Brehm

Question 1

Briefly define enterprise risk management

Answer 1

Ch 1

ERM is defined as the process of systematically and comprehensively identifying critical risks, quantifying their impacts and implementing integrated strategies to maximize enterprise value

Question 2

Briefly describe four aspects of the ERM definition

Answer 2

Ch 1

1) an effective ERM program should be a regular process, not just a one-time event
2) Risks should be considered on an enterprise basis
3) ERM focuses on risks that have a significant impact to the value of a firm
4) Risks must be quantified as best as possible. The impact of each risk should be calculated on an overall, portfolio basis and correlations with other risks should be considered.

Question 3

Briefly describe four risks that an insurer faces

Answer 3

Ch 1

1. Insurance hazard - risk assumed by insurer in exchange for premium. Consists of underwriting risk, accumulation/cat risk, and reserve risk.
2. Asset - risk in the insurer’s asset portfolio related to volatility in interest rates, foreign exchange rates, equity prices, credit quality and liquidity
3. Operational - risk associated with the execution of the company’s business. For example, risks include the execution of IT systems, policy service systems, etc.
4. Strategic - risk associated with making the wrong or right strategic choices. In other words, it is the risk of choosing the wrong plan, given the current and expected market conditions.

Question 4

Briefly describe the four steps in the ERM process

Answer 4

Ch 1

1. Diagnose - company conducts a risk assessment to determine material risks that exceed a company-defined threshold
2. Analyze - risks that exceed a company threshold are modelled as best as possible
3. Implement - implement various activities to manage the risks
4. Monitor - monitor the actual outcomes of the plans implemented in the previous steps against expectations.

Question 5

Provide three characteristics of a good enterprise risk model

Answer 5

Ch 1

1. The model shows the balance between risk and reward from different strategies (such as changing the asset mix or reinsurance program)
2. The model reflects the relative importance of various risks to business decisions
3. The model includes mathematical techniques to reflect the relationships among risks (dependencies)

Question 6

Briefly explain what may happen if a firm employs a weak enterprise risk model

Answer 6

Ch 1

Models without the good characteristics of an ERM model often exaggerate certain aspects of risk while underestimating others. This can lead to overly aggressive or overly cautious corporate decision making

Question 7

Briefly describe four types of parameter risk

Answer 7

Ch 1

1. Estimation risk - misestimation of model parameters due to imperfect data
2. Projection risk - refers to changes over time and the uncertainty in the projection of these changes
3. Event risk - refers to situations in which there is a causal link between a large unpredicted event (outside of the company’s control) and losses to the insurer.
4. Systematic risk - refers to risks that operate simultaneously on a large number of individual policies. Thus, they are non diversifying and do not improve with added volume.

Question 8

a) Provide an example of event risk
b) Provide an example of systematic risk

Answer 8

Ch 1

a) latent exposures such as asbestos
b) inflation

Question 9

Provide three sources of uncertainty in catastrophe models

Answer 9

Ch 1

1. Uncertainty relating to the probabilities of various events
2. Uncertainty relating to the amount of insured damage caused by each event
3. Uncertainty related to data quality

Question 10

Briefly describe a key aspect of asset modeling

Answer 10

Ch 1

A key aspect of modelling is modelling scenarios consistent with historical patterns.

When generating scenarios against which to test a insurer’s strategy, the more probably scenarios should be given more weight.

Question 11

Provide four reasons for holding sufficient capital

Answer 11

Ch 1

Capital must be sufficient to:

• sustain current underwriting
• provide for adverse reserve changes
• provide for declines in assets
• support growth -satisfy regulators, rating agencies, and shareholders

Question 12

Briefly describe four common approaches for setting capital requirements

Answer 12

Ch 1

1. holding enough capital so that the probability of default is remote
2. holding enough capital to maximize the insurer’s franchise value. Franchise value includes an insurer’s balance sheet, customer base, agency relationships, reputation, etc.
3. holding enough capital to continue to service renewals
4. holding enough capital so that the insurer not only survives a major cat but thrives in its aftermath.

Question 13

Provide four advantages of using economic capital for an ERM analysis

Answer 13

Ch 2

1. Provides a unifying measure for all risks across an organization
2. More meaningful to management than risk-based capital or capital adequacy ratios
3. Forces the firm to quantify the risks it faces and combine them into a probability distribution
4. Provides a framework for setting acceptable risk levels for the organization as a whole AND for individual business units

Question 14

An insurer is currently holding capital at the 1-in-4256 VaR level. Given this information, explain why the insurer might select the 1-in-4000 VaR as its target capital level.

Answer 14

Ch 2

The insurer might choose the 1-in-4000 VaR because it is a round number AND because it is slightly less than the current capital level.

Question 15

a) Provide two disadvantages of using standard deviation to measure risk.
b) For each disadvantage above, briefly describe an alternative risk measure that addresses the disadvantage.

Answer 15

Ch 2

Part a:

1. Favorable deviations are treated the same as unfavorable ones
2. As a quadratic measure (i.e. based on the second moment), it may not adequately capture market attitudes to risk

Part b:

1. Semistandard deviation – only uses unfavorable deviations
2. Skewness – since this uses a higher moment, it might better capture market attitudes

Question 16

Briefly describe five types of tail-based risk measures.

Answer 16

Ch 2

• VaR – percentile of the probability distribution
• TVaR (tail value at risk) – expected loss at a specified probability level and beyond
• XTVaR (excess tail value at risk) – calculated as TVaR minus the overall mean
• EPD (expected policyholder default) – calculated by multiplying (TVaR – VaR) by the complement of the specified probability level
• Value of default put option – when capital and/or reinsurance is exhausted, the firm has the right to default on its obligations and put the claims to the policyholders. The market value of this risk is the value of the default put option. It is usually estimated using options pricing methods

Question 17

Briefly describe probability transforms.

Answer 17

Ch 2

Probability transforms measure risk by shifting the probability towards the unfavorable outcomes and then computing a risk measure with the transformed probabilities

Question 18

TVaR is often criticized because it is linear in the tail. Briefly describe a probability transform that can be used to overcome this criticism.

Answer 18

Ch 2

Under transformed probabilities, TVaR becomes WTVaR (weighted TVaR). This is NOT linear in the tail and considers a loss that is twice as large to be more than twice as bad

Question 19

Briefly describe generalized moments.

