Outline the main techniques used to quantify different types of risks.
Enterprise risk - dynamic financial analysis:
- models the risks to which a whole enterprise is exposed and the relationships between these risks
- output is typically in the form of cashflows, and is used to project balance sheets and profit and loss accounts
Enterprise risk - financial condition reports (FCR):
- a report into the current solvency position of the company and its possible future development
- requires the company to consider the risks it is exposed to, and to look at projections of the expected level and profitability of new business
Market risks - VaR, TVaR, interest rate models, scenario tests:
- market and economic risk subject to more quantitative analysis than most other risks. Variety of models have been constructed to model the movement of markets as a whole, individual securities, and the relationships between them
- interest rate risk (short-term rates, long-term rates, full yield curve), foreign exchange risk, and basis risk can also be measured
Credit risk - credit risk models:
- credit risk models exist, largely concerned with single entities rather than a credit portfolio
- credit and counterparty risk are also assessed using quantitative and non-quantitative criteria, for example by banks and some credit rating agencies
Liquidity risk - asset liability modelling:
- method of projecting A & L within the same model, using consistent assumptions, to assess how well the A & L match and to understand the probably evolution of future cashflows
- in the context of liquidity, we are interested in the level of cash held in each period to ensure short-term liabilities can continue to be met with a desired level of confidence
Operational risks - internal and external loss data, scenario analysis, simulations:
- difficult to deal with quantitatively. Not modelled easily with statistical distributions, and ‘worst-case’ scenarios frequently involve the insolvency of the enterprise
- increasingly analysed quantitatively as organisations such as banks collect historical data on operational risk losses
What is a black swan event?
One-off events which are rare, hard to predict and high impact. These are events that often referred to as ‘predictable with hindsight’ e.g. 2008 credit crunch
Outline two processes that could help us respond appropriately to ‘black-swan’ events.
- Use previous experiences and incorporate learning points form past events into our ERM strategy with an aim of becoming better able to react appropriately to surprising events.
- Develop an emerging risks register of potential future issues.
Describe how unquantifiable risks might be analysed.
The use of risk ranges or risk buckets is one possible approach to recognising the lack of granularity in a risk analysis. These buckets may be quantitative (0%-20%, 20%-40% etc.) or qualitative (low, medium, high). The results may be displayed on a risk map.
Outline correlation.
- correlation is a measure of how different variables relate or associate with one another. In the context or ERM, we care about how different risks respond to changes in a given risk factor
- A low level of correlation indicates that risks diversify one another, whilst negative correlation indicates that risks offset one another
- Diversification of risks allows for greater risk to be taken on than would be deemed acceptable if diversification was not recognised
Outline linear correlation.
Pearson’s measure of linear correlation:
px,y = cov(X,Y)/sqrt(var(X)var(Y))
- pearson’s rho takes a value between [-1, 1] and is a measure of linear dependence between the variables
A: - the value is unchanged under the operation of strictly increasing linear transformations
i.e. p(a+bX, b+dY) = p(X,Y)
D: - the value is not unchanged under the operation of a general (non-linear) strictly increasing transformation
- is a valid measure of correlation only if the marginal distributions are jointly elliptical
- not well defined where var(X) or var(Y) is infinite. Hence, cannot be used for some heavy-tailed distributions which would be of interest to ERM
- independent variables are uncorrelated, but not all uncorrelated variables are independent (only implies no linear relationship, not no relationship)
- given the marginal distributions of a pair of random variables and specified correlation, it is not necessarily the case that we will be able to put together a joint distribution
Outline rank correlation.
- calculated empirically by looking at the position (rank) of each item of observed data when ordered, rather than the values of the items themselves
- two main types are spearman’s rho and kendall’s tau
A: - value of linear correlation is dependent not only on the joint distribution, but also on the marginal distribution. The rank correlation of a bivariate distribution however is independent of the multivariate distributions, giving it more attractive properties.
Outline Spearman’s rho.
- measure of rank correlation
- linear correlation of the distribution functions of two random variables
spx,y = 1-6/(T(T^2-1)) x sum((Vt - Tt)^2)
where Vt and Wt are ranks of Xt and Yt
Outline Kendall’s tau.
- measure of rank correlation
tx,y = 2/(T(T-1)) x (pc - pd)
- where pc and pd are the number of concordant and discordant pairs respectively
- a pair of observation (X1, Y1) and (X2, Y2) is concordant if X2-X1 and Y2-Y1 have the same sign
What are the properties of the rank correlations?
- Take values in the interval [-1, 1]
- They are symmetric sp(X, Y) = sp(Y, X)
- They give a value of zero if the random variables are independent
- They take a value of 1 or -1 if the variables are perfectly aligned (comonotonic) and reverse (countermonotonic) respectively
Define tail correlation.
- Focus on the relationship between variables at the points where they take ‘extreme’ values (the lowest or highest k%)
- Defining the tail is subjective and results may be highly sensitive to this choice and potentially unreliable
Outline deterministic modelling.
- Uses a set of assumptions that are predetermined
- Each set of assumptions uniquely determines the value to be taken by each variable in the model
- For each set of assumptions, the output from the model is fully determined - there is no random element
- Prudence is allowed for via the particular choice of assumptions e.g. adding risk margins
Outline sensitivity analysis
- Varying each input assumption one at a time to quantify the effect each variable has independently on the model’s output
- A key limitation is that it has no probabilities assigned to each of the options used
Outline the three key reasons a company may wish to use sensitivity analysis.
