# Impermanent loss on Covered calls pooled with USD

Hello

Here is my problem.

I have some tokens called CHNG. I Write some American calls on it and pool the calls with USD in a liquidity pool.

Let’s say I have 1000 Calls worth 0.1 each = 100 USD that I pool with 100 USDT in a 50/50 pool. 200USD = 100+100.

Price of the call skyrockets to 0.5. Holding separately the 2 assets would be worth 500+100=600USD.

Then the IL for such diff in price appreciation is 25% as a rule of thumb.

Compared to just holding, I would then be worth 600\*0.75=450=225+225 by being in the pool

So now I am having 450 Calls and 225 USD.

It means I now have 550 Calls sold. If I want to cancel my calls, I will get only 450 CHNG.

If the calls I sold are exercised at the exercise price, my PnL is then

* for 550 assets: price at which I sold the calls + exercise price -purchase price
* for 450 assets: market price of CHNG – purchase price

to which I have to add the rewards r for pooling

Whereas if I had held the spot i/o pooling written options: 1000 \*(market price – purchase price)

Doing a bit of equation I find that pooling is more profitable until market price is less than : sum of
1. average premium collected on the 550 options sold

2. exercise price

3. total rewards / 550

Is this correct ?

Thx

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