Risk Based Capital (RBC)
for an Illinois Based Insurance Company
May 11, 2018
Undergraduate Researchers:
Dong Shin (Bill) Seol, Qinxue Liu,
Chuyi Ma, Kexin Liu
Faculty Mentor: Klara Buysse
University of Illinois at Urbana-Champaign
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Risk Based Capital (RBC), Schemes and Mind Maps of Financial Statement Analysis
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Risk Based Capital (RBC)
for an Illinois Based Insurance Company
May 11, 2018
Undergraduate Researchers:
Dong Shin (Bill) Seol, Qinxue Liu,
Chuyi Ma, Kexin Liu
Faculty Mentor: Klara Buysse
University of Illinois at Urbana-Champaign
Table of Contents
- Introduction to RBC System
- Risk Based Capital Ratio
- Required Risk Based Capital
- C- 1 Asset Risk
- C-2 Insurance Risk
- C-3. Interest Rate Risk
- C-4. Business Risk
- Examples: Allstate Cooperation
- Calculation of An Illinois-Based Company
- Reference
Different types of insurance have different kind of risk factors, due to the specificities of
these insurance businesses. NAIC developed distinct RBC models for four major insurance
types: Life, Property/Casualty (P&C), Health, and Fraternal.
Regulators use RBC standards to determine their intervention level on companies. There
are four levels of regulatory action according to the RBC formula:
- company action,
- regulatory action,
- authorized control and
- mandatory control levels.
If the company meets the RBC standard, NAIC regulators take no action; if not, the
greater capital deficiency this company has, the higher control level NAIC regulators will take
on company. In this way, regulators ensure companies have adequate financial solvency under
RBC system.
The levels of regulatory action triggered by the RBC ratio are as follows: NAIC only
takes regulatory action when the ratio becomes less than 250%. If a company’s RBC ratio is
between 250% and 200%, and also fails the trend test (which measures past RBC ratio changes
of the company), Company Action Level is triggered. If the ratio is between 200% and 150%,
the company also triggers Company Action Level, and is required to submit a RBC plan to
improve its RBC ratio into compliance. If the ratio is between 150% and 100%, the company
triggers Regulatory Action Level, and is required to submit a corrective action plan. NAIC will
perform examination or take regulatory action if the commissioner believe it is necessary. If the
ratio is between 100% and 70%, the company triggers Authorized Control Level, and NAIC is
authorized to take regulatory actions, such as rehabilitating or liquidating the insurer. If the ratio
is below 70%, the company triggers Mandatory Control Level, and NAIC is authorized to take
regulatory control, including placing the insurer under regulatory supervision.
In our research project, we look at the basic concepts of the Risk-Based Capital (RBC)
system, investigate RBC regulations, and look into discussions on how to improve companies’
RBC levels. We will then use the knowledge to determine the RBC ratio for a small life
insurance company. The insurance products of this company will be backed by bonds and
equities. This report will show our research progress on RBC system, including our knowledge
on RBC regime, understanding of RBC formulas, and how we put this regulation into practice
with an example.
Required Risk Based Capital
Required Risk Based Capital is intended to calculate the minimum amount of capital an
insurance company should hold in order to not trigger regulatory action, meaning that the
insurance company is solvent enough to do their regular insurance business.
The capital an insurance company should hold differs from the risks it is taken in its
insurance and investment operations. For example, a company that is investing in risky assets
will probably have to hold more capital than a company that is investing in government bonds.
RBC split the risks a company can take in four major classes for life insurers:
- C-1 Asset risk,
- C-2 Insurance risk,
- C-3 Interest rate risk and
- C-4 Business risk.
The Required Risk Based Capital can then be obtained through the formula:
2
- 𝐶 2
2
3
where C-1, C-2, C-3 and C-4 stands for the risk-based capital under that category. Note that this
formula calculates the required Risk Based Capital at Company Action level, that is, when Risk
Based Capital is twice of Total adjusted Capital.
As one can see in the formula, the risks are adjusted for covariance. This is done in order
to take into account the fact that all the four risks categories will not occur at the same time.
In the following sections we will give an overview of the calculation of risk based capital
for each risk.
3
https://math.illinoisstate.edu/krzysio/MAT483/RBC.pdf
C-1 Asset Risk
C-1 Asset Risk measures the risk of default (of bonds and mortgage) or decrease in the
value of the assets (stocks) insurers hold in their investing portfolio. RBC for Asset risk is
calculated by multiplying different risk factors with different types of investments, including
bonds, stocks, mortgages, real estate, and other long term assets and summing up the terms.
Certain types of assets will need an adjustment based on the size of portfolio.
Let’s start with bonds. US government bonds have a risk factor of 0. C-1 risk only
measure the default risk of bonds, and the likelihood of default of a government bond is nearly
zero, because the government may fall behind the repayment of the bonds only if the nation is
under severe financial deficit. Corporate issued bonds are classified into six SVO levels, and risk
factors are related to the rating of the bonds. To classify the bonds into the different classes, one
can obtain the ratings from Standard and. The following table shows the conversion and risk
factors of bonds with different ratings.
