Measures of Financial Risk
3 important questions on Measures of Financial Risk
What are the financial risk measures we can use?
1) Mean-variance or portfolio-theory approach (using SD)
2) VaR (extension of SD to a certain quantile/percentile)
3) Coherent risk measure (ES or even more generic)
Important themes:
- Drive to extend the range of P/L or return distributions that can be handled (applying to non-normal as well).
- Usefulness of the risk measure (VaR is questionable)
- Aggregation of individual risks
2) VaR (extension of SD to a certain quantile/percentile)
3) Coherent risk measure (ES or even more generic)
Important themes:
- Drive to extend the range of P/L or return distributions that can be handled (applying to non-normal as well).
- Usefulness of the risk measure (VaR is questionable)
- Aggregation of individual risks
What are the axioms for a coherent risk measure?
Artzner:
- Monotonicity
- Subadditivity
- Positive homogeneity
- Translation invariance
1,3 and 4 are just to rule out awkward outcomes.
- Monotonicity
- Subadditivity
- Positive homogeneity
- Translation invariance
1,3 and 4 are just to rule out awkward outcomes.
WHat about scenario and stress testing?
Interesting as it turns out that the results of scenario analysis can be interpreted as coherent risk measures. Losses are tail drawings and the expected value is the ES. A solid risk-theoretical justification for stress testing.
Moreover if we have multiple analysis, the maximum of these is a coherent risk measure.
Important as this means that we can always specify a relevant scenario and then taking the average or maxima of the outcomes as that will be a coherent risk measure. It is about the RIGHT risk measure not HOW we measure.
Moreover if we have multiple analysis, the maximum of these is a coherent risk measure.
Important as this means that we can always specify a relevant scenario and then taking the average or maxima of the outcomes as that will be a coherent risk measure. It is about the RIGHT risk measure not HOW we measure.
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