Chapter 14: Introduction to risk measurement

Question 1

The axioms of Coherence – properties of a good risk measure MSPT

Answer 1

1. Monotonicity - a smaller risk portfolio should result in a smaller capital requirement
2. Subadditivity - a merger of risk portfolios has lower capital requirement the sum of individual portfolios
3. Positive homogeneity - the risk of a portfolio should increase proportionally to its size
4. Translation invariance - a change in the size of the loss on a portfolio should result in a capital requirement change of the same amount

Question 2

Merits of notional approach (Factor based model) IS CLAMP

Answer 2

• Implementation is easy
• Standardised across various organisations
• Concentration and diversification not considered
• Long and short positions not considered
• Asset classes not defined are put in a generic “catch all group”
• Market distortions could affect measure
• Probability of change in AL not considered

Question 3

Merits of deviation as risk measure SAA TIM

Answer 3

• Simple calculation
• Applicable to a wide range of risks
• Aggregation is possible if correlation is known
• Tail risk not considered
• Interpretation and comparison may be difficult
• Misleading results if not normally distributed

Question 4

Components of VAR VELC TC

Answer 4

• Volatility - best estimate of future daily price volatility
• Exposure – size of open market position
• Liquidity factor - the tie in days taken to unwind a position in adverse market conditions
• Correlation
• Time horizon
• Confidence level

Question 5

Merits of VaR SATI SMUCH DFS

Answer 5

• Simple expression
• Applicable to a different risk types and classes
• Translatable into a risk tolerance and limit
• Ineligibility of its units
• Sensitive to data and parameters chosen
• Model and measurement error could exist
• Underestimation of skewness and fat tails
• Coherence is absent
• Herding could occur in regulation
• Distribution of losses exceeding the VaR not considered
• Full extent of the risk not measured
• Standard approach to VAR does not exist

Question 6

Merits of the empirical approach SDR BIPS

Answer 6

• Simple
• Distribution error avoided
• Realism
• Boot-strapping reliance
• Interpolation challenges
• Past data reliance
• Stress and scenario testing not possible

Question 7

Merits of parametric approach PEP CASE C

Answer 7

• Past data dependency reduced
• Ease of calculation
• Parameters easily adjusted
• Complex interdependencies not allowed for
• Assumptions made about data and parameters
• Statistical distribution error
• Explanation may be difficult
• Consistency in parameters and distributions is difficult

Question 8

Merits of TVAR/Expected shortfall DEV DICS ARIMS

Answer 8

• Distribution of losses beyond VAR considered
• Easy to calc
• Various calculation approaches
• Diversification benefit allowed for
• Insolvency losses considered
• Coherent
• Sensible behaviour if losses are altered or combined
• Severity of the loss not shown, only the probability
• Assumption sensitivity – not a lot of data in tails
• Relation to current portfolio value is difficult
• Interpretation is difficult
• Modelling is difficult
• Subjectivity in parameter and distribution choice

Question 9

Factors to consider when risk discount rate SINC WACCS

Answer 9

• Systematic risk considered
• Inflation and interest rates
• Nature of cash flows (real vs. nominal)
• Current cost of raising capital
• WACC (Explain fully)
• Alternative investments considered
• Compare riskiness – similar projects, other companies
• Sensitivity testing

Question 10

CAPM Expected return expressed a function of VREC

Answer 10

• Volatility of the market and the project
• Risk free return rate
• Expected market returns
• Correlation between project and the market

Question 11

Variations in VaR CARPT

Answer 11

• Confidence level
• Absolute loss replaced with relative loss
• Returns rather than losses considered
• Percentage rather than monetary losses
• Time horizon can be varied

Question 12

Types of deterministic approaches NFS

Answer 12

Notional approach - RWA approach
Factor sensitivity - Effect of a single underlying factor being changed
Scenario sensitivity approach - Effect of changing a range of factors

Question 13

Merits of Factor sensitivity approach D WAP

Answer 13

• Drivers of risk understood
• Wide range of risks not considered
• Aggregation over several risk factors is difficult
• Probability of change in AL not considered

Question 14

Factors to consider when setting time horizon RRRL

Answer 14

• Regulatory constraints
• Recovery time from loss event
• Reinstate mitigation time
• Liquidity of financial instrument used