Boot Camp: Calcs A

Introduction

This Boot Camp article covers easy versions of the most important types of calculation problems. After reading this article and doing the problems, you'll have a solid foundation for moving ahead to the more difficult problems covered in the Combat Training articles.

Important:The Boot Camp articles are not meant to be comprehensive. The intention is to provide an overview of the syllabus by touching on the most important topics. After finishing Boot Camp, you can move on to Combat Training. That more advanced level involves reading the full BattleWiki articles for each paper, doing the BattleQuizzes, and using the original source readings as appropriate.

Minimum Capital Test Ratio

OSFI.MCT is from the Office of the Superintendent of Financial Institutions. It is the top-ranked paper on the syllabus and accounts for about 10% of the points on the exam, or about 7 points in total. So, you gotta learn it, like, really well! (This paper is in 'Group 1', which includes the top 6 papers. See the BattleBriefings page for the full set of rankings.)

It is entirely about calculating & understanding the MCT ratio. The mechanics of the calculation are covered in detail in the practice templates. Prior exam questions on OSFI.MCT test both calculation & conceptual understanding. Consider this extremely simple example (amts in 000's):

• Capital Available (CapAv) = 62,400
• Capital Required (CapReq) = 50,355 (Assume that the diversification credit has already been taken. This credit is discussed later.)

The formula for the MCT ratio is:

• MCT = CapAv / minCapReq, where minCapReq = CapReq / 1.5

Then MCT = 62,400 / (50,355/1.5) = 185.9% This is comfortably above the supervisery target of 150%, so this insurer is probably doing ok. (In practice, we would need much more info than just a single year's MCT to be able to draw meaningful conclusions about an insurer's overall health. The MSA.Ratios are a great supplement.)

CapAv and CapReq have various components. These are discussed in the mini BattleQuiz below. (Just click on the link.) It is very important to know that CapReq has 4 main components. I use a memory trick to remember the components: IMCO, In My Crummy Opinion. Sounds kind of dumb, right? But I'll never forget it!

• Insurance Risk
• Market Risk
• Credit Risk
• Operational Risk

There's no other way to start than just to dive right in! You should practice the mini BattleQuiz a few times until you feel comfortable with it.

The link will take you to a BattleCard, which is our word for a flash card. Then click on the button with the pencil and the digits 123 to go to the actual problem. When you answer correctly, your BRQ (Battle Readiness Quotient) will rise. This is shown in the navigation bar next to your name.

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Actuarial Present Value

This topic relates to CIA.MfAD, the paper on Margins for Adverse Deviations. It is the #2 ranked paper on the syllabus, and accounts for about 8% of the points on the exam. (So, this paper together with OSFI.MCT comprise almost 20% of the exam. Obviously, you need to learn these 2 papers really, REALLY well!!)

Present Value (PV) accounts for the time value of money. To calculate present value, you need the discount rate. From there, you calculate the corresponding discount factor for each period then multiply by the quantity you wish to discount.

Actuarial Present Value (APV) also accounts for the time value of money but includes something extra called the provision for adverse deviation or PfAD. This is a dollar amount that is added to provide a margin for 3 items: uncertainty surrounding the discount rate, the actuary's liability estimate, and the expected reinsurance recovery. In very general terms:

APV = PV + PfADs

There will almost certainly be a question requiring you to calculate APV(ClmsLiabs) - Actuarial Present Value of the claims liabilities.

• NOTE: Calculating APV(ClmsLiabs) is DIFFERENT from calculating APV(PremLiabs). You would think the methodology would be the same, but APV(PremLiabs) is actually much harder, and is covered in the paper CIA.PrLiabs.

Before you click on the mini BattleQuiz below, you need to know how to calculate the fraction of the amount remaining at 12 months to be paid in a given future period. This is based on the calendar year payment pattern. Suppose you're given:

Age	Cum Paid
12	35%
24	75%
36	100%

Here, the claim is fully paid out after 36 months. For the APV calculation, you first have to calculate the fraction of the amount remaining at 12 months to be paid in the period 12-24.

