FAS 113Considerations on Risk Transfer Testing

Gary Venter & Paul BrehmCLRS 2002

Introduction

Overview of FAS 113

Overview of FAS 113

Establishes the conditions required for a Contract with a reinsurer to be accounted

for as reinsurance and Prescribes accounting and reporting

standards Note “conditions” and “standards” but

not methodology

Risk Transfer Essence

“Contracts that do not result in the reasonable possibility that the reinsurer may realize a significant loss from the insurance risk assumed generally do not meet the conditions for reinsurance accounting and are to be accounted for as deposits.”

Key Issues

Test is on reinsurer gaining risk, not on insurer reducing risk

Reasonable possibility Significant loss These are terms that invite informed

judgment VFIC did not look to draw a line, but

rather explore different methods of measuring risk to provide a consistent framework for such judgments

Reasonable and Significant

FASB only defines them through opposites Insignificant = having little or no

importance; trivial Reasonable = probability is more than

remote (from FAS 5) Test not met if the probability of a

significant variation in either the amount or timing of payments by the reinsurer is remote

Scheduled payments fail this test Reinsurer loss not required here, only

uncertainty

Reasonably Possible to Have Significant Loss

Based on present value of all cash flows Under reasonably possible outcomes

Seems to ask for a scenario generator Irrelevant if cash flows are identified as

premiums, loss shares, profit shares, etc. Interest rates not to vary across

outcomes Significance of loss is relative to amounts

ceded to reinsurer

Evaluating Reasonable, Significant

“Reasonable possibility” and “significant loss” appear closely intertwined

For a smaller loss to qualify, it would have to be more likely to occur

A 5% chance of a 100% loss might be more convincing than a 10% probability of a 25% loss

An Exception

Substantially all the insurance risk relating to the reinsured portions of the underlying insurance contracts has been assumed by the reinsurer

E.g., fronting Possibly any simple quota share

Depends on interpretation of “reinsured portions”

Reinsured Portions

A percentage of all the writings in a line of business would seem to be a reinsured portion

But a capped quota share, such as excluding cat losses, would not appear to take all of the insurance risk for the reinsured portion

It could still meet reasonable and significant tests, but not the exception

Related Statements

Related statements

NAIC Accounting Practices and Procedures Manual for Property and Casualty Insurance Companies Promulgated after FAS 113; draws heavily from

GAAP “Unless the so-called contract contains this

essential element of risk transfer, no credit whatsoever shall be allowed on account thereof in any accounting financial statement of the ceding insurer”

Related statements

SSAP 62 [§12] “Indemnification of the entity company

against loss or liability relating to insurance risk in reinsurance requires both of the following:

a. The reinsurer assumes significant risk under the reinsured portions of the underlying insurance agreements; and

b. It is reasonably possible that the reinsurer may realize a significant loss from the transaction.”

Related statements

IASB Principles for accounting for insurance

contracts (draft only) Principle 1.2 defines an insurance contract.

Reinsurance is simply treated as a sub-set. Principle 1.3 defines the uncertainty required

for a contract to qualify as an (re)insurance contract.

Introduces the word “material” in describing uncertainty

Does not distinguish between underwriting risk and timing

Current Risk Transfer Testing

Practitioner survey  Response 1 Response 2 Response 3 Response 4 Response 5

Official Policy?

No No Yes Don’t know Don’t know

Probability 5% or 10%10% or

20%Reasonable worst case

chance

20% 10%

Significance 5% or 10%10% or

20%10% 20% 10%

Method

Probability distribution of E[ NPV

losses], compare to the present

value of premium.

Compare E[NPV loss]

to E[NPV premiums] by scenario

Scenario testing

NANet present value of all cash flows.

Cat example

Hypothetical cat exposure (left)

Cat program: $15M retention (1 in 10

years) $50M layer (1 in 100

years) Gross AAL = $6M; ceded

layer = $1.625 M Assume 50% target loss

ratio Distribution used to

calculate the distribution of reinsurer profit/loss

NPV calculated at 4%, assuming premiums collected at inception and losses paid at year end

Gross Cat Exposure

0.8000.8200.8400.8600.8800.9000.9200.9400.9600.9801.000

- 50,000,000 100,000,000 150,000,000 200,000,000

Losses in $

Pe

rce

nti

le

Cat example

Return on Premium

-1600.0%

-1400.0%

-1200.0%

-1000.0%

-800.0%

-600.0%

-400.0%

-200.0%

0.0%

200.0%

75.0% 80.0% 85.0% 90.0% 95.0% 100.0%

Cumulative Probability

Ret

urn

Finite example

Assume: E[AY LR] = 75%, with a

c.v. = 10%, distributed lognormally

ER = 32% Payout pattern at

right (industry average)

Finite Program: Cede $15M deposit

prem. 65% AP If LR>75%, cede:

(LR-75%)/(1-.65) S.t. max of 5%/(1-.65)

Distribution of Loss Ratio

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

50.0% 60.0% 70.0% 80.0% 90.0% 100.0% 110.0%

0.0

1.0

2.0

3.0

4.0

5.0

6.0

Cumulative Lognormal Density

Accident Year Payout Pattern

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

12 24 36 48 60 72 84 96 108 120 132 144 156 168 180

Months of Development%

of U

ltim

ate

Finite example – sample cash flows

Inter-Party Cash Flows Loss Ratio = 80%

(60.0)

(40.0)

