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# Impermanent Loss

## Impermanent Loss

Impermanent loss represents the amount of funds lost to changing price action between two tokens in a liquidity pool vs. the value of those tokens if they were held individually. The bigger the change is, the more impermanent loss is experienced. However, it’s important to note that the loss is impermanent, it is not actually realized until the liquidity pair is re-split and the holder reclaims the two tokens they put in.
The cause for the loss is due to how Automated Market Makers (AMMs) work to allow you to trade with the liquidity pool. They use a constant product model, that in its simplest form looks like: x * y = k Where x is the number of token X and y is the number of token Y, and k is some constant decided by the initial creator of the liquidity pool. How this leads to loss is covered in the example(s) below.
Example: Bingo is looking to farm in the BAS-BNB liquidity pool. He has 1000 BAS tokens worth \$1 each for \$1000 total value, and 1 BNB (worth \$1000). To make a liquidity token pairing, he goes to PancakeSwap and pairs them together: 1000 BAS + 1 BNB (pairs need to be made with equal values). ---
Scenario 1: After he makes his pairing, BAS continues to grow, doubling in value to \$2. BNB remains the same. If Bingo didn’t farm, he would have: 1000 BAS * \$2 + 1 BNB * \$1000 = \$3000 (HODL value)
If his tokens were paired together, buy/selling of BAS to get to a value of \$2 would result in a decrease in the number of BAS in the liquidity pool, and an increase in BNB, to keep the value k constant:
~707 BAS * \$2 + ~1.42 BNB * \$1000 = ~\$2828
In this scenario, if Bingo broke his liquidity pair, he would experience an impermanent loss of \$3000 - \$2828 = \$172 (~5.7%). Note that he is still up from his initial \$2000 investment if he farms, but not as much as if he didn’t unless he made more than \$172 from farming. ---
Scenario 2: After he makes his pairing, BAS falls in value, halving in value to \$0.5. BNB remains the same. If Bingo didn’t farm, he would have: 1000 BAS * \$0.5 + 1 BNB * \$1000 = \$1500 (HODL value)
If his tokens were paired together, buy/selling of BAS to get to a value of \$0.5 would result in a increase in the number of BAS in the liquidity pool, and an decrease in BNB, to keep the value k constant:
~1414 BAS * \$0.5 + ~0.7 BNB * \$1000 = ~\$1407
In this scenario, if Bingo broke his liquidity pair, he would experience an impermanent loss of \$1500 - \$1414 = \$86 (~5.7%) in addition to the lower token price.
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Scenario 3: After he makes his pairing, BAS continues to grow, doubling in value to \$2. BNB also doubles in value \$2000 (great day for Bingo!). If Bingo didn’t farm, he would have: 1000 BAS * \$2 + 1 BNB * \$2000 = \$4000 (HODL value)
If his tokens were paired together, there is no effect on the number of BAS or BNB in the liquidity pool because the two token both increased by the same factor (2x).
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Scenario 4: After he makes his pairing, BAS continues to grow, doubling in value to \$2, but BNB drops in value to \$500. If Bingo didn’t farm, he would have: 1000 BAS * \$2 + 1 BNB * \$500 = \$2500 (HODL value)
If his tokens were paired together, buy/selling from the liquidity pool to reach \$2 for BAS and \$500 for BNB would result in a decrease in the number of BAS in the liquidity pool, and an increase in BNB, to keep the value k constant:
~500 BAS * \$2 + ~2 BNB * \$500 = ~\$2000 In this scenario, if Bingo broke his liquidity pair, he would experience an impermanent loss of \$2500 - \$2000 = \$500 (~20%). In this particular case, because the token values have moved 2x in opposite directions, he’s experiencing a lot of impermanent loss.

### Summary

The goal of these scenarios is to illustrate that any relative price movement between BAS and BNB generates some level of impermanent loss. In an ideal world, both tokens increase in value, and at the same rate so you can enjoy the rewards from farming, while also seeing your token values increase. In reality, some level of impermanent loss is likely, so make a profit from staking, the goal is find a farm with a sufficiently high APR and farm it long enough to generate gains that outpace the impermanent loss.
A handy tool for calculating impermanent loss can be found here (https://dailydefi.org/tools/impermanent-loss-calculator/). You can use it to estimate how much impermanent loss you might expect for changing token values and weigh it against the APR of the farm you are considering and how long you might want to stake for.

### A final note on farming strategies and impermanent loss:

A common strategy many apes in crypto follow is to choose liquidity pools that have at least one stablecoin in them to try and minimize impermanent loss, since one token has a fixed value. This strategy can also work against you however, since you are essentially guaranteed to experience impermanent loss since both tokens cannot move together.
This leads to another popular strategy (especially in bear markets) where both tokens in the liquidity pool are stablecoins. In this strategy, there is no potential for impermanent loss since both token prices are fixed. There is also no potential for price growth, but this allows you to hedge against a bear market since the prices will not drop either. The tradeoff is that the APR for staking stable pairs is usually low relative to other tokens.
Farming liquidity pairs whether neither token is a stablecoin comes with the most risk/reward. Both tokens can rise or fall together, leaving you with little impermanent loss, but you are subject to the market forces on two tokens. The risk comes in if the token values move oppositely, as this can generate a lot of impermanent loss. These liquidity pairs usually come with the highest APRs to offset their risk to the holders.