Quote from: BinaryMage on May 26, 2012, 06:28:08 AM

Quote from: coblee on May 26, 2012, 05:54:12 AM

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 BTC

An 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.

Thanks for reminding me that if pirate defaults, PPT still earns the 113.95. I fixed it in my post above. Here it is again:

Quote

Case 1 - Sell 3000 shares of PPT.A at 1.038
  no default: PPT makes 3000 * .038 = 114
  default: PPT loses 960 - 114 = 846

Case 2 - Put 846 btc with pirate
  no default: PPT makes 846 * .28 = 237
  default: PPT loses 846

Difference is 237 - 114 = 123
So you are effectively losing 123 bitcoins for this round. Your loss for if pirate defaults is the same.

Yes, this only is true if pirate defaults within the first week. If pirate defaults after that, PPT will have made more money to cover their loses. In order to do a better apples to apples comparison, it's easier to use compounded interest in this scenario since then it doesn't matter when pirate defaults. 7% interest compounded for 4 weeks is about 31%.

If pirate doesn't default, pirate will payout 1.31 to PPT but PPT only pays 1.28 to bond holders, so PPT makes an addition .03 per share. That's only if no default.

Case 1 - Sell 3000 shares of PPT.A at 1.038
  no default: PPT makes 3000 * (.038 + .03) = 204
  default: PPT loses 960 - 114 = 846

Case 2 - Put 846 btc with pirate
  no default: PPT makes 846 * .31 = 262
  default: PPT loses 846

Difference is 262 - 204 = 58
So if you are do compounding interests, you only lose 58 bitcoins for this round.