CIA.MfAD

This paper is mostly conceptual, but old exam questions are largely computational. Computationally, you'll have to be able to calculcate APV(claims liabilities). Conceptually, you'll need to memorize the characteristics of a good risk margin, and some considerations in their selection.   Forum

Pop Quiz

Can you rank the following reserve analysis situations from lowest to highest in terms of the % risk margin each would require on their point estimates?

1. 1,000 auto physical damage claims (20 year-old accident year) with all claims settled
2. 1 severe earthquake event (1 month old)
3. 1,000 auto liability claims (current accident year @ calendar year-end) for an established & stable company
4. 1,000 auto liability claims (current accident year @ calendar year-end) for a 3-yr-old company
5. 1,000 auto physical damage claims (current accident year @ calendar year-end) for an established & stable company

BattleTable

Based on past exams, the main things you need to know (in rough order of importance) are:

• calculating APV for claims liabilities
• upper & lower limits for MfAD ranges (and interpretation of selected values for a specific company)
• selection considerations for MfAD(inv), also MfAD(clms), MfAD(re)
• difference between PV (Present Value) and APV (Actuarial Present Value)
• calculating undiscounted loss ratios (calculation of discounted loss ratios was removed starting in 2020.Spring)
• calculating MfAD(inv) using explicit quantification (not asked for a long time, but don't ignore!)
• calculating MfADs using quantile methods and stochastic methods

Top Questions ← Questions you absolutely need to know!

Note that in the BattleTable below, you can click E in the left-hand column to open a PDF with the question and answer from the examiner's report for just that question.

Questions held out from Fall 2019 exam: #15. (Skip these now to have a fresh exam to practice on later. For links to these questions, see Exam Summaries.)

 Outdated   → questions highlighted in orange may be partially outdated. See corresponding footnotes.

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Spring #24)	MfAD ranges: - upper & lower limits	risk margins: - desirable traits
E (2018.Fall #16)	ALPHABET CITY: - calculate A,B,C,D,... 4
E (2018.Fall #26)	MfAD selections: - premium vs claim liabilities	OSFI.MCT	CIA.PrLiabs	OSFI.MCT
E (2018.Spring #26)	MfAD ranges: - upper & lower limits	MfAD ranges: - interpretation
E (2018.Spring #15)	see CCIR.ARinstr	calculate: - loss ratios 5, X
E (2017.Fall #14)	calculate: - APV(claim liabilities) 1	see Odo.FinReg
E (2017.Fall #27)	MfAD ranges: - upper & lower limits 2	formula: - PfAD(reinsurance) 2	see CIA.Discnt	see OSFI.AA
E (2017.Spring #25)	MfAD ranges: - upper & lower limits	selecting MfAD(claims): - considerations	MfAD(inv): - selection considerations
E (2016.Fall #15)	calculate: - APV, durations 3
E (2016.Fall #24)	concept: - APV vs undiscounted clms	see BCAR.Cdn	see OSFI.MCT	(d) see ICA.Ch47 (e) see OSFI.ORSA
E (2016.Fall #25)	MfAD ranges: - upper & lower limits	MfADs - comment on selections	MfAD(inv): - selection considerations
E (2016.Spring #13)	calculate: - APV, durations 3
E (2016.Spring #15)	calculate: - PfAD(inv)	see CIA.Discnt
E (2016.Spring #29)	risk margins: - desirable traits	MfADs: - selection considerations
E (2015.Fall #25)	MfAD ranges: - upper & lower limits	MfAD(claims): - higher than 20%	MfAD(claims): - lower than 2.5%
E (2015.Fall #26)	see CIA.Discnt	concept: - PV vs APV
E (2015.Spring #19)	MfAD(re): - calculate	MfAD(re): - comment on value	ceded discount rate: - how to select
E (2015.Spring #25)	calculate: - investment income, LRs 6
E (2015.Spring #30)	MfAD(inv): - explicit quantification	concept: - investment strategies	concept: - investment strategies
E (2014.Fall #17)	calculate: - MfAD(claims)	see CIA.Taxes
E (2014.Fall #21)	concept: - identify "non-MCT" risks	see OSFI.TargCap
E (2014.Fall #27)	MfADs: - quantile methods	MfADs: - stochastic methods
E (2014.Spring #15)	calculate: - APV(claim liabilities)
E (2014.Spring #17)	calculate: - loss ratios X	see CIA.Taxes
E (2013.Fall #19)	concept: - discount rate selection	calculate: - APV(claim liabilities)
E (2013.Fall #36)	concept: - PV vs APV	see CIA.Discnt
E (2012.Fall #22)	calculate: - APV	calculate: - loss ratios X	see CIA.Taxes	see CIA.Taxes

