AIM 1: Distinguish Between Monte Carlo simulation and bootstrapping.
1、The Monte Carlo estimation of VAR:
A) is based on a normal distribution.
B) uses historical data.
C) is based on actual asset price data.
D) is also known as the delta-normal method.
The correct answer is A
Monte Carlo simulation involves the creation of a distribution of pricing paths given randomly generated data. It is accomplished by taking samples from a normal distribution to create distributions of potential future outcomes. For every future outcome (or scenario), a portfolio value can be generated and a corresponding value at risk measure can be estimated.
2、The bootstrapping technique of VAR:
A) is based on a normal distribution.
B) uses historical data.
C) requires lenghty computation time.
D) creates pricing paths.
The correct answer is B
Bootstrapping estimation, on the other hand, utilizes historical data to estimate future outcomes. Both methods use one of two procedures: (1) a single-step procedure and long-term data; this procedure is used when the data has the same time scale as the time horizon of interest, or (2) a multi-step procedure and short-term data to create longer term periods.
3、Which of the following statement about bootstrapping is TRUE?
A) Bootstrapping requires the time scale of the data to be equal to the time scale of interest.
B) Bootstrapping is one method for estimating VaR.
C) Bootstrapping requires a distributional assumption about the data.
D) Bootstrapping uses simulated data to estimate future outcomes.
The correct answer is B
No distributional assumptions are needed to implement bootstrapping. Bootstrapping attempts to use historical data to estimate the future.
AIM 2: Describe the implementation of Monte Carlo simulation for VAR calculations.
VaR is a commonly used risk metric. Typically VaR is estimated via a Monte Carlo simulation or via a bootstrapping method. Implementation of the Monte Carlo simulation for VaR includes all of the following EXCEPT:
I. first a distribution is selected from common statistical methods.
II. samples are made from a Normal distribution and used to build a distribution of future events.
III. hyperparameters are then inserted into the estimation model.
IV. for each event a pricing model is used to determine asset/portfolio values and then approximate VaR.
A) II and IV only.
B) I only.
C) I, II, III, and IV.
D) I and III only.
The correct answer is D
Statement I is incorrect. Random numbers are generated. Statement III is incorrect. Models need not be hierarchical in nature.
AIM 3: Identify the distribution of maxima and minima.
1、Which of the following statements about extreme value theory (EVT) is FALSE?
A) EVT can be used to model everyday occurrences.
B) Cluster analysis is appropriate for financial data with time dependency.
C) POT models determine the cut-off between typical and extreme values.
D) EVT focuses on data that is generally considered outliers.
The correct answer is A
EVT models are appropriate for low probability, high impact events; not everyday occurrences.
2、Extreme value theory can assist with VAR calculations by providing better probability estimates of extreme losses than those indicated by a standard normal distribution. Using the generalized Pareto distribution (GPD), the parameter that indicates the fatness of tails is the:
A) threshold level, μ.
B) scaling parameter, b.
C) slope coefficient, b.
D) shape parameter, ξ.
The correct answer is D
A positive shape parameter, ξ, indicates fat tails.
3、The generalized extreme value (GEV) distribution is useful for: I. estimating VAR. II. stress testing. III. estimating correlation. IV. backtesting.
A) I, II, III, and IV.
B) I and III only.
C) I only.
D) II only.
The correct answer is D
The GEV distribution describes the distribution of the maximums from a large sample of identically distributed observations. It’s not particularly useful for VAR estimation since VAR does not consider the distribution of the maximum, but it is useful for stress testing. GEV also has nothing to do with correlations and would not be used for backtesting to see if a VAR model was effective.
4、Extreme value theory (EVT) can assist with value at risk (VAR) calculations by providing better probability estimates of observing extreme losses than that indicated by a standard normal distribution because empirical distributions exhibit fat tails. If one uses the generalized Pareto distribution (GPD) method to generate parameter estimates for the shape parameter, fat tails will indicate a:
A) positive parameter estimate and VAR calculations that are too small.
B) positive parameter estimate and VAR calculations that are too large.
C) negative parameter estimate and VAR calculations that are too small.
D) negative parameter estimate and VAR calculations that are too large.
The correct answer is A
Fat tails will generate a positive shape parameter, which indicates that VAR estimates are probably too small.
5、Block maxima disaggregates the data into:
A) equal sized, independent subsamples.
B) unequal sized, independent subsamples.
C) unequal sized, dependent subsamples.
D) equal sized, dependent subsamples.
The correct answer is A
The block maxima approach determines the maxima for mutually exclusive, equal sized, independently distributed subsamples of data.
6、Which of the following statements is TRUE?
A) The semi-parametric peaks-over-threshold utilizes the generalized Pareto distribution.
B) Block maxima are a semi-parametric peaks-over-threshold model.
