A question on implied default probability

FRM
#1

Hi All,

I have some problems with the following question about implied default probability:

Suppose you want to estimate the implied default probaility for a BB-rated discount corporate bond.

  • The T-bond (a risk-free bond) yields 12% per year.

  • The 1-year BB-rated discount bond yields 15.8% per year.

  • Year 2-year BB-rated discount bond yields 18% per year.

If the recovery rate on BB-rated bond is expected to be 0%, and the marginal default probaility in year 1 is 5%, which of the following is the best estimate of the risk-netural probability that the BB-rated discount bond defaults within next 2 years?

The answer is 9.91%. Is anyone know how to arrive this answer?

Thanks.

#2

Sam, follow the procedure :

((PD x RR)+ (1-PD)(1-RR)) > 1+R

The above has to hold for the investment in bonds. ( Else one would not invest)

For 2 years this Probability adjusted value must be > than what it would yield if one were to invest in treasury

Hence, ((PD X RR + (1-PD)(-RR)) (1+Yield of 2 years)^2> (1+Risk Free)^2.

Solve the inequality to get the result.

(Note tha the qs. asks for BEST ESTIMATE, … not exact answer i.e. exact probability of default)

#3

Is this Part 2 stuff? I really hope so…

#4

Yeah Very much. Hope you are not talking about it;s relevance.

#5

Thankis ABAL. I still get many chapters and questions on hand not yet revised.

#6

Hi ABAL,

Just encountered a similar problem but it calculates in this way. However, using this methodology, the answer is 6.85%. I wonder what is wrong with th following methodology:

Calculate 1year forward rate for discount bond: (1.18)^2/1.158 = 20.24%

Then PD = 1- [(1+T-bond yield) / (1+1 year forward rate fo discount bond)] = 1 - (1.12/1.2024) = 6.85%

#7

Sam,

Need th entire problem. In the above problem the RR is not mentioned. Quote the qs.

Meanwhile, how are you scoring in the tests?

#8

Hi ABAL,

The question is as folllows:

The rate on a 1-year Treausry note is 3% and the rate on a 2-year T-note is 4.5%. THe rate on a 1-year corporate note is 5% and the rate on a 2-year corporate note is 6.8%. The implied probability of default on the corporate note in year 2 is closest to:

Answer is 2.4%

I haven’t yet started the whole set of questions in 4-hours limited time. Thanks for your help

#9

Sam,

This is way too easy to solve. Frankly, they have just asked for the z- spread. So 6.8%-4.5%=2.3%. Again assuming RR being 0 (this assumption part is tricky) Just equate Instatantenous PD= Zt/(1-RR), put RR 0 and there is your answer.