2009 seminar for the appointed actuary - pfad colloque pour l’actuaire désigné 2009 - ped 2009...
TRANSCRIPT
2009 Seminar for the Appointed Actuary - PfAD
Colloque pour l’actuaire désigné 2009 - PED
2009 Seminar for the Appointed Actuary - PfAD
Colloque pour l’actuaire désigné 2009 - PED
Canadian Institute
of Actuaries
Canadian Institute
of Actuaries
L’Institut canadien desactuaires
L’Institut canadien desactuaires
Outline
• Changes in Standards of Practice• New Educational Note
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 2Page 2
Changes in Standards of Practice
• Three changes in Exposure Draft• Increase claims development’s upper limit to 20%• Decrease investment return risk’s lower limit to 25 basis
points• Recognise of stochastic techniques to be within accepted
actuarial practice in Canada
• Timing • Comments due October 31• Effective December 31
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 3Page 3
Process
• Notice of Intent (NOI) released June 5• Comments from
• 13 individual CIA members• 1 consulting firm with input from 9 members• P&C RMCR
• Very detailed memo from Designated Group (DG) to membership (expected release September 2009) with all comments summarized
• Comments were important input for drafting of PfAD Ed Note
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 4Page 4
Proposed Changes
• Investment return risk – reduction to 25 bp– Focus shift away from current economic environment – Instead consider P&C insurers invested in high quality
government bonds and fully immunized from mismatch risk
• Claims development – increase to 20% reflects feedback and situations like Alberta auto
• Stochastic techniques – accepted, but no proscribed methods or measurements (different from life SOP)
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 5Page 5
Educational Note - Purpose
• Provide guidance to actuaries in selection of MfAD for P&C insurers
• Also valuable to actuaries working with self-insurers and captives
• Flexible enough to allow for future developments in– IFRS – Use of stochastic techniques in valuation of policy
liabilities
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 6Page 6
MfAD Refresher
• MfAD reflects degree of uncertainty of best estimate assumption
• SOP (1740.42): deviations of actual from expected experience may result from one or more of the following:• Error of estimation – past experience data may be
insufficient or unreliable – future conditions may differ from conditions that generated past experience
• Deterioration or improvement of expected experience as result of influences which actuary does not anticipate
• Statistical fluctuation
• MfAD not expected to be so high that probability of unfavourable development is < 1% or 5% (i.e., scenarios under DCAT), purpose of capital
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 7Page 7
Cost of Capital Methods
• Focus of Ed Note is MfAD derived from deterministic or stochastic analyses
• Cost of capital approach – another alternative approach to determining MfAD
• PCFRC believes that cost of capital methods are important area of future development
• Many unresolved issues around the use of such methods• What capital: economic capital, regulatory required capital, rating
agency capital, capital used for pricing, other • How to determine cost, how frequently is cost updated, should it
vary by contract or claim type or vary by duration of contract or claim
• See April 15, 2009 report Measurement of Liabilities for Insurance Contracts: Current Estimate and Risk Margins, prepared by Risk Margin Working Group (RMWG) of IAA for further details (IAA Risk Margin Report)
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 8Page 8
Organization of Educational Note
1. Introduction2. Terminology 3. Desirable risk margin characteristics4. Three categories of margins for adverse deviations5. Explicit assumptions - margins for adverse deviations
using a deterministic analysis 6. Relevant statistical concepts7. Stochastic techniques 8. Three P&C product examples 9. Quantile approaches 10. Comparison of risk margin methods11. Documentation and reporting
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 9Page 9
Information Sources
• IAA Risk Margin Report• Feedback from CIA members received in response
to MfAD NOI• Checklists for MfAD from Appointed Actuary reports
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 10Page 10
Desirable Risk Margin Characteristics - IAIS
• Addressed in Second Liabilities Paper (2006, paragraph 57)
• Does not prescribe any one method• “ … methodology for calculating the risk margin should
share certain characteristics.”• The less that is known about current estimate and its
trend, the higher the margin• Risks with low frequency and high severity will have
higher risk margins than risks with high frequency and low severity
• For similar risks, contracts that persist over longer timeframe will have higher risk margins than those of shorter duration
• Risks with wide probability distribution will have higher risk margins than risks with narrower distribution
• To extent that emerging experience reduces uncertainty, risk margins will decrease, and vice versa
• IASB Identified same properties as desirable
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 11Page 11
IAA Risk Margin Requirements
1. Apply consistent methodology for entire lifetime of contract2. Use assumptions consistent with those used in determination of
