Marshall Flashcards
Current Approaches to Assessing Risk Margins
- Coefficients of variation (CoVs) are determined for individual valuation portfolios or groupings of portfolios, where the groupings are fairly homogeneous
- A correlation matrix is populated with correlation coefficients that reflect expected correlations between valuation portfolios or groupings of portfolios
- CoVs and correlation coefficients are determined separately for outstanding claim liabilities (OSC) and premium liabilities (PL) (Assumptions are made about the correlation between these two types of liabilities as well)
- A distribution is selected and combined with the CoVs and correlation coefficients to determine the aggregate risk margin at a particular probability of adequacy
Determining COVs
- Less sophisticated methods ignore the individual characteristics of the valuation portfolio being assessed. Instead, they are based on “model” portfolios analyzed in two famous papers on risk margin analysis
- More sophisticated methods combine quantitative analysis with qualitative analysis of the sources of uncertainty not captured by quantitative techniques
Populating the Correlation Matrix
- Relies heavily on actuarial judgment
- The key risks that are believed to cause correlation between valuation portfolios are categorized as high, medium or low
- Each category is assigned a correlation coefficient value
Selecting the Distribution
- The most common distribution used to determine the aggregate risk margin is the lognormal distribution
- The normal distribution is used as well, especially at lower probabilities of adequacy where it can generate a higher risk margin than the heavy-tailed lognormal distribution
The Bolt-On Approach
- Separate analyses are used to determine the central estimate and the risk margin - the risk margin is “bolted on” to the central estimate
- Refers to any approach that does not involve a single unified distribution of the entire distribution of possible future claim costs
Claims Portfolio
The aggregate portfolio for which the risk margins must be estimated (ex. XYZ Insurance)
Valuation Classes
The portfolios that are considered individually as part of the risk margin analysis (ex. Property vs. Auto)
Claim Group
A group of claims with common risk characteristics
Systemic Risk
Represents risks that are common across valuation classes or claim groups
- Internal / Model Specification Risk: risks internal to the insurance liability valuation/modeling process
- model structure, model parameterization and data accuracy - External Risk: risks external to the insurance liability valuation/modeling process
- future trends in claim cost outcomes (ex. change in inflation) that may cause actual experience to differ from what is expected based on the current environment and trends
Independent Risk
Represents risks that occur due to the randomness inherent in the insurance process
- Parameter risk: uncertainty in selecting appropriate parameters due to the randomness of insurance
- Process risk: pure effect of randomness due to the insurance process
Quantitative vs. Qualitative Analysis
Quantitative analysis can only reflect uncertainty in historical experience and cannot adequately reflect all possible sources of future uncertainty - best suited for measuring independent risk and past episodes of external systemic risk
To measure internal systemic risk or external systemic risk that differs from historical experience, traditional quantitative techniques should be combined with other quantitative and qualitative analyses
Preparing the Claims Portfolio for Analysis
The claims portfolio should be split into valuation classes based on a number of considerations
- Should the valuation classes be aligned to the valuation portfolios analyzed for central estimate purposes?
- It may not be possible to conduct quantitative analysis at the same granularity used for central estimate purposes
- An approach should be used that balances practicality and granularity and retains as much consistency as possible between the central estimate analysis and the risk margin analysis
Once the claims portfolio has been divided into valuation classes, we must determine whether or not specific classes should be divided further into claim groups
- Cat vs non-cat
- Liability vs Property
Analyzing Independent Risk Sources
Stochastic modeling techniques fail to capture all sources uncertainty for the following reasons:
- Good stochastic models effectively “fit away” past episodes of external systemic risk - if a model does not fully remove these past risks, consideration must be given to whether we should expect similar risks to continue in the future
- Stochastic models do not capture uncertainty arising from internal systemic risk
Analyzing Internal Systemic Risk
- Specification error – the error that arises because the model cannot perfectly model the insurance process
- Parameter selection error – the error that arises because the model cannot adequately measure all the predictors (i.e., parameters) of claim cost outcomes and their trends
- Data error – the error that arises due to poor or unavailable data that’s needed for the reserve analysis
Balanced Scorecard Approach
Used to analyze internal systemic risk
- A balanced scorecard is developed to objectively assess the model specification against a set of criteria
- For each of the sources of internal systemic risk, risk indicators are developed and scored against the criteria
- The scores are aggregated for each valuation class and mapped to a CoV
Analyzing External Systemic Risk
Can identify key potential sources of systemic risk through discussions with business experts as part of the valuation process (underwriting, pricing, claims, expense management)
Risk categories:
- Economic and social risks–the uncertainty associated with inflation, social trends, etc.
- Legislative, political and claim inflation risks–the uncertainty associated with changes in the political landscape, shifts/trends in the level of claim settlements, etc.
- Claim management process change risk–the uncertainty associated with changes in claim reporting, payment, estimation, etc.