4
S&P ratings SVO ratings Risk factor
AAA, AA+, AA-, A+, A, A- Class 1 0.
BBB+, BBB, BBB- Class 2 0.
BB+, BB, BB- Class 3 0.
B+, B, B- Class 4 0.
CCC+, CCC, CCC- Class 5 0.
CC, C, D Class 6 0.
4
http://www.naic.org/documents/svo_naic_aro.pdf
1 - A, with a risk factor of 0.0021. An S&P AA- bond will be classified as NAIC 1-D bond, and
the risk factor is 0.0057.
5
A reason for proposal of the new “granular” is that insurers has the incentive to invest in
higher return bonds rather than the higher rating ones.
6
An investment of AAA bonds requires
the same risk based capital as investing in A- bonds, while A- bonds has higher return rates as
well as higher default risks. The current NAIC classification does not reflect such differences,
and the required risk based capital can be insufficient for the insurers to stay solvent. The
proposal can better eliminate the probability of insolvency by pressurize insurers to redesign
their investment portfolios, optimizing the return and minimizing the risks on the investments.
Mortgage is another common type of investment. There are many types of mortgage
products available in the market: farm mortgages, insured guaranteed mortgages, resident
mortgages, commercial mortgages, etc. These mortgages contain different default risk, because
part of them are guaranteed or insurance, while others don’t. Those with insurance are assigned
with lower risk factor because the risk of default on such investment is lower than the others.
Mortgages in good standing has lower risk factors than the ones are 90 days overdue, since the
past-due mortgage has a higher risk of default. The adjustment factors of mortgages are based on
the size of the portfolio and the yearly experience of insurer dealing with mortgage assets. Any
insurers with less than five years of experience will use 1.0 as the adjustment factor. In this
research paper we will not go into detail about the specific risk factors in mortgage assets We
assume that the small insurance company only invests in bonds and equities.
5
https://www.neamgroup.com/insights/proposed-naic-rbc-c1-factors-for-life-insurers
6
http://www.naic.org/insurance_summit/documents/insurance_summit_160517_financial_risk_based_
capital_update.pdf
Asset risk measures the risk of decrement in value for stocks. Stocks are divided into two
subcategories: affiliated and unaffiliated. For affiliated stock, RBC is calculated by the
percentage of the parent company’s ownership in the subsidiary multiplied by the subsidiary’s
Company Action Level RBC. For example, if company A owns 100% of company B, RBC of
affiliated stock of company A is 100% of the Company Action Level RBC of company B. For
common stocks issued by unaffiliated companies, the risk factor is 0.3 for all. For preferred
stocks of unaffiliated companies, risk factors are again associated with ratings of the preferred
stocks
7
:
S&P ratings NAIC class factor
AAA, AA+, AA-, A+, A, A- 1 0.
BBB+, BBB, BBB- 2 0.
BB+, BB, BB- 3 0.
B+, B, B- 4 0.
CCC 5 0.
CC, C, D 6 0.
Here is an example of the calculation of the Risk Based Capital for stocks:
Assume we have $1,000 of Accenture common stocks and $1,000 of US Bancorp
preferred stock with a S&P rating of BBB+. Then we need the following capital:
C-1 stock risk capital = $1,000 * 0.3 + $1,000 * 0.03 = $
7
http://www.naic.org/documents/svo_naic_aro.pdf
C-2 Insurance Risk
Insurance risk is the risk associated with the mispricing of the products. As the number of
policies written increases, the risk factor will decrease: the risk of loss is diversified. Insurance
risk captures the probability of mispricing, underestimation of expenses, overestimation of
interest rate and investment income, incorrect choice of mortality and morbidity, occurrence of
catastrophe and contagion. These risks are unavoidable for all insurance industry. Risk Based
Capital for this category can be calculated by a risk factor multiplied by net amount at risk. The
net amount of risk is the difference between a claim amount payable if a specific event occurs
and the amount set aside to support the claim
8
NAIC uses computer simulation to come up with the risk factors for different size of
policy written. Portfolios with 10,000, 100,000 and 1 million are generated with selected death
rate and expected lapse rate, and the variations of the actual death rate and selected mortality
table are detected, which is the error of prediction made by insurers. Risk factors are derived
from the variation caught by the stimulation. The risk factors for ordinary life insurances are:
Net amount at risk factor
First $500 million 0.
Next $4500 million 0.
Next $20000 million 0.
Next $25000 million
and above
8
http://rmtf.soa.org/net_amount.pdf
As an example, we created a whole life insurance policy that has a death benefit of
$20,000 payable at the end of the month, and a fixed premium of $200 at the beginning of each
month. Our example was calculated based on a person aged 35 at time = 0, with a guaranteed
interest rate of 3%. At time = 0, considering that the net reserve is the premium received at time
= 0 for simplification, the Net Amount at Risk (NAR) is calculated to be $20,000 - $200 =
$19,800.00. The RBC in this case would be $19,800.00 * 0.0023 = $45.54. When there are more
insurance issued, risk factor of less value will be applied to the excess of the first $500 million.
