Operational risk Margin - DCAT - Spring 2017 Q21

adilvirani

Hi @javid,

In this question, it mentions that "Assume that the MCT total uncapped operational risk margin is less than 30% of the
sum of asset and insurance risk."

How I perceive this is, cap is always 0.30(Insurance + Market + Credit risk margins). So the above statement means that currently the operational risk margin is compA + compB, meaning uncapped is lower than the capped, and hence the operational risk margin is equal to the comp(A) + comp(B). If market risk changes(equity component), it would only affect the cap(CR0)correct? and hence uncapped was lower than capped, we should still use operational risk margin as 5000 which is lower of 5000 and 0.30 of new CR0. So I think operational risk margin should still be 5000 even in DCAT scenario. Please let me know why in examiner report they have decreased the operational risk margin.

Thanks in advance

Cheers
Adil

chrisboersma

all it is trying to say is that:

[1] 5000 = min(30% x (A+I), 8.5% x (A+I) + f(DWP,GWP,CWP)) = 8.5% x (A+I) + f(DWP,GWP,CWP)

Or that 8.5% x (A+I) + f(DWP,GWP,CWP) is not capped by 30% x (A+I) so we can safely ALWAYS use and assume Operational Margin = 8.5% x (A+I) + f(DWP,GWP,CWP) (in both adverse and base scenario). Note: if the cap doesn't affect the base scenario it certainly wont affect the lower adverse scenario.

Which allows us to easily solve for ? (the new Operation Margin):

[2] 5000 = A(market) x 8.5% + C | [before adverse]
[3] ? = (A(market) - Reduction in Market Margin) x 8.5% + C | [after adverse]
[4] = [2] - [3] = 5000 - ? = A(market) x 8.5% - (A(market) - Reduction in Market Margin) x 8.5%
[4] = 8.5% x Reduction in Market Margin = 5000 - ? = 918
.
[3] = ? = 5000 - 8.5% x Reduction in Market Margin = 4082

Given Market Assets = 90,000
reduction = 36,000
Reduction in Market Margin = 36,000 x 30% = 10,800
5000 - 10,800 x 8.5% = 4,082 = ? (Operational Risk Margin AFTER adverse scenario).

We are using equations [2] (base) and [3] (adverse) to calculate the unknown Operation Risk Margin for the adverse scenario.

This can ONLY be done because we assume that:

5000 = min(30% x (A+I), 8.5% x (A+I) + f(DWP,GWP,CWP)) = 8.5% x (A+I) + f(DWP,GWP,CWP)

If we didn't have that statement, we would be left with calculating either:
30% x A(market) + C
OR
8.5% x A(market) + C

Which would leave the answer as ambiguous.

We also could've just as easily calculated C directly:

5000 = 8.5% x A(market) + C = 8.5% x 90,000 x 30% + C
Where, C = 2,705 = C = 8.5% x [I + A(credit)] + f(DWP,CWP,AWP)

We don't need to know what I, A(credit), f(DWP,CWP,AWP) are, we just need to know that the SUM doesn't change in the base and adverse scenarios so it wont impact the operational risk margin calculation.

Then the adverse scenario we have:

? = 8.5% x A(market) + C = 8.5% x (90,000 - 36,000) x 30% + 2,705
= 4,802

Which of course is the same answer.

adilvirani

Oh i completely forgot about that 8.5 percent of the (A+I). lol Thanks @chrisboersma