Chapter 29

Question 1

1. What are the methods of quantifying risk

Answer 1

• Risk scoring
• Rank risks from 1 to 5 in terms of frequency and severity
• Risk score = score for frequency x score for severity
• Assess the risk scores with risk controls and the risk scores without to determine if the score reduced in an amount that justifies the cost of implementing the risk control
• Using a model
• Decide between stochastic and deterministic
• Assign distributions to both frequency and severity
• The choice of parameters is dependent on the risk appetite
• NOTE: it is difficult to model low frequency events due to the lack of data
• Operational risks are difficult to quantify and so these approaches are used:
• Broad bush (adding to other risks ) – does not perform any complex analysis
• Scenario analysis
• Percentage of average income
• Percentage of total risks other than operational risk
• Solvency II standard formulae

Question 2

2. What are the methods of evaluating risks?

Answer 2

• Scenario analysis – looks at the financial impact of adverse plausible scenarios
• Stress testing – projecting the financial condition of a company under extreme adverse events over a period of time
• Combines scenario and stress testing (stress scenario) – scenario analysis identifies the factors which are impacted under chosen scenarios and these factors become the factors to which stress tests are applied
• Reverse stress testing – identifies a scenario that would just be enough to disrupt the company’s business plan
• Stochastic modelling – models the capital necessary to avoid ruin at a desired probability level

Question 3

3. How is scenario analysis done?

Answer 3

• Group risks into broad categories
• Develop plausible adverse scenarios for each group
• The scenario must be representative of all the risks in the group
• The scenario will translate into assumptions for various risk factors (E.g., interest rates fall by 2%, equity markets drop by 30%, unemployment rises by 5%) and these are plugged into the model to simulate the financial impact.
• Total costs calculated are taken as financial costs of all risks represented by chosen scenario (aggregate impact of all risks in that scenario)

Question 4

4. What are the advantages of scenario analysis

Answer 4

• Is used when modelling cannot be used
• Used when modelling cannot be used due to too many subjective parameters eroding the value of using the model
• Can be used to validate models
• It is useful when it is difficult to fit probability distributions to risk events
• Useful in evaluating operational risks
• Good for evaluating global recessions and emerging risks

Question 5

5. What are the disadvantages of scenario analysis and stress testing?

Answer 5

• Only quantifies the severity and not the frequency of the risk

Question 6

6. What are the advantages of stress scenario testing?

Answer 6

• Allow for inter-relationships
• It reveals weaknesses and factors to which the company is most sensitive to and focuses on these factors to which the company is most exposed

Question 7

7. What are the types of stress scenario tests?

Answer 7

• Identifying weak areas by looking at different correlations and volatilities
• Guage the impact of major market turmoil

Question 8

8. What are the disadvantages of stochastic modelling?

Answer 8

• Complex to specify and build
• Run times would be too much with more than one variable being stochastic
• Relies heavily on data

Question 9

9. How can you improve a stochastic model?

Answer 9

• Restrict duration of the model to 2 years (reduce the projection period to 2 years – shorter term is easier to model accurately)
• Design it to automatically allow for programmed correlations between risk events under each simulation
• Limit the number of risk variables that are modelled stochastically (to reduce run time)
• Carry out a number of runs with different single stochastic variable, followed by a single deterministic run using all the worst-case scenarios together (Use Sensitivity Analysis – to identify the variables that have high sensitivity, Before Full Stochastic Runs)

Question 10

10. What are the different methods of aggregating risks to find their capital requirements?

Answer 10

Let
R_j=capital requirement for the jth risk
C_ij=correlation between risks i and j
Fully dependent risk events: Capital requirement= ∑(j=1)^n▒R_j
Fully independent risk events: Capital requirement= √(∑(j=1)^n▒〖R_j〗^2 )
Partially dependent risk events: capital requirement is less than the sum of the individual capital requirements (the lower the correlation, higher the diversification benefit and then the more the extent to which the capital requirement is less than the sum of the individual capital requirements
Stochastic modelling
Correlation matrices – commonly used in insurance industry, used to aggregate risks that are partially dependent, rely on underlying assumptions which may not hold in practice: Capital requirement= √(∑_(i=1,j=1)^(n,n)▒〖C_ij R_i 〗 R_j )
Copulas – function that inputs marginal cumulative distribution functions and outputs joint cumulative distribution functions – provides a way of calculating joint probabilities of risks (how risks move together) and is widely used to model tail risk.

