29.1 Risk measurement Flashcards
Risk quantification
Must assess:
o Prob of event occurring
o Expected loss thereof
Usually RV, may not be esp if there’s a single event insurance risk
Risk quantification methods
- Subjective assessment
- Models
- Operational risk assessment
Subjective assessment
- Either 3-point scale or 5-point scale (5- High; 4- medium-high; etc)
- Product of probability assessment and impact assessment gives scale of 1-25 (or 1-9) as assessment of risk
- Carried out w and w/o controls to assess effectiveness vs cost
Models
- Assign distribution to probability and loss
- E.g. firm may define market risk event from equities as 25% fall in equities over year. Then …
- … research historic data to find prob distr. Parameter chosen for fall in equity market must be consistent with risk appetite.
- Alt, set frequency of loss event in advance, and use it to find size of parameter. E.g. …
- … 0.5% prob of equity fall may involve 40% market movement
Features of a risk that favour use of stochastic modes
Has a high score (high severity and/or frequency)
High variability of possible outcomes
Relates to financial guarantees/options
Involves mismatching of A+L
Operational risk
- Impractical to quantify because so many risk events
- Events rare and independent»_space;> little/no effect on business’ aggregate exposure
Methods:
- Add % uplift to agg risks other than operational risk
- Scenario analysis
Examples of scenario analysis categories for operational risk
o Fraud o Loss of key personnel o Mis-selling of financial products o Calculation error in computer system o Loss of business premises o Loss of company email access for 72 hours
Evaluating risks
- Scenario analysis
- Stress testing
- Stress scenario
- Reverse stress testing
- Stochastic modelling
Scenario analysis uses
Used if: Difficult to fit probability distribution to risk events
- Operational risk
- Impact of fin risks like global recession
Drawback: Doesn’t quantify probability
Steps to scenario analysis
- Group risks into broad categories using senior staff input
- Plausible risk scenario that represents every risk in that group
- Translate each scenario into assumptions for various factors in the model and calculate consequences of risk happening
- Total costs = sum of financial cost from each group
Stress testing
- Model extreme events
•E.g. for market risk, subject asset portfolio to extreme market movements by changing underlying assumptions and characteristics…
•… to get insight on portfolio’s sensitivities to predefined risk factors.
•Esp if asset correlations and volatilities increase in extreme events
Types of stress testing
- Identify weak areas in portfolio and investigate effects of localised stress situations by looking at effect of diff combinations of correlations and volatilities.
- Gauge impact of major market turmoil affecting model parameters while ensuring consistency between correlations while they are stressed.
Stress scenario
- Scenario analysis + stress test
- SA identifies factors impacted under chosen scenario and then stress testing is applied to these
Factors affected by sustained reduction in market movements for unit-linked co
o Income received from fund management charges
o Persistency of existing investment bonds
o New business volumes
o Provider’s regulatory capital requirements
o Value of shareholder’ interests
o Probability of guarantees biting
Reverse stress testing
• Constructing a severe stress test that just allows business to continue to operate its business plan
May be regulatory requirement
Stochastic modelling
- Can determine capital necessary to just avoid ruin at any prob
- Run times may be long + complex to build
Improving run times in stochastic model
- If risk criterion is 1-year ruin probability: restrict duration to 2 years. Some parts of model such as reserve calculations still need projections to run-off.
- Limit # of risk variables modelled stochastically. Variables that have adverse effect when moving in 1 direction can be modelled deterministically.
- Carry out # of runs with diff single stochastic variable, then a single deterministic run using all the worst-case scenarios together.
Aggregating risks
- Sum of individual risks may be > than effect of multiple risks because of diversification or less than perfect (or sometimes) negative correlation.
- Numerical agg of risks is used to agg the capital requirements to cover risk at a pre-determined prob level.
Examples of correlated risks
- Inflation risk and expense risk heavily correlated for long-term fin products.
- Traditionally equity markets moved in opp direction to interest rates (not obvious in recent years)
- Falling equity markets and increasing lapse rates on unit-linked savings products.
- Operational risk likely to be correlated with all other risks.
- Longevity risk on annuity book strongly negatively correlated with mortality risk on term assurance
Other aggregation methods
Copulas
Correlation matrices
Risk measures
Deterministic
- Notional approach
- Factor sensitivity analysis
- Scenario sensitivity analysis
Probabilistic
- VaR
- Ruin probability
- TVar
- Deviation (Tracking error and standard deviation)
- TVaR:Var
Merits of notional approach
Advantage: Simple to implement and interpret across diverse range of orgs.
Disadvantages
- use of “catch all” weighting for undefined asset classes
- Possible distortions to market caused by increased demand for asset classes with high weightings
- Treating short positions as exact opposites of equivalent long position
- No allowance for concentration risk since risk weighting is same irrespective of whether investment in that class consists of single security/variety of diff securities
- Probability of changes A/L isn’t quantified
Merits of factor sensitivity analysis
Advantage: Increased understanding of drivers of risk
Disadvantages
- Not assessing wide range of risks
- Difficult to aggregate over different risk factors
- Probability of changes in A/L isn’t quantified
Merits of VaR
Advantages:
- Simplicity of expression
- Intelligibility of units (money)
- Applicable to all types of risk
- Applicable over all sources of risk so easy comparison between products and businesses
- Ease of transition into a risk benchmark e.g. risk limit
Disadvantages:
- No indication of distribution of losses greater than the VaR
- doesn’t quantify tail =. Can underestimate asymmetric and fat-tail risks
- Sensitive to data, parameters and assumptions
- Not always sub-additive
- If used in regulation, may encourage herding»_space;> increasing systemic risk