^X The calculation of the discounted loss ratio was removed from the syllabus starting 2020.Spring.

¹ Part of a larger problem on calculating net income. See also CCIR.ARinstr, CIA.Accting, but note that CIA.Accting was removed from the syllabus for 2019.Fall, and that reading deals with the accounting treatment of different types of bonds.

² Part of a larger problem on identifying errors by the appointed actuary.

³ Part of a larger problem on calculating MCT interest rate risk margin

⁴ Part of a larger problem on that involves concepts from CCIR.ARinstr but also CIA.Accting which has been removed from the syllabus. That means you will not be able to completely solve this problem with material on the current syllabus.

⁵ There is a minor error in sample answer 1 in the examiner's report. See this forum thread for more information.

⁶ This problem is partially outdated. You no longer have to know how to calculate the discounted loss ratio (quantities E & F in the question) from the "Unpaid Claims and Loss Ratio Exhibit" that is discussed in OSFI.MemoAA.

In Plain English!

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

• NOTE: Calculating APV of claims liabilities is DIFFERENT from calculating APV of premium liabilities. You would think the methodology would be the same, but APV of premium liabilities is actually much harder, and is covered in the paper CIA.PrLiabs.

The other types of questions commonly asked relate to:

• characteristics of good risk margins according to, for example, IAIS (International Association of Insurance Supervisors)
• considerations in selection of margins, which is, of course, the main idea in this paper
• very basic questions on the various methods for actually coming up with a risk margin

Source Readings: BattleActs covers all material from past exams. It also covers significant material that has not appeared on past exams but that I've judged to be important. Still, it's a good idea to spend at least little time reviewing the source readings. You may have a different opinion on what's important and what you can skip. You cannot read all 2,500 pages in depth, but BattleActs give you the necessary background knowledge so that the time you do spend on the source readings will be much more efficient.

Section 1-4: Intro & Risk Margin Traits

The purpose of MfADs (Margins for Adverse Deviations) is:

to reflect a degree of uncertainty inherent in an actuarial best estimate

There are 3 sources of uncertainty that are considered:

• uncertainty surrounding investment return rates
• uncertainty surrounding development on claims
• uncertainty surrounding recovery on losses ceded to a reinsurer

Note that MfAD is a percentage that is applied in some manner to an actuarial best estimate, whereas PfAD (Provision for Adverse Deviation) is the corresponding $-value. In other words, you select an MfAD, then do a calculation to get a $-value PfAD. This distinction is not always clear in the paper.

There are 2 broad methods for calculating MfADs. (Details are discussed later)

• deterministic: select percentages directly based on knowledge of the situation
• stochastic: use quantile methods based on a statistical analysis

Question: What are the characteristics of a good risk margin? There are 3 professional bodies that have addressed this question:

• IAIS: International Association of Insurance Supervisors
• IASB: International Accounting Standards Board
• IAA: International Actuarial Association

There is some discussion regarding how closely these bodies agree on what makes a good risk margin, but that is probably too much detail for the exam. It should be enough to memorize and understand the IAIS characteristics, which are:

• A risk margin applied to an actuarial best estimate should be HIGHER if...