Answer 19

Ch 2

Generalized moments are expectations of a random variable that are NOT simply powers of that variable

Question 20

Describe how the following things affect the amount of capital held by an insurance company:

• Customer reaction
• Capital requirements of rating agencies
• Comparative profitability of new and renewal business

Answer 20

Ch 2

• Customer reaction – some customers care deeply about the amount of capital being held by insurers and/or the financial rating of an insurer. Oftentimes, declines in financial ratings can lead to declines in business
• Capital requirements of rating agencies – different rating agencies require different amounts of capital to be held by an insurer
• Comparative profitability of new and renewal business – renewal business tends to be more profitable due to more informed pricing and underwriting. Thus, it is important to retain renewal business. If renewals comprise 80% of the book, then the insurer should be able to maintain 80% of its capital in a bad year. In this case, the insurer should hold enough capital so that 20% of its capital could cover a fairly adverse event

Question 21

Briefly describe what it means for a risk decomposition method to be “marginal.”

Answer 21

Ch 2

Marginal means that the change in overall company risk due to a small change in a business unit’s volume should be attributed to that business unit

Question 22

Provide two reasons why the marginal property is desirable.

Answer 22

Ch 2

• it links to the financial theory of “pricing proportionality to marginal costs”
• It ensures that when a business unit with an above-average ratio of profit to risk increases its volume, then the overall company ratio of profit to risk increases as well

Question 23

Describe two required conditions for a marginal decomposition.

Answer 23

Ch 2

• Works when business units can change volume in a homogeneous fashion
• Works when the risk measure is scalable. This means that multiplying the random variable by a factor multiplies the risk measure by the same factor (p(aY ) = ap(Y )). This is also known as homogenous of degree 1

Question 24

a) In most cases, firms allocate capital directly. Briefly describe how a firm can allocate the cost of capital.
b) Explain how a business unit’s right to access capital can be viewed as a stop-loss agreement.
c) Provide one approach for calculating the value of the stop-loss agreement.

Answer 24

Ch 2

Part a: Set the minimum profit target of a business unit equal to the value of its right to call upon the capital of the firm. Then, the excess of the unit’s profits over this cost of capital is added value for the firm. Essentially, we are allocating the overall firm value (rather than the cost of capital) to each business unit

Part b: Since the business unit has the right to access the insurer’s entire capital, it essentially has two outcomes – make money or break-even. This is how a stop-loss agreement works as well

Part c: Calculate the expected value of a stop-loss for the business unit at the break-even point

Question 25

Provide two disadvantages of leverage ratios.

Answer 25

Ch 2

They do not distinguish among business classes

They do not incorporate risks other than underwriting risks

Question 26

Briefly describe how IRIS ratios are used to measure firm health.

Answer 26

Ch 2

For each ratio, a range of reasonable values is determined. Any company that has four or more ratios that do not fall within their corresponding reasonable ranges are considered to be at risk and warrant regulatory scrutiny

Question 27

a) Briefly describe how risk-based capital (RBC) models differ from leverage ratios.
b) Provide the four main sources of risk contemplated in RBC models.
c) Briefly describe how RBC models quantify these sources of risk.

Answer 27

Ch 2

Part a: Unlike leverage ratios, risk-based capital (RBC) models combine measures of different aspects of risk into a single number

Part b:

1. Invested asset risk
2. Credit risk
3. Premium risk
4. Reserve risk

Part c: Each of these risks is measured by multiplying factors by accounting values. The magnitude of the factor varies by the quality and type of asset or the line of business

Question 28

a) In terms of risk charges, fully describe one reason why a regulatory RBC model might differ significantly from a rating agency RBC model.
b) In terms of risk charges, fully describe one reason why two rating agency models might differ significantly.

Answer 28

Ch 2

Part a: Use of the models – the A.M. Best and S&P models are used to determine whether the company will be viable in the long term, while regulatory models are used to evaluate the one-year likelihood of insolvency. Thus, the rating agency models should have higher factors

Part b: Presence of a covariance adjustment – many models have covariance adjustments intended to reflect the independence of the various risk components. With this adjustment, the total required capital is less than the sum of the individual risk charges. The reduction in capital depends on the relative magnitudes of the risk charges (greater reductions occur when risk charges are similar in size)

Question 29

An actuary is tasked with projecting his firm’s balance sheet over the next 3 years. Rather than using best estimates, the actuary must project the balance sheet under 5 separate scenarios.

a) Briefly describe the difference between static scenarios and stochastic scenarios.
b) Briefly describe 2 critical features the actuary’s projection model must include.

Answer 29

Ch 2

Part a: Static scenarios are pre-defined scenarios (defined by the firm). Stochastic scenarios are generated through a stochastic process

Part b:

1. The projection model should include correlations among the various moving parts (for example, how do stock returns move with a shock event)
2. The projection model should include reflections of management responses to adverse financial results

Question 30

Briefly describe three ways in which parameter risk manifests itself.

Answer 30

Ch 3

• Estimation risk – arises from using only a sample of the universe of the possible claims to estimate the parameters of distributions
• Projection risk – arises from projecting past trends into the future
• Model risk – arises from having the wrong models to begin with

Question 31

To project future losses, an actuary fit a trend line to historical data. Using standard statistical procedures, the actuary placed prediction intervals around the projected losses. Explain why these prediction intervals may be too narrow.

Answer 31

Ch 3

Historical data is often based on estimates of past claims which have not yet settled. In the projection period, the projection uncertainty is a combination of the uncertainty in each historical point AND the uncertainty in the fitted trend line. Thus, the actuary’s prediction intervals may be too narrow due to the missing uncertainty associated with the historical data

Question 32

a) Describe two approaches for modeling claim severity trend.
b) Explain why projecting superimposed inflation and general inflation separately is advantageous.

Answer 32

Ch 3

Part a:

Approach 1: Model severity trend from insurance data with no regard to general inflation

Approach 2: Correct payment data using general inflation indices. Then, model the residual superimposed inflation. Since any subsequent projection is a projection of superimposed inflation only, a separate projection of general inflation is required

Part b: An advantage of projecting superimposed inflation and general inflation separately is that it reflects the dependency between claim severity trend and general inflation. Most enterprise risk models include a macroeconomic model, which includes future inflation rates. It is essential that the claim severity trend model reflects appropriate dependencies between claim severity trend and inflation. In doing so, inflation uncertainty is incorporated into projection risk

Question 33

Describe the primary difference between modeling projection risk using a simple trend model and modeling projection risk using a time series.

