Goldfarb: Risk-Adjusted Performace Flashcards
Goldfarb issue with general return metrics (ROE, ROA)
Do not distinguish between varying degrees of risk
Can sometimes result in misleading indications of performance
RAROC equation
Income / RAC
Alternate measures of income to use in RAROC calculation
GAAP NI
SAP NI
IASB Fair Value
Economic Profit
Three issues with using economic profit for net income in RAROC equation
- Ignores franchise value
- Complicates reconciliation to GAAP; makes less sense to management
- External parties (only have access to GAAP)
6 alternate measures of capital
Actual committed capital
Market value of equity
Regulatory required capital
Rating agency required capital
Economic capital
Risk capital
Actual committed capital
Actual capital provided by shareholders
Economic capital
Amount of capital necessary to provide firm with certain probability of achieving a specific objective over time horizon
Risk capital
Amount of capital needed to be provided by shareholders to cover risk that L > A
2 objectives to derive economic capital
Solvency objective
Capital adequacy objective
Solvency objective
That firm can meet existing obligations
Capital Adequacy Objective
That firm can continue to grow/pay dividends/maintain rating
Stranded capital
Excess of actual capital over the risk capital (usually driven by regulation or rating agency)
3 ways to derive thresholds used to compare risk measures
- Bond default probabilities at selected credit rating level
- Management risk preference
- Arbitrary default probability
Weaknesses of choosing bond default probabilities for risk measure
- Does not address which credit rating should be targeted
- Does not account for risk of downgrade (AA-rating is based on ability to maintain that level with high probability)
Three points to keep in mind if using bond default probabilities
- Historical vs. current estimates (stability vs. reflective)
- Different sources may indicate different numbers
- Time horizon (default probabilities are annual vs. lifetime)
Disadvantages to using management risk preferences as threshold
- Getting management to articulate/agree
- Differing views from directors/shareholders
- Does not factor in risk, which needs to be considered to compare to reward
- Managers focused on number of issues, difficult to estimate threshold to just probability of default
5 main categories of risk to an insurer
- Market risk
- Credit risk
- Insurance UW risk
- Operational risk
- Strategic risk
Market risk
Potential loss in value that results form impact that changes in equity indices, interest rates, foreign exchange rates, etc. have on current investments
Credit risk
Potential loss in value due to counterparty default, changes in counterparty credit rating, or changes in rating-specific yield spreads
Three most important credit-related risk exposures
- Marketable securities/derivatives/swap positions
- Insureds contingent premiums/deductibles receivable
- Reinsurance recoveries
Uniqueness of reinsurance recoveries for credit risk
- Definition of default (death spiral)
- Substantial contingent exposure (may increase with adverse loss development)
- Reinsurance credit risk is highly correlated with underlying insurance risk
Insurance UW risk (3 categories)
- Loss reserves on prior PYs
- UW risk for current period PY
- Property CAT risk
3 components of total risk that impact loss reserve risk
- Process risk
- Parameter risk
- Model risk
Process risk
Risk that actual results will deviate from expected value due to inherent random variation of claim development process
Parameter risk
Risk that actual deviates from estimate due to inaccurate parameter estimates in models
Model risk
Risk that you used the wrong model
Three methods to quantify UW risk
- Loss ratio distribution model
- Freq/Sev model
- Inference from reserve risk models
5 advantages of Freq/Sev models over loss ratio distribution models
- Easier to account for growth
- Reflects inflation more accurately
- Changes in limit and deductibles reflected
- Impact of deductibles on frequency can be accounted for
- Treatment of split of loss can be mutually consistent
4 methods to derive aggregate distribution from Freq/Sev distributions
Analytical solution (based on freq/sev parameters)
Numerical method (approximation)
Approximation (based on mean, variance of collective risk model)
Simulation
Reasons historical CAT losses not best measure of future losses
- Frequency
- Changes in exposures
- Changes in severities (building materials)
3 modules of CAT models
- Stochastic/Hazard module - generate events
- Damage (vulnerability) module - based on exposure information
- Financial analysis module - applies terms of contracts to determine impact
Correlation vs. dependency
Correlation: measure of linear dependency
Dependency: more general measure of the degree to which different random variables depend on each other
Perfect dependency does not imply perfect correlation
3 methods to quantify dependency between risks
- Empirical analysis of historical data
- Subjective estimates
- Explicit factor models (link variability of risks to common factos)
Disadvantages of empirical analysis to quantify dependency between risks
Data required does not exist
Historical data contains very little insight into correlation/dependency when tail events occur
Advantages/disadvantages to using subjective estimates to quantify dependency between risks
A: Reflects dependency during tail events
A: Reflects user intuition
D: As number of risk categories increases, number of dependency parameter estimates increases exponentially
Four techniques to aggregate the distributions of different risks
- Closed form solutions
- Approximation methods (assume distributions, derive parameters)
- Simulation methods (favored due to intuitiveness, brute forcing of results)
Available methods to allocate capital (Goldfarb)
- Proportional allocation
- Incremental allocation
- Marginal allocation (i.e. Meyers-Read)
- Co-measures
Shortcomings of Meyers-Read
Not developed as a mean for determining risk-adjusted capital requirements
May require more quantitative resources compared to other methods
Significant mathematical challenges
Five applications of risk adjusted performance metrics
- Assessing capital adequacy
- Setting risk management priorities
- Evaluating alternative risk management strategies
- Risk adjusted performance measurement
- Insurance policy pricing
Economic profit, equation
Economic profit = P - E - L / (1 + y) + Investment return
Inconsistent time horizons when assessing aggregate risk profile
Market risk often based on one-year period, whereas insurance risks are based on ultimate liability
Target RAROC when capital is committed for multiple periods
Problems with looking at insurance risks over only one year
Few data/methods to estimate timing of recognition of adverse development
Change in value perspective of loss reserves not consistent with market risk
Likely results in small change in liability valuation, though potential risk over long term (significant)
Problem with quantifying market risk over longer than one-year period
Investment strategies change
Difficult to derive parameters
Importance of economic capital to policyholders and shareholders
Policyholders: Need economic capital to achieve solvency objective
Shareholders: need economic capital to achieve capital adequacy objective
Target RAROC when given cost of capital
Target RAROC = [cost of capital * PV(capital held)] / initial capital
Premium risk
Risk that the expected premium collected will not be enough to pay for expected losses
Interest rate risk vs. tail of business
Longer tail line has more interest rate risk (longer duration)
