Odomirok.19-RBC

The Risk-Based Capital system (RBC) was introduced in 1994 to help regulators detect early signs of insolvency. It is covered in Chapter 19 in Odomirok and is about 60 pages. It includes all kinds of bulls**t details that you don't need to know for the exam. This wiki article provides a framework, including elements tested on past exams. You should work through this article and the mini BattleQuizzes first. You'll then be in a good position to look at the source material and decide whether you want to spend any more time on it.

If after finishing this wiki article you want to deepen your knowledge of RBC, the section on the R₄ risk charge might be a good place to start. I didn't cover the intricate details of R₄ because they have not been tested in the past. That doesn't mean they won't be tested in the future, but if you're playing the odds, you should cover everything else first. The calculations for R₄ are somewhat similar to R₅, which is covered below.

  Forum

BattleTable

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

• calculating RBC charges R_0,1,2,3,4,5 & RBC-ratio
• identifying action level based on RBC ratio & subsequent regulator/company actions
• strategies for reducing RBC charges
• comparison to IRIS ratios

The RBC questions from 2012 appear to be at least partially outdated and are highlighted in tan.

reference	part (a)	part (b)	part (c)	part (d)
E (2018.Spring #18)	calculate: - change in RBC charge	rapid premium growth: - impact on RBC
E (2017.Fall #17)	calculate: - RBC ratio	identify: - RBC action level + actions
E (2017.Fall #18)	financial health: - use of RBC ratios	R0 RBC charge: - difference vs R1,2,3,4,5	RBC vs IRIS: - similarity & difference
E (2017.Spring #19)	calculate: - total RBC1	calculate: - RBC RAL2	RAL actions: - insurer & regulator
E (2016.Fall #16)	RBC risk categories: - identify 2	RBC purpose: - for regulator
E (2016.Fall #17)	calculate: - RBC ratio	identify: - RBC action level	identify: - RBC actions
E (2016.Spring #26)	see Freihaut.Reins	calculate: - R3, R4	see Freihaut.Reins
E (2015.Fall #17)	calculate: - R1	calculate: - R2	reducing R1: - identify 2 ways
E (2015.Spring #19)	components of RBC: - describe	identifying insolvency: - aspects of RBC	interpret RBC ratio: - ratio = 310%	internal capital model: - concerns (vs RBC)
E (2015.Spring #25)	see Freihaut.Reins	see Freihaut.Reins	calculate: - RBC ratio
E (2014.Fall #18)	calculate: - R5, total RBC 3	improving RBC ratio: - reserving practices	limitations of RBC: - for identifying impairment (p607 in pdf)
E (2014.Spring #20)	calculate: - R3	calculate: - RBC	action level: - identify action
E (2013.Fall #21)	RBC risk categories: - identify 2	calculate: - RBC ratio	action level: - identify	action: - describe
E (2012.Fall #14)	see Odomirok.8-9-IS	reduce RBC asset risk: - investment changes
E (2012.Fall #20)	calculate: - R5	see NAIC.IRIS	RBC vs IRIS: - treatment of premium
E (2012.Fall #24)	solvency-based frameworks: - create a new one! W

¹ The examiner's report accepted 10 different answers for this calculation problem. (ASC: This was a very poorly constructed question. The examiner's should be ashamed of themselves.)

² RAL stands for Regulatory Action Level

³ The statement of this problem contains 2 errors. See examiner's comments in examiner's report.

^W Alice thinks this is a totes weird question. (You can look at it, but she thinks it isn't likely to appear again.)

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

  Forum

In Plain English!

Alice's 1st Day (Intro to RBC)

Just for fun, I've organized this wiki article by pretending that Alice is working as a summer intern. Alice's "days" don't necessarily correspond to your own study days. Her "days" are short and you can probably cover several of her days in one of your days.

On Alice's first day of work as an actuarial intern, her mean boss dumped a stack of financial statements on her desk and told her to find out whether the company was healthy. But before she could ask him anything, he was already down the hall issuing orders to someone else. "Jackass," she thought. Poor Alice had no idea what to do. Fortunately the intern in the next cubicle overheard and peeked over the cubicle wall.

"Just calculate the RBC ratio," her new friend said. "It's all in Odomirok. The boss likes to haze the newbies on their first day, but I can help you. We'll tackle it together."

