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
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
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
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).
WP proposed testing framework
• Three-step process
– 1. Determine if contract transfers “substantially all
the risk” – if so, stop.
• Assumed downside essentially same as cedant’s 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.
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
$
0
$ 50,000
$150,000
$250,000
$ 5,000
Probability
96%
2%
1%
1%
Expected value
Cond’l loss severity
NPV(gain)
$ 10,000
($ 38,077)
($134,231)
($230,385)
$ 5,192
($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 chance?”
10/10 rule: VaR(90%) > 10% of premium
Fixes frequency independently of particular contract’s details
Doesn’t measure severity beyond percentile
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”)
“What’s the average loss of capital in the worst 5% of cases?”
Fixes frequency independently of particular contract’s details
Doesn’t 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
Risk coverage ratio (RCR)
• Replace ERD’s premium denominator with expected gain from
NPV distribution (“E[G]” in formulas below)
• Formulas:
As risk per $1 of return:
RCR, % form = pT / E[G]
As expected profit per unit of risk assumed:
RCR = E[G] / pT
• All components come from the economic gain distribution
• 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
– E[G] = Expected gain = $5,192
– RCR % = pT / E[G] = (4%) (110,193) / 5,192 = 84.9%
– Risk concentration embedded in expected return = 84.9%
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)
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
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 = α(RTD)
• α parameter could be between 3 and 5; WP
observed 4 may be too low.
• In example, using α = 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 Wang’s papers
• “Maximum qualified premium” concept opens
door to qualifying part of premium in some
cases, instead of “all or nothing”
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
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.