Akeyinputtothisapproachistheestimateofthecumulative
probability of distress over the valuation period. In this
section,weconsiderthreewaysinwhichwecanestimatethis
probability.Thefirstisastatisticalapproach,wherewerelate
the probability of distress to a firm’s observable
characteristics—firm size, leverage, and profitability, for
instance—by contrasting firms that havegone bankruptin
prior years with firms that did not. The second is a less
data-intensiveapproach,whereweusethebondratingfora
firmand theempirical default ratesoffirms in that rating
classtoestimatetheprobabilityofdistress.Thethirdistouse
thepricesofcorporatebondsissuedbythefirmtobackout
the probability of distress.
Statistical Approaches
The fact that hundreds of firms go bankrupt every year
provides us with a rich database that canbe examinedto
evaluatebothwhybankruptcyoccursandhowtopredictthe
likelihoodoffuturebankruptcy. Oneoftheearlieststudies
thatusedthisapproachwasbyAltman(1968),whereheused
linear discriminant analysis to arrive ata measure that he
calledthe Z-Score.In this first paper,which he has since
updated several times,
11 the Z-Score was a function of five ratios:
AltmanarguedthatwecouldcomputetheZ-Scoresforfirms
andusethemtoforecastwhichfirmswouldgobankrupt,and