Deck 3: Risk Assessment and Pooling

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

Answer 1

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

Answer 2

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

Answer 3

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.

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.

Question 6

Calculate the Expected Value of the following Probability Distribution:

A) -19.6
B) -19
C) -17.8
D) -17.2

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

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.

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.

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.

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.

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.

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.

Question 14

Calculate the Expected Value of the following Probability Distribution:

A) -4.65
B) -5.35
C) -4.67
D) -5.00

Question 15

Calculate the Expected Value of the following Probability Distribution:

A) -38.2
B) -43.8
C) -44.3
D) -49.6

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

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.

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.

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.

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.

Question 21

Which of the following statements about the confidence interval is correct?

A) A confidence interval tells the insurer something about how confident it should be about the calculated risk premium.
B) A confidence interval tells the insurer something about the size of the risk pool.
C) A confidence interval tells the insurer something about how much money it has reserved in the past year to cover potential losses.
D) All of the above are correct.

Question 22

The third step in risk management is:

A) creating large enough pools to diversity risk
B) the process of the assessment of risk
C) the process of identifying risk tools
D) the process of identifying possible risks that can occur

Question 23

Why would "groom decides he doesn't want to get married" not be covered by a typical wedding insurance policy?

A) It is a catastrophic event, and insurance companies do not cover that.
B) The groom has the right to make that decision, and therefore it is not covered under a typical insurance policy.
C) It is not an independent outside event.
D) The risk pool size is too small.

Question 24

Which of the following would be most important in making the decision to provide insurance?

A) Whether or not the probability distribution is normal
B) The current market interest rate
C) Whether or not the losses are independently distributed the accident
D) All are equally important

Question 25

Which of the following statements about the confidence interval is not correct?

A) A confidence interval is based on the outcomes of the probability distribution.
B) A confidence interval is calculated by adding and subtracting the standard deviation to/from the estimate of mean expected loss.
C) A confidence interval tells the insurer something about the size of the risk pool.
D) A confidence interval tells the insurer something about how much money it needs to cover potential losses.

Question 26

The confidence interval:

A) decreases with a larger pool size
B) increases with a larger pool size
C) decreases and increases with a larger pool size
D) does not change with the pool size

Question 27

The probability distribution associated with the role of a die:

A) can be used to forecast the risk of restaurant law suits
B) is a non-normal distribution
C) is known in advance
D) can not be identified

Question 28

A insured person will generally collect on his insurance policy when:

A) he caused the event
B) the event was outside his control
C) the event affected everybody else also, for example a war
D) the event was statistically dependent upon his actions

Question 29

Which of the following is not a risk measure?

A) Standard Deviation
B) Confidence Interval
C) Variance
D) All of the above are risk measures

Question 30

Which of the following statements about the probability distributions is correct?

A) The shape of a probability distribution is not dependent on the number of observations.
B) All probability distributions are normal.
C) A non-normal probability distribution will lead to a better estimate of future losses.
D) All of the above are incorrect.

Question 31

Which of the following would be least important in making a self-insurance decision?

A) The size of the risk pool
B) Social and ethical concerns
C) Historical management policy
D) Financial ability to pay losses

Question 32

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

A) The Risk Charge represents how much an insurance company should charge for people not paying their insurance premium.
B) The Risk Charge can only be calculated when the probability distribution is normal.
C) The Risk Charge is what is added to and subtracted from the Estimated Mean to get to the Confidence Interval.
D) All of the above are incorrect.

Question 33

Which of the following statements about the exposure units and risk pooling is not correct?

A) Exposure units should not be exposed to risk in order to be added to the risk pool.
B) Risk pooling is the ability to reduce the risk of an exposure unit by creating more homogenous pool of units.
C) Risk pooling works best if the number of exposure units is small.
D) Risk pooling is the ability to reduce the risk of an exposure unit by making more accurate predictions about a large pool of units.

Question 34

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

A) Risk pooling works best if the number of parties involved is small.
B) Risk pooling reduces the standard deviation of the loss distribution.
C) Risk pooling increases the loss probability.
D) Risk pooling can be used to increase the cost of bearing risk.

Question 35

Which of the following would not be a reason influencing whether or not an insurance company provides insurance?

A) The size of the pool
B) The current market interest rate
C) Whether or not the losses are independently distributed
D) Whether or not the losses can financially ruin the insurance company

Question 36

If insurers didn't practice pooling, what would happen?