Question 11

11. What are the likely correlations between risks?

Answer 11

• Long term financial products: Inflation risk heavily correlated with expense risk
• Equity markets negatively correlated with interest rates (this relationship has not been obvious is recent years)
• Unit linked savings products: equity markets negatively correlated with lapse rates
• Operational risk weakly correlated with all other risks
• Longevity risk (annuities) negatively correlated with mortality risk (term assurance)

Question 12

12. What are the different risk measures?

Answer 12

Deterministic
* Notional approach – factor-based charges (capital requirement is expressed as a factor/percentage x of the exposure the company has to a certain risk) – prescribed by Solvency II and SAM: Capital Requirement= Exposure × Prescribed Risk Factor
* Factor sensitivity approach – degree to which a company’s financial position is affected by a change in a single factor (similar to stress testing but the risk event does not need to be extreme)
* Scenario sensitivity approach – the degree to which a company’s financial position is affected by a change in a set of factors
Stochastic – can be calculated using an empirical, parametric, scenario analysis or
stochastic approach
* Deviation
- Standard deviation – it measures the deviation from the mean
- Tracking error – it measures the deviation from a benchmark (that is not the mean) – backwards-looking and forwards-looking tracking error
* Value at Risk – maximum potential loss on a pf over a given future period with a given degree of confidence
* Tail Value at Risk – expected shortfall below a certain level, given that the shortfall has occurred
* Probability of ruin – probability that a company’s net financial position falls below 0 over a defined time horizon

Question 13

13. What are the advantages of notional approach?

Answer 13

• Simple to implement
• Simple to interpret across a diverse range of organisations
• Ensures comparability across insurers

Question 14

14. What are the disadvantages of notional approach?

Answer 14

• A single factor is often used for an entire asset class and it does not distinguish between very different risks within that class (leads to misrepresentation of actual risk)
• Potential distortions to the market caused by increased demand for asset classes with lower weightings because the lower the weight, the lower the capital requirements
• Treating short positions as if they were the exact opposite of the equivalent long position (short and long positions have the same capital charge but short positions have unlimited potential loss) - This ignores the asymmetric risk of shorting — short positions can have unlimited losses, unlike long positions.
• No allowance for concentration of risk, as the risk weightings 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 (approach assumes diversification - Problem: Holding R100 million in a single bond is riskier than holding R10 million in ten different bonds — but the capital charge is the same).
• Does not quantify how likely a loss is and so two risks with different likelihoods would have the same capital requirement

Question 15

15. What are the advantages of factor sensitivity approach?

Answer 15

• It increases the understanding of the drivers of risk

Question 16

16. What are the disadvantages of factor sensitivity approach?

Answer 16

• Focuses on a single factor hence does not assess a wider range of risks – ignores interactions between different types of risks
• Is difficult to aggregate over different risk factors – since the sensitivities of different factors are measured independently
• Does not quantify how likely a loss is and so two risks with different likelihoods of loss would have the same capital requirement (Capital might be over-allocated to rare events or under-allocated to more probable ones)

Question 17

1. What are the advantages of scenario sensitivity approach?

Answer 17

• It considers the interactions between different types of risks

Question 18

18. What are the disadvantages of scenario sensitivity approach?

Answer 18

• Does not quantify how likely a loss is (probability of occurrence not taken into account)

Question 19

19. What are the advantages of VaR?

Answer 19

• It is simple to compute
• Easily interpreted as it is expressed in money terms
• It is applicable to all types of risk
• easy comparison between products
• Ease of its translation into a risk limit

Question 20

20. What are the disadvantages of VaR?

Answer 20

• No indication of the losses greater than the VaR level
• Can underestimate asymmetric and fat-tail risks as it does not quantify the size of the tail – solved by Tail VaR (Risk is understated)
• Sensitive to the choice of data, parameters, assumptions
• A merger of risk situations does not increase the overall level of risk (Risk Doesn’t Always Increase When Portfolios Merge – diversification effects do not hold during crisis or tail events)
• If used in regulation, it may encourage ‘herding’ thereby increasing systemic risk (If regulators impose capital based on VaR, firms may be incentivised to structure portfolios to minimise reported VaR, not actual risk.)

Question 21

21. What is a risk portfolio or risk register?

Answer 21

• Categorises various risks to which a business is exposed
• Product of severity and frequency gives an idea of the relative importance of the various risks
• It can also include the responses to the various risks (chapter 28)
• For risks that are retained, the risk register becomes more detailed (detailing risk control measures, the impact of risk control measures, risk owner, managers overseeing the risk)

Question 22

22. What is the importance of risk reporting?

Answer 22

• Identifying new risks
• Quantifying the impact of individual risks
• Determining appropriate risk control systems for specific risks
• Monitoring the effectiveness of existing risk control systems
• Assessing changes to risks faced over time
• Assessing the interactions between risks
• Assisting with pricing, reserving and determining capital requirements
• Assists credit rating agencies determine the appropriate rating for the business
• Gives the regulator a greater understanding of the areas of the business that needs more scrutiny

Question 23

23. What are the advantages and disadvantages of reporting at enterprise level?

Answer 23

• A: by budgeting for risk across the whole enterpirse, maximum use can be made of diversification benefits, and thus minimum capital required to support the risks undertaken.
• D: there is a trade-off between the costs of the additional analysis required to minimize capital requirements in this way and the cost of holding additional capital if risk diversification between business units is not assumed
• D: To accurately capture diversification and dependencies across the enterprise, it Requires more data, systems, expertise, and time

Question 24

24. What are the issues relating to reporting risk externally?

Answer 24

• Whether to use a qualitative or quantitative approach (Should the report describe risks using numbers or narratives)
• How to best communicate:
• The level of uncertainty within the figures given
• The limitation of the assessment approach used
• Tailoring to the needs of the intended audience as with any reporting (Different stakeholders have different levels of technical knowledge and different priorities.)