So Alice and Lakshmi spent the day pulling the relevant information from the financial statements and here is what Alice learned:

Formula: RBC ratio = TAC / ACL (sounds like tackle)

TAC = Total Adjusted Capital = 31,024,000

ACL = Authorized Control Level capital = 5,552,182

==> RBC ratio = 31,024,000 / 5,552,182 = 559%

Ok, so far so good, but WTF does 559% mean? Is that good or bad? (The following table appears near the end of chapter 19 of Odomirok)

action levels [CRAM]	THRESHOLD	insurance dept action	company action	ASCs (Alice's Snarky Comments)
CAL (Company Action Level)	200%	none (initially)	must submit action plan to meet RBC standards	raises & bonuses!
RAL (Regulatory Action Level)	150%	commissioner may take corrective action	must submit action plan to meet RBC standards	small raise, no bonus
ACL (Authorized Control Level)	100%	commissioner may take control of company	none (initially)	take away 3 vacation days
MCL (Mandatory Control Level)	70%	commissioner must take control of company	none (initially)	fire the CEO

For example:

• if a company's RBC ratio drops below 200% to the 150-200% range, they would be at the CAL level
• if a company's RBC ratio drops below 150% to the 100-150% range, they would be at the RAL level

The RBC ratio of 559% for Alice's company is way above the "CAL" threshold, so it looks like the company is doing really well. What a great first day of work for Alice! Go home and relax!

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

Alice's 2nd Day (Trend Test & Risk Categories)

Over morning coffee, Lakshmi pointed out an ommission from the above "action table" that Alice learned about yesterday. If the RBC ratio is above 200% but below 300%, the company is still not in the clear. They would still have to perform the trend test. Let COR denote Combined Operating Ratio:

Trend Test: If a company's RBC ratio is in the 200-300% range and also has a COR > 120% THEN they are subject to the CAL action from the action table.

Reminder: The COR (Combined Operating Ratio) is the sum of:

• Loss & LAE ratio (CY net incurred loss & LAE divided by NEP)
• Expense ratio (other U/W expenses + small miscellaneous items divided by NWP)
• Dividend ratio (policyholder dividends divided by NEP)

Recall that COR does not include investment income. (And next time you see your CEO in the break room, tell him to get the LED out.)

Anyway, Alice's new company is well above the 300% threshold so she was ready to report back to her boss that the company is in great shape, but Lakshmi stopped her.

"Not so fast," Lakshmi said. "The RBC ratio is only 1 metric. For example, what about the IRIS ratios? It's like if you had 98% in calculus on your report card but were failing physics, English, and history. It isn't likely, but when you report back to the boss, you should qualify your conclusion on the health of the company if the only thing you calculated was the RBC ratio."

You can review NAIC.IRIS for the IRIS ratios, but getting back to the RBC ratio, Alice needs to make sure she understands exactly how the 559% value was calculated. It's a long calculation that involves 6 different risk components. The charge for each component represents the amount of capital required to support that particular risk. (Each component has it's own calculation but we'll come back to that later.)

risk category	risk component [Hint: asset→ AFEC]	notation	risk charge for this company
asset risk	Affiliated insurance company risk	R0	0
asset risk	Fixed income risk	R1	553,398
asset risk	Equity risk	R2	4,303,948
asset risk	Credit risk	R3	720,373
U/W risk	reserve risk	R4	9,542,613
U/W risk	NWP risk	R5	3,591,141

You might think you'd sum these 6 charges to find the total required capital, but that isn't how it works. Rather than a simple sum, these risk charges are aggregated using this formula:

Formula: RBC Capital Required = R0 + sqrt(R12 + R22 + R32 + R42 + R52)

The part of the formula with the square root is called the covariance adjustment. (Alice's Canadian cousin told her that in Canada this is called the diversification credit. Risk is reduced by spreading or diversifying it over multiple independent categories.)

Pop Quiz!    :-o

Question: Is the covariance adjustment less than, greater than, or equal to the simple sum of R₁ through R₅?

Answer: The covariance adjustment is less than the simple sum of R₁ through R₅. (Try testing this with some simple numbers. It's a version the triangle inequality you may be familiar with from calculus.)

