Mildenhall Ch 6: Risk measures in practice

Question 1

Identify 3 ways to select risk measures

Answer 1

1. Ad hoc method
2. Economic method
3. Characterization method

Question 2

Briefly explain the adhoc method to select risk measures and provide an example

Answer 2

Start with reasonable risk measure & rationalize it by establishing if it has desired properties or argue against it based on its undesirable properties.

Ex: % loading or % of standard deviation

Question 3

Briefly explain the economic method to select a risk measure and provide an example

Answer 3

Use a rigorous economic theory to select a risk measure.

Ex: utility-based methods that solve optimization problem.

This is the most rigorous selection process but also the hardest to apply in practice.

Question 4

Briefly explain the characterization method to select risk measures.

Answer 4

Start with a list of desired properties and then determine which risk measures have these properties.

This method is more scientific than ad hoc method and easier to apply than economic method.

Question 5

Identify 5 important properties of risk measures from practical point of view

Answer 5

1. Risk measures must reflect diversification (both COH and CONVEX do)
2. When applied in aggregate, risk measure must allow practical allocation to its individual parts (COH does)
3. Risk measure must align with theory (COH does)
4. Risk measure must be easily explained to users (COH does)
5. Backtesting: risk measure should be consistent with observations.
6. Elicitability: risk measure can be estimated by regression-like techniques
7. Robustness & continuity: small change in inputs should result in small change in measured risk
8. MON & TI reflect intuitive concepts of risk & are theoretically and practically sound.

Question 6

Evaluate VaR based on the desired properties.

Answer 6

VaR does not reflect diversification & ignores tail.

However, it is fairly robust.

If we consider VaR for a range of thresholds, we can somewhat capture the tail.

Question 7

Evaluate TVaR based on the desired properties.

Answer 7

TVaR reflects diversification but is hard to elicit and difficult to backtest.

Question 8

List the 5 desirables characteristics of risk margins.

Answer 8

1. The less is known about current estimate and trend, the higher the risk margin should be.
2. Low frequency higher severity risks should have higher risk margins than high frequency low severity risks.
3. For similar risks, longer duration contracts should have higher risk margins than risks with narrower distribution.
4. Risks with wide probability distribution should have higher risk margins than risks with narrower distribution.
5. Risk margins should decrease with emerging experience since it reduces uncertainty (& vice versa)

Question 9

List 3 approaches to estimate risk margins

Answer 9

1. Outcome methods (VaR or TVaR)
2. Cost of Capital
3. Discount-related methods
4. Explicit assumptions
5. Conservative assumptions

Question 10

List the 8 degrees of tail thickness (from thickest to thinnest)

Answer 10

Thick tailed:
1. No mean
2. Mean, but no variance
3. Limited existing moments
4. Subexponential tail

In between:
5. Exponential tail

Thin-tailed:
6. Superexponential tail
7. Log-concave density
8. Bounded

Question 11

For which degrees of thickness do law of large numbers and central limit theorem not apply?

Answer 11

Law of large numbers:
No mean only

Central limit theorem:
No mean and Mean, but no Variance

Question 12

Describe 4 specific uses of risk measures

Answer 12

1. Individual risk pricing: quoting and evaluation of market pricing
2. Classification ratemaking: setting profit margins and allocation CoC
3. Portfolio management: reinsurance purchase, portfolio optimization and ORSA
4. Determining risk capital or evaluation held capital

Question 13

Define intended purpose

Answer 13

Goal addressed by model within context of assignment.

The intended purpose determines the level of detail of modeling (stand alone vs part of portfolio) & appropriate time period for modeling.

Question 14

Define model

Answer 14

Simplified representation of relationship among:
1. real world variables
2. entities
3. events
using:
a. statistical
b. financial
c. economic
d. mathematical
e. non-quantitative
f. scientific
concepts and equations.

Question 15

Briefly explain the 3 components of a model

Answer 15

1. Information inputs: delivers data & assumptions to model
2. Processing: transforms input into output
3. Result: translates output into useful business information

Question 16

Identify 4 users of risk measures

Answer 16

1. UWriters and Pricing actuaries: price adequacy, price competition, fair allocation of CoC
2. Insurer management & ERM function: portfolio optimization, reinsurance strategy, capital structure and estimation of economic capital.
3. Insured: value of insurance and solvency of insurer
4. Regulator: set minimum capital standards
5. Rating agency: evaluate actual capital or adequacy of held capital.
6. Reinsurer: pricing reinsurance contracts
7. Investor: balance and compare risks & returns, franchise value.

Question 17

Define intended user

Answer 17

Refers to any person who will rely on model output

Question 18

Identify random variables targeted by risk measure for:
a. Pricing
b. management
c. regulation

Answer 18

a. Prospective amount or timing uncertainty

b. UW income, Net income or CF at group or legal entity levels

c. Default risk encompassing all sources of risk at legal entity level

Question 19

Briefly describe 5 desirable properties of pricing risk measures

Answer 19

1. PCPs should be reasonable, transparent and explainable
2. PCP parameters should be easy to estimate from market prices
3. PCPs should be easy & efficient to compute
4. PCP values should be robust to ambiguity in underlying risk distribution.
5. Aggregate PCPs should have a logical allocation methodology.
6. PCPs should behave well when used in optimization routines.
7. PCPs should reflect insurance risk diversification.
8. PCPs should be law invariant
9. PCPs should be consistent with economic, financial and behavioural theory

Question 20

Briefly describe 5 desirable characteristics of capital risk measures

Answer 20

1. Robustness to regulatory arbitrage: should balance complexity against data availability
2. Simplicity and explainability: help regulators communicate objectives to stakeholders
3. Standardization: standard approach should be used to ensure comparison across entities
4. Backtesting: should be possible to determine if portfolio was managed to a risk measure tolerance. Any breaches should be explained by chance rather than poor management.
5. Portfolio optimization: against regulatory standard is important for insurers.