Chapter 29: Risk measurement and reporting

Question 1

What are the 2 key features to assess for all risk events?

Answer 1

1. The probability of the event occurring
2. The expected loss if the event occurs

Question 2

Describe how the risk identification “brainstorming” approach can be extended to obtain a subjective assessment of risk exposure

Answer 2

The probability and severity of each risk event are both estimated (separately) using a simple scale.

The product of the probability and severity assessments gives a score on a scale. This provides an assessment of each risk event and allows them to be ranked and prioritised.

The assessment would be carried out with and without possible risk controls

Question 3

Outline how a model could be used to assess a risk event

Answer 3

Distributions need to be assigned to both the probability and severity of the risk event (unless the latter is a fixed amount rather than a RV, such as for a without profit term assurance policy).

To quanitfy the risk simply, the company could define an event and then use historical data to determine a probability distribution for that event. Alternatively, the frequency of the event could be defined and this could be used to determine the loss parameter.

A decision needs to be made as to whether a stochastic or deterministic model is appropriate.

The availability of data to parameterise the model may influence the decision as to which model (if any) is used. This is particularly important when considering rare events

Question 4

Suggest features of a risk that could make it more appropriate to model using a stochastic rather than a deterministic approach

Answer 4

• The risk has a high score (high severity and / or frequency) and therefore is a high priority to assess carefully
• Has a highvariability of possible outcomes
• Has a lot of experience data on which to base the probability distributions
• Relates to financial guarantees or options
• Involves the mismatching of assets and liabilities.

Question 5

State 6 categories into which operational risks might be divided for the purpose of scenario analysis

Answer 5

1. Fraud
2. Loss of key personnel
3. Mis-selling of financial products
4. Calculation error in the computer system
5. Loss of business premises
6. Loss of company email access

Question 6

State 5 ways of evaluating risks

Answer 6

1. Scenario analysis
2. Stress testing
3. Combined stress and scenario testing
4. Reverse stress testing
5. Stochastic modelling

Question 7

Outline 4 steps that should be involved in a scenario analysis to evaluate operational risk

Answer 7

A scenario analysis looks at the financial impact of a plausible and possibly adverse set of events or sequences of events. It is also a deterministic method of evaluating risk.

Scenario analysis involves a number of steps:
1. Group risks into broad categories. This should involve input from a wider range of senior individuals in the organisation
2. Develop a plausible adverse scenario of risk events for each group of risks, which is representative of all the risks in the group.
3. Calculate the consequences / costs of the risk event occurring for each scenario, again involving senior staff.
4. Calculate the total costs of all risks represented by the scenario.

Note: Scenario analysis is limited to quantifying the severity of the scenario but not the probability of it occurring.

Question 8

What is stress testing?

Answer 8

Stress testing is a deterministic method of modelling extreme risk events. It is commonly used to model extreme market movements, but can be applied to other risks (e.g. credit, liquidity)

In relation to market risk it involves subjecting a portfolio to extreme market movements by radically changing the underlying assumptions and characteristics - including changing asset class correlations and volatilities, which are often observed to increase during extreme market events.

Question 9

Outline 2 types of stress scenario test

Answer 9

Two types of tests are designed to:
1. Identify “weak areas” in the portfolio and investigate the effects of localised stress situations by looking at the effect of different combinations of correlations and volatilities
2. Guage the impact of major market turmoil affecting all model parameters while ensuring consistency between correlations while they are stressed

Question 10

Explain what is meant by reverse stress testing

Answer 10

Reverse stress testing is the construction of a severe stress scenario that just allows the firm to be able to continue to operate its business plan.

Equivalently, it is the scenario which would just be enough to stop them doing so.

This scenario might be financial or non-financial

Although, it might be an extreme scenario, it must be plausible

Question 11

Describe how a stochastic model could be used to evaluate a particular risk

Answer 11

The variables that gives rise to the risk are treated as RVs with probability distributions.

The model must be dynamic, with full interactions / correlations between variables

The model can be run to determine the amount of capital that it needs to (just) avoid ruin with a given probability

Question 12

Outline 3 approaches to limiting the ideal scope of a stochastic model in order to make the model more practical

Answer 12

1. Restrict the time horison that the model projects
2. Limit the number of variables that are modelled stochastically and model the other variables deterministically with scenario testing
3. Carry out a number of runs each with a different single stochastic variable, followed by a single deterministic run using all the worst case scenarios together.

Question 13

Explain why the effect of multiple risks may be less than the sum of the individual risks

Answer 13

The overall combined impact may be less than the sum of that for the individual risks due to the impact of diversification or less than perfect (or even negative) correlation.

Less than perfect correlation (i.e. some independence) between the individual risks means that they are very unlikely to occur all at the same time.

Question 14

Outline how the overall capital requirement for a combination of risks relates to the individual risk capital requirements, if the risk events are:
* fully dependent
* fully independent
* partially dependent

Answer 14

Fully dependent:

The overall capital requirement is the sum of the individual capital requirements

Fully independent:

The overall capital requirement is less than the sum of the individual capital requirements (the difference is the diversification benefit). Under certain assumptions, the overall capital requirement can be determined as the square root of the sum of squares of the individual risk capital requirements

Partially dependent:

The overall capital requirement is less than the sum of the individual risk capital requirements. The diversification benefit depends on the degree of correlation (possibly negative) between the risks

Question 15

What are some examples of likely correlations between risks?

