Quantitative Analysis Flashcards
7 cards from real FRM practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Quantitative Analysis flashcards as text
Which VaR methodology directly uses actual historical returns without assuming a specific distribution?
Answer: Historical Simulation VaR
Historical Simulation VaR uses the actual sequence of historical returns to generate a loss distribution, making no parametric assumption about the return distribution.
Expected Shortfall (ES) is considered superior to VaR primarily because:
Answer: It measures the average loss in the tail beyond the VaR threshold and is sub-additive
ES captures the average severity of tail losses beyond the VaR cutoff and satisfies sub-additivity, meaning portfolio ES ≤ sum of individual ESs, unlike VaR.
If a portfolio has a 1-day 95% VaR of $1 million, the approximate 10-day 95% VaR (assuming i.i.d. returns) is:
Answer: $3.16 million
Using the square-root-of-time rule, 10-day VaR = 1-day VaR × √10 = $1M × 3.162 ≈ $3.16 million.
A key advantage of Monte Carlo simulation for VaR estimation over parametric methods is that it:
Answer: Can model complex non-linear payoffs and non-normal distributions
Monte Carlo simulation can incorporate non-linear instruments like options, fat-tailed distributions, and complex correlations, making it far more flexible than parametric methods.
Backtesting a VaR model involves:
Answer: Comparing predicted VaR against actual daily P&L to count exceptions
Backtesting counts how often actual losses exceed the predicted VaR (exceptions) over a historical period to assess whether the model is accurately calibrated.
A copula function in quantitative risk modeling is used to:
Answer: Model the joint dependency structure of risk factors independently of their marginal distributions
A copula separates the dependency structure from the marginal distributions, enabling flexible modeling of joint tail behavior and non-linear dependence between risk factors.
Which VaR calculation approach assumes normally distributed returns and computes risk using mean, standard deviation, and a z-score?
Answer: Delta-Normal (parametric) method
The Delta-Normal parametric method assumes normally distributed returns and computes VaR as: VaR = μ − z × σ, where z is the standard normal quantile for the chosen confidence level.