VRM Credit Risk Chapter 6

Hi David @David Harper CFA FRM

I came across the following exercise:
1635966183288.png
which has the solution
1635966289829.png

This is a simple question but one thing drove me mad (I do not exclude the opportunity my mind went blank due to being tired :D ) But anyway, I calculated variance in 6.11 as E(L^2) - {E(L)}^2 and
E(L^2) = 0.995*0^2 + 0.005* { 1,000,000 * 0.6}^2
Then Variance = 1,791,000 ----------> st.dev = sqrt(1,791,000) = 42,320 ----> this part coincides with the answer an this is OK.

However, when I try to calculate portfolio variance with 3 similar loans I get:

1635966473650.png
Variance = 3*1,791,000 * {1 + 2*0.2} = 7,522,200 (and this also coincides with book , where it is 0.007522

But then I get a mismatch when I take the square out of this: in my case, sqrt(7,522,200) = 2742.67$
whereas sqrt(0.007522) = 0.086729.
There should be a mistake somewhere, but can not find it.
could you please help me?Thanks
 

Attachments

  • 1635966216290.png
    1635966216290.png
    40.6 KB · Views: 4

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi @alexwallace GARP's solution solves for σ as percentage of portfolio size; you can do dollar variance, just like you are doing, but yours is just off by 1,000 as it should be sqrt($600,000^2*0.5%-$3,000^2) = sqrt(1,791,000,000) = $42,320; i.e., it's 1.791 billion not 1.791 million. Then your formula works! In regard to 6.13, 99.82% = 1 - 0.18% and 99.94% = 1 - 0.06%. GARP is using the default probability (e.g., PD of 0.18%) to calibrate the EC level ... oh but wait, that's the math, but it looks to me like their interpretation is incorrect. I think this Q&A is flawed, but I've only just now looked at it. Given the setup (geez the language is just so lazy overall), the question should eliminate "A bank currently has a BBB credit rating." and should ask "If a bank wants to target a BBB credit rating, how much economic capital (i.e., at what confidence level) should it maintain". I'll take a closer look, you can see the math, but I think they whacked the logic. Thanks,
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi @alexwallace Today I took a fresh look at 6.13, and I finally get what they are doing but it's just an awkward (if not inaccurate) way to phrase the question. This concept is really based on prior years' Nocco & Stulz reading, so question 6.13 should be more like:
  • 6.13.a. If the company wants to target a rating of BBB, how much economic (or equity) capital should it hold (or carry)? Answer: Because a BBB-rated company has a one-year (conditional) PD of 0.18%, it should not breach (i.e., fall below) the default threshold with probability of 1 - 0.18% = 99.82% or confidence level. EC confidence level is 99.82% because the implied probability of "insolvency" is 0.18%.
  • 6.13.a. If the company wants to target a rating of A, how much economic (or equity) capital should it hold (or carry)? Answer: Because a BBB-rated company has a one-year (conditional) PD of 0.06%, it should not breach (i.e., fall below) the default threshold with probability of 1 - 0.06% = 99.94% or confidence level. EC confidence level is 99.94% because the implied probability of "insolvency" is 0.06%.
Then you can see how they've taken this concept of "targeting the company to have an as-if rating" to phrase (a) and (b), but I think it's pretty weak. Thanks,
 
Top