Credit Default Swaps question (Bill Ackman)

I am curious about Credit default swaps, specifically the trade of bill ackman (2.6bn) in 2020.
As far as I understand, Bill payed 1.6bn in CDS contracts, and the contracts after spread widening due to corona were worth 4.2bn. The difference would be a 2.6bn profit. However, since the value of the CDS contracts is comprised of the sum of all the periodic payments (In the case of ackman, 27million per month increased to around 70mil monthly payments for 5 years), wouldn’t that mean that ackman still hasn’t received the full 2.6bn in profit? In other words, is my assumption correct that he is still getting payed 70mil every month from the person/institution he sold the CDS to, until the 5years expire? Additionally, i dont quite get why the media used the 27million dollar payment figure when the true price Bill payed was 1.6bn....

 
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I have no idea what the numbers are in real life, but here are mechanics with made up numbers to illustrate*...

1. He bought protection via CDS on an underlying notional of $5bn. At the time, the market determined rate for protection is 2% so he is required to pay 2% per year on that notional for protection. This amounts to a $100m per year in payments he is making to his counterparty.

2. World explodes. Market determined rate for protection is now 10%. He now sells protection on underlying notional of $5bn. For selling this protection, he receives $500m per year for the new trade from counterparty.

3. On net between the two trades, he is owed $400m per year. If trade is done at same bank, he says you owe me a net $400m * 5 years, pay me market equivalent now (let's call it $1.8bn or w/e NPV works out to). If done at different banks, he tells them - go sort this out with each other and pay me market equivalent now. 

Now, he would have been getting marked to market and receiving margin from counterparty the entire time before he exited, but that is the overall mechanism for how it works. I am also taking some liberties with how CDS contracts work as it is a fair bit more complicated and the actual details can vary based on instrument.

 

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