Answer 33

Ch 3

The simple trend model described earlier assumes that there is a single underlying trend rate that has been constant throughout the historical period and will remain constant in the future. A time series assumes that the future trend rate is a mean-reverting process with an autocorrelation coe cient and an annual disturbance distribution

Question 34

Compare the prediction intervals constructed using a simple trend model with those constructed using a time series.

Answer 34

Ch 3

In the simple trend model, the prediction intervals widen with time due to the uncertainty in the estimated trend rate. In the time series model, the prediction intervals widen with time as well, but the effect is more pronounced and the prediction intervals are wider. This is due to the additional uncertainty of the auto-regressive process

Question 35

Briefly describe a consequence of parameterizing a time series with limited data.

Answer 35

Ch 3

If the time period of the data is too limited to exhibit a range of behaviors, the resulting model will be limited as well, and will understate the projection risk

Question 36

Briefly describe how estimation risk is assessed using maximum likelihood estimation (MLE).

Answer 36

Ch 3

To assess estimation risk, we use the covariance matrix that results from the standard MLE procedure (based on second partial derivatives of the parameters), but we assume the parameters follow a joint log-normal distribution with that covariance matrix (works for both large and small datasets)

Question 37

Briefly describe a situation in which estimating parameters using maximum likelihood estimation (MLE) is difficult.

Answer 37

Ch 3

The best-fitting parameters can be di cult to determine if the likelihood “surface” is very flat near the maximum. When the surface is flat near the maximum, a wide range of parameter sets have almost the same likelihood. Thus, the set that maximizes the likelihood might not be any better than one that has slightly smaller likelihood

Question 38

For large datasets, the parameter distributions in the MLE procedure are multivariate normal. Briefly describe two problems that may arise when this normality assumption is used for a small dataset.

Answer 38

Ch 3

1. The standard deviations of the parameters can be high enough to produce negative param- eter values with significant probability
2. The distribution of the parameters may be heavy-tailed (the bi-variate normal is not heavy- tailed)

Question 39

When building a model, various rules and metrics are used to select the best model form. However, the selected form may still be wrong. Describe a process to overcome this problem.

Answer 39

Ch 3

1. Assign probabilities of being right to all of the better-fitting distributions. These probabilities can be based on the Hannan-Quinn Information Criteria (HQIC) metric or a Bayesian analysis
2. Use a simulation model to select a distribution from the better-fitting distributions
3. Select the parameters from the joint log-normal distribution of parameters for the selected distribution
4. Simulate a loss scenario using the parameterized distribution
5. Start the process over again with the next scenario

Question 40

Briefly describe seven types of operational risk loss events. For each event, provide one insurer- specific example.

Answer 40

Ch 4

1. Internal fraud – acts by an internal party that defraud, misappropriate property or circum- vent the law or company policy (ex. claim falsification)
2. External fraud – acts by a third party that defraud, misappropriate property or circumvent the law (ex. claim fraud)
3. Employment practices and workplace safety – acts that are inconsistent with employment, health or safety laws (ex. repetitive stress)
4. Clients, products and business practices – unintentional or negligent failure to meet a pro- fessional obligation to specific clients (ex. bad faith)
5. Damage to physical assets – loss or damage to physical assets from natural disasters (ex. physical damage to insurer’s o ce building)
6. Business disruption and system failures – disruption of business operations due to hardware and software failures, telecommunication problems, etc. (ex. processing center downtime)
7. Execution, delivery and process management – failed transaction processing or process management, and relationships with vendors (ex. policy processing errors)

Question 41

Identify three causes of P&C company impairments.

Answer 41

Ch 4

1. Deficient loss reserves
2. Underpricing
3. Rapid growth

Question 42

An actuary believes the root reason for insurer failures is reserve deficiency. State whether or not the actuary is correct. If the actuary is incorrect, provide the root reason for insurer failures.

Answer 42

Ch 4

Incorrect. The root reason for insurer failures is the accumulation of too much exposure for the supporting asset base

Question 43

A company’s plan loss ratio determination process is considered the “fulcrum” of operational risk. Fully describe a bridging model that could lead to the financial downfall of the company. In your discussion, include three explanations for the company’s downfall and explain how they are related to operational risk.

Answer 43

Ch 4

The plan loss ratio is a forecast of the loss ratio for the upcoming underwriting period. A bridging model determines the plan loss ratio by bridging forward more mature prior-year ultimate loss ratios using year-over-year loss cost and price level changes. If the Bornhuet- ter/Ferguson (BF) method is used for immature prior years with an ELR equal to the initial plan loss ratio for the year, the prior-year ultimate loss ratio will remain close to its plan loss ratio. Once older prior years begin to deteriorate, the BF ELRs for the more recent prior years will increase via the bridging. This could lead to a booked reserve deficiency, a possible rating downgrade, and a large exodus of policyholders

One explanation for the issues described above is that the plan loss ratio and reserve models could not accurately forecast the loss ratio and reserves. If competitors were NOT facing similar problems in forecasting loss ratios or reserves, then this explanation still implies that operational risk exists. Another explanation is that the plan loss ratio and reserve models could have accurately forecasted the loss ratio and reserves, but the models were not properly used. This represents an operational risk due to people failure. The final explanation is that the plan loss ratio and reserve models did accurately forecast the loss ratio and reserves, but the indications were ignored. This represents an operational risk due to process and governance failure

Question 44

a) Briefly describe cycle management
b) Provide an example of naive cycle management.

Answer 44

Ch 4

Part a: Cycle management is the management of underwriting capacity as market prices change with the underwriting cycle

Part b: An example of naive cycle management would be if a company decreased prices and ex- panded coverage in order to “maintain market share” during a soft market. As a result of these actions, price adequacy would drop. As the underwriting cycle hits bottom, the company would begin to recognize increased losses from its increased exposure. This could eventually lead to a rating downgrade, which may drive customers away and lead to stability and availability problems. The company may also become insolvent, which would lead to reliability and affordability problems

Question 45

Describe four areas that a company should focus on to ensure effective cycle management.