1. there is less information known about the estimate
2. the LOB is low frequency & high severity
3. the contract term is 'long'
4. there is a wide probability distribution

• A risk margin applied to an actuarial best estimate should be LOWER with emerging experience.

Calculating APV (Actuarial Present Value)

The mini BattleQuiz includes a calculation problem where you have to calculate APV. Note the difference between PV (Present Value) and APV (Actuarial Present Value):

PV is "normal" discounting, where you take into account the time value of money

APV includes normal discounting, but also includes PfADs (Provision for Adverse Deviations)

APV = PV + PfADs

Notice that:

• PV is always lower than the undiscounted amount (assuming the investment return rate, or discount rate, is positive)
• APV is always higher than PV
• There is no consistent relationship between APV and the undiscounted amount. APV may he higher or lower depending on the magnitude of the MfADs.

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.

This is a very, VERY important type of problem. The APV calculation is often part of a longer problem. Practice it until you find it easy.

mini BattleQuiz 1 You must be logged in or this will not work.

Short Digression on APV & Discounting

Note that the "APV" formulas given below for APV_net, APV_ceded, and APV_gross are actually provided in CIA's reading on Discounting and Cash Flow Considerations for P&C Insures in Section 5.2 on Claim Liabilities, not the MfAD paper. I've included them here, however, because they are so closely related to MfADs.

Error in the examiner's solution to 2015.Spring #19a.

The equation that's incorrect is not used in their solution, but it raises an important difference between the formula for APV_net and APV_ceded.

APV_net = PV_net + PfAD_net(inv) + PfAD_net(clms) + PfAD_ceded(re)

APV_ceded = PV_ceded + PfAD_ceded(inv) + PfAD_ceded(clms) – PfAD_ceded(re)

The trick is that for the ceded formula, the term for PfAD(re) is subtracted. If you sum these 2 equations, you get the formula for APV_gross as given below.

APV_gross = PV_gross + PfAD_gross(inv) + PfAD_gross(clms)

Getting back to the examiner's report, the black font below is what they wrote and the red font is the piece they missed:

Discounted ceded reserves + Pfads = discounted ceded reserve @ 4% + Mfad claims * 13,402,361 – PfAD_ceded(re)

But as I said, they never used that formula so their mistake didn't matter (except for confusing you guys. Thx to jv for noticing this!)

---

Section 5: Explicit Assumptions - Deterministic MfADs

This section discusses considerations for selecting the %-values for the actual risk margins. You MUST memorize the acceptable ranges for each of the 3 MfAD categories: (This seems to be asked on about every second exam)

MfAD Category	Range
investment return rate	[25, 200] bps
claims development	[2.5%, 20%]
reinsurance recovery	[0%, 15%]

The BIG QUESTION is how do you choose an appropriate value within these ranges?

• There are tables within the paper that provide guidance when selecting specific margins within these ranges. Obviously you can't memorize those tables, but I can give you some helpful hints. Basically you should try to get a feel for what types of scenarios would require a require a high margin, and those where a lower margin would suffice. The Pop Quiz at the beginning of this wiki article is a good example of a Bloom's Taxonomy type question on this topic.

MfAD Selection for Investment Return Rates

The following question has been asked several times on past exams. (See entries for MfAD(inv) in BattleTable)

(super-awesome shout-out to michael!!) See his original forum post)

Question: identify considerations in selecting the MfAD for investment return rates [Hint: follow the treasure MAP to investment $$$s!]

Matching (asset & liability) cash flows

unmatched → pick high

Asset risk (credit/default & liquidity)

uncertain → pick high

Payment pattern estimation

if uncertain → pick high

The last part of this section explains two formula-based deterministic methods for calculating MfAD(inv):

• weighted formula (the formula is kind of stupid and it's also never been asked)
• explicit quantification (2015.Spring #30a)

4 Explicit Quantification Practice Problems

MfAD Selection for Claims Development

Ok, this is where the MfAD paper went totally bat-shit crazy. There are literally like 7 gazillion charts on how to select the MfAD for claims development. After I banged my head against the wall for a while, I decided there had to be a better way to explain this. There are 3 broad areas. See below for explanation.

