RBC

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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

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	calculate: - 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 RBC	calculate: - RBC RAL1	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 (2015.Fall #17)	calculate: - R1	calculate: - R2	reducing R2: - 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: - RBC	improving RBC ratio: - reserving practices (error in exam question??)	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 RAL stands for Regulatory Action Level

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

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In Plain English!

Alice's 1st Day

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 level	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 is in the 150-200% 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!

Alice's 2nd Day

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)
• dividend ratio (policyholder dividends divided by NEP)
• expense ratio (other U/W expenses + small miscellaneous items divided by NWP)

Recall that COR does not include investment income.

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, bonds) 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!

Alice's 3rd 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!

Alice's 4th Day

Alice arrived early today so I prepared a special pop quiz she could do while eating her 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 controlled by selecting reinsurers with a high credit rating.

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. 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%)

Alice's 5th Day (TGIF!)

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

E (2017.Fall #17)

It's a very easy problem and I'm surprised that 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	17,00	13,00	1,300
R3 charge	400	500	300
R4 charge	10,300	10,600	8,600
R5 charge	1,400	2,100	1,200

For each scenario, find:

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

Pop Quiz!    :-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 = 10,571
• ACL capital = 5,285
• RBC ratio = 10,000 / 5,285 = 189%

==> action 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 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 level: no action required ( trend test not required because RBC ratio > 300%)

==> regulator action: none

==> company action: none

temp section

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