Answer 45

Ch 4

1. Intellectual property • An insurer’s franchise value is driven by intangible assets (i.e. intellectual property). Managers must focus on retaining top talent during periods of capacity retraction and continue to develop their skills. Managers must also maintain a presence in their core market channels
2. Underwriter incentives • Cycle management requires adaptability and responsiveness. Oftentimes, underwriter incentives are written once a year and are tied to “making the plan.” The problem is that the plan is based on one assumed market situation. Instead, plans should be fluid and change based on the market condition. If prices drop to an unacceptable level, underwriters should be able to stop writing new business without fearing that their bonuses will be in jeopardy
3. Market overreaction • The insurance industry tends to overreact to the underwriting cycle. For example, market prices and coverage tend to soften below reasonable levels. Eventually, market prices and restrictions overcorrect to the other extreme. Firms can take advantage of this overreaction by better managing their underwriting capacity. In general, firms with the most available capacity during the hard market will reap huge profits that can o↵set several years of underwriting losses
4. Owner education • Owners must understand what their financial figures mean AND what to do with that information. Under effective cycle management, financial figures may look out of line when compared with other companies. For example, premium volumes will drop under cycle management. For most firms, this is a bad sign. For an insurer practicing e↵ective cycle management, this is perfectly fine. It’s important that owners NOT make calls for increased market share during the worst possible point in the cycle

Question 46

Briefly explain how agency theory relates to operational risk.

Answer 46

Ch 4

When the interests of management and the interests of a firm’s owners diverge, management may make decisions that are not supported by the firm’s owners. This is an operational risk

Question 47

Describe a situation where the interests of the firm’s owners and management may not be aligned.

Answer 47

Ch 4

A company can agree to pay management a percentage of the increase in its market cap after five years. Although this ties manager compensation to the firm’s performance, management may be more willing to take on risky investments. In their mind, they could either end up incredibly wealthy or right where they are now. This allows them to gamble with the owner’s money

Question 48

Quantifying this operational risk can be extremely di cult. Provide an alternative solution for managing this risk.

Answer 48

Ch 4

Rather than trying to quantify this risk, we should study the incentive plan and make adjustments if necessary

Question 49

Briefly describe control self-assessment.

Answer 49

Ch 4

Control self-assessment is a process through which internal control effectiveness is examined and assessed. The goal is to provide reasonable assurance that all business objectives will be met

Question 50

Identify the primary objectives of internal controls.

(5)

Answer 50

Ch 4

1. The reliability and integrity of information
2. Compliance with policies, plans, procedures, laws, regulations and contracts
3. The safeguarding of assets
4. The economical and e cient use of resources
5. The accomplishment of established objectives and goals for operations or programs

Question 51

Briefly describe key risk indicators.

Answer 51

Ch 4

Risk indicators are measures used to monitor the activities and status of the control envi- ronment of a particular business area for a given operational risk category

Question 52

Briefly explain the difference in review frequency between self-assessments and key risk indicator measurement.

Answer 52

Ch 4

While typical control self-assessment processes occur only periodically, key risk indicators can be measured daily

Question 53

Briefly explain the difference in key risk indicators and historical losses.

Answer 53

Ch 4

Key risk indicators are forward-looking indicators of risk, whereas historical losses are backward-looking

Question 54

Provide four insurer-specific examples of key risk indicators.

Answer 54

Ch 4

1. Production – hit ratios
2. Internal controls – audit results
3. Staffng – employee turnover
4. Claims – frequency

Question 55

Describe the six sigma management framework.

Answer 55

Ch 4

Six sigma is a management framework that focuses on process redesign, project manage- ment, customer feedback, internal communication, design tradeo↵s, documentation and control plans. For the financial services industry, six sigma can help firms identify and eliminate ine ciencies, errors, overlaps and gaps in communication and coordination

Question 56

Provide three insurer processes that might benefit from the six sigma management framework.

Answer 56

Ch 4

• Underwriting – exposure data verification, exposure data capture, price component moni- toring, classification and hazard selection
• Claims – coverage verification, ALAE, use of outside counsel and case reserve setting
• Reinsurance – treaty claim reporting, coverage verification, reinsurance recoverables, dis- putes, letters of credit and collaterization

Question 57

Definitions of strategic risk focus on either strategic risk-taking OR strategic risks. Explain the difference.

Answer 57

Ch 4

Strategic risk-taking refers to intentional risk-taking as an essential part of a company’s strategic execution.

Strategic risks are unintentional risks that occur as a result of strategy planning or execution

Question 58

Briefly describe four categories of strategic risk. For each category, provide an insurance-related example.

Answer 58

Ch 4

1. Industry • Capital intensiveness, overcapacity, commoditization, deregulation, cycle volatility
   
   • Example – Insurers suffer from capital intensiveness
2. Technology • Shift, patents, obsolescence
   
   • Example – Insurers may experience technological advancement in internet distribution (issuing policies over the internet, adjusting claims over the internet)
3. Brand • Erosion or collapse
   
   • Example – Insurance products are fairly homogeneous. At the end of the day, the primary feature of an insurance product is the ability to pay the claim. However, insurers can differentiate themselves on price and service. A reputation for fair claims handling and low prices can certainly improve franchise value
4. Competitor • Global rivals, gainers, unique competitors
   
   • Example – Pricing below the market in order to grab market share is a significant risk to rival insurers

Question 59

a) Describe the traditional planning approach based on “plan estimates.”
b) Briefly describe two issues that may be caused by using the traditional approach.

Answer 59

Ch 4

Part a: The traditional planning approach is based on “plan estimates” (single point estimates). These estimates are often overly optimistic due to the need to meet overall corporate profit or premium volume targets. When actuals deviate from the overly optimistic plan, managers are reluctant to deviate from the plan numbers. This results in booked numbers that are unrealistic for far too long

Part b:

1. The firm may have an unforeseen reserve deficit
2. The overall portfolio mix (combination of written premium and corresponding written loss ratios) may not be what is intended. For example, if leadership had known that the loss ratio would be xx.x% during the planning phase, the target premium volume may have differed

Question 60

c) Describe the scenario planning approach.
d) Briefly describe two advantages of the scenario planning approach.

Answer 60

Ch 4

Part c: In contrast to the traditional planning approach, scenario planning expands the single point estimates to includes various scenarios. The likelihood and response plans for each scenario must be decided in advance. For each option, the firm would need to develop detailed plans that would be activated depending on how market conditions play out

Part d:

1. The firm thinks through responses beforehand. It can prescreen and agree on the best response. It can also save time during crises by having strategic action plans laid out and ready for use
2. Organizational inertia is reduced (i.e. the plan is more flexible). The unrealistic urge to make the numbers at all costs is reduced

Question 61

a) Briefly describe advanced scenario planning.
b) Describe how advanced scenario planning is used in asset management.
c) Provide two examples of insurer-related action rules that could be applied in response to environment changes in advanced scenario planning.