(super-awesome shout-out to michael!!) See his original forum post)

Question: identify considerations in selecting the MfAD for claims development [Hint: in claims development, claims always get OLDer as time moves on]

Operations

(changes, turnovers, no guidelines) → pick high

Line of Business

(long tail coverages, change in legislation) → pick high

Data

(not homogeneous, stable, credible) → pick high

That's probably all you need to memorize, but here's a table with a few more details...

claims MfAD area	pick HIGH when...	pick low when...	comment
operations	there are (operational changes, employee turnover, lack of guidelines)	operations are (stable, strong, consistent)	look at claims management, U/W,...
data	you have the opposite of (stable, credible, homogeneous) data	data is (stable, credible, homogeneous)	look at volume, mix, limits,...
LOB	long-tail coverages, changes in legislation (ON accident benefits)	short-tail coverages (auto physical damage)	just use common sense

Anyway, if you're presented with a situation where you have to choose a claims development MfAD, or if you're asked whether a particular selection is reasonable, these are the kinds of things you might consider. There is no formula – just use your common sense.

A Subtle Distinction:

Here are 2 separate questions that sound similar but HAVE DIFFERENT ANSWERS!

1. When would you choose the highest margin of MfAD(clms) = 20%?
2. When would you choose a margin HIGHER than 20%?

A possible answer to #1 is when there are significant changes like tort reform. A possible answer to #2 is when you're dealing with unusually high uncertainty (2015.Fall #25b)

Cross-reference this with CIA.CSOP, which also discusses when selections can be outside deterministic ranges.

MfAD Selection for Reinsurance Recovery

Ok, this is the final category of MfADs.

Question: identify considerations in selecting the MfAD for reinsurance recovery [Hint: when your risk appetite is FULL, cede your remaining risk to reinsurance]

Financial condition of reinsurer

if poor → pick high

Unregistered reinsurance

if a high proportion of the reinsurance is unregistered → pick high

Loss ratio

if ceded loss ratio is high → pick high

This mini BattleQuiz is long because it covers MfAD selections for all 3 MfAD categories: investment rate of return, claims development, and reinsurance recovery. (sorry!)

mini BattleQuiz 2 You must be logged in or this will not work.

---

Sections 6-10

These sections have been removed from the syllabus for 2019.Fall. They have been archived in the wiki article CIA.MfAD: Sections 6-10.

The next quiz is just a placeholder for the sections that have been deleted. There is no content.

mini BattleQuiz 3 You must be logged in or this will not work.

---

Section 11: Documentation & Reporting

This section answers the 2 main questions related to documentation on any topic (not just MfADs):

• What should be disclosed?

- process for margin selection (whether explicit assumptions from Section 5, or based on a stochastic analysis as in Sections 7 & 9)

• What level of detail is appropriate?

- consider what qualitative & quantitative info best serves the user's understanding & decision-making

mini BattleQuiz 4 You must be logged in or this will not work.

Exam Problems

Here are two final mini-BattleQuizzes of old exam problems for extra practice.

• The first has to do with calculating PfADs
• The second quiz has a problem that asks you to calculate the loss ratio on both a discounted and undiscounted basis.

Interest Rate Risk Margin

There are two other problems that I left out: (2016.Fall #15), (2016.Spring #13), worth 6.25 pts, and 7.75 pts respectively!! Crazy! They were both extremely difficult problems that combined concepts from MCT, MfADs, and premium liabilities. Obviously you have to study these problems thoroughly, but some of what you need is in the premium liabilities paper, (which you haven't covered yet, if you're doing the papers in order of importance.) Please note: The solutions in the examiner's reports for these problems are outdated. In particular, the duration calculation for the premium liabilities has been changed. This is explained in detail in CIA.PrLiabs.

mini BattleQuiz 5 You must be logged in or this will not work.

