AIM 1: Describe the loss distribution approach, its components, and its estimation.

1、The mass of the tail of a distribution is key when computing VaR. When estimating the operational VaR, one only needs to focus on the right tail. This concept is important because:

Basel II standards require VaR calculations based exclusively on the tail of the severity distribution.
for high confidence intervals it suggests that operational risk is dependent upon only the tail of the severity distribution.
because frequency is only input as an expectation, it is not essential to calibrate a particular counting process.
symmetry of the distributions.
A) II and III only.
 
B) I, II, and III only.
 
C) II only.
 
D) IV only.

The correct answer is A

For high confidence intervals it suggests that operational risk is dependent upon only the tail of the severity distribution. Frequency is only input as an expectation, it is not essential to calibrate a particular counting process.

2、Which of the following statements is (are) TRUE regarding the loss distribution approach (LDA)?

It is the most popular way to satisfy the AMA standards.
It is commonly used by endowments and foundations.
It requires an estimate of the probability distribution function.
It cannot be used if the frequency process is Poisson.
A) II and IV only.
 
B) I only.
 
C) I and III only.
 
D) None of these.

The correct answer is B

Statement I is correct. LDA is the most common way to satisfy AMA standards.

3、The most popular method to be in compliance and satisfy the AMA standards is:

A) Value at Risk.
 
B) loss distribution approach.
 
C) basic risk estimation.
 
D) total risk method.

The correct answer is B

Loss Distribution Approach (LDA) is the most popular method.

A) basic indicator approach.
 
B) standardized approach.
 
C) advanced measurement approach.
 
D) limited distribution approach.
 

The correct answer is C

Advanced measurement approach offers the greatest flexibility.

5、In the LDA process, the severity process describes:

A) the term of the operational loss.
 
B) the distribution of the operational loss.
 
C) the size of the operational loss.
 
D) the number of losses that occur.

The correct answer is C

The severity process describes the magnitude, or size, of the loss.

6、In the LDA process, the frequency process describes:

A) the number of losses that occur.
 
B) the distribution of the operational loss.
 
C) the size of the operational loss.
 
D) the term of the operational loss.

The frequency describes the number of loss events that occur over a specific time interval.

7、As a result of the Basel standards every bank must now, calculate explicit capital charges to cover operational risk by one of three approaches: the basic indicator approach (BIA), the standardized approach (SA), and the advanced measurement approach (AMA). Which of the following statements are TRUE with respect to the operational risk approaches?

In practice the AMA approach is the most flexible approach for operational risk.
The most popular method to satisfy the AMA standards is the loss distribution approach (LDA).
The AMA method allows a bank to build its own operational risk model and measurement system, comparable to market risk standards.
BIA is widely used in insurance and actuarial science.
A) I, II, and III only.
 
B) I, II, and IV only.
 
C) II and IV only.
 
D) None of these.

The correct answer is A

LDA is widely used in insurance and actuarial science.

It is the most popular way to satisfy the AMA standards.
It is commonly used by insurance companies.
It requires an estimate of the probability distribution function.
It cannot be used if the frequency process is Poisson.
A) None of these.
 
B) I and II only.
 
C) II and IV only.
 
D) I and III only.
 

The correct answer is B

An estimate of the PDF is not needed. Poisson is a common frequency process.

AIM 2: Define various forms of subexponential severity distributions.

1、The sub exponential distribution:

A) is modeled with lots of small losses.
 
B) has tails that decay faster than the exponential distribution.
 
C) is similar to the normal distribution.
 
D) is heavy tailed in nature.

The correct answer is D

A key feature of the sub exponential distribution is that its tails decay more slowly than the exponential distribution. Hence, the correct answer is that they are heavy tailed in nature.

2、Three of the most common sub exponential distributions are:

A) Lognormal, Weibull, and Pareto.
 
B) Normal, Weibull, and Gamma.
 
C) Normal, Weibull, and Poisson.
 
D) Lognormal, Weibull, and Poisson.

The correct answer is A

As defined in the reading, the most common sub exponential distributions are Lognormal, Weibul, and Pareto.

3、Empirical research suggests that most severity distributions for operational risk are extremely “heavy” tailed. To be compliant with Basel II, the extreme heavy-tailed property of operational losses needs to be accounted for in the choice of the severity distribution. Which of the following statements are TRUE with respect to severity distributions?

Three well-known heavy-tailed distributions are the Poisson, Weibull, and the Pareto distribution.
Of the Poisson, Weibull, and Pareto distribution only the Pareto is consider subexponential.
Subexponential distributions are distinct statistically in that their tails decay more slowly than any exponential distribution.
Heavy-tailed distributions have large, but well-defined means and variances.
A) II only.
 
B) I only.
 
C) All of these.
 
D) III only.
 

The correct answer is D

Poisson is not considered a “heavy” tailed distribution. The Poisson, Weibull, and Pareto distributions are all in the subexponential class. The natural logarithm of 1 is 0, since e0 = 1.

AIM 3: Discuss the implications the closed-form operational VAR has on the general class of LDA models.

1、Operational losses are best approximated with:

A) exponential distributions.
 
B) skewed distributions.
 
C) heavy tailed distributions.
 
D) bimodal distributions.

The correct answer is C

Operational losses are best captured with heavy-tailed distributions as these losses tend to be sizable.

2、Past Research has shown, very conclusively, that when it comes to modeling operational risk:

heavy tailed distributions are not needed.
extreme events occur frequently enough that the mean is often undefined.
standard deviation is remarkably consistent.
standard deviations are likely undefined.
A) II and IV only.
 
B) II and III only.
 
C) I and II only.
 
D) III only.

The correct answer is A

Heavy tailed distributions are needed. Standard deviation is often undefined.

AIM 4: Explain the time-scaling in the Pareto Severity Model and its implications.

1、In the case of the Pareto-LDA model, typical values for α imply that the threat of losses due to operational risk increases very quickly, notably faster than the result of the square-root-rule. This result suggests:

A) operational risk rapidly decreases with time.
 
B) operational risk is greatest at time, t = 0.
 
C) operational risk increases with time.
 
D) operational risk is independent of time.

The correct answer is C

As time increases operational risk increases.

2、In practice one can derive multi-period VAR measures from 1-period values by:

A) using the LDH approach.
 
B) using the square root of time rule.
 
C) multiplying the VAR measures.
 
D) adding the VAR measures.

The correct answer is B

In practice multiperiod VaR measures can be derived by using the square-root of time rule.

3、In the case of the Pareto LDA approach we obtain a _______ rule for operational risk

A) sum of VAR.
 
B) time squared.
 
C) square root of time.
 
D) nth root of time.

The correct answer is D

In the case of a Pareto LDA model a nth root of time rule is obtained for OpVar measures.

4、In the case of OpVAR, the Pareto LDA approach implies that:

A) OpVAR is independent of time.
 
B) OpVAR increases constantly in time.
 
C) OpVAR increases exponentially in time.
 
D) OpVAR increases linearly in time.

The correct answer is C

The Pareto LDA approach implies that OpVar increases very rapidly, or exponentially, with time.

5、In the case of the Pareto-LDA model, typical values for α imply that the threat of losses due to operational risk increases very quickly, notably faster than the result of the square-root-rule. This result suggests?

A) Operational risk increases linearly with time.
 
B) Operational risk increases exponentially with time.
 
C) Operational risk is greatest at time, t = 0.
 
D) Operational risk is independent of time.

The correct answer is B

Time tends to magnify operational risk. Operational risk grows with time. As time increases operational risk increases exponentially.