ERM Chapter 15 Flashcards
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
