Bond Math

Daniel Davies dsquared at al-islam.com
Fri Oct 25 10:49:32 PDT 2002



>Date: Fri, 25 Oct 2002 01:28:58 -0400 (EDT)
>From: Michael Pollak
>Subject: Bond math

Doing the actual sums on this is hellish, and I'm certainly not going to attempt it after lunch on a Friday. But the intuition behind Michael's calculation is right, and something like it is certainly the best way to think about this sort of thing. A few comments:

The bond that people are talking about in the blatts is the Brazilian "C-Bond". The C-Bond is the biggest and most liquid of the Brazilian government bonds; it isn't a Brady Bond and the majority of its interest is capitalized rather than paid out as a cash coupon (the "C" stands for "Capitalisation". Details are available on http://eve.bradynet.com/cgi-bin/cyberexchange?ticker=brcbond , and the "Colour of the Market" discussion boards on bradynet are a fine place to find out all sorts of things about emerging market debt.

The C-Bond is a Brady Bond, so the yield quoted on it is a "stripped yield". Basically, the coupons on Brady Bonds are protected by "collateral"; a special series of US Treasury bonds printed for the purpose and held at the NY Fed. This shouldn't matter so much though, because the C-Bond has low coupons and doesn't amortise.

So yeh, basically, the product of the probability of default and the loss in event of default ought to be such as to make the expected return on a C-Bond equal to the expected return on a Treasury bond (plus a small residual risk premium of maybe 1-2% for various technical reasons). I haven't checked Michael's multiplication but it looks right.

NB that the 50% loss-in-event is most likely some broker's back of envelope number which has been elevated into a parameter precisely by its use in "probability of default" calculations printed in the newspapers. In general, recovery rates are more like 60-70%.

John's almanac was fascinating. I'd note additionally that not listed there were the bonds of the Kingdom of Siam (Thailand), which have always paid every single coupon in history, but which still typically trade at a discount to Latin American bonds.

dd

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