We can illustrate the use of this approach with Global
Crossing. At the end of 2001, Global Crossing had been
assignedabondratingofCCCbyS&P.Basedonthisbond
ratingandthehistoryofdefaultsbetween 1971 and2001,we
wouldhaveestimatedacumulativeprobabilityofbankruptcy
of 51.38 percent over the next 10 years for the firm.
Based on Bond Price
The conventional approach to valuing bonds discounts
promisedcashflowsbackatacostofdebtthatincorporatesa
default spread to come up with a price. Consider an
alternativeapproach. Wecoulddiscount theexpectedcash
flowsonthebond,whichwouldbelowerthanthepromised
cash flows because of the possibility of default, at the
risk-free rate to price the bond. If we assume a constant
annualprobabilityofdefault,wecanwritethebondpriceas
follows for a bond with fixed coupon maturing inNyears.
Thisequationcannowbeusedinconjunctionwiththeprice
on a traded corporate bond to backout theprobability of
default. We are solving for an annualized probability of
defaultoverthelifeofthebond,andignoringtherealitythat
theprobabilityofdefaultwillbe higherintheearlieryears
and decline in the later years.
Whilethisapproachhastheattractionofbeingasimpleone,
we wouldhasten to add thefollowingcaveats in using it.
First,notethatnotonlydoweneedtofindastraightbond
issued by the company—special features such as