C) Tail events are more likely under the generalized Pareto distribution relative to a normal distribution.
D) The generalized Pareto distribution provides a non-linear estimate of the tail.
The correct answer is C
Generalized Pareto distribution generates a linear approximation to the tail distribution. Block maxima and peaks-over-threshold are two general classes of extreme value modeling. The generalized Pareto distribution is a parametric approach.
7、All of the following are extreme value theory models EXCEPT:
A) block Maxima.
B) semi-parametric peaks-over-threshold.
C) generalized Pareto distribution.
D) stressed VAR.
The correct answer is D
Stressed VAR is not an EVT model.
8、Under the Extreme Value Theorem (EVT), which of the following is (are) TRUE regarding the modeling of market risk?
I. The three key resulting distributions are: Gumbel, Weibull, and Frechet.
II. EVT permits the analysis of maxima and minima distributions.
III. EVT is does not account for “heavy” tails observed in the market place.
IV. EVT is dependent upon the normal distribution.
A) I and III only.
B) I only.
C) None of these.
D) I and II only.
8、Under the Extreme Value Theorem (EVT), which of the following is (are) TRUE regarding the modeling of market risk?
I. The three key resulting distributions are: Gumbel, Weibull, and Frechet.
II. EVT permits the analysis of maxima and minima distributions.
III. EVT is does not account for “heavy” tails observed in the market place.
IV. EVT is dependent upon the normal distribution.
A) I and III only.
B) I only.
C) None of these.
D) I and II only.
The correct answer is D
Statement III is incorrect because EVT allows for “heavy” tails as we see in the market place. Statement IV is incorrect because EVT is not dependent upon the normal distribution.
9、Which of the following statements is (are) FALSE concerning extreme value distributions?
Using block maxima, local maxima may not resemble extreme observations.
Small tails reduce the variance of the estimator in cluster analysis.
The two classes of EVT models are block maxima and generalized extreme value distribution.
A) I and II only.
B) I and III only.
C) I, II, and III.
D) II and III only.
The correct answer is D
Small tails decrease the number of extreme observations increasing the variance. Block maxima and peaks-over-threshold are the two classes of EVT distributions.
10、Extreme value theory (EVT) can assist with value-at-risk (VAR) calculations by providing better probability estimates of observing extreme losses than that indicated by a standard normal distribution because:
A) the observed empirical distribution of most asset returns tends to be platykurtic.
B) extreme losses appear to occur less frequently than indicated by a normal distribution.
C) extreme losses appear to occur more frequently than indicated by a normal distribution.
D) EVT is the most efficient method for estimating extreme losses.
The correct answer is C
Extreme losses appear to occur with a higher frequency than indicated by a normal distribution. EVT has been shown to generate more realistic probability estimates for extreme losses than a normal distribution.
11、Under the Extreme Value Theorem (EVT), which of the following is (are) TRUE regarding the modeling of market risk?
I. The three key resulting distributions are: Lognormal, Weibull, and Pareto.
II. EVT permits the analysis of maxima distributions.
III. EVT does nto account for "heavy" tails observed in the market place.
IV. EVT is dependent upon the normal distribution.
A) I and IV only.
B) None of these.
C) I and II only.
D) I and III only.
The correct answer is B
Gumbel, Weibull, and Frechet are common results. EVT allows for analysis of maxima and minima. EVT allows for “heavy” tails as we see in the market place. EVT is not dependent upon the normal distribution.
AIM 4: Calculate the peaks over threshold.
1、The Peaks Over Threshold (POT) approach serves as a basis for an expanded model of risk estimation. Which of the following statements are false regarding POT?
I. Under the POT method, in the case of “fat” tails, not all moments are defined.
II. POT is often estimated with a Generalized Pareto Distribution.
A) Both I and II.
B) Neither I nor II.
C) I only.
D) II only.
The correct answer is B
Both statements are correct (i.e., neither are false).
2、Which of the following is TRUE comparing VAR and extreme value theory (EVT)?
A) VAR and EVT assume normality of the return distribution.
B) Only EVT considers losses beyond a specified threshold.
C) The generalized Pareto distribution is fully parameterized by the mean and variance.
D) EVT focuses exclusively on the upper half of the return distribution.
The correct answer is B
The principal shortcoming of VAR is that it does not consider losses beyond a specified threshold.
AIM 5: Discuss the coherence property of risk measures.
1、Which of the following are properties of a Coherent risk metric?
A) Positive homogeneous.
B) All of these.
C) Monotonicity.
D) Sub-additivity.
The correct answer is B
All of these are properties of a Coherent risk metric.
2、Which of the following is a property of a coherent risk metric?
A) Sub-Additive.
B) Sub-Monotonic.
C) Positive Heterogeneous.
D) All of these.
The correct answer is A
Only Sub-Additive is a coherent risk metric.
辛苦了！
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