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Risk Transfer Testing of Reinsurance Contracts

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CAS formed Working Party on Risk Transfer Testing to respond to AAA request ... Paper on Working Party Report published in ... Pricing and strategic planning ... – PowerPoint PPT presentation

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Title: Risk Transfer Testing of Reinsurance Contracts


1
Risk Transfer Testing of Reinsurance Contracts
  • A Summary of the Report by the CAS Research
    Working Party on Risk Transfer Testing
  • CAS Ratemaking Meeting
  • March 2008
  • David L. Ruhm, FCAS

2
Background
  • AAA Committee on Property and Liability Financial
    Reporting (COPLFR) requested input on risk
    transfer testing, 2005
  • CAS formed Working Party on Risk Transfer Testing
    to respond to AAA request (Michael Wacek, chair)
  • Working Party Report issued, Summer 2005
  • More developments since see AAA and NAIC
    websites

3
Background, continued
  • Paper on Working Party Report published in
    Variance, Spring 2007 (Ruhm Brehm)
  • Paper briefly describes 2 risk measurement
    methods in Working Party Report
  • Expected reinsurer deficit (ERD)
  • Right-tailed deviation (RTD)
  • Paper also describes risk coverage ratio (RCR)
    method, which is related to ERD

4
Scopes of WP report, Variance paper
  • Working Party took accounting rules as given
  • Merits of accounting rules not debated
  • Focus was on risk transfer testing methods
  • Variance paper provides a brief summary of some
    key material from WP Report
  • Also includes risk coverage ratio (RCR)
  • Interested parties should read the full WP Report

5
Risk measurement Practical uses
  • Better risk control, including ERM context
  • You can manage only what you can measure
  • Pricing and strategic planning
  • Ensure expected profit is adequate compensation
    for amount of risk assumed
  • Risk-based capital allocation
  • Capital risk ? adequate price adequate ROC

6
Risk measurement Accounting
  • If a contract transfers risk it can receive
    insurance accounting treatment
  • If not, premiums are treated as deposits and
    net results are amortized into earnings over time
  • Insurance accounting is often preferred
  • Risk transfer requirements are similar for GAAP
    and Stat
  • GAAP FAS 113
  • Stat SSAP 62

7
SSAP 62 highlights
  • Reinsurer must assume significant insurance
    risk
  • Requires non-remote probability of significant
    variation in amount timing of payments by
    reinsurer
  • Reasonably possible that reinsurer may realize
    a significant loss
  • Based on NPV of all cash flows between ceding
    assuming companies under reasonably possible
    outcomes (emphasis added).

8
WP proposed testing framework
  • Three-step process
  • 1. Determine if contract transfers substantially
    all the risk if so, stop.
  • Assumed downside essentially same as cedants
    original
  • 2. Determine whether or not risk transfer is
    reasonably self-evident if so, stop.
  • E.g., cat x/s, x/s w/no loss sensitive features
  • 3. Calculate recommended risk metrics and compare
    values to critical threshold values.

9
Expected reinsurer deficit (ERD)
  • Uses probability distribution of net economic
    outcomes (NPV of cash flows)
  • Critical point 0 gain economic breakeven
  • Formula
  • ERD pT / P
  • p probability of net loss
  • T average conditional loss severity
  • P expected premium

10
Expected reinsurer deficit (ERD)
  • Concepts inherent in ERD
  • Risk zone is area in distribution where
    economic loss exists in terms of negative NPV
  • Risk loss frequency x average loss severity
  • Base in denominator expected premium, measuring
    risk per 1 premium

11
ERD example
  • Simple example of ERD calculation
  • Aggregate excess 250m excess of 500m
  • Settlement 1 year after inception
  • Investment yield 4.00 (1-yr risk-free rate
    available at inception)
  • Premium 10m at inception

12
ERD example
  • Loss distribution (dollars in 000)
  • Ceded loss Probability NPV(gain)
  • 0 96 10,000
  • 50,000 2 ( 38,077)
  • 150,000 1 (134,231)
  • 250,000 1 (230,385)
  • 5,000 Expected value 5,192
  • Condl loss severity (110,193)

13
ERD example
  • Simple example of ERD calculation, continued
  • Probability of net loss p 4
  • Average conditional loss severity
  • (38,077 x 2 134,231 x 1 230,385 x 1) / 4
  • T TVaR(96) 110,193
  • ERD pT / P (4) (110,193) / 10,000 44.1
  • By comparison, 10 chance of 10 loss 1.0 ERD

14
ERD steps
  • 1. Produce the probability distribution of net
    present value gain, including all flows (real
    examples have more flows).
  • 2. Identify the risk zone part of the
    distribution containing net losses.
  • 3. Measure probability of loss and average
    conditional severity when it occurs.
  • 4. Apply the ERD formula.

