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Risk Transfer Testing of Reinsurance Contracts


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

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

  • 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

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

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

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

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

SSAP 62 highlights
  • Reinsurer must assume significant insurance
  • Requires non-remote probability of significant
    variation in amount timing of payments by
  • 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).

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
  • 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.

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

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

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

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)

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

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.

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
  • 10/10 rule VaR(90) gt 10 of premium
  • Fixes frequency independently of particular
    contracts details
  • Doesnt measure severity beyond percentile

Comparison to other metrics
  • TVaR (tail value-at-risk), CTE (conditional tail
  • 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
  • 10/10 rule A contract passing 10/10 will pass a
    1 ERD test, but not the other way around cat
    excess example

Risk coverage ratio (RCR)
  • Replace ERDs premium denominator with expected
    gain from NPV distribution (EG in formulas
  • 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
  • Risk / return metric on economic value

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
  • Risk concentration embedded in expected return

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
  • RCR is not affected by traded dollars in
  • RCR measures the risk/return tradeoff in terms of
    economic gain
  • Applications of RCR
  • Risk-based pricing
  • Risk-based capital allocation (see paper for

Right-tailed deviation (RTD)
  • Some Working Party members prefer risk measures
    based on distributional transforms over ERD
  • Transforms may have added benefits, some added
  • Right-tailed deviation (RTD) proposed by Shaun
  • 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

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

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

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

  • 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

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