Answer 61

Ch 4

Part a: In basic scenario planning, scenarios and strategies are manually generated. In advanced scenario planning, the best strategy for each scenario is found by maximizing some performance metric and reducing downside risk

Part b:

• For each scenario, various asset strategies are tested by simulating the returns of portfolios selected by different strategies
• Each strategy is represented as a set of asset selection rules, where the rules are repeatedly applied to rebalance the portfolio in response to the environment changes as the scenario progresses
• Rebalancing measures include selling bonds, changing investment allocations and buying tax-exempt investments in response to the portfolio tax position
• The selected portfolio is the one that maximizes a performance metric (ex. net income, economic value) and reduces downside risk (ex. TVaR)

Part c:

1. Hold price in response to market price decreases. This reduces premium volume and market share
2. Allocate underwriter capacity in various ways based on anticipated price adequacy levels

Question 62

a) Briefly describe how the interaction between multiple firms might be handled in scenario planning.
b) Provide an example of how one firm’s strategy might conflict with another firm’s strategy.

Answer 62

Ch 4

Part a: In order to capture the interactions between firms during scenario planning, firms must employ agent-based modeling (ABM). ABM is a method for studying systems of interacting “agents.” These “agents” are independent entities capable of assessing the environment, selecting courses of action and using those selections to effect change on the environment

Part b:

One firm might plan (in isolation) to target a market segment identified as profitable. The firm would create detailed plans outlining the target premium volume and loss ratio. However, they fail to recognize the fact that other competitors have also noticed the profitable segment. When all of the competitors attempt to grow in the same segment, prices drop and the profitability of the line decreases

Question 63

a) Briefly describe three deterministic reserve models.
b) Explain how the deterministic reserve models described in part a. ignore calendar year effects.

Answer 63

Brehm EP#42 Part a: ⇧ Expected loss method – ultimate losses determined by multiplying earned premium times the expected loss ratio. Subtracting paid losses to date results in an estimated reserve ⇧ Link ratio method – uses development factors (or link ratios) to project losses-to-date to ultimate. Subtracting paid losses to date results in an estimated reserve ⇧ Bornhuetter/Ferguson – applies an unpaid loss percentage (determined using a development pattern) to an expected loss to determine the reserve Part b: ⇧ The methods mentioned above assume that losses for each accident year emerge based on a constant underlying development pattern. They also assume that trends have been con- stant throughout the historical period and will remain so throughout the projection period. Thus, the models ignore calendar year e↵ects and only consider the risk of misestimating development factors. In reality, trends are not usually constant and data adjustments are required. These adjustments may be necessitated by changes in case reserve adequacy or general inflation

Question 64

a) Describe the four stages of the underwriting cycle for a single LOB.
b) For each stage, state whether the primary driver is competition, data lags or both.

Answer 64

Ch 5

Part a:

1. Emergence – when a new LOB arises, data is thin, demand grows quickly and pricing is erratic. Price wars set in as competitors enter the market. Eventually, a sudden price correction occurs and weak competitors leave the market. A period of profitability follows, which brings in more competitors and “restarts” the cycle
2. Control – stabilization of the LOB is eventually gained through collective coercive control (ex. restricting entry, standardizing insurance products, stabilizing market shares, etc.). Rating bureaus and state DOIs regulate price changes
3. Breakdown – due to technological and societal changes, new types of competitors enter the market and take business away. This causes a breakdown in the control regime
4. Reorganization – this is a return to the conditions of the “emergence” phase, as a new version of the old LOB emerges

Part b:

• Emergence – dynamics driven by competition
• Control – dynamics driven by data lags
• Breakdown – dynamics driven by competition and data lags
• Reorganization – dynamics driven by competition

Question 65

Describe how data lags might influence the underwriting cycle.

Answer 65

Ch 5

Since insurance pricing involves forecasting based on historical results, there are time lags between the compilation of the historical data and the implementation of the new rates. One theory is that these time lags lead to poor extrapolation by actuaries during the ratemaking process. Due to the lags, historical data may suggest that further rate increases are needed when rates have actually returned to adequate levels

Question 66

Describe how competition might influence the underwriting cycle.

Answer 66

Ch 5

Not all competitors have the same view of the future. Inexperienced firms may have poorer loss forecasts than mature firms. As a result, inexperienced firms may drop prices based on poor forecasts. This eventually pushes the market toward lower rates

Question 67

Provide three examples of economic drivers that affect insurance profitability.

Answer 67

Ch 5

1. Insurance profitability is linked to investment income
2. The cost of capital is linked to the wider economy
3. Expected losses in some LOBs are a↵ected by inflation

Question 68

Provide two quantities that could be used as the dependent variable in an underwriting cycle model.

Answer 68

Ch 5

Potential dependent variables include loss ratio and combined ratio

Question 69

Provide four quantities that could be used as independent variables in an underwriting cycle model.

Answer 69

Ch 5

Potential independent variables include the

• historical combined ratio,
• reserves,
• inflation, and
• GNP

Question 70

Provide four sources of competitor intelligence that could be used to inform an underwriting cycle model.

Answer 70

Ch 5

Sources of information include

• customer surveys,
• trade publications,
• news scanning and
• rate filings

Question 71

a) Identify three styles of modeling the underwriting cycle.
b) The styles identified in part a. vary by three dimensions. Briefly describe the three dimensions. For each dimension, state how each style compares.

Answer 71

Ch 5

Part a:

• Soft approaches,
• behavioral modeling and
• technical modeling

Part b:

• Dimension 1 – data quantity, variety and complexity: soft > behavioral > technical
• Dimension 2 – recognition of human factors: soft > behavioral > technical
• Dimension 3 – mathematical formalism and rigor: technical > behavioral > soft

Question 72

Describe three soft approaches to modeling the underwriting cycle.

Answer 72

Ch 5

• Scenarios – A scenario is a detailed written statement describing a possible future state of the world. Multiple scenarios are used to define a space of possible future outcomes. Once this space has been defined, firms can organize their thinking about the future and how they might respond to these scenarios. These scenarios are different from “simulations”, which are more numerous and processed by computers rather than humans
• Delphi method – the Delphi method is a method of obtaining expert consensus on an issue. Experts are given background information and asked for their opinions in a questionnaire. The answers are aggregated and then summaries are given back to the participants. Based on the summaries, participants can changes their answers or articulate their reasons for disagreeing. This process is repeated until consensus is reached
• Competitor analysis – competitor analysis attempts to discern the states, motives and likely behavior of individual competing firms. It starts with a database of competitor information, key financials, news items and behavioral metrics. For predicting turns in the underwriting cycle, the goal is observing unusually profitable or distressed financial conditions over a large number of firms (basically, has the state of the market changed)

Question 73

Briefly describe how scenarios and the Delphi method feed off of each other.

