Mod 14: Introduction to risk measurement Flashcards
Outline the axioms of coherence ©
A risk measure, F , is coherent if it satisfies the following four axioms:
- monotonicity
- subadditivity
- positive homogeneity
- translation invariance
Explain the implications of a risk measure being (or not being) subadditive
Subadditivity
A risk measure being subadditive implies that a merger of risk situations does not increase the overall level of risk. Indeed it may decrease the overall level of risk, as a consequence of diversification.
Subadditivity makes decentralisation of risk-management systems possible, since constraints can be placed on business units and if they stay within these constraints then the overall risk level cannot exceed the sum of the parts.
By contrast, non-subadditive risk measures incentivise the breaking up of organisations or portfolios to reduce risk.
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Describe two groups of risk measures and state at least three examples of each
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Deterministic and probabilistic risk measures
Deterministic risk measures are simplistic, giving only a broad indication of the level of risk. They include:
1. notional approach (eg ratio of risk-weighted assets to liabilities)
2. factor sensitivity approach (sensitivity of financial position to single risk factor)
3. scenario sensitivity approach.
Probabilistic risk measures involve applying a statistical distribution to a risk (risks) and measuring a feature of that distribution. They are potentially more accurate, but they are more complex (greater model risk), and can imply inappropriate levels of confidence (especially with respect to tail-risk estimation). They include:
1. deviation (eg standard deviation, tracking error)
2. VaR and probability of ruin (looking at a ‘cut off’ to the tail) 3.TVaR and ES (looking beyond a ‘cut off’ – into the tail).
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List the potential advantages and disadvantages of the notional approach to risk measurement which compares the risk-weighted value of assets to the value of liabilities
The notional approach
The advantages of this notional approach include:
1. simple to implement and interpret across a diverse range of organisations.
The disadvantages include:
1. ‘catch all’ weighting for (possibly heterogeneous) asset classes
2. possible distortions to the market caused by increased demand for asset classes with high weightings
3. short positions treated as exact opposite of the equivalent long position (but they might affect capital requirements to different extents)
4. no allowance for concentration risk (same risk weighting irrespective of a single security or a variety of different securities)
5. approach quantifies severity but not probability
State formulae for three risk measures based on deviation ©
State the main advantages and disadvantages of risk measures based on deviation
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Advantages and disadvantages of deviation-based risk measures
Advantages:
1. simplicity of calculation
2. applicability to a wide range of financial risks
3. can generally be aggregated, if correlations are known
Disadvantages:
1. difficulty in interpreting comparisons (other than as a simple ranking)
2. potentially misleading if the underlying distribution(s) is/(are) skewed
3. do not focus on tail risk
4. specifically, underestimates tail risk if the underlying distribution(s) is/(are) leptokurtic (ie thicker tails)
5. aggregations of deviations can be misleading, eg if the component distributions are not normally distributed.
6. risk measures quantify severity but not probability
Describe Value at Risk (VaR) ©
Value-at-Risk
Value at Risk (VaR) is defined (in SP9) as the maximum potential loss with a given (high) probability (alpha ) over a given time period.
The time period (or horizon) will typically be chosen to comply with any contractual and legislative constraints and also having regard to liquidity considerations and portfolio stability.
A high probability (or confidence level) is typically used for capital adequacy purposes. Often multiple levels are considered, eg 99%, 99.5%, 99.9%.
Three general approaches to its calculation are: empirical (or historical), parametric (or variance-covariance) and stochastic.
List the main advantages and disadvantages of VaR as a risk measure
Advantages and disadvantages of VaR
Advantages:
1. the simplicity of its expression
2. the intelligibility of its units, ie money
3. its applicability over all sources of risk – facilitating comparison its
4. inherent allowance for risk interaction
5. its ease of translation into a risk benchmark, eg risk limit
Disadvantages:
1. it gives no indication of the distribution of losses beyond VaR
2. it can under-estimate asymmetric and fat-tail risks
3. it can be very sensitive to the choices of data, parameters and assumptions
4. it is not a coherent risk measure – VaR is not sub-additive
5. regulatory use may encourage ‘herding’, so increasing systemic risk
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List the factors to be considered when choosing how to perform a VaR calculation (ie empirical, parametric, stochastic)
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Factors to use when comparing approaches to calculating a VaR
- simplicity of calculation
- speed of calculation
- ease of explanation
- need to / ease of specifying distribution and (consistent) parameters
- ability to reflect (explicitly) complex distribution features, eg skewness
- ability to reflect (explicitly) complex inter-dependencies
- degree to which future loss distribution is assumed constant
- use of past data (objectiveness? reliance upon?)
- backward or forward looking
- facilitation of stress and/or scenario testing ©
Describe the probability of ruin
Probability of ruin
The probability of ruin is the probability that the net financial position of an organisation or line of business falls below zero over a defined time horizon.
It is closely linked to the Value at Risk. For example, if the current net financial position is less than the 95% VaR, then we can infer that the probability of ruin is greater than 5% over the same time horizon used to calculate the VaR.
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Describe Tail Value at Risk (TVaR or Conditional Value at Risk)
Tail Value at Risk, TVaR (or Conditional Value at Risk, CVaR) The expected loss given that a loss over the specified VaR has occurred.
Like VaR, it can be calculated using an empirical, parametric or stochastic approach.
List the main advantages and disadvantages of TVaR as a risk measure
Advantages and disadvantages of TVaR
Advantages:
1. it considers the losses > VaR − − it is 2. a coherent risk measure, so it facilitates aggregation
Disadvantages:
1. the choice of distribution and parameter values is subjective and difficult to determine
2. it is highly sensitive to assumptions – a significant concern as we are using information from further into the tail of the loss distribution than for VaR, and we are more uncertain of this
Define expected shortfall (ES) ©
Expected shortfall
The expected shortfall is the probability of loss multiplied by the expected loss given that a loss has occurred.
little intuitive meaning,otherwise similar advantages and disadvantages as for TVaR
State two ‘rules of thumb’ relating to VaR
Two ‘rules of thumb’
- The number of days that a mark-to-market loss might exceed
VaR_alpha
might be estimated as [ 100%-alpha] times 250 , where alpha is the confidence level and 250 is the number of trading days in a year. - square root of n times VaR
Outline factors that will affect the choice of time horizon for risk measurement
Choice of time horizon
The choice will be influenced by expectations as to the time period over which an organisation is committed to holding its portfolio, (and hence the time exposed to the risk). This in turn is affected by:
1. contractual / legal constraints, eg a general insurance company is typically bound to a claims portfolio for one year
2. liquidity considerations, ie the time taken to liquidate an investment portfolio, which, in adverse conditions, may be longer than is usual
3. the time to reinstate risk mitigation, eg re-establish a derivatives hedge
4. the time to recover from a loss event, eg for operational risks such as fire
