Finance Junkie
Posts: 205
Joined: Mon Feb 04, 2013 3:35 pm


Postby » Sat Nov 01, 2014 4:03 pm

Under Malz's single-factor credit model, a(T) = beta*m + SQRT(1-beta^2)*epsilon, a
firm has a beta of 0.40 and an unconditional default probability of 3.0%. If we enter a
modest economic downturn, such that the value of (m) = -1.0, what is the (downturn)
conditional default probability?
a) 3.0%
b) 4.6%
c) 5.3%
d) 6.8%

Since the unconditional PD = 3.0%, k = NORM.S.INV(3%) = -1.88.
The mean of the conditional distribution is (-beta*m) and the distance to default = k -
beta*m = -1.480;
As the conditional variance is (1-beta^2), the conditional standard deviation = SQRT(1-
beta^2) = 0.9165
and the normalized distance to default = (k - beta*m)/SQRT(1-beta^2) = -1.480/0.9165 = -
1.615, and the implied PD = NORM.S.DIST(-1.615) = 5.318%.

Here how did they find K

Finance Junkie
Posts: 730
Joined: Wed Apr 09, 2014 6:28 am


Postby edupristine » Tue Nov 04, 2014 9:55 am

The Excel NORM.S.INV function calculates the inverse of the Standard Normal Cumulative Distribution Function for a supplied probability value.

The format of the function is : NORM.S.INV( probability )

Where the probability argument is the probability value (between 0 and 1), for which you want to calculate the inverse of the standard normal cumulative distribution function.

You enter the “probability that a value Z is up to…” and it returns that value Z (in terms of “sigmas”, because it is the standardized distribution with average 0 and sigma 1).

Example: NORMSINV(0.5)=0, NORMSINV(0.00135)=-3, NORMSINV(0.9772)=2

NORMSINV(0) and NORMSINV(1) will return error, because they correspond to – infinte sigmas and +infinte sigmas.

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