corresponding current estimates3. Be determined in manner consistent with sound insurance pricing
practices4. Vary by product (class of business) based on risk differences
between products5. Be easy to calculate6. Be consistently determined between reporting periods for each
entity that is, risk margin varies from period to period only to extent that there are real changes in risk
7. Be consistently determined between entities at each reporting date, that is, two entities with similar business should produce similar risk margins using the methodology
8. Facilitate disclosure of information useful to stakeholders9. Provide information that is useful to users of financial statements10. Be consistent with regulatory solvency and other objectives11. Be consistent with IASB objectives
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 12Page 12
CIA Risk Margin Characteristics
• Characteristics cited by both IAIS and IAA are consistent with characteristics noted in CIA SOP
• Section 1740.42 and 1740.43:• A larger margin for adverse deviations (compared to the
best estimate assumption) is appropriate if• the actuary has less confidence in the best estimate assumption,• an approximation with less precision is being used, • the event assumed is farther in the future,• the potential consequence of the event assumed is more severe, or• the occurrence of the event assumed is more subject to statistical
fluctuation.
• A smaller margin for adverse deviations is appropriate if the opposite is true.
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 13Page 13
CIA SOP - MfAD
• Three categories of MfAD• Claims development – % of claim liabilities excluding
PfAD• Recovery from reinsurance ceded – % of amount
deducted on account of reinsurance ceded excluding PfAD
• Investment return rates – deduction from expected investment return rate per year
• SOP note that according to how considerations so vary, selected margins should vary between:• Premium liabilities and claim liabilities• Lines of business• Accident years, policy years, or underwriting years
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 14Page 14
Explicit AssumptionsMFAD Using a Deterministic Analysis
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
• New concept – not excessive
• May be circumstances for MfAD above high margin • SOP: “for unusually high uncertainty or if the resulting
provision for adverse deviations is unreasonably low because the margin for adverse deviations is expressed as a percentage and the best estimate is unusually low.”
• (See attachments to presentation material – new SOP and consideration tables)
Category Low Margin High Margin Claims development 2.5% 20% Recovery from reinsurance ceded Zero 15% Investment return rates 25 basis points 200 basis points
Page 15Page 15
Considerations – Deterministic Approach (Explicit Assumptions)
• Ed Note contains numerous tables with considerations for explicit assumptions approach
• Not exhaustive list, but representative of key issues to consider
• In some situations, considerations may not be relevant or applicable
• May be additional unique considerations specific to organization
• For each consideration, spectrum between situation necessitating low margin or high margin
• For many insurers, particular circumstances for any one consideration may dictate selection of margin between low and high values set out in SOP
• When faced with situation in which some considerations indicate low margin and others indicate high margin, actuary would use professional judgment to determine priority of considerations and resulting final margin20
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
920
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
9
Page 16Page 16
MfAD for Investment Return Rates
• Addresses several different types of risk:• Mismatch risk between payment of claims and availability
of liquid assets• Error in estimating the payment pattern of future claims• Asset risk including credit/default risk and liquidity risk
• In economic environment of low interest rates, mismatch risk and credit/default risk still remain
• Following CIA SOP, could derive discount rate adjusted by MfAD less than 0%• In practice, actuaries may limit discount rate to 0% in such
situations
• Two examples of alternative formula-based approaches presented in Ed Note
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 17Page 17
Relevant Statistical Concepts
• Not intent to present detailed description of statistics
• Expected that actuaries using stochastic methods for determination of MfAD have expertise in fundamentals of statistical modeling
• Key concepts:• Risk distribution• Normal distribution• Standard deviation• Coefficient of variation (CV)• Skewness
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 18Page 18
Stochastic Techniques
• Stochastic simulations can be powerful techniques for quantifying risk exposures underlying P&C insurance policies
• Users require full understanding of stochastic risk modelling for successful implementation and rational interpretation
• Expect actuaries who use stochastic approaches to determine MfAD would generally use stochastic methods to determine policy liabilities
• Beyond scope of Ed Note to address stochastic modeling techniques except as applicable to determination of PfAD
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 19Page 19
Stochastic Techniques (cont’d)
