Module 14: Introduction to risk measurement Flashcards
Axioms of coherence (4)
Properties that a good risk measure should have.
These are:
- monotonicity
- subadditivity - reflecting the effects of diversification
- positive homogeneity
- translation invariance
A consequence of subadditivity and positive homogeneity is convexity.
Axiom 1: Monotonicity
If risk portfolio 2 exhibits greater losses under all future scenarios than the losses on risk portfolio 1, then a monotonic risk measure will indicate that a greater amount of capital should be held in respect of the former, although how much more is not specified.
Axiom 2: Subadditivity
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.
Note:
- non-subadditive risk measures incentivise the breaking up of organisations or portfolios to reduce risk
- subadditivity makes decentralisation of risk-management systems possible, since constraints can be placed on business units and if they stay within these contraints, then the overall risk level cannot exceed the sum of the parts.
Axiom 3: Positive Homogeneity
If we double the size of the loss situation we double the risk - no reduction being given for non-existent diversification.
Axiom 4: Translation Invariance
If we add (or deduct) an amount to (or from) the loss, then the capital requirement needed to mitigate the impact of the loss increases (or decreases) by the same amount.
A consequence of subadditivity and positive homogeneity
convexity
2 Major types of risk measure
- deterministic
- probabilistic
Deterministic risk measure
Gives a broad indication of the level of the risk taken.
3 Examples of deterministic risk measures
- notional approach
- factor sensitivity approach
- scenario sensitivity approach.
Probabilistic risk measure
Involves applying a statistical distribution to a risk (risks) and measuring a feature of that distribution.
5 Examples of a probabilistic risk measure
- deviation measures (eg standard deviation, tracking error, information ratio)
- Value at Risk (VaR)
- ruin probability
- Tail Value at Risk (TVaR)
- expected shortfall
A time horizon chosen may depend on any contractual / regulatory constraints.
The choice of a suitable time horizon will be influenced by expectations as to: (2)
- the time to recover from a loss event
- the time to reinstate risk mitigation (eg re-establish a derivatives hedge)
5 Factors to consider when setting a discount rate for a project
- the organisation’s cost of capital
- the level of inherent risk exposure
- inflation rates
- interest rates
- investment returns in the economy
Outline the notional approach
The notional approach is a broad-brush risk measure.
E.g. risk weightings might be applied to the market value of assets, the results then summed and this total then compared to the value of liabilities in order to determine a notional (‘risk-adjusted’) financial position.
Discuss the advantages and disadvantages of the notional approach
ADVANTAGE
- simple to implement and interpret across a diverse range of organisations
DISADVANTAGES
- potential undesirable use of a “catch all” weighting, for (possibly heterogeneous) undefined asset classes
- possible distortions to the market caused by increased demand for asset classes with high weightings
- treading short positions as if they were the exact opposite of the equivalent long position (in practices, they might affect the capital requirements to different extents).
Outline the factor-sensitivity approach
Determines the degree to which an organisation’s financial position (eg solvency or funding) is affected by the impact that a change in a single underlying risk factor (eg short-term interest rates) has on the value of assets and liabilities.
Discuss the advantages and disadvantages of the factor sensitivity approach
ADVANTAGE:
- Increased understanding of the drivers of risk
DISADVANTAGES:
- Not assessing a wider range of risks, by focusing upon a single risk factor
- Being difficult to aggregate over different risk factors
- The probability of the changes considered (in the values of assets and/or liabilities) is not quantified
Scenario sensitivity approach
Similar to that of factor sensitivity, but rather than changing a single underlying risk factor, the effect of changing a set of such factors (in a mutually consistent way) is considered.
Tracking error
Deviation is measured relative to a benchmark other than the mean.
Deviation measured on a portfolio of assets can be calculated in two ways:
Retrospectively (ex post) - calculating past deviations based on actual historic asset allocations.
Prospectively (ex ante) - based on current asset allocations by using either:
- the observed historic covariances of the returns on different asset classes (ie semi-prospectively), or
- estimated future covariances (ie fully-prospectively)
Discuss the advantages and disadvantages of deviation measures
ADVANTAGES:
- simplicity of calculation
- applicability to a wide range of financial risks
- can be aggregated, if correlations are known
DISADVANTAGES
- difficulty of interpreting comparisons, other than in terms of simple ranking
- potentially misleading if the underlying distribution(s) are skewed
- do not focus on tail risk and, specifically, underestimates tail risks if the underlying distributions are leptokurtic (thicker tails)
Value at Risk (VaR)
The maximum loss which is not exceeded with a given high probability (α) over a given time period.
Discuss the advantages and disadvantages of VaR
ADVANTAGES:
- the simplicity of its expression
- the intelligibility of its units, ie money
- its applicability to all types of risk
- its applicability over all sources of risk - facilitating easy comparisons between products and across businesses its inherent allowance for the way in which different risks interact to cause losses
- the ease of its translation into a risk benchmark, eg risk limit
DISADVANTAGES:
- it gives no indication of the distribution of losses greater than the VaR, eg does not reveal how much is likely to be lost should a loss occur that is greater than the VaR
- it can under-estimate asymmetric and fat-tail risks
- it can be very sensitive to the choices of data, parameters and assumptions
- it is not a coherent risk measure - VaR is not sub-additive
- if used in regulation, it may encourage ‘herding’ thereby increasing systemic risk.
3 General approaches to the calculation of VaR
- empirical (or historical)
- parametric (variance-covariance)
- stochastic
