Chapter 29 - Risk measurement and reporting Flashcards
What are the key features to be assessed when quantifying risks? (Note terminology)
Probability/Frequency of risk event
Expected loss/Severity of risk event
Read through section 1.2 p. 3.
This is about subjective assessment and the 1-5 or 1-3 scoring system and how this can be used.
- Multiply scores of frequency and probability to get number from 1-25 or 1-9
- Do this with and without risk controls to judge approximate effectiveness of proposed controls
Read through section 1.3 p.4
This is about using modelling to quantify risks
- Require appropriate data
- Need to assign distribution to frequency and severity of risks
Discuss the main tools for evaluating risks.
Scenario analysis
- The steps in scenario analysis are:
1) Risk exposures grouped into broad categories
2) Develop adverse scenarios for each group of risks
3) Each scenario is translated into assumptions for valuing the likely cost of the risk event
4) Total expected cost of risk events are calculated - Looks at financial impact of a plausible and possibly adverse set of scenarios or events
- Deterministic method of evaluating risks, which is useful when assigning full distributions to events is difficult or impossible
- Frequently used for evaluating operational risks as well as financial risks (e.g. recession)
- Weaknesses include reliance on subjective inputs and lack of probabilistic interpretation of results
Stress testing
- Project financial condition of a company under a specific adverse event (i.e. for a specific risk factor) over a period of time
- Deterministic method
- Frequently used to model extreme market movements, as well as credit modelling and modelling liquidity risks
- Aim is to gain insight as to the sensitivities of a portfolio or product to predefined risk factors
Combination of scenario analysis and stress testing
- aka stress scenarios
- Use scenario analysis to determine important risk factors, and then stress tests are applied using these factors.
- Need to keep in mind how other areas of the business and general environment will react to stress scenarios
- Scenarios should focus on risk exposures to which business is most exposed
Reverse stress testing
- Construction of a severe, but plausible, stress scenario that just allows the firm to be able to continue to operate its business plan
- Could be internal and external scenarios
- Firm needs to consider both short-term and long-term plan in the event of business plan failure
Stochastic modelling
- All variable assigned stochastic distribution, as well as correlation matrices for these variables (i.e. a fully specified joint-probability distribution)
- Weaknesses are that model is complex to specify and build, run times of code can be impractical
- Results are only good if the model is good
- Therefore ways to combat these weakness are to limit the scope of the model by:
1) Restricting model duration (i.e. time horizon)
2) Limit number of risk variables that are modelled stochastically
3) Run simulation with one variables at a time, followed by running the worst-case scenarios together
Briefly discuss the methods for aggregating risks when setting capital requirements.
The method will change based on the relationship or correlation between the risks being considered.
Fully dependent risk events
- Capital requirement is the sum of the capital required for each risk at a pre-determined probability level
Fully independent risk events
- Capital requirement for a combination of risks that occurs with a given probability is less than the sum of the individual capital requirements (as in the previous dependent scenario)
Partially dependent risk events
- This is most likely to occur in practice
- Capital requirement is again less than the sum of the capital requirements for each risk
- Can use correlation matrices to aid calculation
- Difference between capital requirements in fully dependent scenario and the actual scenario is known as the diversification benefits
- This diversification benefit is maximised if correlation between risks are negative
Stochastic models can also be used to aggregate risks, however these are noted to be very impractical
Copulas are another way of aggregating risks
- Useful when company approximately knows individual probability distributions (i.e. marginal distributions) of risks.
- Copula is a function that inputs marginal cumulative distributions and outputs a joint cumulative distribution function
- Different copulas used to describe different degrees of dependence between random variables
- Used widely in quants to model tail risk
List some of the important correlations between common risk events.
Inflation risk is highly correlated with expense risk for most long-term financial products
Equity markets are generally negatively correlated with interest rates (however not so obvious in recent years)
Falling equity markets are correlated with increasing lapse rates (i.e. investment risk and persistency risk)
Operational risks are usually weakly correlated with other risks
Longevity risk on annuity book is strongly negatively correlated with mortality risk on a term assurance book.
- Company could reduce capital requirements by writing both of these products to diversify risks.
Discuss the main methods to measure risk.
Read through section 4 starting on p.16 also.
Two main groups of measures are deterministic and stochastic measures
DETERMINISTIC APPROACHES TO MEASURING RISK:
Notional approach
- See advantages and disadvantage on p. 17
Factor sensitivity approach
- Basically stress testing but scenarios do not need to be extreme
- See advantages and disadvantages on p. 18
Scenario sensitivity approach
- Similar to factor sensitivity but risk factors are varied in unison instead of just one factor at a time
- Should be changed to represent a specific scenario
STOCHASTIC/PROBABILISTIC MEASURES TO MEASURING RISK:
Deviation (from mean) and tracking error (from other benchmark)
- Forwards and backwards-looking tracking error
Value at risk (VaR)
- See advantages and disadvantages p. 20
- empirical approach
- parametric approach
- stochastic approach (simulation or bootstrap)
Probability of ruin
Tail Value at risk (TVaR) or Conditional Tail Value at risk (CVaR)
What does the ration of TVaR to VaR represent?
Indication of skewness of distribution. Higher ration indicates asymmetric distribution with a fat tail.
Discuss the main features of a risk portfolio or risk register.
Risk categorisation and quantification
- Each risk awarded score for impact/severity and probability/frequency
Risk response
- The response to each risk identified is recorded
- E.g. retained, shared, diversified, mitigated etc.
Additional details
- Details of control measures
- Reassessment of value and impact after controls
- Risk owner, i.e. who takes on the risk
- Designate risk managers
- Identification of risk concentrations and highlight ways to manage risk in these areas
List the reasons to carry out regular risk reporting.
Can help management to:
- Identify new risks
- Obtain better understanding of the nature of the risks being faced
- Determine appropriate level of risk to take on and develop appropriate control systems
- Proactively monitor and manage the effectiveness of risk control systems
- Pre-emptively identify possible changes in the nature of the risks
- Assess the interaction between risks
- Appropriately price, reserve and determine any capital requirements
Can also help other stakeholders:
- Create understanding of risks to shareholders and potential shareholders, which may increase attractiveness of business
- Help rating agencies determine an appropriate credit rating for the business
- Give regulator a greater understanding of areas within a business which could require more scrutuiny
Read through sections 6.2 and 6.3 on pp. 25-27
About reporting risk at an enterprise level and issues with reporting risk externally
Read through section 1.4 p. 5
About difficulties of valuing operational risks
- Due to so many possible operational risk events
- Events are rare and often independent so impractical to value all of them
- Can use broad-brush approach (e.g. add on a percentage to total risk) or scenario analysis after grouping risk events