Question 1: what is the reason for the covariance adjustment

The reason is that risks R₁ through R₅ are assumed to be independent. It's unlikely that all 5 risks would reach their maximum value at the same time. The covariance adjustment reduces the required capital to reflect this assumption of independence. For example, the level of equity risk (performance of stocks) is likely not related to reserve risk. A company would be unlikely to experience both very bad investment returns and very bad underwriting results at the exact same time.

Question 2: why is R0 excluded from the covariance adjustment

Well, R₀ is not indepedent of the other risks. In other words, R₀ is correlated with the other risks. It represents the charge for an affiliated company (subsidiaries) and investment in an affiliate does not provide a diversification benefit.

Let's end day 2 by applying the above formula to find that:

• RBC Capital Required = 11,104,365

We can now calculate the denominator for the RBC ratio:

RBC denominator: ACL capital = 50% x (RBC Capital Required)

So ACL Capital = 5,552,182 (See Alice's 1st Day.) You might also want to take a quick look at part (b) of:

E (2017.Fall #18)

Do the mini BattleQuiz then go home and relax!

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

Alice's 3rd Day (Review Day)

Alice really bonded with Lakshmi so she decided to stop at Dunkin' Donuts on her way to work and get Lakshmi coffee and a bear claw. As the new best friends were chomping through their morning snacks, Lakshmi leaned in a whispered,

"RBC usually counts for about 4-5% of the points on Exam 6. It's a good idea if we spend a few more days on this RBC assignment for the boss, but don't forget that the Statement of Actuarial Opinion is by far the biggest topic on the exam. You should probably spend today reviewing Odomirok.16-17-SAO and COPLFR.SAO. I've got a meeting on IRIS ratios anyway so I'll be busy today. See you tomorrow and happy studying! Slay the beast!"

So Alice spent her 3^rd day reviewing the SAO material. Time well spent!

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

Alice's 4th Day (Ranking of Risk Charges)

Alice arrived early today so I prepared a special pop quiz she could do while eating her morning bear claw.

Pop Quiz!    :-o

Question: Based on industry totals, rank the risk charges R₁ through R₅ according to their relative magnitude. (You can find this information on page 233 of Odomirok)

Answer:

	risk	relative magnitude
R4	U/W risk - reserves	54%
R2	asset risk - equity	29%
R5	U/W risk - NWP	16%
R3	asset risk - credit	1%
R1	asset risk - fixed income	0%

Of course, you should also be able to explain why these rankings are the way they are. Let's start at the bottom and work up.

• asset risk - fixed income: Although fixed-income investments can have risks (for example, inflation risk) they are generally considered very safe so their RBC charge is very close to 0. An example of a fixed income investment is a government bond. Insurance companies generally have over half of their investments in this category.
• asset risk - credit: Aside from slow-paying customers, a significant portion of credit comes from reinsurance, but this can be at least partly controlled with sensible reinsurance arrangements.

Now let's consider the "high-value" categories:

• U/W risk - NWP: The total U/W risk, which is the risk associated with writing policies, is by far the most significant source of risk for an insurer. The total U/W risk accounts for 54% + 16% = 70% of the total. Also, the biggest component of liabilities on the balance sheet is the reserves. The intuitive reason the NWP portion of the UW risk is smaller than the reserve portion is that NWP risk is related to the unexpired portion of written policies. So if we're dealing with annual terms, the unexpired portion will be less than 1 year. Compare this to the reserves for claims that have actually been incurred: These incurred claims may span many accident years, so the risk (and associated charges) should be greater.
• asset risk - equity: The exact reason that equity risk lies between reserve risk and NWP risk relates to technical considerations behind the RBC formulas and is beyond the scope of the reading. But you should note that equity risk (stocks, for example) is much greater than the risk from fixed income investment (government bonds, for example)
• U/W risk - reserves: This is the business of insurance companies and is the biggest item on the balance sheet. Insurers have the expertise (actuaries!) to take on significant risk in this category and manage it for the mutual benefit of both the insurer and society.

Just for fun, go back to the example from Alice's 2nd day and calculate how the percentages there compare to the table above. (Answer: The ordering is the same but the percentages are slightly different: 51%, 23%, 19%, 4%, 3%)

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

Alice's 5th Day (An Exam Problem. Also TGIF!)

