Statistics Risk Assessment & Management 2 ā Questions and Answers
Question 1: Which statistical measure is most commonly used to quantify the spread of potential losses in a risk distribution?
- Mean
- Standard deviation (Correct answer)
- Mode
- Median
Correct answer: Standard deviation
Standard deviation measures the dispersion of outcomes around the expected value, making it the primary metric for quantifying risk spread.
Question 2: Value at Risk (VaR) at a 95% confidence level means that losses will exceed the VaR estimate in approximately what percentage of cases?
- 5% (Correct answer)
- 95%
- 50%
- 1%
Correct answer: 5%
A 95% VaR means losses exceed the threshold in 5% of scenarios ā the remaining 5% tail of the distribution.
Question 3: In risk management, Expected Shortfall (ES) improves on VaR because it:
- Is always lower than VaR
- Averages losses beyond the VaR threshold (Correct answer)
- Ignores extreme tail events
- Uses only historical data
Correct answer: Averages losses beyond the VaR threshold
Expected Shortfall (also called CVaR) computes the mean of all losses exceeding the VaR cutoff, capturing tail severity that VaR ignores.
Question 4: A risk analyst models losses with an exponential distribution. If the mean loss is $200,000, what is the probability that a single loss exceeds $400,000?
- eā»Ā² ā 13.5% (Correct answer)
- eā»Ā¹ ā 36.8%
- 50%
- eā»ā°Ā·āµ ā 60.7%
Correct answer: eā»Ā² ā 13.5%
For an exponential distribution, P(X > 2Ī¼) = e^(ā2) ā 0.135, because the rate Ī» = 1/Ī¼ and P(X > t) = e^(āĪ»t).
Question 5: Which technique randomly samples from probability distributions to simulate thousands of possible risk outcomes?
- Bootstrapping
- Monte Carlo simulation (Correct answer)
- Regression analysis
- Bayesian updating
Correct answer: Monte Carlo simulation
Monte Carlo simulation generates large numbers of random scenarios by sampling input distributions, producing an empirical loss distribution.
Question 6: In a risk matrix, a risk with HIGH probability and LOW impact would typically be categorized as:
- Critical risk requiring immediate mitigation
- Moderate risk to monitor and control (Correct answer)
- Negligible risk to accept
- Catastrophic risk to transfer
Correct answer: Moderate risk to monitor and control
High-probability, low-impact risks fall in the moderate zone ā they occur often but losses are manageable, warranting monitoring rather than urgent action.
Question 7: Beta in the Capital Asset Pricing Model (CAPM) is a measure of:
- Total portfolio variance
- Systematic (market) risk relative to the market (Correct answer)
- Idiosyncratic firm-specific risk
- Credit default probability
Correct answer: Systematic (market) risk relative to the market
Beta quantifies how much an asset's returns move relative to market returns, measuring non-diversifiable systematic risk.
Statistics Risk Assessment & Management 2
Which statistical measure is most commonly used to quantify the spread of potential losses in a risk distribution?