• Refer reader to CIA’s August 2001 Research Paper Use of Stochastic Techniques to Value Actuarial Liabilities under Canadian GAAP prepared by Working Group on the use of Stochastic Techniques (Working Group) of CLIFR
• Specifically, recommend review of:• Section 3. When to Use Stochastic Simulation Methods for
Actuarial Liability Valuation• Section 4. General Overview of the Stochastic Valuation
Method for Actuarial Liability Valuation• Section 6.5. Correlation• Section 7. Practical Issues
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 20Page 20
Stochastic Techniques (cont’d)
• Reference to Mack and bootsrapping – no details – refer to literature
• Actuaries using stochastic techniques for developing MfAD would also take into account considerations presented in Section 5 of Ed Note
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 21Page 21
Stochastic Techniques (cont’d)
• Actuaries considering change from deterministic approach to stochastic approach would engage in discussion with insurer’s management and auditors to determine if such change represented potential change in accounting policy important consideration would be materiality of any resulting change
• Since stochastic techniques may be more subject to variability from valuation date to valuation date, ongoing communication between actuary and insurer’s management and auditors may be required
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 22Page 22
Stochastic Techniques (cont’d)
• When using stochastic models, important to recognize that MfADs do not cover inherent or statistical volatility arising from particular model expected that large and small insurers would generate similar MfAD when using same model
• MfADs do, however, cover uncertainty in whether actuary has the “right” model or “right” parameters
• Thus, actuary working with large volumes of data or more years of experience will likely have more confidence that the selected model is “correct” and resulting margins will likely be lower for larger volume or more established data than for smaller volume or less reliable data
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 23Page 23
Mandating Assumptions for Stochastic Techniques
• In the CIA 2001 Research Paper, the Working Group struggled with issue
• Impractical, inappropriate, and unmanageable for following reasons:– Would entail significant and time-consuming testing and
review of experience data from across the industry– Would potentially require large number of possible
assumptions or variations in assumptions to be covered– Would be difficult to anticipate all unique company
circumstances that can legitimately affect valuation results and therefore cause prescription to be inappropriate
– Ranges would need periodic updating to reflect emerging experience
– Would undermine integrity and responsibility of Appointed Actuary
• Considerations equally applicable to P&C insurers today• Actuary reminded of his/her responsibilities20
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
920
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
9
Page 24Page 24
Sample Products – Discussion
• Stochastic modelling will typically be beneficial for products with skewed cost distributions with low frequency of occurrence but high severity and/or material variability in the cost distribution
Examples:• Stop loss reinsurance• Catastrophic P&C insurance risks• Credit, warranty, and mortgage guarantee insurance• Long-tail lines of business such as professional liability
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 25Page 25
Three P&C Product Examples20
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
920
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
9
Sample Lines of Business Product A Product B Product C 1. Notional Coverage Type Automobile
Third Party Liability General Liability “Risky Liability”
Catastrophe Coverage
2. γ (gamma) (Measure of Skewness) 0.4 0.8 8 3. Coefficient of Variation (CV) 13.3% 26.1% 151.3% 4. Settlement pattern Medium Longer Medium 5. Risk distribution Normal Power Normal Power Lognormal
Page 26Page 26
Quantile Approaches
• Establishing which statistical measurement is most appropriate for determination of MfADs based on stochastic techniques is important decision
• Difference between selected measurement and mean result establishes dollar PfAD
• Following approaches reviewed:• Multiples of standard deviation
• Percentile or confidence levels, Value at Risk or VaR
• CTE, Tail Value at Risk or TVaR
• Currently, no generally accepted method (from regulatory, accounting, or actuarial perspective) for determining appropriate quantile for purpose of determining risk margins 20
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
920
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
9
Page 27Page 27
Quantile Approaches (cont’d)
Multiples of Standard Deviation • Simplicity • Practicality
Percentile or Confidence Levels • Most commonly used• Australia, Singapore, South Africa – 75%
confidence level requirement (Australia, at least equal to ½ std deviation)
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 28Page 28
Quantile Approaches (cont’d)
CTE• The 2001 Research Paper states:
Setting the liabilities for life insurers in excess of CTE(80%) would not normally be an acceptable practice as the resulting coverage would be excessive and inconsistent with GAAP. Provision for more catastrophic, implausible or unknown events is done through required capital, which would normally be established at a much higher CTE percentage.
