
Deviation of actual from expected experience may result from
 Error of estimation
 Unexpected change in experience
 Statistical fluctuation

MfAD  Defn
Difference btw the assumption for a calculation and corresponding BE assumption

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

MfAD may be expressed as
 Difference btw assumption for valuation and BE assumption (investment return)
 Multiplier to liabilities without PfAD (claim dev't)
 Addition to liabilities without PfAD, determined thru scenario testing

Desirable risk margin characteristics
 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

A risk margin methodology should
 Consistent for lifetime of contract
 Use assumptions consistent with those for current estimates
 Determined based on sound insurance pricing practices
 Vary by product based on risk differences
 Easy to calculate
 Consistent btw periods and varies from period to period only for real changes in risk

Situations appropriate to select larger MfAD and examples
 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

Categories of MfAD
 Claims development (2.5%20%): % of claim liabilities excl PfAD
 Recovery from reinsurance ceded: (0%15%) % of reinsurance recovery excl PfAD
 Investment return rates (25bp200bp): deduction from expected investment return

Claims development MfAD considerations
 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)

Situations that support claims dev't MfAD outside the range
 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

Recovery from Reinsurance Ceded MfAD considerations
 Ceded LR
 Reinsurers in runoff
 Unregistered reinsurance
 Reinsurers in weak financial condition
 Unregistered reinsurance
 Claim disputes with reinsurers

Risks that MfAD for investment return rates addresses
 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

MfAD for investment return rates considerations
 Matching of assets and liabilities
 Quality of assets
 Asset default risk
 Eco conditions
 Investment expenses
 Concentration by type of investments

When may MfAD change
when some of the considerations in determination of MfAD change

2 formulabased / quantitative approaches for deriving MfAD for investment return (subject to min/max)
 Weighted Formula
 Explicit Quantification – Three Margins

Weighted Formula
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 riskfree 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 riskfree bonds and other investments removed for discounting purposes
 k directly related to size of MfAD
 Advantage: easily adaptable to principlesbased approach of IFRS

Explicit Quantification  3 Margins
 Sum of:
 Asset/liability mismatch risk margin
 Timing risk margin
 Credit risk margin

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

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

Credit Risk Margin
 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)

MfAD Stochastic techniques  Why prescription around assumptions / ranges for broad use is impractical
 Timeconsuming 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

Types of products suitable for stochastic modelling and examples
 Examples:
 Stop loss reinsurance
 CAT insurance
 Credit, warranty, and mortgage insurance
 LT LOB (prof liability)
 Skewed cost distributions due to:
 low frequency / high severity
 extend for many years
 LT
 correlation between lines, e.g. dependent on eco forces

Stop Loss Reinsurance  Why stochastic
 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

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

Credit, warranty, and mortgage guarantee insurance  Why stochastic
 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

LT LOB  Why stochastic
 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.

Quantile approaches for the determination of MfAD based on stochastic techniques
 Multiples of the standard deviation
 Percentile or confidence levels (VaR)
 CTE / TVaR

Multiples of Standard Deviation  Advantages
Simplicity and practicality

Percentile or Confidence Levels  defn
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

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

2 aspects of insurance liabilities be considered to measure risk margin
 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

Practical Issues and Partial Solutions of Quantile Approaches
 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

