BK.Reins

Blanchard & Klein covers the mathematics of reinsurance, specifically, the impact on the ceding company's financial statements and key financial metrics.

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Study Tip

This reading has been on the syllabus for a long time but it has never appeared on the exam, at least as far back as 2012. The only reason I can think of is that there are already 3 other readings on the topic of reinsurance: Klann.ReinsComm, Odomirok.14-F, and Freihaut.Reins. They are color-coded  tan  on the BattleBriefings page. They are heavily tested and there may not be room for any further questions on reinsurance. Of course then you have to wonder why it's on the syllabus at all. Anyway, this reading is also on the Canadian Exam-6 so I've included references to problems that have appeared on the Canadian exam. But unless you have already covered everything else really well, I don't recommend spending a lot of time on Blanchard.

BattleTable

• this reading has not been tested on any exam from the year 2012 and subsequent

reference	part (a)	part (b)	part (c)	part (d)
no prior questions

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In Plain English!

Intro

The first thing to cover is an obvious list-type question. Note that I reordered the list so that the hint would spell something that's easier to remember.

Question: identify the 6 functions of reinsurance [Hint: cat-SWIGS]

catastrophe protection (a very large loss will be mostly absorbed by reinsurance)

Stabilize loss experience (reinsurance 'cuts the right tail off' the loss distribution)

Withdrawal from market is facilitated (off-loading risk to reinsurance is quicker than runoff)

Increase large-line capacity (but minimize associated risk)

Guidance from reinsurer (with expertise in U/W & pricing for that particular line)

Surplus relief (reinsurance reduces net leverage ratio)

A further explanation of these items is probable not necessary, but is given in the BattleCards of lower exam probability. A better type of question is the impact of each type of reinsurance on financial statements. That's what this paper is all about. In particular, it looks at the impact of reinsurance on each of the following quantities:

Balance Sheet items: assets, liabilities, surplus

Income Statement items: premiums, losses

other financial statistics: leverage ratios (premium-to-surplus, reserves-to-surplus)

One strategy for studying this paper is to go through each of the 5 spreadsheets to understand on a detailed level the impact of reinsurance on the various quantities. (The 6^th example does not provide a spreadsheet.) But given that this is not a high-ranked paper, that would be a lower priority than the Frei.RskTrans paper. If you were asked to perform the types of calculations in these exhibits, you could probably make an educated guess based on common sense and get decent partial credit.

In the next sections we'll take a quick look at the following calculation problems, but for now, just make sure you know cat-SWIGS or the 6 functions of reinsurance.

E (Cdn - 2018.Spring #16b)

E (Cdn - 2017.Fall #17b)

E (Cdn - 2013.Fall #32ab)

This is a really easy mini BattleQuiz.

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[Blanchard Example 2] Cat Protection (Cdn - 2017.Fall #17b)

Link to Canadian problem:

E (Cdn - 2017.Fall #17b)

Note: This statement of this problem contains an error. The given information is internally inconsistent and the examiner's report accepted 2 answers for part (ii) NEP (Net Earned Premium) More on this below.

This exam question feels like a simplified version of catastrophe protection, Example 2. The treaty described in the problem is much simpler than the cat treaty described in the paper. This is a question that almost takes longer to read than it does to solve. There are 8 bullet points of given information but only 2 of them will be used in meaningful way in the solution:

• the aggregate excess-of-loss treaty covers 100% of losses above 600
• reinsurance premium = 100

You also need a couple of formulas that people often forget (especially the first one):

• NEP = NWP – chg(UEP)
• U/W income = revenue – losses – expenses

Using the table of values for Scenario C without reinsurance, we can calculate as follows:

(i) NWP = GWP – reinsurance premium = 1550 - 100 = 1450

(ii) NEP = NWP – chg(UEP) = 1450 – (700 – 0) = 750

Or alternately, NEP = 750 – 100 = 650 (This is because the reinsurance treaty was purchased on Jan 1, so NEP drops by the full amount of the premium. If the treaty were purchased half-way through the year, NEP would have gone down by only half that amount.) But the point is that this gives a different answer for NEP. If the problem had been constructed with internally consistent information then both methods would have produced the same answer.

(iii) net UEP = 700 (No change because if reinsurance hadn't been purchased, the 100 in reinsurance premium would have resulted in unearned = 0 at the end of the year anyway.)

(iv) net IL = 600 (Incurred losses were 800, but the limit under the treaty is 600, so losses are capped at 600.)

(v) U/W income = revenue – losses – expenses = NEP – net IL - operating expenses = 750 – 600 – 200 = -50

(vi) net unpaid = incurred – paid = 600 – 200 = 400 (You have to assume that the paid of 200 doesn't depend on whether reinsurance was purchased. I'm not so sure this is true, but if you don't assume that then you can't solve the problem. Always state your assumptions.)