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 29Page 29
Quantile Approaches (cont’d)
CTE (cont’d)• Unlike life insurance, no specific statistical
measurement or percentile mandated by CIA SOP for P&C insurance
• Examples prepared by RMWG of IAA, indicate that range of CTE(60%) to CTE(80%) is likely too high for many traditional P&C lines of insurance
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 30Page 30
Three P&C Product Examples20
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
920
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
9
Table 9.2 Risk Margins at Selected Confidence Levels Risk Margin as % of Discounted Current Estimates
Product
γ
(gamma)
Percent of Discounted Current Estimate Confidence Level CTE
65% 75% 90% 40% 75% A 0.4 4.4% 8.5% 17.6% 8.4% 17.6% B 0.8 7.1% 15.7% 35.7% 16.2% 33.9% C 8.0 -16.0% 15.1% 123.2% 51.7% 164.6%
Table 9.1 Risk Margins at Selected Confidence Levels Number of Standard Deviations
Number of Standard Deviations Above the Mean Required to Reach Selected Level of Confidence Confidence Level CTE
Product
γ
(gamma) 65% 75% 90% 40% 75% A 0.4 0.33 0.64 1.32 0.63 1.33 B 0.8 0.27 0.60 1.37 0.62 1.30 C 8.0 (0.11) 0.10 0.81 0.38 1.08
Page 31Page 31
Evaluation of Quantile Methods
• In evaluating various methods for developing risk margins, IAA Risk Margin Report suggests that two aspects of insurance liabilities be considered to measure risk margin: • Time – the rate at which risk is released over time (i.e.,
settlement pattern) • Shape – the risk distribution of possible outcomes around
the mean value, at the reporting date, over a specified time horizon
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 32Page 32
Comparison of Risk Margin Methods
• Summary of observations regarding the various methods
• Comparison of methods from quantitative perspective
• Comparison of methods from qualitative perspective• Qualitative review includes comparison of each method to
desirable characteristics of risk margins identified by IAIS and IAA
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 33Page 33
Summary Observations
• In quantile family of methods, CTE approaches theoretically more sound than confidence level approaches
• Differences can be significant for products with more skewed risk distributions
• Regulatory oversight or actuarial practice could apply higher confidence levels for products whose risk distributions are more highly skewed
• Explicit assumptions best considered as useful approximations for implementing a quantile method
• Consistency among insurance products and between insurance and other industries is challenging using purely explicit assumption approach
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 34Page 34
Quantitative Comparison20
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
920
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
9
Table 10.1 Comparison of Risk Margins from Different Methodologies Risk Margin as % of Discounted Current Estimate
Risk Margin Approach Product A Product B Product C
1. 0.5 standard deviations 6.7% 13.1% 75.7%
2. 1.0 standard deviations 13.3% 26.1% 151.3%
3. 65% confidence 4.4% 7.1% -16.0%
4. 75% confidence 8.5% 15.7% 15.1%
5. 90% confidence 17.6% 35.7% 123.2%
6. 40% CTE 8.4% 16.2% 51.7%
7. 75% CTE 17.6% 33.9% 164.6%
Notional Coverage Type Automobile Third Party Liability
General Liability “Risky Liability”
Catastrophe Coverage
Page 35Page 35
Qualitative Comparison –Compliance with 5 IAIS Characteristics
• The less that is known about current estimate and its trend, the higher the margin
• Risks with low frequency and high severity will have higher risk margins than risks with high frequency and low severity
• For similar risks, contracts that persist over longer timeframe will have higher risk margins than those of shorter duration
• Risks with wide probability distribution will have higher risk margins than risks with narrower distribution
• To extent that emerging experience reduces uncertainty, risk margins will decrease, and vice versa
