Question 1

Which of the following is not a benefit of forecasting future losses?
A) Better estimate of insurance costs
B) More appropriate budgeting of financial impact of the losses
C) Better selection of optimal risk-handling techniques
D) Better monitoring of trends and impact of change in trend

Accepted Answer

A

Question 2

The Expected Value of a probability distribution is calculated by:
A) adding up all expected losses
B) adding up all expected losses and dividing the result by the number of observations
C) multiplying the expected losses with their probability and dividing the result by the number of observations
D) multiplying the expected losses with their probability and calculating the sum of all outcomes

Accepted Answer

The Expected Value of a probability distribution is calculated by multiplying each possible outcome by its probability and then summing all these values. This is accurately described in option D.

Question 3

Risk Assessment:
A) is the first step in the Risk Management Process
B) is the process of identifying the broad range of risk exposures
C) is the process of estimating the financial impact of each risk
D) deals with risk identification

Accepted Answer

C

Question 4

If the Average Loss Severity is $1,150 and the Average Loss Frequency is 0.12, what is the Average Loss?
A) $9,583.33
B) $104.35
C) $138
D) There is not enough information to calculate the Average Loss.

Accepted Answer

The answer of If the Average Loss Severity is $1,150...

Question 5

Which of the following statements about the average loss severity and average loss frequency is not correct? A) The average loss severity represents the average size of losses that might occur. B) The average loss frequency represents the average number of losses that might occur. C) Both the average loss severity and the average loss frequency are outside the control of the risk manager. D) The average loss can be estimated by multiplying the average loss severity with the average loss frequency.

Accepted Answer

The average loss severity and the average loss frequency can be influenced by the risk manager through various risk management techniques such as loss control and loss financing.

Question 6

Calculate the Expected Value of the following Probability Distribution: 
A) -19.6
B) -19
C) -17.8
D) -17.2

Accepted Answer

The answer of Calculate the Expected Value of the following...

Question 7

A random variable:
A) is a variable whose future value is known with certainty
B) can be given a probability of occurrence by the risk manager
C) is completely outside the control of the risk manager
D) is not measurable

Accepted Answer

A random variable is a variable whose future values are uncertain and depend on some probability distribution. It cannot be known with certainty. The probability of occurrence of a random variable can be assessed by the risk manager, which makes option B the correct choice. Option C is not always true, as there may be some ways in which the risk manager can influence or control a random variable. Option A is incorrect, as we have just discussed, and Option D is also incorrect as random variables are measurable using statistical tools.

Question 8

Which of the following statements about the Probability Distribution is correct?
A) A Probability Distribution deals with random variables.
B) A Probability Distribution shows the probability of occurrence of a variable.
C) A Probability Distribution shows all possible outcomes of a variable.
D) All of the above are correct.

Accepted Answer

A Probability Distribution deals with random variables and shows the probability of occurrence of a variable. It also shows all possible outcomes of a variable. Therefore, all the given statements are correct.

Question 9

Which of the following statements about the standard deviation is correct?
A) The standard deviation measures the expected loss for the firm.
B) The standard deviation is calculated by taking the square root of the variance.
C) The standard deviation is a subjective measure of risk.
D) All of the above are correct.

Accepted Answer

The standard deviation is calculated by taking the square root of the variance. Option A is incorrect because the standard deviation is a measure of the variability in the data, not the expected loss. Option C is incorrect because the standard deviation is an objective measure of risk based on the actual data, not subjective. Option D is incorrect because options A and C are incorrect.

Question 10

If the Average Loss Severity is $925 and the Average Loss Frequency is 0.17, what is the Average Loss?
A) $183.78
B) $157.25
C) $5,441.18
D) There is not enough information to calculate the Average Loss.

Accepted Answer

The formula for the calculation of average loss is: 
Average Loss = Average Loss Severity x Average Loss Frequency

Putting the values given in the question, we get:

Average Loss = $925 x 0.17 = $157.25

Therefore, the answer is B.

Question 11

Which of the following is not a characteristic of a Probability Distribution?
A) The probability of occurrence of a variable is assigned randomly.
B) The maximum probability for any one outcome will be less than 1.
C) The minimum probability for any one outcome will be greater than 0.
D) The sum of all probabilities must be equal to 1.

Accepted Answer

Probability distribution is a function that assigns probabilities to each possible outcome of a random variable. The probability of occurrence of a variable is not assigned randomly, but it is based on the nature of the process being modeled or observed. The other options are characteristics of probability distributions. The sum of probabilities must be equal to 1, as the total probability of all possible outcomes must be 1. The minimum probability must be greater than 0, as it is not possible for an outcome to have a negative probability. The maximum probability for any one outcome cannot exceed 1, as the probability cannot be greater than the total probability of all possible outcomes.

Question 12

Which of the following statements about the risk pooling is correct?
A) Risk pooling works best if the parties involved have heterogeneous risk characteristics.
B) Risk pooling works best if the number of parties involved is small.
C) Risk pooling works best if the loss experience of the parties involved is statistically dependent.
D) Risk pooling, assuming some assumptions are met, reduce overall risk.