For example, with 30,000 insurance issued, the total NAR at time 0 will be equal to $19,800 *
30,000 = $594 million. The RBC in this case is $500 million * 0.0023 + $94 million * 0.0015 =
C-3. Interest Rate Risk
Interest Rate Risk is basically the risk caused by the possible changes in interest rate
levels during the investment period. This can result in an insurer earning fewer returns than
expectation on its investments and thus cannot pay the policyholder. In this situation, interest
obligations under various insurance and annuity contracts cannot be met and disintermediation
will spur: if interest rates go up, more people will surrender their contract which is not good for
the insurance company because they will have less business and thus less profit; on the contrary,
if interest rates go down, less people will surrender their contract which is not good either
because the insurance company have to pay the policyholder, but doesn’t receive a lot of return
from the market.
This risk depends heavily on how closely the assets and liabilities are matched in time.
For example, if the cash inflows from assets (maturity values are included) exactly equals to the
b. Medium/High Risk Category: the assumed asset/liability duration mismatch in this category
should be larger than 0.125. It determined by measuring the value of the additional risk from
the more discretionary withdrawal provisions based on assumptions of policyholder behavior
and random interest rate scenarios. For medium risk category particularly, supplementary
contracts not involving life contingencies (SCNI) and dividend accumulations are also
included because the historical tendency of these policyholders is relatively insensitive to
interest rate changes. The category usually includes:
i. including annuity reserve with surrender charge
ii. exhibit 10 reserve not included in item 10D of the Notes to Financial Statement
(excluding reserve not related to specific policies)
iii. structured settlement annuities
iv. annuity reserve with no adjustment (for high risk category only)
During calculation, low risk category is first determined, followed by adding medium and
high risk categories, which are derived from the low one.
The risk factor for all these three categories of interest rate risks are demonstrated in the
following table
11
:
Class Factor
Low Risk 0.
Medium Risk 0.
High Risk 0.
The conditions for calculating RBC under C3 are:
11
http://www.naic.org/documents/prod_serv_statistical_rsn_lb.pdf
a. General account funded:
○ because interest rate risks will be meaningless without a founded general
account;
b. Reserve interest rate or fund long-term interest guarantee must be less or equal to
○ because the one-year swing in interest rates that is used to measure low
risk category is possibly 4 percent;
c. Experience rating mechanism is immediate participation, retroactive credits of
other technique other than participating dividends:
○ because such an action can give a more credible estimation for the risk;
d. The investment is not subject to discretionary withdrawal or is subject to market
value adjustment:
○ only if the portfolio experience and current interest rates can be reflected
in the lump sum market value adjustment reflect, which is expected to
pass both credit risk and rate risk to the policyholder on withdrawal.
Here is an example for calculating interest rate risks
12
For an insurance company investing $3,500 million in a project that is classified in low-
risk categories, the risk factor is 0.75%, and the RBC under C3 Interest Rate Risk, should be
$3,500 * 0.75% = $26.25 million.
12
https://math.illinoisstate.edu/krzysio/MAT483/RBC.pdf
Example: Allstate Corporation
In this section, we are going to introduce an example of RBC calculation on Allstate
Corporation, according to the historical data of Allstate’s assets and liabilities. Using data from
annual statement of Allstate, the Required Risk-Based Capital can be calculated.
We first evaluate the C-1 (asset default) risk by summing up default risks of Allstate’s
various investments, including bond, preferred stock, common stock, mortgage on real estate,
cash, and reinsurance of Allstate Corp., each adjusted with its corresponding NAIC risk factor.
C-2 (insurance) risk evaluates the policy mispricing risk Allstate takes, and can be
calculated by subtracting face value of policy in force from reserve for life contracts.
C-3 (interest rate) risk measures the how sensitive Allstate’s investments are under
changing interest rate. Unfortunately, the interest rate risk rating information of Allstate’s
investments remains private, and we have no access to it. So C-3 risk cannot be calculated.
C-4 (business) risk represents Allstate’s normal business management and operation risk
and can be calculated by multiplying Allstate’s investment in life and annuity to the
corresponding risk factor.
The chart below in the next page illustrates the calculation of Allstate’s risks for Risk-
Based Capital.
Using the RBC formula, the required risk-based capital comes out to be $2.7 billion,
which is reasonable compare to Allstate’s $2.8 billion in annual report. The number is smaller
than $2.8 million mainly because we are lack of data of calculating C3.
According to Allstate’s 2017 annual report, the company has a total adjusted capital of
$17.70 billion. Dividing the total adjusted capital by the authorized control level RBC, the RBC
ratio comes to be approximately 6.32. This significantly exceeds the authorized control level, and
shows that Allstate has sufficient amount of capital, based on its risk level, to support its
operations. As a conclusion, Allstate trigger no regulatory intervention in 2017.