Answer 73

Ch 5

A Delphi process can create a set of scenarios and scenarios can form the input to a Delphi assessment about the likelihood of each scenario

Question 74

List two types of technical models that can be built to model the underwriting cycle.

Answer 74

Ch 5

Basic Autoregressive time series General Factor model

Question 75

a) Provide four questions that must be answered before an econometric model can be built.
b) Once an econometric model is built, describe how it can be used to create an empirical distribution of possible future market equilibrium prices.

Answer 75

Ch 5

Part a:

1. How do economic factors (ex. interest rates, inflation, cost of capital) influence the supply and demand curves?
2. How does capital influence the supply and demand curves?
3. How do the supply and demand curves jointly determine price and quantity?
4. How does profitability affect external capital flows?

Part b: An econometric model is comprised of various components such as supply curves, demand curves, capital flows, inflation, etc. Each component influences the equilibrium price in specific ways. Various component changes can be simulated to create an empirical distribution of possible future equilibrium prices

Question 76

Explain why it is important to use arbitrage-free models when modeling bonds.

Answer 76

Brehm EP#60 Arbitrage-free models should be used because models will always favor arbitrage strategies if they are allowed in simulated scenarios. In reality, arbitrage opportunities do not last long and may not still be there after running the model

Question 77

State an advantage of modeling the short-term rate r.

Answer 77

Brehm EP#64 An advantage of modeling that short-term rate is that it can be used to model the entire yield curve

Question 78

a) Explain how traditional exchange rate modeling contradicts historical data. b) Provide one way to model correlation between exchange rates for di↵erent countries.

Answer 78

Brehm EP#69 Part a: ⇧ One theory of foreign exchange movement assumes that it is a stochastic process with a “drift” that, on average, equalizes government bond returns across currencies. Thus, a country with lower bond returns has a higher expected growth in the value of its currency. Historically, the opposite has been true; countries with higher interest rates have had higher growth in the value of their currency Part b: ⇧ One option for modeling foreign exchange correlation is a t-copula

Question 79

Describe the three evolutionary steps of the decision analysis process

Answer 79

Ch 2

1. Deterministic project analysis - uses a single deterministic forecast for project cash flows to produce an objective function like present value or internal rate of return. Uncertainty is handled judgmentally rather than stochastically. This analysis may demonstrate some sensitivities to critical values.

2. Risk Analysis - forecasts of distributions of critical variables are input into a Monte Carlo simulation process to produce a distribution of the present value of cash flows. Risk judgment is still applied intuitively.

3. Certainty Equivalent - expands upon risk analysis by quantifying the intuitive risk judgment using a utility function. The utility function does not replace judgment. Instead, it formalized judgment so that it can be consistently applied.

Question 80

Explain how the efficient market theory removes the need for the certainty equivalent step of the decision analysis

Answer 80

Ch 2

The certainty equivalent attempts to quantify corporate risk preferences. Since investors can diversify away firm-specific risk, it does not have a risk premium and should be ignored. Since the goal of firm managers is to maximize shareholder value, then they should ignore firm-specific risk as well.

Question 81

Provide two counterarguments to the theory that [efficient market theory removes the need for the certainty equivalent step of the decision analysis]

Answer 81

Ch 2

1. It is difficult to determine which risks are firm-specific and which risks are systematic. Attempts have been made to determine which corporate decisions affected the stock price and which did not, but the results were inconclusive.
2. Market-based risk signals (such as the risk-adjusted rate) often lack the refinement needed for managers to mitigate or hedge the risk.

Question 82

Briefly explain corporate risk tolerance

Answer 82

Ch 2

Corporate risk tolerance refers to the organization’s size, financial resources, ability, and willingness to tolerate volatility.

Question 83

Describe how an efficient frontier can be used to select an insurance portfolio.

Answer 83

Ch 2

An efficient frontier plot shows risk on the x-axis and reward (or return in this case) on the y-axis. The efficient frontier curve graphs the portfolios that maximize return for a given risk level. If the current portfolio has the same return as on of the efficient portfolios but more risk, then it is sub-optimal. In order to select one of the efficient portfolios, firms must decide how much risk they are willing to tolerate and how much reward they are willing to give up for a reduction in risk (or visa versa)

Question 84

Briefly describe how return on risk adjusted capital (RAROC) is determined

Answer 84

Ch 2

First, allocate risk capital to portfolio elements. Then, multiply the allocated risk capital by a hurdle rate to determine the RAROC for each portfolio element.

Question 85

Explain how RAROC can be used to determine if an activity is worth pursuing

Answer 85

Ch 2

Calculate the economic value added (EVA) by subtracting the RAROC from the NPV of the activity’s cash flows. If the EVA is positive, then the activity should be pursued.

Question 86

Assuming risk capital itself has been allocated, explain how cost-benefit analysis can be used to determine which risk mitigation strategies should be pursued.

Answer 86

Ch 2

Pursue activities where the benefit (ie. decrease in required capital) exceeds the costs of implementation.

Question 87

Assuming the cost of capital has been allocated, explain how cost-benefit analysis can be used to determine which risk mitigation strategies should be pursued.

Answer 87

Ch 2

Pursue activities that produce positive incremental EVA

Question 88

Explain how investment risk differs in each of the following asset/liability mixtures:

• Asset portfolio with no liabilities
• Asset portfolio with fixed duration liabilities
• Asset portfolio with variable duration liabilities

Answer 88

Ch 2

Asset portfolio with no liabilities: in this case, short term treasuries are considered risk free while high-yield assets are considered risky

Asset portfolio with fixed duration liabilities: short term treasuries have durations shorter than the liabilities and introduce reinvestment risk to the equation. If interest rates drop, total investment income may not be sufficient to cover the liabilities. If interest rates rise, longer-term investments (with durations longer than the liabilities) introduce risk as well if depressed assets have to be liquidated to fund liabilities. Duration matching would be a good strategy to neutralize interest rate changes.

Asset portfolio with variable duration liabilities: in this case, duration matching is no longer possible because the duration of the liabilities in unknown. A model incorporating asset and liability fluctuation would be needed at this point to determine the optimal investment portfolio.

