Ch 29: Risk Management And Reporting

Question 1

Risk quantification

Question 2

For all risk events, assess:

Answer 2

• Probability of occurrence (frequency)
• Expected loss (severity)
• Normally treated as random variables

Question 3

Subjective assessment:

Answer 3

• Risks commonly assessed using simple scales
• Ranking frequency and severity from low to high
• Product of two scales = overall score for that risk
• enabling them to be ranked
• Assessment would be done with and without
  controls - assess efficiency
• May be recorded in risk register

Question 4

Using a model

Answer 4

Note! It is difficult to model low frequency events due
to lack of data. Stochastic approach more
appropriate if risk:
* Has a high score - high priority to assess
carefully
* High variability of possible outcomes
* Lot of experience data on which to base
probability distributions
* Relates to financial guarantees / options
* Involves mismatching of assets and liabilities

Question 5

Operational risks:

Answer 5

• Difficult to quantify
• Typical approaches
• Broad-brush addition to other risks (for
  capital requirements)
• Scenario analysis
• Banking - add % uplift to total aggregated
  risks other than operational risks
• Insurers - Solvency II standard formula uses
  factor-based approach, taking specified % of
  provisions and premiums

Question 6

Operational risk categories examples:

Answer 6

• Fraud
• Loss of key personnel
• Mis-selling of financial products
• Calculation error in computer system
• Loss of business premises
• Loss of cpy email access for 72 hours

Question 7

Scenario analysis

Answer 7

Looks at financial impact of plausible and possibly adverse set / sequence of events
* Useful when it is difficult to fit full probability distribution to risk events
* Typically, deterministic and straight forward
- May be adapted to contain probabilistic and advanced mathematical elements
- Frequently used - operational risks, global recession
- Assessing emerging risks - climate change
* Drawback - does not indicate likelihood of estimated severities

Question 8

Scenario analysis process:

Answer 8

1. Risk exposures grouped into categories - input from senior individuals in organisations
2. Develop plausible adverse scenario for each group of risk
3. Determine financial cost of each scenario - involving senior staff
4. Total cost represents a “worst-case” loss scenario

Question 9

Stress testing

Answer 9

• Involves assessing impact of a specific
  adverse event
• Form of scenario analysis, focusing on
  extreme scenarios
• Radically change assumptions and
  characteristics
• Deterministic method
• Application
• Extreme market movements
• Credit and liquidity risks
  Note! Sensitivity testing works the same,
  except that you don’t “stress”.

Question 10

Stress scenario

Answer 10

• Combine stress and scenario testing
• Stress test is performed by considering the impact of a
  set of related adverse conditions that reflect the chosen
  scenario
• Decisions need to be made as to how other aspects of the
  business will react if stress event occurs
• Types of stress scenario tests:
• Identify “weak areas” in the portfolio and investigate
  effects of localised stress situations by looking at the
  effect of different combinations of correlations and
  volatilities
• To gauge the impact of major market turmoil affecting
  all model parameters, while ensuring consistency between
  correlations while they are stressed

Question 11

Stochastic model

Answer 11

Ideal model
- All risk variables modelled through probability
distributions
- Dynamic interaction between variable specified
- Potentially very complex / impractical
* In theory, correct required capital to avoid ruin (at given
confidence level) calculated
Practical ways to reduce complexity of stochastic models:
* Restrict time horizon for model
* Limit number of stochastic variables
* Carry out a number of runs with a different single
stochastic variable and then a single deterministic run using
all the worst-case scenarios together
Note! All methods are used to understand a company’s
vulnerability to various risks.

Question 12

Reverse stress testing

Answer 12

• Often required by regulators
• Construction of severe stress
  scenario that just allows firm to be
  able to continue to meet its business
  plan
• May be extreme scenario, but must
  be plausible

Question 13

Capital requirements and relationships between risks

Answer 13

Generally, most important aggregation is for capital
requirements
* In many regulatory regimes, capital requirement is set in
respect of an event occurring within 12 months with a
probability of 0.5% (“1 in 200-year event”)
* Aggregate individual risks to allow for correlations and
inter-actions

Question 14

Risk can be aggregated through:

Answer 14

• Stochastic modelling - although
  this may be impractical
• Single formulae - fully
  independent / fully dependent
• Correlation matrices
• Copulas

Question 15

Fully dependent risks:

Answer 15

• Aggregate risk is the sum of individual
  risks (at a given probability level)
• Capital requirement = sum RJ for n
  dependent capital requirements

Question 16

Independent risks:

Answer 16

• Aggregate capital requirement < less than sum of its
  constituent parts – cancel out
  *
• For fully independent risks, a simplified approach
  such as is often used
  Note! In most real-world problems, risks are partially
  correlated.