(20.0)

-

20.0

40.0

60.0

80.0

100.0

Time in Months

Do

llars

in M

illio

ns

Cash Flow 15.0 92.9 - - (39.9) (36.8) (23.1) (15.5) (10.6) (7.1) (5.2) (2.8) (1.6) (0.2) - -

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180

Finite example

-20.0%

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 100.0%

Cumulative Probability

Ret

urn

on

Pre

miu

m

Considerations

Burden of proof is on the cedant; “proof” is that the reinsurer can lose money, not that cedant risk is reduced

Analysis should include: Distribution of possible results Cash flow estimates Appropriate, common discount rate Thorough understanding of contract terms

Analysis does not include: Taxes Reinsurer expenses

The 10-10 rule, or VaR tests in general are “sufficient, but not necessary.” Risk assessment could/should consider the whole distribution…other risk metrics can be considered.

Alternatives to VaR Tests

Alternative Measures of Risk

Expected Deficit Tail Value at Risk Other Coherent Measures Exponential Transforms Transforming the 10-10 Rule

Expected Deficit

Loss x Probability Single loss: 10-10 ~ 5-20 ~ 2-50 etc. Or average deficit: expected value over

all scenarios of the reinsurers loss in the losing scenarios = E(P – L)+

From examples: Property Catastrophe = -40% Quota Share = -3% Finite = -3%

Coherent Risk Measures

1. Sub-additivity: (X+Y) (X) + (Y)2. Monotonicity: If X Y, (X) (Y)3. Positive Homogeneity: for 0 (X) =

(X)4. Translation Invariance: (X+a) = (X)+a Examples:

Means under transformed probabilities, i.e., E*(X) = xf*(x)dx, where f* is a transformation of f

TVaR

Tail Value at Risk

TVaR = E[X |x > VaR ] = x(

xf(x)dx/(1–)

That is, expected losses when loss exceed threshold

= E*(X) where f* is 0 below x( and f/(1–) above

Examples at 90th percentile Property Catastrophe = -319% Quota Share = -42% Finite = -23%

Distinguishes last two, which deficit did not Maybe 20% – 25% right target range

Problems with and Alternatives to TVaR

Problems No risk attributed to losses below the threshold Linear impact above the threshold

Alternatives E* with some other f*

E.g., F*(x) = (b–1(F(x))+a) = Wang transform where is the standard normal distribution

Example of Wang Transform

Wang Transform for Pareto 1-(1+x/100)^-1.01 with 0.7u - 1.3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 10 100 1,000 10,000 100,000 1,000,000 10,000,000 100,000,000

TransformedOriginal

Measuring Risk with Wang Transform

Determine transform parameters Test different parameters with known treaties

Look at expected reinsurer profit under transformed distribution

If negative, there is risk

Risk with Parameters from Example, i.e., 0.7u – 1.3

From examples: Property Catastrophe = -440% (P = $3.25M) Property Catastrophe = -2% (P = $25M) Quota Share = -19%

Cat treaty that is too expensive won’t pass risk transfer by this test Reinsurance premium levels:

Good deal Bad deal So bad it doesn’t qualify for risk transfer No risk at all

Van Slyke – Kreps Approach

Uses a market pricing approach to find the market risk load to retrocede the entire contract P & L

Uses an exponential risk-adjusted value of losses:RAV = c ln{E[exp(X/c)]} with capital c

Then they show the risk load should obey: = E[Y] + (/s) ln E[e – sY/], where s is an industry parameter (they suggest about 0.4) and Y is return on premium

Solve for and use c = /s to find RAV Set a cutoff like RAV(Y)>–70% for risk transfer

Van Slyke – Kreps Test

From examples: Property Catastrophe = 75% (P = $3.25M) Property Catastrophe = -67% (P = $25M) Quota Share = 25%

Again if cat pricing gets too high, risk transfer fails

Initial cat price looks small by market risk Quota share has a good deal of risk

Transformed 10-10 Rule

Transforms normal distribution to make rule more applicable for heavy tails

Let X be ROP– i.e., ROP if negative, else 0

F is distribution of X; define F*: 1. For a pre-selected security level =10%, let =

1()= 1.282, which is the -th percentile of the standard normal distribution

2. Apply the Wang Transform: F*(x) = [1(F(x)) ]. 3. Calculate the expected value under F*: WT() =

E*[X] 4. If WT() < 10%, it passes the test, otherwise it

fails

Application

For normal distributions this gives the 10-10 rule

For the cat example, risk transfer fails at a premium of $35M

For the quota share, WT(0.10) = 14.39% < 10%, so it passes

Risk Transfer Tests Summary

All based on measures of risk All have to be calibrated to judgment

level All work on regular and finite deals Can calibrate using contracts where risk

transfer can be more confidently judged

Conclusions

Conclusions

FAS 113 is a standard, not a methodology; requires: A reasonable possibility Of a significant loss

FAS 113 does dictate some considerations: Cash flows between parties Appropriate, common discount rate Thorough understanding of contract terms

Risk associated with “possibility” and “significance” are typically measured with a VaR measure using 10% and 10% as the critical values

Conclusions

Other risk measures exist and could be applied to the risk transfer question -- EPD, TVaR, and distributional transforms

Regardless of risk measure, critical values need to be established – judgment will still be required

There is a disconnect between FAS 113 (reinsurer loss) and risk testing for Index Securitization (reduction in cedant risk)