KMV Distance to Default

[ChadWOB]

This formula seems to be pretty straightforward, but I'm not getting the correct answer (this is a practice question from Schweser)

Asumming l/t to s/t debt ratio is less than 1.5. Have assets of $700mm, s/t liabilities of $120mm and l/t liabilities of $300m. The standard deviation of asset value is $76mm. Using KMV model, what is the distance to default?

This is how I approach the problem:

1) Calculate Default Threshold = s/t debt + .5 * l/t debt

2) Calculate DD = Assets - Default Threshold / StDev.

Answer should be 5.66 StDevs -HOWEVER I have trouble with the default threshold calculation. I take the 120 plus .5, which is 180 correct (half of 120 is 60)? Multiply by 300 which gives me 54,000.

If I take 700 - 54,000/76 I get a huge number, way off base. This seems like it should be very easy, what is wrong with my approach?

 

[ChadWOB]

Please disregard....order of operations problem. Time for a break!!!

 

[shanlane]

Hello,

Is it just me or are there MANY iterations of this formula?

I have seen the first term in the numerator written as Expected return on assets, expected value of equity and expected value of the assets.

What is the proper formula?

Thanks!

Shannon

 

[David Harper CFA FRM]

i'll make a summary post to my notebook at the top (@ http://forum.bionicturtle.com/forums/davids-notebook.54/), since it appears to be too much to ask some of you to conduct a search (i.e., this is one of the most-answered questions on the forum)

 

[ChadWOB]

Shannon,

I have seen numerous variations as well. Including (Assets PLUS Liabilities - Default Theshold) in the numerator. David, can you clarify why the first term would be Assets plus Liabilities would be the term used for Assets in the numerator?

I am unclear as to the proper formula, but am aware of the variations of it so will go by trial and error on the actual exam when I see this question.

 

[David Harper CFA FRM]

Yes, when i get a chance, i will post a summary; if you search "Merton", you should find about two dozen answer to this (or 173, whichever is higher), in the meantime, but i will put up a condensed summary post, when i get a chance, thanks,

 

[David Harper CFA FRM]

for those with spreadsheet access, and the inclination, as i mentioned in the T6.c. video, this learning XLS contains the total Merton on one spreadsheet:
http://www.bionicturtle.com/how-to/spreadsheet/2011.t6.c.1.-merton
... reconciling all the manifestations (there is really only one Merton model, in two big steps, only the perspective, and alas the notation, around it vary).

But i will make a summary post ASAP.

 

[dev]

Was trying to implement KMV model for PD estimation. One doubt, after estimating the DD (distance to default) how to map the same to Expected default frequency.

For example, “For a particular company we compute and get a DD of 3. To compute EDF, 2000 companies last year has a DD of 3, and 15 of these firms defaulted after one year. The expected default frequency for the company = 15/2000 i.e. 0.75%”

While surfing through net, i got an diagram mapping of EDF to DD.




The diagram is obtained based upon historical DD mapped to EDF. Hence when we compute DD, by using the graph we can directly compute the EDF.
We are not having co ordinates for the same or not know to compute the same.

We require the co ordinates to map the dd computed. Can you guide us in plotting the EDF – DD graph or any other method to map DD to EDF.