Fall 2018 Q15 - Unregistered reinsurance deduction

ineedcoffee

I'm a bit confused by the part of the examiner's report for this question where the deduction for XYZ is being calculated.
The question states that for reinsurer XYZ, we have
UEP = 500
O/S recoverables = 750
Reinsurance receivable = 300
Total Reinsurance collateral = 1200

Wouldn't D = max(500 + 750 + 300 - 1200, 0) = 350?

The examiner's report calculates it as D = max(1200 - 500 - 750 - 300, 0) = 0.

chrisboersma

Yes your calculation is A deduction from the MCT guide, but it is the deduction for "Capital Available", which is actually a given in this particular question. The question does require we calculate the deduction from the "margin required for unregistered re insurers". Note: we are also given "Margin for Credit Risk" so we don't need to worry about the deduction for super excess collateral (see [9]).

Details

There are three potential deductions for reinsurance:
1. deduction from margin required: (this question's equation) - excess collateral [6].
2. deduction from capital available: (your equation) - shortfall in collateral [8]. In this case you pay the full 15% margin and deduct shortfall from capital available.
3. deduction from LOC/NOC credit risk margin - super excess collateral [9]

In the table above - I just increase the NOC+LOC in each row from 0 to 1750 and do all the other calculation based on a changing NOC+LOC amount.

[1] col = Acceptable Collateral (input variable) = SUM(Collateral)
[2] U + CL = unearned premiums ceded and outstanding losses recoverable
[3] rec-pay = Receivable from assuming insurer less payables to a assuming reinsurer
[4] 15% Risk Margin for Reinsurance = 15% x [2]
[5] Collateral Required = [2] + [3] + [4]
[6] Deduction from margin = min (max ([1] - [2] - [3]; 0) ; [4])
[7] Margin Required (unregistered re) = [4] - [6]
[8] Cap.A = Deduction to Capital Available = max ([2] + [3] - [1]; 0)
[9] Excess = max ([1] - [5]; 0)
[10] Excess % = [9]=[1] - used to reduce capital required for credit risk

The notation I used to simplify my notes: Omega = Reinsurance

ineedcoffee

Thanks @chrisboersma !
I was focused on getting the deduction required for capital available since the question doesn't state whether it is already gross or net deductions. I went off the assumption that the "capital available" was gross of deductions, and I was interested in seeing how much to deduct from capital available if that was the case. If capital available was gross of deductions, then I'm correct in saying we'd deduct 350 for unregistered reinsurance?

chrisboersma

yes

Also,

you'll find these problems significantly easier when you start by calculating the "shortfall in collateral" right off the bat (no deduction required if there is a negative shortfall): [2] + [3] - [1]

(Unearn + Unpaid + Rec) - (Payables + NOC + LOC*)

• LOC* is always capped at 30% of Unearned + Unpaid

Then calculate the (maximum) margin required for unregistered reinsurance as 15% x ([2] + [3])

javid

Hi,

The use of the word "deduction" may not be the most appropriate here as we are calculating "required capital". If you look at 4.3.3.2 of http://www.osfi-bsif.gc.ca/Eng/fi-if/rg-ro/gdn-ort/gl-ld/Pages/mct2018.aspx#fnb26, they list the "deduction from capital available" which is what you gave above. However, in the exam question, you are looking to calculate the capital required, and as such the margin required.

As per 4.3.3.3 of http://www.osfi-bsif.gc.ca/Eng/fi-if/rg-ro/gdn-ort/gl-ld/Pages/mct2018.aspx#fnb26,

The margin requirement for each unregistered reinsurer may be reduced to a minimum of 0 by payables to the reinsurer and acceptable collateral (as defined in section 4.3.3.2) that are in excess of the amount of ceded policy liabilities and receivables from the assuming insurer.

So, in this case, if you write D = (Unearn + Unpaid + Rec) - (Payables + NOC + LOC*), what you need to calculate for this exam question is max(0, -D).

You can see this being done in 70.60 of http://www.osfi-bsif.gc.ca/Eng/Docs/PC_qrt_2018.xlsx.

chrisboersma

The margin is 20% of “Unearned premiums ceded to assuming insurer” and “Outstanding losses recoverable from assuming insurer” (collectively, “ceded policy liabilities”). The margin requirement for each unregistered reinsurer may be reduced to a minimum of zero by payables to the reinsurer and acceptable collateral (as defined in section 4.3.3.2) that are in excess of the amount of ceded policy liabilities and receivables from the assuming insurer.

Margin of 20% x [Unearned + Unpaid] is the baseline capital required for unregistered reinsurance (always charged). This amount (the 20% x [Unearned + Unpaid] ) can be reduced to zero using excess collateral as calculated as

MAX((Payables + NOC + LOC*) - (Unearn + Unpaid + Rec) ,0)

Which I refer to as a deduction from the standard capital required for unregistered reinsurance, because unless you have the excess collateral you must charge at least the 20% (15% for policies prior to December 31, 2019 - there's a good chance they will test the transition rules).

This is the same language as the CAS exam committee is using and is how it was presented in Fall 2018 Q15

Margin unreg reins = 0.15 × (UEP + O/S) – deduction 
For ABC:  
deduction = Max (0, 1,000 + 2,000 – 1,500 – 1,500) = 0 
margin = 0.15 × (1,500 + 1,500) – 0 = 450 
For XYZ: 
Deduction = Max (0, 1,200 – 500 – 750 – 300) = 0 
Margin = 0.15 × (500 + 750) – 0 = 187.5 

chrisboersma

As per page 70.60 the deduction (or subtraction, or reduction, or removal of etc.) we are referring to is column 44:

Acceptable collateral in excess of recoverables
(39-20-22-24+26) where positive

And you can see it is being deducted from the "15% Margin on unearned premiums and outstanding losses recoverable" (column 40) to calculate to total "margin required" (column 46)

Margin Required
(40-44) where positive

javid

Thanks @chrisboersma