# Do liquidity pools reduce downside?

Entering liquidity pools can cause loss of upside when one side of a pair goes up, called impermanent loss. I was reading binance’s resource on impermanent loss which states: “Impermanent loss happens no matter which direction the price changes.”

This sounds like it means if e.g. you had entered an LP between a stable and ETH and ETH’s price drops, you’d lose more (not accounting for farming rewards) than if you simply held the ETH and stable.

This didn’t make sense to me since LPs seem to basically just average your holdings of each. I made an example to see for myself (forgive my scratch math, hope it’s clear enough):

Your initial position, 10% of pool:
1500 DAI 150 ETH |
10\$ price of ETH |
Total LP: 15000 DAI 1500 ETH

xy=k:
15000 + 1500 = 16500 |
10x + 1x = 16500 |
x= 1500 |
Price of ETH changes to 5\$ |
5x + 1x = 16500 |
x=2750 |
New pool amounts |
ETH = 2750 |
DAI = 2750 x 5 = 13750

Your position if you entered LP:
275 ETH and 1375 DAI |
1375 x 2 = 2750\$

Your position if you held/stayed out of LP:
1500 + 150×5 = 1500 + 750 = 2250\$

This seems to contradict binance’s claim, LP is basically hedging from ETH downside. Is my math or understanding wrong? Would be great if anyone can confirm.

EDIT: my math was very wrong. My ape brain did x + y = k instead of xy = k. The new math works out with LP lower as expected.

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### 6 thoughts on “Do liquidity pools reduce downside?”

1. I’m still working through the math and will update my post once I wrap my head around it, but wanted to point this out. You summed when you should’ve multiplied.

`xy=k` -> `x * y = k` -> `15000 * 1500 = 22500000`

You did `xy=k` -> `x + y = k` -> `15000 + 1500 = 16500`

Ok I followed this guide: https://chainbulletin.com/impermanent-loss-explained-with-examples-math/

Constant product = `x * y = 15000 * 1500 = 22500000`

After price change, 1 ETH = 5 DAI, ratio is 5.

x = sqrt(22500000/5) = 2121.32034 ETH

y = sqrt(22500000*5) = 10606.6017 DAI

2121.32034 * 10606.6017 ~= 22500000

We own 10% of the pool, so we withdraw 212.132034 ETH and 1060.66017 DAI, worth \$2121.
Value if held is \$2250.

Impermanent loss is `(2121 – 2250)/2250` = 5.7%

To check our work, plug numbers into https://dailydefi.org/tools/impermanent-loss-calculator/ and verify the same result.

2. I’m not sure about your math here, not that it’s wrong but I dont see what you’re trying to say clearly.

Keep it simple 200 dai and 200 dollars of eth. Fuck a price.

Eth goes up 20% but over 2 days, 10% a day

200 dai and 220 dolla of eth is re balanced into 210 dai and 210 dolla eth.

Then the second 10% jump occurs. You have 210 dai and 231 dolla of eth.

This is rebalanced to 220.5 dai and 220.5 dolla eth

Total value 441

If you just held both separately, you’d have 200 dai and 200>10%>220>10%>242

You’d have more money if you held eth. In reality the rebalancing occurs quickly with smaller changes so in this example there is less IL. Irl its deff worse than the 1 dollar diff in this example.

Hope this help.

3. I’m not too good in maths and to prevent myself from doing unnecessary calculations I always do stick to staking. Presently I’m using UwUFUFU and I prefer its staking feature to liquidity pool since it’s a single token staking feature