Question 89

For each of the following accounting systems, explain how bonds and liabilities are valued and state whether assets successfully hedge against liabilities:

• Statutory accounting
• GAAP accounting
• Economic accounting

Answer 89

Ch 2

Stat accounting - bonds are amortized and liabilities are not discounted. Assets provide little hedging to liabilities

GAAP accounting - bonds are marked to market and liabilities are not discounted. Assets provide little hedging to liabilities

Economic accounting - bonds are marked to market and liabilities are discounted. Assets hedge against liabilities

Question 90

Briefly describe three paradigms for measuring the value of reinsurance.

Answer 90

Ch 2

1. Reinsurance provides stability: stability refers to protection of surplus, improved predictability of earnings, and customers’ assured recovery of their insured losses. The cost of this stability is the ceded premiums minus loss and expense recoveries.
2. Reinsurance frees up capital: by purchasing reinsurance, insurers are able to hold less capital. Thus, the important comparison is the amount paid to purchase the reinsurance versus the amount of capital freed up. If we calculate the ratio of amount paid to capital freed up, we obtain a return on equity number. As long as this ROE is less than the firm’s target return, the purchase was a good decision.
3. Reinsurance adds market value to the firm.

Question 91

Explain why it is misleading to analyze the distribution of the differences in underwriting results between two reinsurance companies.

Answer 91

Ch 2

Analyzing the distribution of differences is misleading, it assumes that the percentiles of each individual distribution relate to the same loss event. For example, the 99th percentile of distribution of one reinsurance program is probably not the same event as the 99th percentile of another distribution. Thus, the 99th percentile of the distribution of differences between the programs would be misleading because the percentiles of the individual distributions do not line up.

Question 92

Briefly describe a more useful way (than analyzing the distribution of the differences in two uw results bw two reinsurance companies) to compare the distributions of two reinsurance programs.

Answer 92

Ch 2

It is more useful to analyze the differences in the individual probability distributions

Question 93

Briefly explain why using combined ratio to compare reinsurance programs is misleading

Answer 93

Ch 2

If a reinsurance program has slightly stronger underwriting results but far more ceded premium, then the combined ratio will actually be worse (even though the absolute underwriting income is better)

Question 94

Briefly describe two classes for required capital

Answer 94

Ch 2

1. Theoretical models - those that derive required capital and changes in it based on the calculated risk metrics from the enterprise risk model (such as VaR, TVaR, etc)
2. Practical models - those that derive required capital based on rating agencies (ex. BCAR, S&P CAR), regulatory requirements (ex. RBC, ICAR), or actual capital.

Question 95

a) Identify and briefly describe one disadvantage of using practical models for required capital.
b) Briefly describe how this disadvantage can be overcome

Answer 95

Ch 2

a) Practical models rely on risk proxies (such as premiums and reserves) rather than relying on the risk itself. Thus, a reinsurance program may not result in a large change in required capital because it has little impact on premiums and/or reserves
b) We can compensate for this disadvantage by building the practical models into the enterprise risk model. A capital score can be calculated for each scenario and a probability distribution of capital scores can be produced. Then, required capital can be set at different probability levels.

Question 96

Explain how accumulation risk is created

Answer 96

Ch 2

Accumulated risks result from elements of an insurer’s business that absorb capital over multiple periods. Loss reserves are an example of something that produces accumulation risk

Question 97

Briefly describe the concept of as-if loss reserves and explain how it can be used to approximate accumulation risk.

Answer 97

Ch 2

For an accident year of new business, the as-if loss reserves are the reserves that would exist at the beginning of the accident year, if that business had been written in a steady state in all prior years. This acts as a proxy of the accumulation risk from the prior years of reserves

Question 98

Provide two advantages of as-if loss reserves

Answer 98

Ch 2

They can measure the impact of accumulated risk caused by correlated risk factors across accident years

The reinsurance being considered can be applied to the accident year and as-if reserves, providing a more valid measure of the impact of reinsurance on accumulated risk and on capital absorbed over the full life of the accident year.

Question 99

Briefly describe how the tails of the distribution of underwriting results changes when including accumulation risk

Answer 99

Ch 2

By including accumulated risk, the distribution of underwriting results is less compressed and has bigger tails.

Question 100

Provide two co-measures for standard deviation. Include h(X), L(Y), p(Y) and r(X_j) in your response.

Also, briefly describe each co-measure in words and state which one is preferred.

Answer 100

Ch 2

Version 1 ► Spreads the standard deviation in proportion to the mean of the components.

Let h(X) = X and L(Y) = stdev(Y) ÷ E[Y]

p(Y) = E[(Y•stdev(Y))÷E[Y]] = stdev(Y)

r(X_j) = E[(X_j•stdev(Y))÷E[Y]] = stdev(Y)•E[X_j] ÷ E[Y]

Version 2 ► decomposes the standard deviation in proportion to the covariance of the component of the total. This is the prefferred co-measure.

Let h(X) = X - E[X] and L(Y) = (Y - E[Y]) ÷ stdev(Y)

p(Y) = E[(Y - E[Y])²÷stdev(Y)] = stdev(Y)

r(X_j) = Cov(X_j,Y) ÷ stdev(Y)

Question 101

See Image

Answer 101

Ch 2

See image

Question 102

The following efficient frontier plots the collection of efficient investment portfolios, as well as the company’s current portfolio:

a) determine if the company’s current portfolio is optimal or sub-optimal.
b) briefly describe how this efficient frontier plot violates one of the tenants of the asset-liability approach described in Brehm.

Answer 102

Ch 2

a) since there are portfolios on the efficient frontier that provide more return for the same level of risk as the current portfolio, the current portfolio is sub-optimal
b) when plotting return by risk, the accounting systems shoudl be consistent. In this efficient frontier plot, the reutrn is measured based on GAAP accounting and risk is measured based on statutory accounting.

Question 103

An insurer is considering two reinsurance options. The insurer ran 25,000 simulations of its underwriting results under each option to aid in the selection process. Here are the results:

a) using the table, identify two statistics that support option 2
b) using the table, identify two statistics that support option 1
c) briefly describe why the statistics identified in part b. might be misleading

Answer 103

Ch 2

a)

• the mean shows that the uw results under option 2 are better than option 1 on average
• the safety level is the uw result at the 1 in 100 level. It shows that option 2 outperforms option 1 in an extremely good year.

b)

• the standard deviation suggests that option 1 is preferred
• The worst possible scenario under option 1 is better than the worst possible scenario under option 1

c) the standard deviation is misleading becasue it can be reduced by eliminating favorable deviations. Regarding the worst possible scenario, it is a 1 in 25,000 year event. This is an unreasonable probability level to manage to. Instead we need to compare the programs at more realistic probability levels.

