Post
Topic
Board Securities
Re: [GLBSE] MORE Pirate Pass Through Bonds!
by
coblee
on 26/05/2012, 18:40:48 UTC
Can you show the math behind that break-even value?

1.28 / 1.07^4

Oh, we were discussing break-even in comparison to simply investing 960 BTC with Pirate, not general break-even for a non-default.

1.28 / 1.31 does not take into consideration the lost opportunity cost of 960 btc sitting there doing nothing. So that's not the true break even cost. Because PPT would earn more if they took the 960 btc and invested directly with Pirate since they are risking to lose that anyways if pirate defaults.

Here's the algebra for calculating the true break-even with compounding:

Case 1 - Sell 1 share of PPT at 1+x (if sold at 1.038 then x=.038)
  no default: PPT makes x+.03 (.03 is the extra you get for compounding)
  default: PPT loses .32-x

Case 2 - Put .32-x btc with pirate
  no default: PPT makes (.32-x)*.31 = .0992-.31x
  default: PPT loses .32-x

So break-even is when the 2 "no default" cases are equal.

  x + .03 = .0992 - .31x
  1.31x = .0692
  x = .0692 / 1.31
  x = .05284427

For the compounding case, true break-even is 1.0528 btc per share.
Selling shares less than 1.0528 is a losing proposition for PPT.