[Blanchard Example 2] Cat Protection (Cdn - 2013.Fall #32ab)

Link to Canadian problem:

E (Cdn - 2013.Fall #32ab)

This question is a simplified version of Example 2 in the paper. It concerns the effect of buying reinsurance to provide catastrophe protection, and the answer is just common sense:

Part (a): what is the impact on (surplus, net loss reserves, investment income) when insurer purchases (versus doesn't purchase) catastrophe reinsurance but DOES NOT suffer a catastrophe?

surplus: down - the company pays the cost of reinsurance but gets no benefit (because there is no catastrophe)

net loss reserves: no effect - the purchase of reinsurance has no effect on the net loss reserves (because there is no catastrophe)

investment income: down - investment income is down because the cost of reinsurance lowers assets so there is less to invest (whether or not there is a catastrophe)

Part (b): what is the impact on (surplus, net loss reserves, investment income) when insurer purchases (versus doesn't purchase) catastrophe reinsurance but DOES suffer a catastrophe?

surplus: up - the company is at least partially shielded from the effect of the catastrophe

net loss reserves: down - because some of the losses are ceded (versus not having purchased reinsurance)

investment income: down - investment income is down because the cost of reinsurance lowers assets so there is less to invest (whether or not there is a catastrophe)

[Blanchard Example 3] Stabilizing Loss Experience

Let's take a quick look at a spreadsheet example from the paper without the benefit of an exam problem as guidance: stabilizing loss experience, Example 3. Note that the type of reinsurance in this case would an excess-of-loss treaty. It protects the insurer in a year with unusually high losses.

Question: what is the impact on (surplus, net loss reserves, investment income) when insurer purchases (versus doesn't purchase) reinsurance to stabilize loss experience, assuming a normal loss year.

surplus: down - the company pays the cost of reinsurance but gets no benefit (assuming "normal" losses don't trigger excess-of-loss treaty)

net loss reserves: no effect - the purchase of reinsurance has no effect on the net loss reserves (assuming "normal" losses)

investment income: down - investment income is down because the cost of reinsurance lowers assets so there is less to invest (whether or not treaty is triggered)

Question: what is the impact on (surplus, net loss reserves, investment income) when insurer purchases (versus doesn't purchase) reinsurance to stabilize loss experience, assuming a high loss year and treaty is triggerred.

surplus: up - the company is at least partially shielded from the high loss year

NLR: down - because some of the losses are ceded (versus not having purchased reinsurance)

investment income: down - investment income is down because the cost of reinsurance lowers assets so there is less to invest (whether or not treaty is triggered)

I solved this problem by reading the numerical values from the spreadsheet, but you can easily reach the same conclusions using common sense.

[Blanchard Example 4] Surplus Relief (Cdn - 2018.Spring #16b)

Link to Canadian problem:

E (Cdn - 2018.Spring #16b)

This question refers to the surplus relief function of reinsurance. It's just like Example 4 from the paper but with different numbers. The question describes a quota-share reinsurance treaty and asks if the treaty will provide surplus relief. This is just another way of asking you to calculate the leverage ratios from the exhibit in the paper, both before and after the purchase of reinsurance:

• before reinsurance you need to calculate these leverage ratios:

GWP / surplus

(gross loss reserves) / surplus

• after reinsurance you need to calculate these leverage ratios:

NWP / surplus

(net loss reserves) / surplus

If the net leverage ratios after reinsurance are lower than the gross leverage ratios before reinsurance, you can conclude there has been surplus relief. Once you realize that, it's pretty easy because they give you the surplus before and after reinsurance (654 to 495). Your part is to calculate the effect of the quota-share reinsurance on the premiums and loss reserves:

• GWP = 1,500 before, and the quota-share ratio is 50%, so NWP = 750 after
• gross loss reserves = 850 before, and the quota-share ratio is 50%, so net loss reserves = 425 after

Now just substitute these values into the formulas to see that the leverage ratio for premiums dropped from 233% to 152%, and the leverage ratio for reserves also dropped from 132% to 86%. You can therefore conclude there has been surplus relief.

Note: One small point is that the ceding commission of 15% is a red herring. You don't need it. If you check the example in the paper, they give a ceding commission of 20% but then say parenthetically that it's consistent with the gross expense ratio. The ceding commission then doesn't affect the calculations.

This question was poorly done on the exam. The actual calculation of the leverage ratios is not hard, but I think a lot of people didn't realize that's what you had to do. Questions that haven't been asked before are often poorly done. If it appears again, I'm sure everyone will perform much better!

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