As a Friday treat, we're going to cover a calculation problem similar to the following exam problem:

E (2017.Fall #17)

It's a very easy problem and I'm surprised people didn't ace it. (According to the examiner's report, exam-takers made a lot of different kinds of mistakes.)

Pop Quiz!    :-o

Given:

description	scenario 1	scenario 2	scenario 3
company net loss & LAE ratio	85%	85%	85%
company expense ratio	35%	35%	35%
policyholder dividend ratio	10%	10%	10%
Total Adjusted Capital	10,000	12,000	14,000
R0 charge	0	0	0
R1 charge	800	900	1,000
R2 charge	1,700	1,300	1,300
R3 charge	400	500	300
R4 charge	13,300	10,600	8,600
R5 charge	1,400	2,100	1,200

For each scenario, find:

• RBC ratio
• RBC action or control level
• appropriate regulator & company action.

Pop Quiz Answers!    :-D

Recall:

• RBC ratio = TAC / ACL (sounds like tackle)
• ACL capital = 50% x (RBC Capital Required)
• RBC Capital Required = R₀ + sqrt(R₁² + R₂² + R₃² + R₄² + R₅²)

Scenario 1:

• RBC Capital Required = 13,511
• ACL capital = 6,756
• RBC ratio = 10,000 / 6,756 = 148%

==> action or control level: RAL (Regulator Action Level)

==> regulator action: commissioner may take corrective action

==> company action: must submit action plan to meet RBC standards (to commissioner of domiciliary state explaining how to increase capital or decrease risk)

Scenario 2:

• RBC Capital Required = 10,933
• ACL capital = 5,466
• RBC ratio = 12,000 / 5,466 = 220%

==> action/control level: depends on results of trend test because RBC ratio is in the 200-300% range

• COR = 85% + 35% + 10% = 130% > 120% ==> action level is CAL (Company Action Level)

==> regulator action: none (initially)

==> company action: must submit action plan to meet RBC standards (to commissioner of domiciliary state explaining how to increase capital or decrease risk)

Scenario 3:

• RBC Capital Required = 8,842
• ACL capital = 4,421
• RBC ratio = 14,000 / 4,421 = 317%

==> action or control level: none (trend test not required because RBC ratio > 300%)

==> regulator action: none

==> company action: none

Tip: For the practice template in the mini BattleQuiz, I sometimes like to just keep pressing the New and Cheat buttons without actually doing the calculation. I find that seeing the answer immediately helps build my intuition on how the RBC ratio corresponds to the action level (without having to stop and do the whole calculation every time.)

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

---

Week 2: Day 1 (Another Exam Problem)

We covered lots of useful information above about RBC and how to do basic calculations, but we did it in a different order from Odomirok. Let's now take a step back and look at how Odomirok organized the RBC chapter. In the problems we've already done, you were directly given R₀ thru R₅. Now you have to learn how to calculate these charges directly from financial statement information. Something I've noticed, however, is that more recent exam problems on RBC are less difficult/detailed than problems from 2015 & prior. Is this an intentional change by the exam committee? If so, you could spend less time on these details but I can't say for sure. Better not skip them entirely!

page	topic	comment
227	Overview	covered above
228	RBC Formula	covered above
233	R0	detailed calculation (Odomirok states there are issues with the R0 methodology and detailed examples will be provided in a future version of the text.)
239	R1	detailed calculation: bond size, asset concentration
250	R2	detailed calculation: asset concentration
256	R3	detailed calculation: reinsurance recoverable allocation
260	R4	detailed calculation: excessive premium growth, reinsurance recoverable allocation, loss-sensitive discount, loss concentration
274	R5	detailed calculation: excessive premium growth, loss-sensitive discount, premium concentration
280	RBC Model Act	covered above

As a start, let's look at an old exam problem. I didn't like how the examiner's report explained the solution, so I solved it myself in a way that made more sense to me. You can see what I did in the link below. You could have almost figured it out from what we've already covered, plus a little bit of commons sense.

Solution to 2017.Spring #19

Now, here are a couple of similar practice problems but with different numbers:

2 practice problems like 2017.Spring #19

And finally, here is the link to the actual exam problem and answer. They accepted 10 different answers because they didn't provide enough information in the statement of the problem. (You had to make certain assumptions.) Anyway, it might be instructive to take a quick look at some of the alternate answers. Don't spend too long on this though.

