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# PD of default

#### caramel

##### Member
Whats the difference between probability of default and marginal probability of default. Was trying the below

45. A portfolio consists of 17 uncorrelated bonds, each rated B. The 1-year marginal default
probability of each bond is 5.93%. Assuming an even spread of default probability over the year
for each of the bonds, what is the probability of exactly 2 bonds defaulting in the first month?
a. 0.0325%
b. 0.325%
c. 0.024%
d. 0.24%
2006 FRM Practice Exams 39
Given a 1-year marginal default rate of 5.93%, the 1-month marginal default rate
is 1 – (1 – 0.0593)(1/12) = 0.00508.
The number of combinations of 2 bonds from 17 bonds is 17*16/2, and so the
probability of exactly 2 bonds defaulting in the first month is:
(17*16/2) * (0.00508)2 * (1 – 0.00508)15 = 0.325%

#### David Harper CFA FRM

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

As an old question, it relies on Saunders' definition of marginal PD as the probability of default in any given full year, or during a given year.

(I am not very keen on marginal PD, and have long since asked GARP to replace with conditional PD: http://www.bionicturtle.com/forum/threads/cumulative-probability-of-default.573/
... i think it is confusing because statistically "marginal" is synonymous with "unconditional" yet in the PD context it is often used to mean conditional PD)

but note, this question arguably works even if "marginal" is deleted, or even replaced with "unconditional" or even "conditional"

A better question, IMO, would simply ask "if the annual default probability is 5.93% ..."
Thanks,

#### inderjeet.chandnani

##### New Member
What is the difference in approach if I calculate monthly probability 1st 5.93^1/12 then we calculate monthly probability of not defaulting, answer seems to be different so I was just trying to figure out difference between approaches