They don't need to, but it doesn't affect the numbers, because they have to pay it out if pirate defaults. You can strike out the line (which I did in the quote above) and just compare the 2 cases. Instead of selling 3000 shares at 1.038, they should instead invest 960 btc with pirate because the profit would be greater with the same loss if pirate defaults.
If what you are saying is that they should do case 1 AND case 2 at the same time, then that means if pirate defaults they will lose 1920 bitcoins. Then in that case, why not just put 1920 btc with pirate instead?
I agree putting 1920 BTC with Pirate is financially more profitable than this round of PPT bonds in all cases, but I'm not sure how that's relevant - no investment needed to be made initially by any of them other than the 960 BTC in the PPT fund. (PPT.A is simply being reused, no 8 BTC asset creation fee)
More importantly, we're ignoring a few key aspects of this.
Assuming the 113.95 BTC above the 3000 BTC is not invested with Pirate
and not earning any interest (unlikely), if Pirate defaults, they will lose 960 - 113.95 BTC =
846.05 BTC - but only if he defaults before the first payment.
If he defaults after the first payment, they will lose 960 - 113.95 - (.07 * 3000) =
636.05 BTC.
After the second payment, 960 - 113.95 - (.14 * 3000) =
426.05 BTC.
After the third payment, 960 - 113.95 - (.21 * 3000) =
216.05 BTC.
If he does not default, they will make 3113.95 - 3000 =
113.95 BTCAn investment of 960 BTC into Pirate would lose
960 BTC if Pirate defaults before the first payment.
960 - (.07 * 960) =
892.8 BTC loss if Pirate defaults after the first payment.
960 - (.14 * 960) =
825.6 BTC loss if Pirate defaults after the second payment.
960 - (.21 * 960) =
758.4 BTC loss if Pirate defaults after the third payment.
And finally a .28 * 960 =
268.8 BTC profit if Pirate does not default.
Effectively, the first usage of 960 BTC is better if Pirate defaults before all 4 payments, the second if he does not default. I'm not necessarily arguing for PPT's choice here, but it seems to me to have a similar effect to a partial hedge. They make less if Pirate pays out, but lose less if he defaults.