Accepted Answer

Risk pooling, assuming some assumptions are met, reduces overall risk. This is because pooling risks across a larger group of individuals or entities allows for the sharing of potential losses, which spreads the risk and reduces the impact on any one party. This is the basis for insurance and other risk-sharing mechanisms. Heterogeneous risk characteristics and statistically dependent loss experience can also benefit from risk pooling, but they are not the most critical factors for its effectiveness. The number of parties involved can also vary depending on the context and purpose of the risk pooling.

Question 13

The Expected Value of a Loss Exposure:
A) can be used by an insurance company to calculate the insurance premium
B) can be used by a firm to save enough to cover the expected losses
C) is an estimate, and not absolute value, of future losses
D) All of the above are correct.

Accepted Answer

All of the choices are correct. The expected value of a loss exposure is an estimate of future losses and can be used by insurance companies to calculate premiums and by firms to save enough to cover the expected losses.

Question 14

Calculate the Expected Value of the following Probability Distribution: 
A) -4.65
B) -5.35
C) -4.67
D) -5.00

Accepted Answer

The answer of Calculate the Expected Value of the following...

Question 15

Calculate the Expected Value of the following Probability Distribution: 
A) -38.2
B) -43.8
C) -44.3
D) -49.6

Accepted Answer

The answer of Calculate the Expected Value of the following...

Question 16

"Independence" in an insurance pool means:
A) the bad risks pay more for insurance than good risks
B) the members of the pool exhibit the same level of risk
C) those who experience losses have their premiums raised
D) the occurrence of one event makes it neither more nor less probable that the other occurs

Accepted Answer

"Independence" refers to the statistical concept that the occurrence of one event has no impact on the probability of another event occurring. In an insurance pool, independence means that the risks of each member are not influenced by the risks of the other members, and the occurrence of a claim by one member does not increase or decrease the likelihood of claims by other members. Therefore, choice D is the correct answer.

Question 17

Which of the following statements about the expected average loss is not correct? A) The average loss is guaranteed to happen in the upcoming year. B) The average loss will be expressed in dollars. C) The average loss is a tool for risk managers to handle future risks. D) The average loss can be estimated by multiplying the average loss severity with the average loss frequency.

Accepted Answer

The expected average loss is an estimate or prediction of the average loss that may occur in the future. It is not a guarantee that the loss will definitely happen in the upcoming year.

Question 18

Which of the following statements about the standard deviation is correct?
A) The standard deviation is calculated by squaring the variance.
B) The standard deviation is a number between 0 and 1.
C) The standard deviation is a quantified measure of risk.
D) All of the above are correct.

Accepted Answer

The standard deviation is a quantified measure of risk, as it measures the amount of variability or dispersion of a set of data from its mean. Option A is incorrect because the variance is calculated by squaring the standard deviation, not the other way around. Option B is incorrect because the standard deviation can be any positive number, not just between 0 and 1.

Question 19

Which of the following statements about the loss severity distribution is correct?
A) The loss severity distribution estimates the average size of an expected loss.
B) The loss severity distribution can be used to estimate the average severity of loss if a loss occurs.
C) The loss severity distribution represents the number of losses likely to happen.
D) The loss severity distribution is measured as a percentage of loss.

Accepted Answer

The loss severity distribution estimates the probability distribution of potential loss sizes, allowing for estimation of the average severity of loss if a loss occurs. It does not represent the number of losses likely to happen or the percentage of loss. Option A is incorrect because the average size of an expected loss is estimated using the expected loss distribution.

Question 20

Which of the following statements about convolution is not correct? A) Regardless of the number of possible outcomes, risk managers still perform convolution calculations by hand. B) Convolution uses joint probabilities to estimate the combined effects of frequency and severity. C) The outcome of the calculation using convolution will be expressed in dollars. D) The total probability of all loss combinations have to add up to 1.

Accepted Answer

Risk managers typically use software to perform convolution calculations as they can involve a large number of possible outcomes and can be time-consuming to perform by hand.

Quiz 3: Risk Assessment and Pooling

Which of the following is not a benefit of forecasting future losses?

The Expected Value of a probability distribution is calculated by:

Risk Assessment:

If the Average Loss Severity is $1,150 and the Average Loss Frequency is 0.12, what is the Average Loss?

Which of the following statements about the average loss severity and average loss frequency is not correct?

Calculate the Expected Value of the following Probability Distribution:

A random variable:

Which of the following statements about the Probability Distribution is correct?

Which of the following statements about the standard deviation is correct?

If the Average Loss Severity is $925 and the Average Loss Frequency is 0.17, what is the Average Loss?

Which of the following is not a characteristic of a Probability Distribution?

Which of the following statements about the risk pooling is correct?

The Expected Value of a Loss Exposure:

Calculate the Expected Value of the following Probability Distribution:

Calculate the Expected Value of the following Probability Distribution:

"Independence" in an insurance pool means:

Which of the following statements about the expected average loss is not correct?

Which of the following statements about the standard deviation is correct?

Which of the following statements about the loss severity distribution is correct?

Which of the following statements about convolution is not correct?