• The answer is (75% - 35%) / (100% - 35%) = 0.6154. The trick is that the basis (denominator) excludes the %paid at 12 months.
• Similarly, the proportion paid in the period 24-36 is (100% - 75%) / (100% - 35%) = 0.3846.

The first time you try this problem, you'll probably have to click on the Cheat button to see how to do it. (It's a tough problem to get right because there are so many small steps.)

Remember that in the practice templates like the one below, you can generate new random problems by clicking on the New Problem button. That means you can redo the problem with different numbers until you get it consistently correct!

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Excess (Deficiency) Ratio

Calculating the excess (deficiency) ratio appears on every exam. But the way they give you the information varies considerably from exam to exam. The mini BattleQuiz has the easiest possible version of this problem, but if you can do it confidently, you'll have a fighting chance at any tricks they may throw at you. At the very least, you can write down the relevant formulas and get partial credit. (Even if you think you don't know how to answer a particular question, you can usually get partial credit by taking an educated guess. That's a very useful skill to develop, both for exams, and in general.)

The most basic version of the problem is modeled on (2015.Spring #21). You're given 3 chunks of information:

• investment yields for the relevant CYs
• paid loss triangle (incremental)
• unpaid loss triangle (discounted & including PfADs, which is that same as saying APV)

You need to get those 3 things into your head! And quick!

I don't have much more to say here since the practice template in the mini BattleQuiz explains in detail how to do this type of problem. It usually counts for 1-2 points on the exam. (It's part of the CCIR.ARinstr reading, the Annual Return Instructions, which is the #3 ranked paper on the syllabus.)

Good luck!

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DCAT (Dynamic Capital Adequacy Testing)

CIA.DCAT is from the Canadian Institute of Actuaries. It's ranked in Group 2, which includes papers ranked in the range 7-12. I've included it here because the question discussed below has appeared at least 5 times on previous exams.

This paper details a methodology for stress-testing. One of the purposes of stress-testing is to identify and control risks. The basic idea is to run simulations for various adverse scenarios and assess the impact on financial metrics such as MCT ratio and capital (also sometimes approximated by equity).

Consider this important question: Based on a DCAT analysis involving base & adverse scenarios, when can the AA (Appointed Actuary) report that an insurer is in good financial condition?

Answer:

• for the BASE scenario: must have MCT >150%   (all yrs)
• for the BASE scenario & all PAS: must have A > L   (all yrs)

Note that PAS = Plausible Adverse Scenarios, A = Assets, L = Liabilities

Here's a really basic question that often appears on the exam:

(a) Given the following, can the AA report that the insurer is in good financial condition?

Scenario	Component	2018	2019
Base Scenario	MCT Ratio	220%	190%
	Capital (A-L)	500m	460m
Adverse Scenario: Earthquake	MCT Ratio	155%	150%
	Capital (A-L)	405m	-15m

(b) Given the following, can the AA report that the insurer is in good financial condition?

Scenario	Component	2018	2019
Base Scenario	MCT Ratio	220%	190%
	Capital (A-L)	500m	460m
Adverse Scenario: High Inflation	MCT Ratio	140%	130%
	Capital (A-L)	435m	310m

Answer:

(a) No. Capital is negative for the adverse scenario in 2019.

(b) Yes. Base scenario has MCT ≥ 150% for all years. Base and adverse scenario have capital ≥ 0 for all years.

(It always seemed a bit STRANGE to me that the MCT ratio for the adverse scenario isn't relevant to the appointed actuary's decision! But whatever...)

Note that in the mini BattleQuiz below, the question in the BattleCards says [setup required]. This means that it is an old exam problem but the question is too long to fit in the actual BattleCard. Click E in the left-hand column to open a PDF with the full exam question and answer.

The mini BattleQuiz link below will take you to a self-scored BattleCard. If you know the answer, click the "check"; otherwise click the "x". Your score will be updated accordingly. You have to be honest!

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Summary

The Full BattleQuiz shows the BattleCards for previous mini BattleQuizzes all at the same time.

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