15
Comparisons to other metrics
  • Other popular metrics have a similar structure
  • Based on distribution of a key financial item
  • Specific threshold point of the distribution
  • Measurement of frequency and/or severity
  • VaR (value-at-risk)
  • Key financial item net gain / (loss) of capital
  • Threshold point Percentile, such as 5th
  • Measurement is severity of percentile point
  • What level of loss is possible at an outside
    chance?
  • 10/10 rule VaR(90) gt 10 of premium
  • Fixes frequency independently of particular
    contracts details
  • Doesnt measure severity beyond percentile

16
Comparison to other metrics
  • TVaR (tail value-at-risk), CTE (conditional tail
    expectation)
  • Key financial item net gain in capital, or net
    economic gain
  • Threshold point Percentile, such as 5th
  • Measurement is average severity beyond percentile
    point (tail)
  • Whats the average loss of capital in the worst
    5 of cases?
  • Fixes frequency independently of particular
    contracts details
  • Doesnt capture the likelihood of a net loss
  • ERD connection T TVaR(1-p), p probability of
    loss
  • 10/10 rule A contract passing 10/10 will pass a
    1 ERD test, but not the other way around cat
    excess example

17
Risk coverage ratio (RCR)
  • Replace ERDs premium denominator with expected
    gain from NPV distribution (EG in formulas
    below)
  • Formulas
  • As risk per 1 of return
  • RCR, form pT / EG
  • As expected profit per unit of risk assumed
  • RCR EG / pT
  • All components come from the economic gain
    distribution
  • Risk / return metric on economic value

18
RCR example
  • Same example as above
  • Probability of net loss p 4
  • Average conditional loss severity T 110,193
  • EG Expected gain 5,192
  • RCR pT / EG (4) (110,193) / 5,192
    84.9
  • Risk concentration embedded in expected return
    84.9

19
Advantages / applications
  • Advantages of ERD and RCR
  • Cutoff point is economic breakeven, rather than a
    statistical percentile
  • Realized impact of risk on companies is in
    dollar, rather than percentile, terms
  • Includes all loss events, rather than only the
    most extreme events
  • Captures both frequency and severity in one
    metric
  • RCR is not affected by traded dollars in
    premium
  • RCR measures the risk/return tradeoff in terms of
    economic gain
  • Applications of RCR
  • Risk-based pricing
  • Risk-based capital allocation (see paper for
    reference)

20
Right-tailed deviation (RTD)
  • Some Working Party members prefer risk measures
    based on distributional transforms over ERD
  • Transforms may have added benefits, some added
    complexity
  • Right-tailed deviation (RTD) proposed by Shaun
    Wang
  • Define F(x) 1 1 F(x) 0.5
  • F is F with the tail stretched out a
    risk-loaded distribution
  • F(x) F(x), which means E E
  • RTD E E risk load

21
RTD example
  • Loss distribution (dollars in 000)
  • Ceded loss F(x) F(x)
  • 0 96 80
  • 50,000 98 86
  • 150,000 99 90
  • 250,000 100 100
  • Expected value 5,000 34,000
  • RTD 34,000 - 5,000 29,000

22
RTD example
  • RTD risk transfer test
  • Maximum qualified premium a(RTD)
  • a parameter could be between 3 and 5 WP observed
    4 may be too low.
  • In example, using a 5
  • Maximum qualified premium 145m

23
RTD advantages
  • F(x) is a new loss distribution all the
    usual methods apply
  • Easy to risk-price layers of coverage
  • Other advantages see Wangs papers
  • Maximum qualified premium concept opens door to
    qualifying part of premium in some cases, instead
    of all or nothing

24
Conclusion
  • The WP Report is a significant contribution to
    the literature on risk transfer
  • Defined a structured process to narrow down
    contracts that have to be tested
  • Described two risk metrics that appear superior
    to the 10-10 test ERD and RTD
  • 1 ERD suggested as one possible threshold

25
Conclusion
  • Further research recommended
  • Level 1 Consensus thresholds
  • Level 2 Other methods, including quantitative
    definitions of terms and incorporating parameter
    uncertainty
  • (Paper only) 3rd research area Develop the
    actuarial perspective on risk transfer,
    independent of current accounting rules.
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