Provision of Risk Margin for Adverse Deviation (PRAD) Models - Characteristics, Pros and Cons

1. Many countries in the region are using the RBC (Risk Based Capital) approach to determine the capital requirements.

2. The PRAD shall be determined such that the overall valuation of guaranteed liabilities secures 75% sufficiency.

3. Why do we need risk margins? As we progress, we are facing an Increased uncertainty in the current estimate of liabilities and its trends. 

4. Different countires have different names for risk margins.


UNCERTAINTY IN CLAIMS LIABILITY ESTIMATION
1. PRADs are required due to uncertainty in Estimating Claim Liability such as:

i. Parameter error such as Error in determining the values of the parameters of the claims run-off process and the parameter might evolve over time.

ii. Process error - Future payments are random and unknown.

iii. Model specification error

iv. Data error 

v. Future trends variability from Inflation, interest rate, claims run-off patterns, claims management process, exposure, business mix, staff departure, legislation, insurance market cycle, technology etc

vi. Reinsurance risk

2. Methods used to derive PAD for Claim Liability

i. Mack Method

ii. Bootstrapping

iii. Stochastic Chain Ladder Method

iv. Industry Benchmark


PRAD CLAIMS LIABILITY METHODOLOGIES - MACK METHOD
1. Based on chain-ladder assumptions and Measures the Mean Square Error (MSE) of the overall claims reserve, which is the sum of the MSE of individual accident year’s claims reserve and the covariance of the claims reserve between accident years.

2. Pros of this method is it measures parameters, process and total risk with stable results

3. Cons are:

i. Model provides, only, the mean and standard error of the claim distribution

ii. Does not explicitly measure tail variability

iii. Does not model well the situation when actuary selects factor other than weighted or simple average

iv.  Outliers distort results greatly 


PRAD CLAIMS LIABILITY METHODOLOGIES - BOOTSTRAPPING METHOD
1. Outliers distort results greatly. Catogerised into two types: Non-parametric Bootstrapping and Parametric Bootstrapping

2. Pros are:

i. Does not need to make assumptions about underlying distribution (i.e. Non-parametric Bootstrapping)

ii. Actual data “guides” the simulation

iii. Generates a distribution of the estimate of unpaid claims, as opposed to just a point estimate

iv. A powerful procedure in that it allows us to estimate the distribution with very little data

3. Cons are:

i. Variability limited to that which is in the historical data

ii. Data outlier can have a leveraged effect on the results

iii. Residuals might needed to be divided into similar resampling group


PRAD CLAIMS LIABILITY  METHODOLOGIES - STOCHASTIC CHAIN LADDER METHOD
1. Development Factors assumed to be lognormal distributed.

2. Parameters such as mean, Standard Deviation and Coefficient of Variation are estimated and then used to generate multinomial random variables (𝐹_(𝑖,𝑛+1−𝑖)+⋯+𝐹_(𝑖,𝑛) ) through Cholesky decomposition process
.
3. Pros of this methods are Correlations across periods can be accommodated and Flexible, can incorporate the development period effect explicitly

4. Cons are:

i. Requires standard statistical software for faster means of calculation.

ii. Simulating with Excel is relatively slower as this method involved simulation

iii. Costs more for making the model


PRAD CLAIMS LIABILITY METHODOLOGIES - INDUSTRY BENCHMARK
1. Adoption of PAD loading according to Industry Benchmark by Line of Business (eg. Simple average of risk margin from different companies.)

2. Pros are :

i. Simple to use

ii. Useful for company which lacks of claim historical data

iii. Can be apply to volatile data

iv. Can be use as reasonableness check on the other methods.

3. Cons are:

i. Estimated PAD might not be reflecting the Company’s true variability of claim liability estimated

ii. Mix of business is assumed to be similar with the benchmark


PRAD FOR PREMIUM LIABILITY
1. PRAD for Premium Liability is expected to be greater than that of Claims Liability due to the larger degree of uncertainty in determining the potential liabilities developing during the unexpired period of the policies, such as:

i. Greater reliance on assumptions relating to unknown future events and experience (e.g. changes in Claims Frequency and Average Claims Size

ii. Possible exposure to catastrophes

iii. Potential changes in claims procedures

iv. Uncertainty increases with decreasing age of accident period

2. Can be derived either via  Multiple of PAD for Claim Liability or Time Series Analysis Of historical ULR (Uninsured Loss Recovery)


PRAD PREMIUM LIABILITY METHODOLOGY - MULTIPLE OF PRAD FOR CLAIMS LIABILITY
1. Set PAD for Premium Liability as multiple of PAD of Claim Liability and Multiple can also be chosen based on Coefficient of Variation (CoV) of Premium Liability.

2. Rule of thumb: 1.75 for short tailed classes, 1.25 for long tailed classes (Tillinghast – Towers Perrin, 2001)

3. Pros are easy to apply and takes into account claims deterioration

4. Cons are:

i. Exposure might be very different for Earned portion and Unearned portion of premium (e.g. due to exposure to event risk)

ii. Multiple may need to be adjusted in an arbitrary manner to reflect changes in claims environment

iii. Volatility can be lower for Unexpired Risk Reserve (URR) than for Claim Liability for certain classes

iv. The process driving the volatility of the premium liability is largely unrelated to the process driving the volatility in the claim liability

5. Effective if high correlation between volatility of Claims and Premium Liability 


PRAD PREMIUM LIABILITY METHODOLOGY - TIME SERIES ANALYSIS OF HISTORICAL ULR 
1. Comparison of the historical projections of URR with the latest estimates. Determines distribution of the standard errors and select the appropriate confidence level

2. Pros are:

i. Utilises data of many prior years

ii. Able to determine the most appropriate method to project URR for different classes

iii. Does not rely on any assumptions on distribution of claims

3. Cons are this method is complex and difficult to understand and outliers can distort results

4. Suitable if claims distribution is unknown and  if nature of volatility of Claims and
Premium Liability dissimilar

5. Example 

THOUGHTS
1. Companies should choose the most appropriate method based on the nature of their portfolios.

2.  The confidence level adopted by companies should reflect their risk appetite 

3. Calculation of PAD also helps companies gain a better understanding of their risk.

4. Stochastic Chain Ladder is not common in the industry due to its costs and complexity.

5. Industry Benchmarks are not popular due to:

i. Different regulatory environment o product features / tariff o economic environment o distribution channel.

ii. Every company operates differently – benchmark risk margins may not reflect the true volatility of the liabilities

6. Volatility Drivers are claims settlement process for claims liability and Claims experience for premium liability.

7. Industry benchmark and Judgement are regulators’ and auditors’ least favourite especially if its referred and subsequently a loading iss added to the Claim Liability risk margin to determine the Premium Liability’s.

(Source: Singapore Act. Soc, nmg)