Question 104

An insurer is considering two reinsurance options. Given the following:

Calculate marginal ROE’s for each option and use them to identify the preferred option.

Answer 104

Ch 2

Option 1: marginal ROE = -0.2 ÷ 1.5 = -13.33%

Option 2: marginal ROE = 0.9 ÷ 1.8 = 50%

Option 2 is the better option

Question 105

Given the log-normal density graph:

Which copula does it belong to?

a. Gumbel
b. Normal
c. Frank
d. HRT

Answer 105

Ch 3

A

Question 106

Given the log-normal density graph:

Which copula does it belong to?

a. Gumbel
b. Normal
c. Frank
d. HRT

Answer 106

Ch 3

B

Question 107

Given the log-normal density graph:

Which copula does it belong to?

a. Gumbel
b. Normal
c. Frank
d. HRT

Answer 107

Ch 3

C

Question 108

Given the log-normal density graph:

Which copula does it belong to?

a. Gumbel
b. Normal
c. Frank
d. HRT

Answer 108

Ch 3

D

Question 109

Briefly escribe four organizational details that need to be addressed when developing an internal model.

Answer 109

Ch 3

1. Reporting relationship - modeling team reporting line, solid line vs. dotted line reporting
2. Resource commitment - mix of skill set (actuarial, UW, communication, etc.), full time vs. part time
3. Inputs and outputs - control of input parameters, control of output data, analyses and uses of output
4. Initial scope - prospective UW year only, or including reserves, assets, operational risks? low detail (on the whole company) or high detail (on specific segment)?

Question 110

For each organizational detail (that needs to be addressed when developing an internal model), provide a recommended course of action.

(4)

Answer 110

Ch 3

1. Reporting relationship: the reporting line for the internal model team is less important than ensuring they report to a leader who is fair.
2. Resource commitment: since an internal model implentation is considered a new competency, it’s best to transfer internal employees or hire external employees for full-time positions.
3. Inputs and outputs: controlled in a manner similar to that used for general ledger or reserving systems
4. Scope: prospective UW period, variation around plan

Question 111

Briefly describe four parameter development details that need to be addressed when developing an internal model.

Answer 111

Ch 3

1. Modeling software - capabilities, scalability, leaning curve, integration with other systems
2. Developimg input parameters - process is heavily data driven, requires expert opinion (especially when data quality is low), many functional areas should be involved
3. Correlations - line of business representatives cannot set cross-line parameters, corporate-level ownership of these parameters is required
4. Validation and testing - no existing internal model with which to compare, multi-metric testing is required

Question 112

For each parameter development detail (that need to be addressed when developing an internal model), provide a recommended course of action.

(4)

Answer 112

Ch 3

1. Modeling software: compare existing vendor software with user-built options, ensure final software choice aligns with capabilities of the internal model team
2. Developing input parameters: include product expertise from UW, claims, planning and actuarial; develop a systematic way to capture expert opinion
3. Correlations: have th einternal model team recommend correlation assumptions, which are ultimately owned at the corporate level.
4. Validation and testing: validate and test over an extended period, provide basic education to interested parties on probabilities and statistcs.

Question 113

Briefly describe four model implenetation details that need to be addressed when developing an internal model.

Answer 113

Ch 3

1. Priority setting - importance of priority (company may not immediately make the necessary improvements to support implementation), approach and style (ask vs. mandate), priority and timeline must be driven from the top
2. Interest and impact - implement communication and education plans across the enterprise
3. Pilot test - assign multidisciplinary team (actuarial, UW, finance, etc.) to provide real data and real analysis on the company as a whole or on one specific segment, important to remember that piloting means model indications receive no weight (just a learning excercise).
4. Education process - run in parallel with pilot test, bring leadership to same point of understanding regarding probability and statistics.

Question 114

For each model implementation detail (that need to be addressed when developing and internal model), provide a recommended course of action.

(4)

Answer 114

Ch 3

1. Priority setting: have top management set the priority for implementation
2. Interest and impact: plan for regulator communication to broad audiences
3. Pilot test: assign multidisciplinary team to analyze real company data; prepare the company for magnitude of change resulting from using an internal
4. Education process: target training to bring leadership to similar BASE level of understanding

Question 115

Briefly describe three integration and maintenance details that need to be addressed when developing an internal model

Answer 115

Ch 3

1. Cycle - integrate model runs into major coporate calnedar (planning, reinsurance purchasing, capacity allocation), ensure that internal model output supports major company decisions
2. Updating - determine frequency and magnitude of updates
3. Controls - ensure that there is centralized storage and control of input sets and output sets (date stamping vial), ensure there is an endorsed set of analytical templates used to manipulate internal model outputs for various pruposes (such as decision making and reporting)

Question 116

For each integration and maintenance detail (that need to be addressed when developing an inernal model), provide a recommended course of action.

(3)

Answer 116

Ch 3

1. Cycle: integrate into planning calendar at a minimum
2. Updating: perform major input review no more frequently than twice a year. Minor updates can be handled by modifying the scale of the impacted portfolio segments.
3. Controls: maintain centralized control of inputs, outputs and application templates

Question 117

A consultant has been asked to model projection risk for two independent firms. Based on the number of annual claims, one firm is considered “small” and the other firm is considered “large”. Given the following assumptions:

• Projected losses are determined by multiplying aggregate losses by a factor 1 + J
• Claims frequency is Poisson distributed for both firms
• The severity CV for both firms is 5

a) assuming the projection risk is zero (ie. CV(1+J) = 0), compare the overall uncertaintiy for each firm.
b) for each firm, explain how the overall uncertainty changes as projection risk increases

Answer 117

Ch 3

a) When the frequency and severity distributions are known, the CV of total losses is calculated as the square root of “the frequency variance to mean ration plus the square of the severity CV, all divided by the frequency mean”. Thus, the small firm should have more uncertaintiy since we are dividing by a smaller number (ie. the number of claims).
b) as the projection risk increases, the overall uncertaintiy for the large firm is more significanly impacted. This is because the small firm is already volatile to begin with.

Question 118

For the following technical models that can be built to model the underwriting cycle, provide the underlying equations that drive th model.

• Basic autoregressive time series
• General Factor Model

Answer 118

Ch 5