E (2017.Spring #19)

About R₀: You should probably know that it measures the risk associated with subsidiary insurance companies based on the following:

1. stocks & bond in the subsidiary
2. investments in alien insurance company affiliates
3. off-balance sheet or other items

There have not been any detailed calculation questions regarding R₀ on recent exams.

Week 2: Day 2 (R₁)

Today we're covering the detailed calculations for R₁. We'll be basing the discussion on the exam problem below from 2015.Fall. It gives you financial statement info on stocks and bonds then asks you to calculate R₁ and R₂.

E (2015.Fall #17)

Before going through the solution, I have a story about 2 of Alice's friends, Lucky and Unlucky. Lucky is an FCAS. Unlucky isn't (yet.) They were both preparing to take Exam 6 in 2016.Spring. And of course they both noticed the above RBC question from the previous exam. Unlucky said,

"It looks like the CAS really wants us to know the details of the RBC calculation. I'm going to learn it really well. Also, there was nothing on the IRIS ratios on the last exam, so I'm going to spend less time on IRIS."

Lucky thought about this and said,

"Screw that. The RBC calculations are way too detailed. I'm just going to study the question from the last exam and if they ask any more than that, I'll just take an educated guess."

Of course you know what happened. On the 2016.Spring exam there a fairly easy question on RBC and 6 points on IRIS. Lucky passed and got her FCAS. Unlucky is still trying to pass Exam 6, always making wrong predictions as to what is going to be asked.

Moral of the Story: There is a lot of luck involved in passing this exam. The most important thing is to know how to do the questions from past exams, but not every question is a repeat of the past. Obviously you can't study the whole syllabus in detail. Use past exams as a guide and try to make good predictions regarding questions that might appear in the future. Be like Lucky!

Just to be absolutely clear: Alice's advice is that you study a little beyond what's been asked in the past (use your judgment) but don't go too far. Even if you don't know the exact answer to a question, write down any related formulas and concepts you can think of. You can often squeeze out partial credit, even if it's only 0.25 points. The difference between passing and failing can be razor thin.

Anyway, let's get back to R₁. Consider a simplified version of the exam problem:

quantity	notation	value	description
bond charge	BC	406	this is the basic RBC charge for the bonds owned by the insurer
bond size charge	BSC	609	an extra charge reflecting the level of diversification of the bond portfolio
asset concentration charge	ACC	379	reflects increased risk of large concentrations of bonds (doubles the RBC charge for the 10 largest issuers)

Given the information in the above format, calculating R₁ is trivial:

Formula: R1 = BC + BSC + ACC

The answer is:

R₁ = 406 + 609 + 379 = 1,394.

But in the exam problem, you are not given these quantities directly - you have to calculate them. If BSF stands for Bond Size Factor then here's what you need:

quantity	formula
BC =	SUM over n: [ (total bonds of class n) x (RBC factor for class n) ]
BSC =	[ BSF - 1 ] x BC
ACC =	(total bonds from TOP 10 issuers) x (RBC factor)

Notes on the BSF term (Bond Size Factor):

==> Since we have at most 12 issuers in this problem, BSF always equals 2.5

==> In general BSF = sumproduct [ (# issuers, weights) / sum(# issuers) ]   * Odomirok has an example in tables 84 & 85

==> if (bond count) > 1300 then BSF is set to 0.

==> BSF decreases as (bond count) increases

Notes on the RBC factor:

• depends on the class of bond
• bonds are classified according to their credit-worthiness from highest quality down to in/near default
• this problem considers only class 02 bonds, which are high credit quality

So you see that calculating R₁ can get messy really quickly. It isn't that the concept is hard. It really all boils down to this:

• RBC charge = SUM [ (value of bond) x (RBC factor) ]

...summed over all bonds...along with modifications for bond size and asset concentration. It gets messy in the real world because you could have hundreds of bond issuers all with different levels of credit-worthiness. The challenge is finding a way to keep track of everything. Let the computer do it!!

