Portfolio Unexpected Loss (ULp) & Risk Contribution (RC)

[frmengineer]

Hi David,

Can you please show (expand) the ULp formula for 4 assets ? I want to know how the formula works (or how it looks like in 4 assets) instead of just memorizing the formula you provide us for 2 assets ? What if we were asked to find ULp for 5 assets...how would the formula looks like ?

2) Can you please also expand/show the Risk Contribution (RC) formula to 4 assets ?

Thanks a lot !

 

[David Harper CFA FRM]

Hi frmengineer, The exam is highly (extremely?) unlikely to go beyond 2-asset wrt RC/UL.

Risk contribution is already in notes & video

I just entered UL(p) from Ong p 133 ... actually looks similar to portfolio variance:

Thanks,

 

[frmengineer]

Hi David,

Thank very much for your reply.

I do notice the two formulas for RCi and ULp are in the notes, but I have been spending over one hour and a half trying to expand the above ULp formula for 3 or 4 assets. On your notes, you expanded the ULp formula for two assets, but I want to know how to expand it to 3 or 4 assets. I want to know how I can expand both RCi and ULp formulas to 3 assets and above. Can you please show me as I try many time but don't really understand how the two summations work in the ULp. Thanks a lot !!! I always appreciate your great work, David!!

 

[David Harper CFA FRM]

Hi frmengineer,

Thanks for your kind words. I started a fresh update to the Ong spreadsheet, with a tab that extends the above to three assets. The implements UL(3 assets) and RC for each of three assets. You will notice that the input changes from a single default correlation to a small correlation matrix. I just did it quickly and haven't yet vetted or published, but it is internally consistent and should give you examples for each, thanks!

https://www.dropbox.com/s/kztn0cs9yghj0hx/6.d.2.Ong_portfolio_UL.xlsx

 

[frmengineer]

Thank you so much David !! You have been always very helpful.

 

[Maximus_FRM2012]

Hi David,

With respect to the portfolio unexpected loss, why is the weights of the unexpected losses not included? For example, when you have two assets in a portfolio and you want the portfolio standard deviation, you would include the weight of the assets in the calculations.

I guess on a bigger level, I've noticed sometimes weights are included in VAR calculations and sometimes weights are excluded. Can you please let me know how we differentiate between when to include weights and when to exclude them for VAR calcs involving more than 1 component.

Its frustrating because I keep having to second guess myself every time I do a VAR calculation.

Maximus

 

[David Harper CFA FRM]

Hi Maximus,

In the case of portfolio unexpected loss (UL), the weights are implicitly included in the unexpected loss of each exposure. I just 5 minutes ago answered a question that is quite related, can you take a look, because I just compare two ways to compute the portfolio VaR, and I think it's related in the sense that the weights are always there, they are just sometimes "implicit:" http://forum.bionicturtle.com/threads/portfolio-variance-quick-last-minute-question.6525/

Thanks,

 

[Maximus_FRM2012]

Hi David,

Thank you for your response. The post you referenced was exactly what I needed. This now makes total sense with the unexpected loss as well.

Maximus

 

[logicpad]

Sorry, cannot find Portfolio Unexpected Loss (ULp) or Risk Contribution for asset i (RCi) for two assets, in the 2013.P2.Credit-Risk notes, could you please let me know chapter and pages? Thank you.

 

[David Harper CFA FRM]

Hi logicpad: They aren't in 2013 notes. Ong's Chapter 6 (Portfolio Effects: Risk Contributions and Unexpected Losses) was an assigned reading in FRM 2012 Credit Risk (Topic 6) but was dropped in the 2013 syllabus. Thanks,

 

[logicpad]

Thank you David.

 

[southeuro]

Hi David, hope all's well.

I am confused with reg. to unexpected loss formulae. I have 2, namely from Jorion and Ong.
Ong's is fairly straight forward: AE * sq.root of [(EDF*var of LGD) + (LGD^2 * Var of EDF)]
Jorion's is AE * sq. root of [(EDF*var of LGD) + (LGD^2 * (EDF) (1-EDF)]

seeming to imply that Var of EDF = (EDF) * (1-EDF)... My mind may be blurred at this point (b/c of hours of study) but am not sure if that's true mathematically, or otherwise. Your thoughts?

Thanks as always.

 

[David Harper CFA FRM]

Hi @southeuro Yes, those formulas are equivalent! variance(EDF) = EDF*(1-EDF) because EDF (which is essentially another way to say "default probability" such that EDF = PD) and is a Bernoulli http://en.wikipedia.org/wiki/Bernoulli_distribution; aka, a binomial with n=1 and the binomial has variance = n*EDF*(1-EDF), so a Bernoulli has variance = 1*EDF*(1-EDF). I hope that helps!

 

[lianne]

Hello, guys,
May I just confirm that the risk contribution and unexpected loss calculations are all dropped in 2014 part 2 exam?
I couldn't find those formulae anywhere... I'm just a little worried as I saw them a few times in the past FRM practice exams.
Thanks a lot in advance!

 

[Nicole Seaman]

Hello @lianne,

Yes, the risk contribution and unexpected loss calculations (Ong, Chapter 6) were dropped after 2012 so they are not in the 2014 syllabus.

Thank you,

Nicole

 

[David Harper CFA FRM]

It is true that Ong Chapter 6 was dropped but please note that the Primary Topics (the list of concepts that begin each Topic before the reading list) does include: "Expected and unexpected losses"
In this way, I think unexpected loss remains on the table (where Ong's dropped reading covered the special case where UL is one standard deviation) but risk contribution is not under examination. Thanks,

 

[lianne]

It is true that Ong Chapter 6 was dropped but please note that the Primary Topics (the list of concepts that begin each Topic before the reading list) does include: "Expected and unexpected losses"
In this way, I think unexpected loss remains on the table (where Ong's dropped reading covered the special case where UL is one standard deviation) but risk contribution is not under examination. Thanks,

Thank you, Nicole and David!
It's really helpful.

 

[umarpak]

Dear Harper,

Hope you are doing good. I need to calculate Credit VaR for my loan Portfolio while working in a bank. My bank has thousands of loans on its books but just for illustration I am giving an example below. Kindly guide if I can proceed with this approach to calculate and present Credit VaR to my Board.

If I need to calculate Credit VaR for my loan portfolio with 3 Loan Assets (assuming default correlation of 1 Flat). Can I do the following:-

For Loan 1 e.g. EL = PD X LGD X EAD = Rs. 120, UL = EAD * sq.root of [(EDF*LGD*(1-LGD)/4 + (LGD^2 * PD (1-PD))] = Rs. 700

For Loan 2 e.g. EL = PD X LGD X EAD = Rs. 150, UL = EAD * sq.root of [(EDF*LGD*(1-LGD)/4 + (LGD^2 * PD (1-PD))] = Rs. 800

For Loan 3 e.g. EL = PD X LGD X EAD = Rs. 180, UL = EAD * sq.root of [(EDF*LGD*(1-LGD)/4 + (LGD^2 * PD (1-PD))] = Rs. 900

Can we say that Portfolio Credit VaR = (120+700)+(150+800)+(180+900) = 820+950+1080 = Rs. 2,850 (under Basel Approach)

What is the confidence level of this Credit VaR? Can we convert this to 99.9% Confidence?

Regards,

Umar