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).