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 36Page 36
Explicit Assumptions
• Although could be constructed in manner to address characteristics, do not necessarily satisfy any
• As an implementation approach, explicit assumptions, selected by product, could be made to approximate percentile method
• If approximation sufficiently close, explicit assumption approach would satisfy characteristics to same extent as method it approximates
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 37Page 37
Quantile Methods
• All quantile methods fail characteristic (c-2)
• Confidence level method does not necessarily satisfy characteristics (a), (b), (d) or (e)
• Highly skewed distributions (e.g., Product C) can result in negative risk margins
• Examples show that as distributions become more dispersed and more skewed, risk margins implied by a fixed confidence level include fewer standard deviations
• Violates spirit of characteristics (a), (b), (d), and (e) throughout and letter of those in the extreme
• CTE and methods based on multiples of standard deviation generally satisfy characteristics (a), (b), (d), and (e) better than do confidence level method 20
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
920
09 S
emin
ar f
or t
he A
ppoi
nted
Act
uary
Col
loqu
e po
ur l’
actu
aire
dés
igné
200
9
Page 38Page 38
Table 10.2 Comparison of Risk Margins with IAA Desirable Characteristics
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
IAA Desirable Characteristics Explicit Deviation Level CTE Consistent methodology for lifetime of contract achievable achievable achievable achievable
Assumptions consistent with current estimates achievable achievable achievable achievable
Consistent with sound pricing practices not typically
used not typically
used not typically used not typically
used
Vary by product based on risk differences by product yes yes yes yes
Easy to calculate yes relatively easy relatively easy relatively easy Consistently determined between reporting periods achievable achievable achievable achievable
Consistently determined between entities achievable
difficult without mandated
assumptions
difficult without mandated
assumptions
difficult without mandated
assumptions
Facilitate useful disclosure to stakeholders achievable achievable achievable achievable
Provide useful information to users of financial statements achievable achievable achievable achievable
Consistent with regulatory solvency and other objectives yes yes yes yes
Consistent with IASB objectives (i.e., market consistent) unknown unknown unknown unknown
Page 39Page 39
Documentation and Reporting
• CIA SOP: “Documentation is an integral part of work that affects the application of nearly all standards. ... Appropriate documentation describes the course of the work and the actuary’s compliance with accepted actuarial practice.”
• Actuary would document his/her process for determining MfADs
• Important regardless of whether actuary uses explicit assumptions or stochastic techniques
• Documentation for both explicit assumptions and stochastic techniques would include support for key decisions
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 40Page 40
Documentation and Reporting (cont’d)
• With respect to reporting, normally in user’s interest to be aware of MfADs selected by actuary
• Accordingly, reasonable that actuary would usually at least consider some disclosure regarding MfADs within actuarial work product for both internal user and external user reports
• Must also take into account complexity of concept, potential importance of concept to user, as well as sophistication of user who will be receiving work product
• Also important for actuary to communicate with insurer’s auditors, particularly regarding any significant change either in value of MfADs or process for determining such values
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
2009
Sem
inar
for
the
App
oint
ed A
ctua
ryC
ollo
que
pour
l’ac
tuai
re d
ésig
né 2
009
Page 41Page 41