CIA MfAD

• Error of estimation
• Unexpected change in experience
• Statistical fluctuation

Difference btw the assumption for a calculation and corresponding BE assumption

Difference btw result of a calculation and corresponding result using BE assumptions

1. Difference btw assumption for valuation and BE assumption (investment return)
2. Multiplier to liabilities without PfAD (claim dev't)
3. Addition to liabilities without PfAD, determined thru scenario testing

• Higher when
  • Less is known about current estimate
  • Risks with low frequency / high severity (than high frequency / low severity)
  • Contracts that persist over a longer time
  • Risks with a wide probability distribution
• Should decrease as emerging experience reduces uncertainty

1. Consistent for lifetime of contract
2. Use assumptions consistent with those for current estimates
3. Determined based on sound insurance pricing practices
4. Vary by product based on risk differences
5. Easy to calculate
6. Consistent btw periods and varies from period to period only for real changes in risk

• Situations
  • Significant degree of uncertainty in assumptions used
  • Event assumed farther in the future
  • Potential consequence more severe
  • Occurrence more subject to stat fluctuation
• Examples
  • Reinsurer financial distress
  • Hyperinflation
  • New LOB / lack of data to use
  • Change in tort system affecting future claims
  • Recession - high investment return risk
  • Company experience volatile
  • High uncertainty on the future development for Asbestos

• Claims development (2.5%-20%): % of claim liabilities excl PfAD
• Recovery from reinsurance ceded: (0%-15%) % of reinsurance recovery excl PfAD
• Investment return rates (25bp-200bp): deduction from expected investment return

• Insurer’s operations
  • claims handling (stable and consistent; sig changes)
  • adequacy of staffing
  • UW guideline (specific; lack of)
• Data on which the estimate is based
  • data volume (high; sig YoY changes)
  • stability of loss experience
  • homogeneity in data grouping
• LOB
  • environment (stable; changes)
  • tail (short; long)
  • latent claims (low potential; high)

• higher:
  • significant changes from tort reform
  • new LOB / lack of data to use for reserving
  • recession and effect on LT lines
• lower:
  • LOB in runoff (100% ceded to a reinsurer)
  • Insurer has stop loss coverage that is reserved at stop loss limit
  • LOB where all payments are certain

• Ceded LR
• Reinsurers in runoff
• Unregistered reinsurance
• Reinsurers in weak financial condition
• Unregistered reinsurance
• Claim disputes with reinsurers

• Mismatch risk btw payment of claims and availability of liquid assets
• Error in estimating the payment pattern of future claims
• Asset risk incl:
  • credit/default risk
  • liquidity risk

• Matching of assets and liabilities
• Quality of assets
• Asset default risk
• Eco conditions
• Investment expenses
• Concentration by type of investments

when some of the considerations in determination of MfAD change

• Weighted Formula
• Explicit Quantification – Three Margins

MfAD = iPM – iAM = iPM – min (iPM, iRFM x (1- k))

• iPM = interest rate for discounting based on matching of assets to claim liabilities before MfAD
• iAM = interest rate for discounting after MfAD
• iRFM = interest rate of risk-free bonds with reasonable match to payout of claim liabilities (at least duration)
• k = factor to adj for possible shortening of claim liabilities duration due to misestimated payment pattern and shift in yield curve
• market spread btw risk-free bonds and other investments removed for discounting purposes
• k directly related to size of MfAD
• Advantage: easily adaptable to principles-based approach of IFRS

• Sum of:
  • Asset/liability mismatch risk margin
  • Timing risk margin
  • Credit risk margin

• A/L Mismatch Risk Margin
  • = coverage ratio
  • × (A duration – L duration)/L duration
  • × interest rate movement in run-off period
• Coverage ratio = (premium liability + claims liability) / (investments + installment premiums)
• Interest rate movement in run-off period = base year bond yield * 1 stdev of change in investment yield
• Where the bond is a risk-free bond with a similar duration to that of L

• If duration of liabilities D is shortened by x%, then margin =
• method #1: discount rate (d) * x%
• method #2: (1+d)^((1-x%)*D) = (1+d adjusted for timing risk)^D
  • margin = d - d adjusted for timing risk

• Difference btw yield on high quality (e.g. corp) bonds and risk free gov bond with similar duration
• Rationale: higher than risk free implies credit risk (dif = credit risk spread)

• Time-consuming review of industry experience
• Need to cover large # of assumptions
• Difficult to anticipate all company circumstances
• Ranges need regular update to reflect emerging experience
• Undermine integrity of AA

• Examples:
  • Stop loss reinsurance
  • CAT insurance
  • Credit, warranty, and mortgage insurance
  • LT LOB (prof liability)

1. Skewed cost distributions due to:
   • low frequency / high severity
   • extend for many years
   • LT
2. correlation between lines, e.g. dependent on eco forces

• to limit losses for an agg # of risks over a specified period
• evaluated by simulation and skewness of the cost distribution will increase as threshold increases

Evaluated by simulation of effects of CAT to provide a representation of the severity

• Extend for many years -> significant premium liabilities at financial reporting date.
• Results highly dependent on eco forces (inflation, interest rates), with significant correlation btw classes -> subject to losses driven by high frequency related to eco
• Stochastic modeling of premium liabilities and MfAD more appropriate than deterministic

• Distribution of unpaid volatile and subject to external forces (eco and social inflation, judicial changes)
• Stochastic analyses of LDFs / frequency / severity may be beneficial when estimating claim and premium liabilities.

• Multiples of the standard deviation
• Percentile or confidence levels (VaR)
• CTE / TVaR

Simplicity and practicality

Extra amount added to expected value so probability of actual outcome < amount of liability (including risk margin) over selected time period = target level of confidence

• Conditional expected value based on downside risk
• Avg of outcomes that exceed (Qth percentile)

• Time: rate of risk being released over time (i.e., settlement pattern)
• Shape: distribution of possible outcomes around mean, at reporting date, over a specified time horizon

• How to select Confidence Level: no theory
• Dif Confidence Levels for dif Products: difficult to achieve consistency.
• During claim runoff, distribution wider and more skewed (fewer claims and larger) -> need dif confidence intervals by year.
• Insufficient info on extreme events. possible solution: Weighted avgs of extreme scenarios; Judgment on operational issues