum, any more than that, the pool will pay less than 350 dollars and the trader will begin to lose money. This trader paid 1365 dollars for the ethereum he sold to the pool, which you can get by multiplying 3.9 times 350. By doing some more calculations we find out that the pool paid 1631.
8 tether tokens for the trader, which means that he made a profit of approximately 267 after what happened the pool now has 23.9 ethereum and 8368.2 tether tokens you own 10 of the pool so when you cash out your tokens you will get 2.39 ethereum and 836.8 tether tokens we can get the value of these tokens by multiplying 2.39 times 350 which will give us 836.5 and you also have another 836.
8 dollars in tether making a total of 1673.3 dollars which means that you took a loss of 326.7 dollars. To calculate your impermanent loss in this case, let’s see what could have happened if you held your tokens. First you would still have the 1000 tether tokens, plus the 2 ethereum which would have been worth 700 dollars. Adding the two together $1,700.
So you still would have taken a loss of $300 from the initial $2,000. But you lost an additional $26.7 by investing in the pool, which is your impermanent loss. But still, if we assume that you earned the same $120 in returns from the pool, you will have a total of $1,793.3, which means that by investing in the pool, you reduced your loss by $93.
As you can see, the fees can sometimes cover the impermanent loss, but that is not always the case. Pulls with no stablecoins are much riskier than the Ethereum tether pool we talked about. pools with no stable coins the two tokens can move in price and the impermanent loss in this case could easily exceed the returns earned from the pool let’s see an example let’s say that you want to invest two thousand dollars into an ethereum monopole the price of ethereum currently is five hundred dollars and the price of mana is two dollars which means that the price of 1 ethereum equals 250 mana
tokens. So you deposited 2 ethereum and 500 mana tokens, and you now own 10% of the pool. After a while, the price of ethereum rises to 750 and the price of mana falls to 50 cents. At that new price, 1 ethereum is equal to 1500 1500 mana but the pool still has the old price so the traders will do their arbitrage by buying the cheap ethereum from the pool and selling it at a high price on other exchanges by doing the same calculations we find that after the arbitrage the pool will have 8.16 ethereum and 12 254okens and when you cash out you will get your 10 which equals 0.816
ethereum and 1225 monotokens at the new prices these tokens are equal to 1224.5 dollars so you took a big loss of 775 dollars but let’s see what could have happened if you held the tokens. The two Ethereum are worth now one thousand five hundred dollars and the five hundred mana are worth two hundred fifty dollars, making a total of one thousand seven hundred fifty dollars.
So in this case you also took a loss, but much smaller than the first case. Your impermanent loss here is five hundred.5 and this loss is very unlikely to be covered by the returns of the pool even if you are getting a 20 apy and left the tokens for an entire year as you can see from the previous example impermanent loss is very large when the prices of the two tokens move in opposite directions to make easy for you, let’s quickly go over the different scenarios that could happen in a liquidity pool. Let’s start with the first case which is when the
two tokens move in different directions. This is the worst case for any liquidity provider. For example, if a token rises in price by 50% and the other one drops by 7-5%, the liquidity provider will suffer an impermanent loss of 30%. The second case is when the two tokens move in the same direction with equal movements, or when you wait for the prices to return to the initial prices, this case is very unlikely to happen due to the volatility of cryptos, but if does happen, in this case, the impermanent
loss will be zero or very close to zero. The third case we have is when the two tokens rise in price but with different percentages. For example, if one token rises in price 50% and the other one rises by 7-5%, the impermanent loss in this case will be very low at 0.3%. This is the best scenario you can hope for when investing in liquidity pools as you will benefit from the price increase and you will not lose much to impermanent loss the last case we have is when the prices of the two tokens fall but with different percentages in this case the
impermanent loss will also be very small but still larger than the previous case for example if the price of one token falls by 50 and the other token falls by seven to five percent then the impermanent loss in this case will be 5.72 so as we have said the best scenario to hope for is that the prices of both tokens increase with close movements or if that doesn’t happen then at least both prices move in the same direction with close movements in the next part we will explain how we got the numbers we used in
the previous examples so these liquidity pools use a mathematical formula to determine prices this formula is called the automated market maker formula as you can see in an ethereum tether pool the z equals the number of ethereum coins in the pool times the number of tether tokens in the pool which we can easily calculate to get 200 000.
this z is a constant number that doesn’t change unless someone comes and invest more tokens in the pool as we have said before as the number of ethereum coins in the pool decreases the price of each ethereum will increase so to get the number of ethereum coins that need Ethereum coins in the pool decreases, the price of each Ethereum will increase.
So, to get the number of Ethereum coins that need to remain in the pool for the price to reach 650, we use this formula. We take the square root of the Z divided by the new price, which will give us 17.5 Ethereum. So, when there are only 17.5 Ethereum coins, the pool will have a price of 650 Tether tokens per Ethereum. Buying any more from the pool will increase the price even more. So the arbitrage traders can buy a maximum of 2.5 Ethereum from the pool.
To find out how much Tether they pay to the pool, we return to the automated market maker formula. We have the Z and the new number of Ethereum, we can then easily find the new number of Tether tokens, which will be 11,401. So, the traders paid 1,401 Tether for the 2.5 Ethereum they bought from the pool.