Answer 15

• Inflation risk is heavily correlated with expense risk for most long-term financial products
• Traditionally equity markets have moved in the opposite direction to interest rates, but in recent years this correlation has not been so obvious
• Falling equity markets are likely to be correlated with increasing lapse rates on unit-linked savings products
• Operational risk is likely to be weakly correlated with all other risks, because if management are concentrating on some other issue they may not be concentrating on routine operational matters
• In life insurance, the longevity risk on an annuity book is strongly negatively correlated with mortality risk on a term assurance book (not perfectly negative correlation because the typical ages are different)

Question 16

List 3 methods of aggregating partially dependent risks

Answer 16

1. Stochastic model
2. Correlation matrix
3. Copulas

Question 17

How can liability risks be measured?

Answer 17

Liability risks can be measured by an analysis of experience, e.g. actual deaths divided by expected deaths.

It is important to ensure consistent classification and measurement of the risk event and the exposure to risk

Question 18

What are the advantages and disadvantages to the notional approach of deterministic approaches to measuring risk?

Answer 18

Advantages:
* Simple to implement and interpret across a diverse range of organisations

Disadvantages:
* Potential undesirable use of a “catch all” weighting for (possibly heterogeneous) undefined asset classes
* Possible distortions to the market caused by increased demand for asset classes with high weighting
* Treating short positions as if they were the exact opposite of the equivalent long position
* No allowance for concentration risk, as the risk weighthings for an asset class is the same irrespective of whether the investment in that asset class consists of a single security or a variety of different securities
* The probability of the changes considered is not quantified.

Question 19

What are the advantages and disadvantages of the factor sensitivity approach?

Answer 19

Advantages:
* Increased understanding of the drivers of risk

Disadvantages:
* Not assessing a wider range of risks, by focusing upon a single risk factor
* Being difficult to aggregate over different risk factors
* The probability of the changes considered (in the values of assets and/or liabilities) is not quantified

Question 20

What are the 4 probabilistic approaches to measuring risk?

Answer 20

1. Deviation
2. Value at Risk
3. Probability of ruin
4. Tail Value at Risk

Question 21

Deviation

Answer 21

Deviation can be measured as:
- standard deviation: where deviation is measured from the mean
- Tracking error: where deviation is measured relative to a benchmark other than the mean

Question 22

Value at Risk (VaR)

Answer 22

VaR generalises the likelihood of underperforming by providing a statistical measure of downside risk. VaR represents the maximum potential loss on a portfolio over a given future period with a given degree of confidence.

VaR can be measured either in absolute terms or relative to a benchmark.

Question 23

What are the advantages and disadvantages of VaR?

Answer 23

Advantages:
* The simplicity of its expression
* The intelligibility of its units, i.e. money
* Its applicability to all types of risks
* Its applicability over all sources of risk - facilitating easy comparisons between products and across businesses its inherent allowance for the way in which different risks interact to cause losses
* The ease of its translation into a risk benchmark

Disadvantages:
* It gives no indication of the distribution of losses greater than the VaR
* It can under-estimate asymmetric and fat-tail risks as it does not quanitfy the size of the “tail”
* It can be very sensitive to the choices of data, parameters and assumptions
* VaR is not always sub-additive (Subadditivity means that a 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 24

Probability of ruin

Answer 24

The probability of ruin is the probability that the net financial position of an organisation or line of business falls below zero over a defined time horizon.

Question 25

Tail VaR

Answer 25

The TVaR is the expected loss given that a loss over the specified VaR has occurred. The ratio of TVaR and VaR can be used as an indication of the skewness of a distribution. A higher ratio can indicate that the loss distribution is asymmetric with a fatter tail

Question 26

Describe what is mean by a "risk portfolio" and what it might contain

Answer 26

The risk portfolio categorises the various risks to which the business is exposed. Against each risk would be recorded a quantification of impact and probability. The product of the impact and the probability measures gives an idea of the relative importance of the various risks The risk portfolio can then be extended to indicate how the risk has been dealt with. For example: * avoided * retained * diversified * mitigated For risks that are retained, the risk portfolio becomes a more detailed risk register. It would include: * details of control measures * reassessment of value and impact after controls * the risk owner * the board committee or senior manager with oversight of the risk * identification of concentrations of risk and the need for management action in these areas.

Question 27

Give the reasons why regular risk reporting is important within a business

Answer 27

The production of regular risk reporting allows the management of a business to: * identify any new risks faced by the business * obtain a better understanding of the risks faced by the business in terms of quantifying the materiality and financial impact of individual risks * determine appropriate risk and control systems to manage specific risks * proactively monitor and manage the effectiveness of risk and control systems within its business * assess whether the risks faced by a business are changing over time * assess the interaction between individual risks * appropriately price, reserve and determine any capital requirements for its business * give shareholders or potential shareholders in a business a greater understanding of the attractiveness of that business for investment * help credit rating agencies determine an appropriate rating for the business * give a regulator a greater understanding of the areas within a business which could require more scrutiny

Question 28

Explain why, if risk is managed at the enterprise level, it is necessary to have a coherent system of risk reporting across the whole enterprise

Answer 28

If 2 business units are allocated risk exposures that diversify away at the enterprise level, but one of the two units does not take on the risk exposure allocated, this could increase the capital requirements of the enterprise.