- To develop an understanding of the risks faced
- To provide insight into the dependence of the output on subjective assumptions
- To satisfy a supervisory authority’s requirements
Outline scenario analysis.
- Similar to sensitivity analysis, except multiple inputs are changed simultaneously
- A scenario is a set of model inputs that represent a plausible and internally-consistent set of future conditions
A: - facilitates evaluation of the potential impact of plausible future events on an organisation
- not restricted to consideration of events that have happened in the past and can therefore include assessment of its vulnerabilities to high impact, low probability events
- provides useful additional information to supplement traditional models based on statistical information
- facilitates production of action plans to deal with possible future catastrophes by assessing the impact pre and post mitigation
D: - potential complexity as a process
- reliance upon generating hypothetical extreme but also plausible events
- uncertainty as to whether the full set of scenarios considered is representative or exhaustive
- absence of any assigned probabilities to any of the scenarios
Outline the four steps a company should take when conducting a scenario analysis within a RM framework.
- Decide (top-down) on the scenarios to be modelled. Could be based on historical events, or generated by asking participants what the worst plausible events imaginable are to the organisation.
- Establish the impact on risk factors i.e. model inputs
- Take action based on the results. This involves reviewing the results from step 2 and deciding what plans to put in place to minimise the effects of the scenario. Company may also look to identify early warning indicators.
- Review the scenarios to ensure they remain relevant over time.
Outline stress testing.
- similar to scenario and sensitivity testing, but focuses on extreme scenarios or very large changes in input assumptions
- two main categories are top-down stress-scenario tests and bottom-up stress-variable tests
- process involves deciding which stresses to consider, how extreme they are to be, and then running the risk models to quantify the impact
A: - ability to compare the impact of the same stresses on differing organisations
- explicit examination of extreme events which may not otherwise be considered
- use in assessing the suitability of any response strategies, by assessing the expected impact of the stress in absence of any response, and in the presence of the proposed response
D: - subjective to which assumptions to stress and the degree of stresses to consider
- assigns no probability to the events considered
- only looks at extreme situations, so needs to be coupled with other techniques
Outline stochastic modelling.
- used when inputs to a model are uncertain
- key benefit is that it provides a probability distribution for the model outputs
- achieved by running the model repeatedly (simulations) and accumulating the results to give a distribution of potential outcomes. This allows estimation of the mean, variance, and probabilities associated with the outcome being more or less than a certain value
Outline historical simulation (bootstrapping).
- each simulation is generated through direct reference to historical data e.g. random sampling
A: - applicable to many situations, provided past data is available
- does not require large amounts of past data if the sampling is done with replacement
- does not require the specification of probability distributions for the inputs
- reflects the characteristics of the past data without the need for parameterisation
D: - cannot be performed in the absence of relevant past data
- assumes past data is indicative of the future
- does not take into account inter-temporal links between past data items e.g. auto-correlations
- may underestimate uncertainty as it is based on what actually happened rather than what potentially could have happened
Outline Monte Carlo simulation.
- each simulation uses random numbers to generate variates from a statistical distribution and the model is then run using these variates
A: - computer packages are widely available to do most of the work, and these can be easily adapted and updated
- increasing the number of simulations increases the accuracy of the output by reducing the estimation error
- possible to simulate the interdependence of risks
- widely understood technique as it used relatively simple mathematics
- it can be used to model complex financial instruments, such as derivatives
D: - random selection of parameter values may lead to a set of simulations which are not representative of the full range of possibilities - unless the set is sufficiently large
- large sets of simulations may be time consuming to perform
Outline two advantages of using a factor-based approach over a data-based approach.
- The discipline imposed on understanding what drives the key variables
- Making the relationships between the drivers explicit
D: Additional effort required, which in some applications, is not justified.
Outline pseudo-random numbers.
- those which appear to follow no pattern but which are the result of an underlying mathematical process
- properties that make them appropriate for the purpose of simulation include:
> be replicable - to facilitate checking
> repeat only after a long period - to create valid lengthy simulations
> be uniformly distributed over a large number of dimensions
> exhibit no serial correlation
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ERM Chapter 19
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ERM Chapter 25
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ERM Chapter 327
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ERM Chapter 413
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ERM Chapter 516
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ERM Chapter 69
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ERM Chapter 77
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ERM Chapter 88
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ERM Chapter 917
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ERM Chapter 1010
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ERM Chapter 1129
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ERM Chapter 1214
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ERM Chapter 1318
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ERM Chapter 1417
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ERM Chapter 1522
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ERM Chapter 1631
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ERM Chapter 1725
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ERM Chapter 1821
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ERM Chapter 1911
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ERM Chapter 2012
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ERM Chapter 2111
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ERM Chapter 2214
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ERM Chapter 2313
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ERM Chapter 2416
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ERM Chapter 2511
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ERM Chapter 2613
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ERM Chapter 2720
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ERM Chapter 2814
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ERM Chapter 2918
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ERM Chapter 3023
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ERM Chapter 314
