Goldfarb: Risk-Adjusted Performace

Question 1

Goldfarb issue with general return metrics (ROE, ROA)

Answer 1

Do not distinguish between varying degrees of risk

Can sometimes result in misleading indications of performance

Question 2

RAROC equation

Answer 2

Income / RAC

Question 3

Alternate measures of income to use in RAROC calculation

Answer 3

GAAP NI

SAP NI

IASB Fair Value

Economic Profit

Question 4

Three issues with using economic profit for net income in RAROC equation

Answer 4

1. Ignores franchise value
2. Complicates reconciliation to GAAP; makes less sense to management
3. External parties (only have access to GAAP)

Question 5

6 alternate measures of capital

Answer 5

Actual committed capital

Market value of equity

Regulatory required capital

Rating agency required capital

Economic capital

Risk capital

Question 6

Actual committed capital

Answer 6

Actual capital provided by shareholders

Question 7

Economic capital

Answer 7

Amount of capital necessary to provide firm with certain probability of achieving a specific objective over time horizon

Question 8

Risk capital

Answer 8

Amount of capital needed to be provided by shareholders to cover risk that L > A

Question 9

2 objectives to derive economic capital

Answer 9

Solvency objective

Capital adequacy objective

Question 10

Solvency objective

Answer 10

That firm can meet existing obligations

Question 11

Capital Adequacy Objective

Answer 11

That firm can continue to grow/pay dividends/maintain rating

Question 12

Stranded capital

Answer 12

Excess of actual capital over the risk capital (usually driven by regulation or rating agency)

Question 13

3 ways to derive thresholds used to compare risk measures

Answer 13

1. Bond default probabilities at selected credit rating level
2. Management risk preference
3. Arbitrary default probability

Question 14

Weaknesses of choosing bond default probabilities for risk measure

Answer 14

1. Does not address which credit rating should be targeted
2. Does not account for risk of downgrade (AA-rating is based on ability to maintain that level with high probability)

Question 15

Three points to keep in mind if using bond default probabilities

Answer 15

1. Historical vs. current estimates (stability vs. reflective)
2. Different sources may indicate different numbers
3. Time horizon (default probabilities are annual vs. lifetime)

Question 16

Disadvantages to using management risk preferences as threshold

Answer 16

1. Getting management to articulate/agree
2. Differing views from directors/shareholders
3. Does not factor in risk, which needs to be considered to compare to reward
4. Managers focused on number of issues, difficult to estimate threshold to just probability of default

Question 17

5 main categories of risk to an insurer

Answer 17

1. Market risk
2. Credit risk
3. Insurance UW risk
4. Operational risk
5. Strategic risk

Question 18

Market risk

Answer 18

Potential loss in value that results form impact that changes in equity indices, interest rates, foreign exchange rates, etc. have on current investments

Question 19

Credit risk

Answer 19

Potential loss in value due to counterparty default, changes in counterparty credit rating, or changes in rating-specific yield spreads

Question 20

Three most important credit-related risk exposures

Answer 20

1. Marketable securities/derivatives/swap positions
2. Insureds contingent premiums/deductibles receivable
3. Reinsurance recoveries

Question 21

Uniqueness of reinsurance recoveries for credit risk

Answer 21

1. Definition of default (death spiral)
2. Substantial contingent exposure (may increase with adverse loss development)
3. Reinsurance credit risk is highly correlated with underlying insurance risk

Question 22

Insurance UW risk (3 categories)

Answer 22

1. Loss reserves on prior PYs
2. UW risk for current period PY
3. Property CAT risk

Question 23

3 components of total risk that impact loss reserve risk

Answer 23

1. Process risk
2. Parameter risk
3. Model risk

Question 24

Process risk

Answer 24

Risk that actual results will deviate from expected value due to inherent random variation of claim development process

Question 25

Parameter risk

Answer 25

Risk that actual deviates from estimate due to inaccurate parameter estimates in models

Question 26

Model risk

Answer 26

Risk that you used the wrong model

Question 27

Three methods to quantify UW risk

Answer 27

1. Loss ratio distribution model 2. Freq/Sev model 3. Inference from reserve risk models

Question 28

5 advantages of Freq/Sev models over loss ratio distribution models

Answer 28

1. Easier to account for growth 2. Reflects inflation more accurately 3. Changes in limit and deductibles reflected 4. Impact of deductibles on frequency can be accounted for 5. Treatment of split of loss can be mutually consistent

Question 29

4 methods to derive aggregate distribution from Freq/Sev distributions

Answer 29

Analytical solution (based on freq/sev parameters) Numerical method (approximation) Approximation (based on mean, variance of collective risk model) Simulation

Question 30

Reasons historical CAT losses not best measure of future losses

Answer 30

1. Frequency 2. Changes in exposures 3. Changes in severities (building materials)

Question 31

3 modules of CAT models

Answer 31

1. Stochastic/Hazard module - generate events 2. Damage (vulnerability) module - based on exposure information 3. Financial analysis module - applies terms of contracts to determine impact

Question 32

Correlation vs. dependency

Answer 32

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

Question 33

3 methods to quantify dependency between risks

Answer 33

1. Empirical analysis of historical data 2. Subjective estimates 3. Explicit factor models (link variability of risks to common factos)

Question 34

Disadvantages of empirical analysis to quantify dependency between risks

Answer 34

Data required does not exist Historical data contains very little insight into correlation/dependency when tail events occur

Question 35

Advantages/disadvantages to using subjective estimates to quantify dependency between risks

Answer 35

A: Reflects dependency during tail events A: Reflects user intuition D: As number of risk categories increases, number of dependency parameter estimates increases exponentially

Question 36

Four techniques to aggregate the distributions of different risks

Answer 36

1. Closed form solutions 2. Approximation methods (assume distributions, derive parameters) 3. Simulation methods (favored due to intuitiveness, brute forcing of results)

Question 37

Available methods to allocate capital (Goldfarb)

Answer 37

1. Proportional allocation 2. Incremental allocation 3. Marginal allocation (i.e. Meyers-Read) 4. Co-measures

Question 38

Shortcomings of Meyers-Read

Answer 38

Not developed as a mean for determining risk-adjusted capital requirements May require more quantitative resources compared to other methods Significant mathematical challenges

Question 39

Five applications of risk adjusted performance metrics

Answer 39

1. Assessing capital adequacy 2. Setting risk management priorities 3. Evaluating alternative risk management strategies 4. Risk adjusted performance measurement 5. Insurance policy pricing

Question 40

Economic profit, equation

Answer 40

Economic profit = P - E - L / (1 + y) + Investment return

Question 41

Inconsistent time horizons when assessing aggregate risk profile

Answer 41

Market risk often based on one-year period, whereas insurance risks are based on ultimate liability

Question 42

Target RAROC when capital is committed for multiple periods

Answer 42

Question 43

Problems with looking at insurance risks over only one year

Answer 43

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)

Question 44

Problem with quantifying market risk over longer than one-year period

Answer 44

Investment strategies change Difficult to derive parameters

Question 45

Importance of economic capital to policyholders and shareholders

Answer 45

Policyholders: Need economic capital to achieve solvency objective Shareholders: need economic capital to achieve capital adequacy objective

Question 46

Target RAROC when given cost of capital

Answer 46

Target RAROC = [cost of capital \* PV(capital held)] / initial capital

Question 47

Premium risk

Answer 47

Risk that the expected premium collected will not be enough to pay for expected losses

Question 48

Interest rate risk vs. tail of business

Answer 48

Longer tail line has more interest rate risk (longer duration)