Loss Ratios: Discounted & Undiscounted

Syllabus Change 2020.Spring: The calculation of the discounted loss ratio has been removed from the OSFI.MemoAA source text. It is provided below for informational purposes only. This calculation has appeared on prior exams but should not appear on any exams starting with 2020.Spring.

The formulas for the discounted and undiscounted loss ratios are actually part of the paper OSFI Memorandum or OSFI.MemoAA in the wiki. They are given on p28 and are based on something called the Unpaid Claims and Loss Ratio Analysis Exhibit. I've included that material here, because it's related to the APV calculation. Here are questions where this has been asked:

E (2018.Spring #15b)

E (2015.Spring #25)

E (2012.Fall #22) This problem is old and it's a total pain to solve. If you understand the other problems of this type you should be fine.

The formula for the undiscounted loss ratio is pretty easy:     (Thx to xQEDx for the formula correction)

LRundiscounted = (Paid Loss + UCAEundiscounted) / EP.

But the formula for the discounted loss is less familiar:     (Thx to xQEDx for the formula correction)

LRdiscounted = (Paid Loss + UCAEAPV – investment income from UCAE) / (EP + investment income from UPR)

The way I remember the undiscounted formula is that discounting gives you a "credit". The discounted LR is often (not always) lower than the undiscounted LR. So, you subtract investment income from the numerator, but add it to the denominator.

There is a forum discussion on this topic. I also worked out a simple example just to make sure I understood everything myself. I uploaded the example as a PDF available here.

Remember: As of 2020.Spring, the calculation of the discounted loss ratio has been removed from the OSFI.MemoAA source text.

mini BattleQuiz 6 You must be logged in or this will not work.

BattleCodes

Memorize:

• Deterministic ranges for each category of risk margin: claims development, reinsurance recoverables, investment rate
• Characteristics of a good risk margin according to IAIS (if you're ambitious, you can also memorize the characteristics according to IASB & IAA, and compare them to each other, but this extra detail probably won't be on the exam.)
• Considerations in selection a risk margin:
  • MfAD(clms): operations (leadership, guidelines,..), DATA (stable, consistent, homogeneous), LOB (tail length, judicial environment, retention level,..)
  • MfAD(re):      ceded LR, proportion of unregistered reinsurance, financial condition of reinsurer
  • MfAD(inv):    cash flow-matching between assets and liabilities, payment pattern errors, credit risk

Conceptual:

• Given a specific situation, you should have a feel for whether a high or low margin is required.

Calculational: (just go over all the old exam problems)

• APV (claims liabilities): extremely important!!!
• LR: both discounted & undiscounted: important, but only the undiscounted LR is still on the syllabus    ← shout-out to bkmlocks!
• MfAD(inv) using either the weighted formula method, never asked or explicit quantification has been asked: (of lesser importance, but I wouldn't skip it entirely)
• investment income: important (as an intermediate step in a larger calculation)
• duration of liabilities: important (as an intermediate step in a larger calculation)

You can expect roughly 4-5 pts from this paper on the exam

Full BattleQuiz You must be logged in or this will not work.

  Forum

POP QUIZ ANSWERS

• A < E < C < D < B
• Explanation: (in terms of the risk profile of each situation)
  • margin(A) = 0 since all claims are settled
  • margin(E) = small since auto physical damage is short-tailed; usually settled within weeks or a few months
  • margin(C) = moderate since auto liability has a longer tail than auto physical damage
  • margin(D) = higher than C for many reasons: a new company has inexperienced mgmt, thin data, smaller proportion of renewal business...
  • margin(B) = highest since earthquakes are costly and difficult to accurately estimate (low frequency & high severity)