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# Altman's Z score

#### shanlane

##### Active Member
Hello,

I have two simple questions about Alman's Z score I ws hoping you could answer for me.

Are we supposed to memorize the formula for this or just how to interpret it? It seem s a little silly to have to memorize a bunch of betas and their corresponding variables, but if that's what they want I guess I will do it.

What do you mean by the "Ignorant zone"? I assume this just means that we just have no decision as far as default or no default is concerned. Is this accurate?

Thanks!!
Shannon

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Shannon,

No, the test will *never* ask you to know the Altman's Z coefficients; it's use to us is merely that it's the leading example of a linear discriminant (a linear combination of independent variables gives a line used to divide "probably will not default" from "probably will default").

The "zone of ignorance" (it occurs to me this would make a nice question!) functions like the YELLOW ZONE in the Basel backtest: in both cases, there cannot be certainty, there are two errors that can be made. So these zones represent zones where the power/size of the test is insufficient such that, in a sense, the model does not want to make a formal decision.

In Altman's I *think* the null hypothesis is "the firm will default" such that:
• Z of less than 1.81 (http://en.wikipedia.org/wiki/Altman_Z-score; interesting, looks like it's also called a "Grey zone") signifies "let's accept the null;" i.e., we predict default
• Z of greater than 2.99 signifies: reject the null and predict NON-default
So (this part i am just musing), maybe they decided that, under this definition of the null, a Type I error (predict non-default when the firm does; i.e., mistakenly reject a true null) is worse than a Type II error (predict default but the firm does not).
... in which case maybe a 2.50 predicts non-default (a firm with this score falls on the "wrong side" of the line), but the probability of a Type I error is just too high. So they carve out a zone, bumping up the score to 2.99 is the way, even after crossing the point where the line would predict "non-default," of simply reducing the probability of costly Type I error.

Thanks, David

Great.

Thanks!!

Shannon