# some formulas

Discussion in 'P2.T6. Credit Risk (25%)' started by ravishankar80, Jun 23, 2008.

1. ### ravishankar80New Member

A couple of questions on credit risk

I do not have the 3 chapters of Ong in the core reading material and I am relying entirely on your notes for these. I was going through the edit grids for portfolio loss;could you provide the formulas for
-Portfolio unexpected loss
-Risk contribution of exposure

-Also could you post the answers to Practice question 5 for credit risk
Thanks a lot.

Ravi

2. ### David Harper CFA FRMDavid Harper CFA FRM (test)

Hi Ravi,

The credit notes will publish this week...

I just added images of the formula (for portfolio UL and RC) directly into the EditGrid. Please let me know if you think images-in-EditGrid is helpful, I'd do more of that if it helps?

http://www.bionicturtle.com/images/editgrid/ong6_port_ul_rc.png

Note the Portfolio UL is maybe easier than it looks. It sums the following product for every pairwise asset:
(UL asset 1)(UL asset 2)(correlation between #1 and #2).
That product for all permutation of assets.

So, in a two asset portfolio, there are four permutations:

(UL #1)(UL #1)(correlation #1 with #1) +
(UL #1)(UL #2)(correlation #1 with #2) +
(UL #2)(UL #1)(correlation #2 with #1) +
(UL #2)(UL #2)(correlation #2 with #2)

The second and third above reduce to:
(2)(correlation #1 with #2)(UL#1)(UL#2)

So you get the formula in the XLS (a thing's correlation with itself = 1)

(UL #1)(UL #1)(correlation #1 with #1) +
(UL #2)(UL #2)(correlation #2 with #2)
(2)(correlation #1 with #2)(UL#1)(UL#2)

which =
(UL #1)^2 + (UL #2)^2 +
(2)(correlation #1 with #2)(UL#1)(UL#2)

and take the square root, finally.

Sorry about Credit A, Q5, an oversight, it is posted now.

Thanks,
David

3. ### David Harper CFA FRMDavid Harper CFA FRM (test)

....Although, it occurs the RC formula is not as helpful as Ong's 6.5b
(you will see this in the notes):

http://www.bionicturtle.com/images/forum/ong6_rc_65b.png

where i'd suggest focusing on the correlation (rho) such that the asset i's risk contribution is a function of it's pairwise correlation with other portfolio assets. It is the only thing that matters. Idiosyncratic risk (specific to the bond) is eliminated via the "free lunch" that is diversification. At an extreme, if the bond had only idiosyncratic risk and no pairwise correlations, its RC would be zero! Ong: "Risk contribution is a measure of un-diversified risk of an asset in the portfolio" That undiversified risk is measured in rho above.

David

4. ### ravishankar80New Member

That was clearly explained and very helpful .Thanks a lot.