Question 17

Correlation matrices:

Answer 17

• Reflects diversification benefits
• Commonly used in insurance
• n x n symmetrical matrix
• Overall capital can be expressed

Question 18

Copulas:

Answer 18

• Function - joint cumulative distribution function from
  marginal cumulative functions
• Reflects dependence explicitly
• Used in quantitative finance, starting in insurance
• Useful to model tail risks
• Describe different degrees of dependence between random
  variables, including in the tails of distributions

Question 19

Deterministic approach

Answer 19

• Notional approach
• Factor sensitivity approach
• Scenario sensitive approach

Question 20

Notional approach:

Answer 20

• Broad-brush measure – weights for
  different assets
• Factor-based charges – factor x exposure
  measure
• Advantage - simple to implement and
  interpret across diverse range of
  organisations
• Disadvantages
• Potential undesirable use of a ‘catch all’
  weighting, for undefined asset classes
• Possible distortions to the market -
  demand for assets with high weightings
• No allowance for concentration risk –
  same weighting irrespective of whether the
  investment consists of single security /
  variety of different securities
• Probability of changes considered is not
  quantified

Question 21

Scenario sensitivity approach:

Answer 21

Scenario sensitivity approach:
* Effect of changing a set of factors in a mutually
consistent way is considered
* Disadvantage – probability of changes considered
not quantified

Question 22

Factor sensitivity approach:

Answer 22

• Determines degree to which financial position is
  affected by impact that change in a single
  underlying risk factor has on the value of assets
  and liabilities
• Advantage - Increased understanding of the drivers
  of risk
• Disadvantages
• Not assessing a wider range of risks, by focusing
  on a single risk factor
• Being difficult to aggregate over different risk
  factors
• Probability of changes considered is not quantified

Question 23

Probabilistic approach

Answer 23

• Deviation
• Value at risk
• Probability of ruin
• Tail Value at Risk

Question 24

Deviation:

Answer 24

• Standard deviation – deviation is measured from mean
• Tracking error – deviation is measured relative to a benchmark other than mean

Question 25

Value at Risk:

Answer 25

* Statistical measure of downside risk * Maximum potential loss on portfolio over given future period with given degree of confidence * Calculated using an empirical, parametric / stochastic approach / scenario analysis * Maximum potential loss which is not exceeded with a given high probability over a given time period * Absolute terms / relative to benchmark

Question 26

Disadvantages:

Answer 26

* Gives no indication of distribution of losses greater than VaR * Can under-estimate asymmetric and fat-tail risks - does not quantify size of the tail * Can be very sensitive to choices of data, parameters, and assumptions * Not always sub-additive (Subadditivity = merger of risk situations does not increase the overall level of risk * If used in regulation it may encourage herding, thereby increasing systemic risk

Question 27

Advantages:

Answer 27

Simplicity of expression * Intelligibility of results * Applicability to all types of risks * Applicability over all sources of risk * Ease of its translation into a risk benchmark

Question 28

Three general approaches to calculation of VaR:

Answer 28

1. Empirical / historical 2. Parametric 3. Stochastic

Question 29

Probability of ruin:

Answer 29

* Probability that the net financial position of an organisation / line of business falls below 0 over a defined time horizon

Question 30

Tail Value at Risk / Conditional Value at Risk:

Answer 30

* Expected loss given that a loss over the specified VaR has occurred Note! Higher ratio of Tail VaR / VaR → asymmetric distribution with a fatter tail

Question 31

Risk categorisation and quantification:

Answer 31

Risk categorisation and quantification: * Impact and probability * Product of impact & probability gives idea of relative importance of various risks

Question 32

Risk response:

Answer 32

Extend risk portfolio to indicate how risk was dealt with: * Avoided * Retained + capital needed to support it * Diversified + assessment of remaining combination of risks * Mitigated + assessment of remaining risk - Internal actions / transfer to another party

Question 33

For risks that are retained, the risk portfolio would also contain details of:

Answer 33

* Control measures * Reassessment of value and impact after controls * Risk owner * Board committee / senior manager with oversight of the risk * Identification of concentrations of risk and related actions

Question 34

Risk reporting allows management to:

Answer 34

* Identify new risks * Obtain better understanding of risks faced i.t.o quantifying the impact of individual risks * Determining appropriate control systems for specific risks * Monitoring the effectiveness of existing control systems * Assessing changes to risks faced * Assessing the interaction between risks * Assisting with pricing, reserving, and determining capital requirements ## Footnote Note: It is also helpful for external stakeholders – shareholders, credit rating agencies, and regulators

Question 35

Reporting at enterprise level

Answer 35

* Should be consistent across the enterprise in order to - Optimise the allocation of risk appetite - Make the best use of diversification for capital efficiency