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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


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 loss ratios both discounted and undiscounted
  • calculating MfAD(inv) using explicit quantification (not asked for a long time, but don't ignore!)
  • calculating MfADs using quantile methods and stochastic methods
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.
reference part (a) part (b) part (c) part (d)
E (2018.Spring #26) MfAD ranges:
- upper & lower limits
MfAD ranges:
- interpretation
E (2018.Spring #15) see CCIR.ARinstr calculate:
- loss ratios
E (2017.Fall #14) calculate:
- APV(claim liabilities) 1
see Odo.FinReg
E (2017.Fall #27) MfAD ranges:
- upper & lower limits 2
- PfAD(reinsurance) 2
see CIA.Discnt see OSFI.AA
E (2017.Spring #25) MfAD ranges:
- upper & lower limits
selecting MfAD(claims):
- considerations
- 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
- comment on selections
- 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
- selection considerations
E (2015.Fall #25) MfAD ranges:
- upper & lower limits
- higher than 20%
- lower than 2.5%
E (2015.Fall #26) see CIA.Discnt concept:
- PV vs APV
E (2015.Spring #19) MfAD(re):
- calculate
- comment on value
ceded discount rate:
- how to select
E (2015.Spring #25) calculate:
- investment income, LRs
E (2015.Spring #30) MfAD(inv):
- explicit quantification
- investment strategies
- 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
- stochastic methods
E (2014.Spring #15) calculate:
- APV(claim liabilities)
E (2014.Spring #17) calculate:
- loss ratios
see CIA.Taxes
E (2013.Fall #19) concept:
- discount rate selection
- APV(claim liabilities)
E (2013.Fall #36) concept:
- PV vs APV
see CIA.Discnt
E (2012.Fall #22) calculate:
- loss ratios
see CIA.Taxes see CIA.Taxes
1 Part of a larger problem on calculating net income. See also CCIR.ARinstr, CIA.Accting.
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

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.

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.

Note that the "APV" formulas given below for APVnet, APVceded, and APVgross 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 APVnet and APVceded.
APVnet = PVnet + PfADnet(inv) + PfADnet(clms) + PfADceded(re)
APVceded = PVceded + PfADceded(inv) + PfADceded(clms) PfADceded(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 APVgross as given below.
APVgross = PVgross + PfADgross(inv) + PfADgross(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 PfADceded(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!)
Note that in the mini BattleQuiz below, some of the BattleCards are actually old exam questions. Click E in the left-hand column to open a PDF with the full exam question and answer.

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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

For some reason, this has been asked at least 3 times: (2017.Spring #25c), (2016.Fall #25c), (2016.Spring #29b). There are 3 considerations as follows:

  • MATCHING of cash flows from assets & liabilities (if unmatched: pick MfAD high)
  • ERROR in estimating payment patterns (if uncertain: pick MfAD high)
  • ASSET risk (credit/default & liquidity) (if high risk: pick MfAD 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 of consideration for the claims development MfAD:

  • operations
  • data
  • LOB (Line of Business)

The paper then breaks these areas down further into sub-areas, and that's where they lost me. Here's a table that summarizes how I made sense of it:

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

Again, the considerations in selecting an MfAD for reinsurance recovery is just a list to memorize:

  • consider ceded Loss Ratio (if high: pick MfAD high)
  • consider proportion of unregistered reinsurance (if high: pick MfAD high)
  • consider financial condition of reinsurer (if poor: pick MfAD 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!

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Section 6: Relevant Statistical Concepts

This section is a very brief discussion of statistics as it applies to P&C insurance. It covers:

  • when a normal distribution works well (high volume of risks, limited correlation between risks)
  • when a normal distribution DOESN'T work well (low volume of risks, high correlation between risks.)

That's about it.

Section 7: Stochastic Techniques

For Section 7, you need to know what a stochastic technique is (produces a loss distribution using simulation) and where it works well (with skewed loss distributions such as catastrophe insurance.)

Section 8: Three P&C Product Examples

  • The examples are: TPL (third party liability), GL (general liability), and catastrophe insurance.
  • They are compared according to the criteria of skewness, CV (coefficient of variation), and length of settlement pattern.
  • The PURPOSE of introducing these examples is that they are used in Section 10 to compare various methods for calculating risk margins.
  • Here's a little secret: None of the methods work very well on ANY of these examples!

Section 9: Quantile Approaches (Stochastic)

This feels like it should be an important section, but it's been only very lightly tested. I found it interesting, but you probably shouldn't spend too much time on it. You definitely need to know the names of the 3 quantile methods:

multiples of SD (standard deviation)
VaR (Value at Risk), also called the percentile method or confidence interval method
TVaR (Tail Value at Risk), also called CTE (Conditional Tail Expectation)

It's less likely you'd be asked for any details of these methods OR to evaluate how well they perform OR what to do in the case of an extreme event like an earthquake. These points are all covered in the Level 3 BattleCards anyway, if you're interested.

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Section 10: Comparison of Risk Margin Methods

This section is quite interesting, but it's probably too detailed to be asked. It compares the 3 methods from Section 9 on both a quantitative & qualitative basis. Surprisingly, none perform particularly well. This highlights the inherent difficulty in assessing risk, and, by implication, setting an appropriate risk margin.

It would be nice to have a general method for coming up with risk margins that satisfies the traits discussed in Section 3; in practice, however, many situations have unique characteristics that must be take into account, above and beyond any generalized methodology.

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

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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.

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Loss Ratios: Discounted & Undiscounted

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 + UCAEAPVinvestment 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.

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  • 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


  • 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
  • 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.



  • 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)