A) They would save a lot of time and money by not having to do difficult calculations.
B) They would make a handsome profit since they would get to sell a lot of insurance to a lot of people.
C) The insurance mechanism would become unfeasible.
D) The insurance mechanism would become the largest money-making venture in the United States.

Question 37

Given the requisites of risk pooling, which of the following exposures would make the best subject of a profitable insurance pool? Assume a premium appropriate to the exposure is charged and analyze the exposure from the insurer's standpoint.

A) Insuring all the lives of college seniors in the U.S. for $10,000 each, without an initial medical exam
B) Insuring college students against their GPA falling below a 3.0
C) Insuring all the dorms on a single college campus against property damage
D) Insuring students against the theft or disappearance of textbooks

Question 38

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

A) When the probability distribution is non-normal, risk cannot be reduced by increasing the pool size.
B) After the pool size has reached 36, risk can no longer be reduced any further.
C) Risk is reduced as the pool size increases.
D) All of the above are correct.

Question 39

What is the so-called Risk Charge?

A) Risk Charge represents how much an insurance company should charge for people not paying their insurance premium.
B) Risk Charge represents the margin of error arising from estimating an unknown variable.
C) Risk Charge represents the standard deviation of the variance.
D) Risk Charge represents how much an insurance company should charge for uncertainty.

Question 40

Which of the following statements about probability of occurrence is correct?

A) The range of values found by adding and subtracting one standard deviation to the mean of the random variable accounts for 68.26 percent of the area under the curve.
B) The range of values found by adding and subtracting two standard deviations to the mean of the random variable accounts for 68.26 percent of the area under the curve.
C) The range of values found by adding and subtracting two standard deviations to the mean of the random variable accounts for 99.74 percent of the area under the curve.
D) All of the above are incorrect.

Question 41

Risk Pooling is the ability to reduce the risk of a unit by making more accurate predictions about a large pool of units.

Question 42

One reason insurable losses must be definite is to allow measurability of the losses.

Question 43

Homogeneous Risk Characteristics refer to the concept that the parties in a pool exhibit the same level of risk.

Question 44

When assessing the financial impact of a firm's pure risks, a risk manager is interested in calculating a measure of the long-run average loss that is expected in the future.

Question 45

The formula for the confidence interval is Estimated Mean + Estimated Standard Deviation.

Question 46

If the Average Loss Severity is $457 and the Average Loss Frequency is 0.21, the Average Loss is $95.97.

Question 47

The range of values found by adding and subtracting three standard deviations to the mean of the random variable accounts for 99.74 percent of the area under the curve.

Question 48

The use of loss distributions lead to a subjective estimate of risk exposure.

Question 49

An insurance applicant dying from cancer is not likely to be able to get insurance because:

A) it is impossible to estimate the loss
B) the probability of loss is extremely high and thus the price for coverage would be uneconomical
C) the confidence interval is very high
D) the risk pool is very large

Question 50

A risk pool needs a small group of similar exposures for predictive accuracy.

Question 51

The standard deviation measures the degree to which the actual losses from a loss distribution deviate from the expected loss.

Question 52

The frequency with which losses occur and their severity are two key statistical measures for evaluating loss exposure.

Question 53

When the variance of a probability distribution is $81,000 the risk equals:

A) $900
B) $6,561,000,000
C) $284.61
D) There is not enough information to calculate the risk.

Question 54

A Risk Manager needs more information than just the loss frequency and loss severity to assess the risk exposure of their firm.

Question 55

The confidence interval increases with a larger pool size.

Question 56

When the variance of a probability distribution is $360,000, the standard deviation equals:

A) $600
B) $3,600
C) $180,000
D) $12,000

Question 57

The Risk Charge represents the error arising from estimating a known variable.

Question 58

When a probability distribution of a variable is not known, it can be estimated using prior experience.

Question 59

Why does a risk manager typically focus on the upper tail of the probability distribution?

A) The upper tail shows the amount of coverage of the risk a firm faces.
B) The upper tail shows the total risk pool.
C) The upper tail shows the confidence interval of the loss distribution.
D) The upper tail shows the sum of the estimated mean loss plus the risk charge.

Question 60

The variance is independent of the shape of the probability distribution.

Question 61

Explain why the standard deviation represents risk.

Question 62

Why is risk reduced by creating a large pool of exposure units?

Question 63

Large employers with a large number of employees often use pooling to self-insure some of their risk.

Question 64

Discuss how probability distributions are used in estimating future losses.

Question 65

What are the requirements for an "ideally" insurable group of exposures?

Question 66

How do insurers use a confidence interval?