Finally, here is my solution to the exam problem referenced above:

Solution to 2015.Fall #17

And here are a couple of similar practice problems but with different numbers:

2 practice problems like 2015.Fall #17

One last thing you might want to do is glance at these examples in Odomirok:

• tables 84-85: calculation of the BSF (Bond Size Factor)
• tables 86-87: calculation of ACC (Asset Concentration Charge) for R₁ and R₂ for a company with multiple classes of fixed income and equity assets
• tables 86-87: calculation of total R₁ for a company that has multiple classes of fixed income and equity assets

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

Week 2: Day 3 (R₂)

This section is about calculating R₂. It's similar to the R₁ calculation except easier because there's no BSF term (Bond Size Factor.) The only modification to the basic charge is the ACC (Asset Concentration Factor.)

If you're given SC = 1,365 (basic Stock Charge) and ACC = 1,335 then calculating R₂ is child's play!

Formula: R2 = SC + ACC

The answer is:

R₂ = 1,365 + 1,335 = 2,700.

Of course in the exam problem, you're not given these quantities directly - you have to calculate them. But this too is easy because it's very similar to the calculation for R₁.

quantity	formula
SC =	SUM over i: [ (total bonds of type i) x (RBC factor for type i) ]
ACC =	(total stocks from TOP 10 issuers) x (RBC factor)

Now, calculating R₂ can still get messy for the same reasons that R₁ gets messy. But it isn't conceptually difficult.

Pop Quiz!    :-o

Go back to the practice problems from the previous section and calculate R₂.

Pop Quiz Answers!    :-D

practice 01: R₂ = SC + ACC = (21,900 x 0.15) + (21,900 - 200 - 500) x 0.15 = 6,465

practice 02: R₂ = SC + ACC = (51,100 x 0.15) + (51,100 - 600 - 500) x 0.15 = 15,165

Now that we've covered R₁ and R₂, there's a comment I made in Week 2: Day 1 about allocation of the ACC (Asset Concentration Charge) that should now make more sense. Recall that the exam problem we looked at had 10 different sample answers in the examiner's report. One source of ambiguity was that they didn't tell how to allocate ACC between R₁ and R₂. You now know that the ACC is calculated separately for R₁ and R₂, but the exam problem only provided the total ACC. To properly solve the problem, you had to know how much went into R₁ and how much went into R₂. Since they didn't tell you, you had to make an assumption:

• The examiners accepted any allocation of ACC between R₁ and R₂.

The simplest thing to do is put it all either in R₁ or R₂, and I opted to put it all in R₂.

Week 2: Day 4 (R₃ & R₄)

Here's a problem from way back in 2014 where you have to calculate R₃. It's pretty easy (aside from 1 small trick) because they explicitly tell you which financial statement amounts relate to credit risk and they give you the associated RBC factors.

E (2014.Spring #20)

Without even studying this section, you could guess that to calculate R₃ you have to multiply (amount held) by (RBC factor), and you'd probably get half the points just doing that. But here's the trick:

R3 Trick: The RBC charge for reinsurance recoverable is split 50/50 between R3 and R4 1

¹ Use this split only if:

R₄ > (RBC charge for non-invested assets) + (RBC charge for reinsurance recoverables)

Note that R₃ is always greater than the right-hand-side of this inequality since the right-hand-side contains only 2 of the 3 components of R₃. The 3 components of R₃ are (see Addendum on R₃): non-invested assets, reinsurance recoverables, health credit risk.

Remember that R₄ is the biggest component of RBC (54% industry-wide) and R₃ is a small portion of the total (1% industry-wide). Therefore, this inequality should virtually always be true. And in fact, the examiner's report never even checked – they just went ahead and did the 50/50 allocation. (If by some freak occurrence this inequality were false, then 100% of the charge for reinsurance recoverable would go to R₃.)

In this problem you also have to calculate R₄ but it's very easy because they give you all the components. You just have to recognize them:

• basic loss reserving charge: 400,000
• excessive growth charge/penalty for loss reserves: 75,000

Just add them up then throw in the 50% allocation for the reinsurance recoverable charge. (See the R₃ trick above.)

Alice's Story Time: Remember Alice's friends Lucky and Unlucky? Well, Unlucky noticed that the section on R4 in Odomirok was very long (about 15 pages). She panicked and spent a week learning all the calculations in detail. On the other hand Lucky realized that all of that was just too detailed for the exam and decided to spend her time studying topics closer to what had been asked in the past. Can you guess what happened?

The detailed calculations for R₄ (not covered in this wiki article) are kinda-sorta similar to the calculations for R₅ which we do cover in detail in the next section. It's an extremely hard problem.