- Expense risk–the uncertainty associated with the cost of managing the run-off of the insurance liabilities or the cost of maintaining the unexpired risk until the date of loss
- Event risk–the uncertainty associated with claim costs arising from events (i.e. cats), either natural or man-made
- Latent claim risk–the uncertainty associated with claims that arise from sources that are not currently covered (i.e.,asbestos)
- Recovery risk–the uncertainty associated with recoveries, either reinsurance or non-reinsurance
Correlation Effects
- Independent Risk: uncorrelated with other sources of uncertainty both within and between valuation classes
- Internal Systemic Risks: uncorrelated with independent risk and external systemic risk sources but correlated between classes or between outstanding claim and premium liabilities
- Same actuary effect causes correlation between classes due to common valuation approaches
- Link between premium liability methodology and outcomes from outstanding claim valuation cause correlation between the two liability types - External Systemic Risks: uncorrelated with independent risk, internal systemic risk, and (in general) with other risk categories but correlated between classes or between outstanding claim and premium liabilities in the same risk category
Consolidation of Analysis Into Risk Margin Calculation
- Normal Risk Margin = Z * CoV
- Lognormal Risk Margin = exp(Z * sigma - sigma^2 / 2) - 1
where sigma^2 = ln(1 + CoV^2)
The risk margins above can be converted into dollars by multiplying them by the central estimates for the liabilities in question
Aggregate Independent Risk CoV
Comes from the variance formula for the sum of independent random variables
CoV = SQRT[SUM((w_i * CoV_i)^2)] / SUM(w_i)
Each w_i * CoV_i term represents the variance of the ith liability where w_i is the weight
Aggregate Internal Systemic Risk CoV
Comes from the variance formula for the sum of dependent random variables
CoV = SQRT[SUM((w_i * CoV_i)^2) + 2 * w_i * w_i+1 * CoV_i * CoV_i+1 * p] / SUM(w_i)
Create a table with each cell = w_i * w_j * CoV_i * CoV_j * p_i,j and square root the sum of the table for the aggregate CoV
Considers covariance between liabilities - must be a term for each pair of liabilities
Aggregate Total CoV
CoV = SQRT(CoV_Ind^2 + CoV_Int^2 + CoV_Ext^2)
Each overall source of risk (i.e., independent, internal systemic, external systemic) is assumed to be uncorrelated
Sensitivity Testing
Goal is to gain insights about the sensitivity of the final risk margin to key assumptions
- Vary each key assumption (i.e., the CoVs and correlations) and monitor the impact on the risk margin
- Review key assumptions that have significant impact on the risk margin
Scenario Testing
Goal is to tie the risk margin to a set of valuation outcomes
- Adjust the assumptions used for the central estimate in order to align the central estimate with the assessed provisions including the risk margin
Scenario testing asks the question: “What scenario (ex.higher frequency or severity) would result in the central estimate increasing to the current central estimate plus the risk margin?”
Independent Risk CoV Selection
- Portfolio size: larger portfolios should have lower CoVs due to lower volatility from random effects
- Length of claim run-off: longer-tailed lines should have higher CoVs due to more time for random effects to have an impact
Internal Systemic Risk CoV Selection
If template models are used for similar valuation classes, we would expect similar CoVs
If a similar valuation methodology is used on both short and long-tail classes, then we would expect a higher CoV for the long-tail class since they tend to be more complicated classes
External Systemic Risk CoV Selection
Long-tailed portfolios should have higher CoVs than short-tailed portfolios in most cases (exceptions include event risk and liability risk for home classes)
Hindsight Analysis
Goal is to compare the past reserve estimates of liabilities against the latest view of the same liabilities to review the actual volatility in the past
- Models may have improved significantly since previous valuations
- Future external sources of systemic risk may be significantly different from past episodes, which could make it appear as though estimates were off
- More useful for short-tailed portfolios where serial correlation between consecutive valuations is less significant
Mechanical Hindsight Analysis
- Apply the chain ladder method to data as of the valuation date to calculate a current unpaid estimate
- Iteratively, remove a diagonal of data and apply the same method to calculate unpaid estimates for prior valuation dates
- Compare the past estimates to the current estimate for the same accident years. The relevant payments made between the past valuation dates and the current valuation date should be added to the current unpaid estimate
Used to analyze:
- Independent risk, by focusing on the periods with stable experience
- Internal systemic risk, by applying this technique using a number of actuarial methods and observing the differences in volatility
- All past sources of uncertainty, by applying the approach across all past periods
Properties of CoV scales
- The minimum CoV for best practice is unlikely to be less than 5%
- The maximum CoV for worst practice could be greater than 20%
- The scale should not be linear – model improvements show diminishing returns
- CoVs for long-tail lines should be higher than short-tail CoVs for the same score
- It’s reasonable to use the same scale for outstanding claim liabilities and premium liabilities
