Statistics Risk Assessment & Management 5 — Questions and Answers
Question 1: An analyst uses a 99% one-day VaR of $1 million. Under Basel III, the minimum capital requirement multiplier applied to this VaR for market risk is typically:
- 1×
- 3× (Correct answer)
- 10×
- 0.5×
Correct answer: 3×
Basel III requires banks to hold capital equal to at least 3 times the 99% 10-day VaR (the multiplication factor) to buffer against model risk.
Question 2: Which graphical tool plots cumulative probability of loss on one axis and loss amount on the other to display the full loss distribution?
- Gantt chart
- Probability-Impact matrix
- Cumulative Distribution Function (CDF) plot (Correct answer)
- Pareto chart
Correct answer: Cumulative Distribution Function (CDF) plot
A CDF plot of losses shows, for any loss value, the probability that losses will not exceed that amount, enabling VaR and ES to be read directly.
Question 3: In Failure Mode and Effects Analysis (FMEA), the Risk Priority Number (RPN) is calculated as:
- Severity + Occurrence + Detection
- Severity × Occurrence × Detection (Correct answer)
- Severity × Probability of Failure
- Detection / (Severity × Occurrence)
Correct answer: Severity × Occurrence × Detection
RPN = Severity × Occurrence × Detection, where each factor is rated on a scale (typically 1–10), with higher scores indicating higher priority for corrective action.
Question 4: Operational risk under Basel II/III is defined as the risk of loss from:
- Changes in interest rates and exchange rates
- Counterparty credit defaults on derivatives
- Inadequate processes, people, systems, or external events (Correct answer)
- Systemic collapse of the financial system
Correct answer: Inadequate processes, people, systems, or external events
The Basel Committee defines operational risk as arising from failures in internal processes, human error, system failures, or external events such as natural disasters.
Question 5: A loss severity distribution is modeled with a lognormal model. If the underlying normal variable has μ = 10 and σ = 1, the median loss is:
- e¹⁰ ≈ $22,026 (Correct answer)
- e¹⁰·⁵ ≈ $36,315
- e¹¹ ≈ $59,874
- e⁹ ≈ $8,103
Correct answer: e¹⁰ ≈ $22,026
For a lognormal distribution, the median equals e^μ (not e^(μ+σ²/2), which is the mean), so median = e^10 ≈ $22,026.
Question 6: Which approach to quantifying risk involves subject-matter experts assigning probabilities when historical data is scarce?
- Frequentist probability estimation
- Bayesian subjective probability elicitation (Correct answer)
- Maximum likelihood estimation
- Bootstrapped resampling
Correct answer: Bayesian subjective probability elicitation
Bayesian subjective probability elicitation converts expert judgment into prior probability distributions when empirical frequency data is unavailable.
Question 7: A company buys a put option on its raw material to hedge against price spikes. This risk management strategy is best classified as:
- Risk avoidance
- Risk acceptance
- Risk transfer via financial derivative (Correct answer)
- Risk mitigation through process improvement
Correct answer: Risk transfer via financial derivative
Using derivatives like put options to cap downside exposure transfers the financial risk of adverse price movements to the option seller.
Statistics Risk Assessment & Management 5
An analyst uses a 99% one-day VaR of $1 million.
Under Basel III, the minimum capital requirement multiplier applied to this VaR for market risk is typically: