Credit analysis, Reduced Form Models

[Sparrow]

Hey guys,
I’m a little confused. CFA book 5 page 414 says: “It can be shown that this maximum likelihood estimation is equivalent to running the following simple linear regression to estimate the coefficients:
ln (d / (1-d)) = a + ∑bx, where the dependent variable includes the default flag (d = 1 if default, 0 if no default).
This is called a logistic regression…”
Is it ok that if d equals 1, we divide 1 by 0? Or am I missing something?
Thanks

 

[tickersu]

Sparrow wrote:
Hey guys,
I’m a little confused. CFA book 5 page 414 says: “It can be shown that this maximum likelihood estimation is equivalent to running the following simple linear regression to estimate the coefficients:
ln (d / (1-d)) = a + ∑bx, where the dependent variable includes the default flag (d = 1 if default, 0 if no default).
This is called a logistic regression…”
Is it ok that if d equals 1, we divide 1 by 0? Or am I missing something?
Thanks

The given model is for the ln(odds) for default (probability of d, default, is between 0 and 1). For example, if the probability of default is 0.8, then the value of your DV would be Ln[0.8/(1-0.8)]= Ln(4).
They’re also explaining that when you enter data, a default is coded as a 1, and no default is coded as 0.
Hope this helps.

 

[Sparrow]

Oh, I see.. I think I got it now. Thanks for a quick response!

 

[tickersu]

Sparrow wrote:
Oh, I see.. I think I got it now. Thanks for a quick response!

Glad to help.