Addendum on R₃

I would have said what we covered above this is very likely all you need to know about R₃, but Alice reminded me about part (b) of the following rather unfair problem:

E (2016.Spring #26)

The reason it's unfair is that you had know the RBC factors for the components of R₃. In mini BattleQuiz 6, there was a practice template on calculating total RBC. To solve it, you had to know which of the financial statement items related to R₃, but I gave you the factors. Let's step back for a moment and list all the possible R₃ items. (Items in green relate to this exam problem.)

1. Non-Invested Assets:

• Investment income due and accrued (factor = 0.01)
• Amounts Receivable related to uninsured plans (0.05)
• Federal income tax recoverable (0.05)
• Guaranty funds receivable or on deposit (0.05)
• Recoverable (parent/subs/affiliates) (0.05)
• Aggregate Write-ins for other than Invested Assets (0.05)

2. Reinsurance recoverable (0.1)

3. Health Credit Risk (accounts for 0% of P&C insurer risk)

Now, in (2016.Spring #26), you weren't given the actual RBC charges, you were given the financial statement amounts. To get the charges you had to multiply each by the correct RBC factor, which was not given. (The correct factors are in parentheses in the above list.) In other words, they expected you to memorize these factors. If you didn't memorize these factors, my advice would be to make up something reasonable like 0.1 and just use that across the board. If you did everything else correctly, you would still get most of the points. (Alice thinks it was ridiculous to expect you to memorize the RBC factors. Don't get her started!)

R₃ trick: The solution in the examiner's report explicitly checked the inequality for the R₃ trick. I wonder if they deducted points for not checking, even if you correctly did the 50/50 allocation. They didn't mention it.

Week 2: Day 5 (R₅)

Unfortunately there have been exam problems that test the details for calculating R₅. Note however that these problems were from 2018, 2014 and 2012. The syllabus has changed since 2012 and the reference to the claims-made discount in that problem is no longer relevant. Alice's advice is to ignore the problem from 2012 since it's very similar to the 2014 problem.

Recall the comment I made in Week 2: Day 1 - that recent RBC exam questions are less difficult/detailed than problems from 2015 & prior. I was guessing that the detailed calculations for R₅ wouldn't show up again, but then they did in (2018.Spring). You can try your hand at that problem in the mini BattleQuiz, but take a quick look at the 2014 problem first:

E (2014.Fall #18)

And here's my solution to the calculation of R₅ for that problem. (Once you have R₅, calculating the total RBC is easy because they directly give you R₁ thru R₄.) I've included a lot more explanatory details than were in the examiner's report:

Solution to 2014.Fall #18

And finally, here are 4 PDFs with practice problems similar to the 2014 exam problem but with different numbers:

4 practice problems like 2014.Fall #18

Note 1: These 4 problems were generated with random numbers and problem #2 had a negative base RBC charge for WC. This negative charge for WC should probably be set to 0 before combining it with the charges for the other lines.

Note 2: In the above problems, you were given the $-value for the excessive growth charge, but it's possible you may have to calculate it from the raw data. If so, you need to know the following:

Formula: (excessive premium growth charge) = (excess growth) x 0.225 x NWP

==> (excess growth) = (average growth over last 3 years) – 10%

==> (average growth over last 3 years) is capped at 40% for each year

Pop Quiz!    :-o

Given:

year	NWP
2016	100,000
2017	120,000
2018	174,000
2019	191,400

Calculate the NWP excess growth charge.

Pop Quiz Answers!    :-D

(average growth over last 3 years)

= average (120000/100000 - 1 , 174000/120000 - 1, 191400/174000 - 1)

= average (20%, 45%, 10%)      (but the growth must be capped at 40%)

~ average (20%, 40%, 10%)

= 23.3%

excess growth charge

= (excess growth) x 0.225 x NWP

= (23.3% – 10%) x 0.225 x 191,400

= 5,742

And here's the mini BattleQuiz for the Alice's last 3 "days":

mini BattleQuiz 7 You must be logged in or this will not work.

Alice's Summer Performance Review (Old Exam Problems)

mini BattleQuiz 8 You must be logged in or this will not work.

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

BattleCodes

Memorize:

Conceptual:

Calculational: