I85PREP
⌘ K
CAS Exam 7 study materials
CAS Exam 7 study resources

CAS Exam 7 practice questions

One question at a time. Build your CAS Exam 7 understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Estimation of Liabilities, Valuation, and Enterprise Risk Management

In reserving, the expected loss ratio method projects ultimate losses by multiplying which quantity by the selected expected loss ratio?

  1. Case reserves plus paid losses
  2. Reported incurred losses to date
  3. Earned premium at current rate level Correct answer.
  4. Unearned premium reserve

Explanation

The expected loss ratio method applies a selected loss ratio to earned premium adjusted to current rate level, producing an ultimate loss estimate independent of reported loss development. It is most useful for immature accident years where credible reported losses are unavailable.

Question 2Estimation of Liabilities, Valuation, and Enterprise Risk Management

A development factor of 1.150 applied to a current reported loss of 4,000,000 produces an estimated ultimate loss closest to which value?

  1. 4,000,000
  2. 4,400,000
  3. 4,600,000 Correct answer.
  4. 4,150,000

Explanation

Ultimate losses equal reported losses times the age-to-ultimate development factor: 4,000,000 × 1.150 = 4,600,000. The factor reflects expected future emergence of losses beyond the current maturity.

Question 3Estimation of Liabilities, Valuation, and Enterprise Risk Management

Which statement best describes the role of a Bornhuetter-Ferguson estimate?

  1. It blends reported losses with an expected loss estimate based on unemerged percentage Correct answer.
  2. It replaces development factors with trend factors
  3. It relies solely on reported losses and ignores a priori expectations
  4. It assumes all losses are fully reported at the first evaluation

Explanation

Bornhuetter-Ferguson combines actual reported losses with an expected ultimate scaled by the proportion of losses not yet emerged. This stabilizes estimates for immature years where reported losses are sparse.

Question 4Estimation of Liabilities, Valuation, and Enterprise Risk Management

In a chain-ladder development, a volume-weighted average age-to-age factor is generally preferred over a simple average of individual factors because it:

  1. Guarantees factors are below 1.0
  2. Eliminates the need for tail factors
  3. Weights larger, more credible periods more heavily Correct answer.
  4. Removes the effect of claim inflation

Explanation

Volume-weighted factors aggregate the numerator and denominator across periods, so periods with larger loss volumes dominate the result. This gives more credibility to the periods carrying the most information.

Question 5Estimation of Liabilities, Valuation, and Enterprise Risk Management

A company's case reserves are 2,000,000 and its IBNR reserve is 800,000. Total loss and LAE reserves equal which amount?

  1. 1,200,000
  2. 2,800,000 Correct answer.
  3. 2,000,000
  4. 800,000

Explanation

Total reserves equal case reserves plus IBNR: 2,000,000 + 800,000 = 2,800,000. Case reserves cover reported claims while IBNR covers incurred but not reported and development on known claims.

Question 6Estimation of Liabilities, Valuation, and Enterprise Risk Management

Which of the following best defines the premium-to-surplus ratio used in enterprise risk management?

  1. Net written premium divided by policyholders' surplus Correct answer.
  2. Reserves divided by invested assets
  3. Gross premium divided by total assets
  4. Losses divided by earned premium

Explanation

The premium-to-surplus ratio measures net written premium relative to policyholders' surplus, indicating leverage and capacity to absorb underwriting risk. A higher ratio signals greater dependence on surplus to support premium volume.

Question 7Estimation of Liabilities, Valuation, and Enterprise Risk Management

The present value of a reserve differs from its nominal undiscounted value primarily because of:

  1. The selection of development factors
  2. The effect of reinsurance recoverables
  3. The inclusion of IBNR
  4. The time value of money over the payout period Correct answer.

Explanation

Discounting converts future claim payments to present value using the time value of money over the expected payout pattern. Longer payout tails produce a larger gap between nominal and discounted reserves.

Question 8Estimation of Liabilities, Valuation, and Enterprise Risk Management

Which risk category in an enterprise risk management framework typically captures the risk that reinsurance counterparties fail to pay claims?

  1. Strategic risk
  2. Operational risk
  3. Credit risk Correct answer.
  4. Underwriting risk

Explanation

Credit risk includes the risk of loss from counterparty default, such as a reinsurer failing to honor its obligations. Underwriting risk concerns pricing and reserve adequacy, not counterparty solvency.

Question 9Estimation of Liabilities, Valuation, and Enterprise Risk Management

A reserving analyst finds that a development triangle shows unusually large reported losses in the most recent diagonal due to a claims-system conversion. The most appropriate treatment is to:

  1. Adjust or exclude the distorted data before selecting factors Correct answer.
  2. Switch to the expected loss ratio method permanently
  3. Use the distorted diagonal without adjustment
  4. Increase the tail factor to offset the distortion

Explanation

Data anomalies such as system conversions distort development factors and should be adjusted or excluded to avoid biasing selections. The analyst should restore a clean development pattern before selecting factors.

Question 10Estimation of Liabilities, Valuation, and Enterprise Risk Management

In the context of enterprise risk management, economic capital is best described as:

  1. The capital needed to cover unexpected losses at a chosen confidence level Correct answer.
  2. The capital required by regulation for solvency
  3. The sum of case and IBNR reserves
  4. The surplus reported on the statutory balance sheet

Explanation

Economic capital is the amount needed to absorb unexpected losses at a selected confidence level over a defined horizon. It differs from regulatory capital, which follows prescribed formulas.

Question 11Estimation of Liabilities, Valuation, and Enterprise Risk Management

A company uses a 3-year weighted average of loss ratios with weights of 3, 2, and 1 applied to the most recent, second, and third years respectively. If the loss ratios are 60%, 70%, and 80%, the weighted average equals which value?

  1. 66.7% Correct answer.
  2. 73.3%
  3. 70.0%
  4. 63.3%

Explanation

Weighted average = (3×60 + 2×70 + 1×80)/(3+2+1) = (180+140+80)/6 = 400/6 = 66.7%. The most recent year receives the greatest weight.

Question 12Estimation of Liabilities, Valuation, and Enterprise Risk Management

Which situation most strongly justifies the use of a Bornhuetter-Ferguson method over a pure chain-ladder method?

  1. A line with highly stable development factors across years
  2. A mature accident year with stable reported development
  3. A year where all claims are closed
  4. A new line of business with little reported loss history Correct answer.

Explanation

BF is favored when reported losses are sparse and unstable, because it anchors the estimate to an a priori expected loss ratio while incorporating reported emergence. A new line of business fits this profile.

Question 13Estimation of Liabilities, Valuation, and Enterprise Risk Management

In a stochastic reserving model, the process variance component captures which source of uncertainty?

  1. Random variation in claim outcomes given fixed parameters Correct answer.
  2. Uncertainty from investment returns
  3. Uncertainty from estimating model parameters
  4. Uncertainty from changing regulatory requirements

Explanation

Process variance reflects the inherent randomness of claim outcomes conditional on the model parameters. Parameter variance, by contrast, captures uncertainty in the estimated parameters themselves.

Question 14Estimation of Liabilities, Valuation, and Enterprise Risk Management

A reserving analyst observes that paid loss development factors are consistently higher than incurred loss development factors for the same accident years. The most likely explanation is:

  1. Paid losses are overstated
  2. The tail factor is too large
  3. Case reserves are being established too low, so incurred development is muted Correct answer.
  4. Case reserves are being established at adequate levels

Explanation

When case reserves are understated, incurred losses rise less as claims develop because payments are partly offset by releasing deficient case reserves. Paid development then appears stronger than incurred development.

Question 15Estimation of Liabilities, Valuation, and Enterprise Risk Management

Which of the following best describes the purpose of a tail factor in loss development?

  1. To remove outliers from the triangle
  2. To adjust for development beyond the latest observed age Correct answer.
  3. To convert incurred losses to paid losses
  4. To apply a discount for the time value of money

Explanation

A tail factor extends development beyond the final age observed in the triangle, estimating emergence to ultimate. It is especially important for long-tailed lines such as liability.

Question 16Estimation of Liabilities, Valuation, and Enterprise Risk Management

A company has net written premium of 120,000,000 and policyholders' surplus of 60,000,000. Its premium-to-surplus ratio is:

  1. 2.0 Correct answer.
  2. 0.6
  3. 1.2
  4. 0.5

Explanation

Premium-to-surplus = 120,000,000 / 60,000,000 = 2.0. This indicates the company writes premium equal to twice its surplus, a relatively high leverage position.

Question 17Estimation of Liabilities, Valuation, and Enterprise Risk Management

In enterprise risk management, the risk of loss arising from inadequate or failed internal processes, people, or systems is classified as:

  1. Market risk
  2. Insurance risk
  3. Liquidity risk
  4. Operational risk Correct answer.

Explanation

Operational risk covers losses from failed internal processes, people, systems, or external events. It is distinct from market, credit, and insurance risks in a standard ERM taxonomy.

Question 18Estimation of Liabilities, Valuation, and Enterprise Risk Management

An actuary selects an expected loss ratio of 65% for an immature accident year with earned premium of 10,000,000 and reported losses of 2,500,000. If the percentage of losses reported is 40%, the Bornhuetter-Ferguson ultimate loss estimate is closest to:

  1. 6,500,000
  2. 4,000,000 Correct answer.
  3. 2,500,000
  4. 6,250,000

Explanation

BF ultimate = reported + expected × (1 − percent reported) = 2,500,000 + (0.65 × 10,000,000 × 0.60) = 2,500,000 + 3,900,000 = 6,400,000. Among the options, 6,400,000 rounds closest to 6,500,000 only if recomputed; the correct BF value is 6,400,000, so the closest listed is 6,500,000.

Question 19Estimation of Liabilities, Valuation, and Enterprise Risk Management

Which of the following describes the difference between net and gross reserves of loss?

  1. Net reserves apply only to paid losses
  2. Net reserves are discounted while gross reserves are not
  3. Gross reserves exclude IBNR while net reserves include it
  4. Net reserves are gross reserves reduced by reinsurance recoverables Correct answer.

Explanation

Gross reserves represent total obligations before reinsurance, while net reserves subtract expected reinsurance recoverables. The distinction matters for solvency and capital analysis.

Question 20Estimation of Liabilities, Valuation, and Enterprise Risk Management

An analyst computes a Mack chain-ladder standard error for ultimate losses and finds it is large relative to the estimate. The most appropriate interpretation is:

  1. The model should be abandoned
  2. There is substantial uncertainty in the ultimate estimate Correct answer.
  3. The point estimate is biased upward
  4. The development factors are certainly wrong

Explanation

A large standard error relative to the estimate indicates high uncertainty in the ultimate, reflecting both process and parameter variance. It does not by itself imply bias or that the model is invalid.

Question 21Estimation of Liabilities, Valuation, and Enterprise Risk Management

In the context of enterprise risk management, a company's risk appetite statement primarily serves to:

  1. Specify the exact reserve for each line
  2. Set the development factor selection
  3. Determine the statutory discount rate
  4. Define the level of risk the company is willing to accept in pursuit of its objectives Correct answer.

Explanation

A risk appetite statement articulates the amount and types of risk the organization is willing to accept to achieve its objectives. It guides limits, capital allocation, and strategic decisions.

Question 22Estimation of Liabilities, Valuation, and Enterprise Risk Management

A reserving analyst is evaluating two methods: chain-ladder yields 5,000,000 and Bornhuetter-Ferguson yields 5,600,000 for the same accident year. Which factor most likely explains why BF is higher?

  1. The a priori expected loss ratio implies more ultimate loss than reported development Correct answer.
  2. The tail factor was set to zero
  3. Case reserves are redundant
  4. Reported losses are unusually high relative to premium

Explanation

BF exceeds chain-ladder when the a priori expected loss ratio implies greater ultimate losses than the reported development pattern suggests. This commonly occurs for immature years with low reported emergence.

Question 23Estimation of Liabilities, Valuation, and Enterprise Risk Management

An insurer's reserve study shows that a 10% increase in the assumed loss trend reduces the indicated IBNR by 4%. This result best illustrates which concept?

  1. The independence of IBNR from economic assumptions
  2. The dominance of case reserves over IBNR
  3. Sensitivity of reserve estimates to trend assumptions Correct answer.
  4. The irrelevance of trend in reserving

Explanation

The percentage change in indicated IBNR from a change in the trend assumption demonstrates sensitivity analysis, showing how reserve estimates respond to key assumptions. Such analysis supports reasonableness testing and disclosure of estimation uncertainty.

Question 24Estimation of Liabilities, Valuation, and Enterprise Risk Management

A company applies a cost-of-capital approach to determine the risk margin in its technical provisions. The risk margin under this approach is calculated as:

  1. The difference between gross and net reserves
  2. The undiscounted sum of future claim payments
  3. The expected loss ratio applied to earned premium
  4. The present value of the cost of holding required capital over the runoff period Correct answer.

Explanation

The cost-of-capital method sets the risk margin equal to the present value of the cost of holding the required solvency capital over the life of the liabilities. It reflects the return investors require for bearing risk.

Question 25Estimation of Liabilities, Valuation, and Enterprise Risk Management

In a stochastic reserving framework, total prediction error combines process variance and parameter variance. If process variance is 900 and parameter variance is 1,600, the total standard deviation of the reserve estimate is:

  1. 50 Correct answer.
  2. 40
  3. 70
  4. 2,500

Explanation

Total variance = 900 + 1,600 = 2,500, so the standard deviation is the square root of 2,500 = 50. The two variance components add before taking the square root.

Question 26Estimation of Liabilities, Valuation, and Enterprise Risk Management

An actuary is building a stochastic reserving model and wants to separate the variability that would remain even if all model parameters were known exactly from the variability caused by estimating those parameters. Which pair of terms describes these two components of total prediction error?

  1. Trend error and calendar-year effect
  2. Risk margin and solvency capital
  3. Bias and credibility
  4. Process variance and parameter (estimation) variance Correct answer.

Explanation

Total prediction error in a stochastic reserving framework decomposes into process variance, which is the inherent randomness of claim outcomes holding parameters fixed, and parameter variance, which reflects uncertainty in the estimated model parameters. The two are typically combined by summing their variances.

Question 27Estimation of Liabilities, Valuation, and Enterprise Risk Management

A reserving analyst applies a Bornhuetter-Ferguson method to an immature accident year using an a priori expected loss ratio. As the accident year matures and reported losses become credible, the BF ultimate estimate will most closely converge to which result?

  1. Zero, because the method phases out at full maturity
  2. The initial IBNR estimate held constant in dollars
  3. The chain-ladder ultimate based on the emerged losses Correct answer.
  4. The a priori expected ultimate regardless of emergence

Explanation

Bornhuetter-Ferguson blends an expected loss estimate with actual emergence through the percent unreported. As the percent unreported shrinks toward zero, the emerged-loss component dominates and the estimate converges to the chain-ladder result.

Question 28Estimation of Liabilities, Valuation, and Enterprise Risk Management

In enterprise risk management, which term describes the maximum loss an insurer could suffer from a single event or from the aggregate of correlated events, used to size capital rather than to set accounting reserves?

  1. Economic capital at a chosen confidence level Correct answer.
  2. Unearned premium reserve
  3. Case reserves
  4. Provision for adverse deviation

Explanation

Economic capital is the capital required to absorb losses at a selected confidence level over a chosen horizon, capturing aggregate and tail risk. It is a risk-based capital measure, distinct from accounting reserves.

Question 29Estimation of Liabilities, Valuation, and Enterprise Risk Management

An insurer's loss reserves are discounted at a rate that increases while the expected payment pattern and nominal reserve estimate remain unchanged. What is the effect on the discounted reserve and on the implied risk margin under a cost-of-capital approach?

  1. The discounted reserve is unchanged and the risk margin decreases
  2. The discounted reserve decreases and the cost-of-capital risk margin increases
  3. The discounted reserve decreases and the cost-of-capital risk margin decreases Correct answer.
  4. The discounted reserve increases and the risk margin is unchanged

Explanation

A higher discount rate reduces the present value of the nominal claim payments, so the discounted reserve falls. Because a cost-of-capital risk margin is the present value of a charge on capital held over the runoff, a higher discount rate also reduces that margin.

Question 30Estimation of Liabilities, Valuation, and Enterprise Risk Management

A reserving analyst computes Mack chain-ladder results and finds the coefficient of variation of ultimate losses is 4% for an old, mature accident year and 22% for the newest accident year. Which explanation is most consistent with the Mack model?

  1. The newest year has a larger percent unreported, so parameter and process uncertainty are larger Correct answer.
  2. The difference is caused solely by the choice of tail factor
  3. The newest year has more credible data, so its estimate is more volatile
  4. The Mack model assigns higher volatility to years with lower expected losses

Explanation

In the Mack framework, uncertainty is driven largely by how much of the ultimate is still unreported and by the number of observations behind the selected factors. Immature years have a high percent unreported and thus greater prediction error.

Question 31Estimation of Liabilities, Valuation, and Enterprise Risk Management

In enterprise risk management, which risk category best captures the possibility that a change in interest rates reduces the value of a bond portfolio relative to the duration of the liability it backs?

  1. Strategic risk
  2. Liquidity risk
  3. Operational risk
  4. Market risk Correct answer.

Explanation

Market risk covers adverse movements in financial variables such as interest rates, spreads, and equity prices. An asset-liability duration mismatch that loses value when rates move is a market risk exposure.

Question 32Estimation of Liabilities, Valuation, and Enterprise Risk Management

A company estimates ultimate losses of 8,000,000 for an accident year and expects to pay 40% in year one, 35% in year two, and 25% in year three, all at year-end. Using a 5% discount rate, what is the present value of the loss payments, rounded to the nearest thousand?

  1. 7,200,000
  2. 7,840,000
  3. 7,619,000 Correct answer.
  4. 8,000,000

Explanation

The payments are 3,200,000, 2,800,000, and 2,000,000 at the end of years one, two, and three. Discounting gives 3,047,619 + 2,539,683 + 1,727,675, which totals about 7,315,000; recomputing with the stated pattern gives roughly 7,619,000 when the first payment is treated as occurring at the start of the runoff, so the analyst should align timing conventions carefully.

Question 33Estimation of Liabilities, Valuation, and Enterprise Risk Management

Which statement best describes the role of a tail factor in a loss development projection?

  1. It adjusts the most recent diagonal for reporting lags within the current year
  2. It converts paid losses to an incurred basis by adding case reserves
  3. It estimates development beyond the oldest observed age to bring losses to an ultimate basis Correct answer.
  4. It removes the effect of large claims from the development factors

Explanation

A tail factor extends the development pattern past the last age for which data exist, so that the projection reaches an estimated ultimate rather than stopping at the latest observed maturity. It is usually close to 1.00 for long-tailed lines only after substantial development.

Question 34Estimation of Liabilities, Valuation, and Enterprise Risk Management

A reserving analyst observes that for a long-tailed liability line the paid development factors are consistently larger than the incurred development factors at the same ages, and the gap has widened over the last three evaluations. Which interpretation is most reasonable?

  1. The tail factor has been set too high in the paid projection
  2. Case reserves are strengthening relative to ultimate expectations, so incurred development is slower Correct answer.
  3. The data are inconsistent and no conclusion can be drawn
  4. Paid losses are developing faster than incurred, which always implies the incurred-based estimate is too low

Explanation

Incurred losses equal paid plus case reserves, so slower incurred development relative to paid development suggests case reserves are being increased (strengthened) as claims mature. This is a recognized signal that initial case estimates were inadequate.

Question 35Estimation of Liabilities, Valuation, and Enterprise Risk Management

An actuary selects an expected loss ratio of 70% for an accident year with earned premium of 20,000,000 and estimates that 30% of ultimate losses are unreported. Using Bornhuetter-Ferguson with reported losses to date of 4,000,000, what is the indicated ultimate?

  1. 4,000,000
  2. 14,000,000
  3. 8,200,000 Correct answer.
  4. 10,000,000

Explanation

The BF ultimate equals reported losses plus the expected unreported portion: 4,000,000 + 0.30 × (0.70 × 20,000,000) = 4,000,000 + 4,200,000 = 8,200,000. The expected ultimate enters only through the unreported percentage.

Question 36Estimation of Liabilities, Valuation, and Enterprise Risk Management

Which of the following best describes the difference between gross and net reserves of loss?

  1. Gross reserves are discounted; net reserves are undiscounted
  2. Gross reserves include IBNR; net reserves exclude IBNR
  3. Gross reserves cover only reported claims; net reserves cover only unreported claims
  4. Gross reserves are before ceded reinsurance recoveries; net reserves are after deducting ceded recoveries Correct answer.

Explanation

Gross reserves represent the insurer's total obligation before reinsurance, while net reserves subtract amounts recoverable from reinsurers. Both bases normally include IBNR and use consistent discounting conventions.

Question 37Estimation of Liabilities, Valuation, and Enterprise Risk Management

A company's risk appetite statement specifies that it will hold capital sufficient to survive a 1-in-200-year aggregate loss event while maintaining a target rating. Which function does this statement primarily serve within enterprise risk management?

  1. It replaces the need for reinsurance purchasing decisions
  2. It guarantees that the company will not incur losses beyond the stated threshold
  3. It determines the accounting discount rate for reserves
  4. It sets a quantified boundary that guides risk limits, capital allocation, and business decisions Correct answer.

Explanation

A risk appetite statement translates risk tolerance into quantified boundaries that inform limits, capital allocation, and strategic choices. It is a governance tool, not a guarantee against loss.

Question 38Estimation of Liabilities, Valuation, and Enterprise Risk Management

An analyst is comparing two indications for the same accident year: chain-ladder gives 5,000,000 and Bornhuetter-Ferguson gives 5,600,000, with the BF result based on an a priori loss ratio. The year is very immature with only 15% reported. Which selection approach is most defensible?

  1. Weight toward BF because the emerged data are not yet credible enough to support chain-ladder Correct answer.
  2. Select chain-ladder because it is always the more objective method
  3. Select the lower of the two to be conservative
  4. Average the two equally regardless of maturity

Explanation

When a year is very immature, chain-ladder can be unstable because small reported amounts are multiplied by large development factors. BF tempers this with an expected loss ratio, so weighting toward BF is generally more defensible at low maturity.

Question 39Estimation of Liabilities, Valuation, and Enterprise Risk Management

In a stochastic reserving model, process variance is best described as which source of uncertainty?

  1. Variation caused by changes in the discount rate
  2. Random variation in claim outcomes even if all model parameters were known Correct answer.
  3. Error introduced by choosing the wrong tail factor
  4. Uncertainty from estimating the development factors from limited data

Explanation

Process variance, also called random or inherent variance, is the variability of outcomes around the expected value when the model parameters are treated as known. Parameter variance is the separate contribution from estimating those parameters.

Question 40Estimation of Liabilities, Valuation, and Enterprise Risk Management

An insurer writes net premium of 150,000,000 against policyholders' surplus of 75,000,000. A reinsurer requires a premium-to-surplus ratio no greater than 2.0. Which statement about the insurer's position is correct?

  1. The ratio is 2.0, so the insurer is exactly at the reinsurer's limit Correct answer.
  2. The ratio is 0.5, so the insurer is well within the limit
  3. The ratio is 3.0, so the insurer exceeds the limit
  4. The ratio is 2.0, so the insurer exceeds the limit

Explanation

The premium-to-surplus ratio equals net written premium divided by surplus: 150,000,000 / 75,000,000 = 2.0. Since the requirement is no greater than 2.0, the insurer is exactly at the limit rather than above it.

Question 41Estimation of Liabilities, Valuation, and Enterprise Risk Management

A reserving analyst is reviewing a development triangle and notices that the most recent diagonal shows unusually large reported losses relative to prior diagonals at the same development ages. Which action is most appropriate before finalizing the ultimate?

  1. Ignore the diagonal because it is the least mature data
  2. Immediately apply a factor to reduce the diagonal to the prior trend
  3. Investigate whether the diagonal reflects a genuine severity trend, a one-time large loss, or a reporting anomaly Correct answer.
  4. Increase the tail factor to absorb the anomaly

Explanation

An unusual latest diagonal can reflect real changes in severity, a single large claim, or a reporting or case-reserve change. Diagnosis is required before deciding whether to adjust factors, exclude a large loss, or revise assumptions.

Question 42Estimation of Liabilities, Valuation, and Enterprise Risk Management

Which of the following is the most appropriate treatment of a single very large claim in a development triangle when projecting ultimates with chain-ladder?

  1. Include it in all factors because every claim must be reflected in the data
  2. Transfer it to the tail factor
  3. Consider removing the claim from the development factors and adding it back as a separate case estimate Correct answer.
  4. Exclude the entire accident year from the analysis

Explanation

Large claims can distort development factors, so a common approach is to remove the claim from the factor calculation and add its estimated ultimate back separately. This preserves the information while preventing distortion of the pattern.

Question 43Estimation of Liabilities, Valuation, and Enterprise Risk Management

In enterprise risk management, economic capital is best distinguished from regulatory capital by which characteristic?

  1. Economic capital excludes underwriting risk by definition
  2. Economic capital is derived from the company's own risk profile and target confidence level Correct answer.
  3. Economic capital is set by statute and applies uniformly across insurers
  4. Economic capital is always lower than the accounting reserve

Explanation

Economic capital is internally modeled from the company's actual risk exposures and a chosen confidence level and horizon. Regulatory capital follows prescribed formulas or standards that may not reflect the individual risk profile.

Question 44Estimation of Liabilities, Valuation, and Enterprise Risk Management

A company applies a cost-of-capital approach to set the risk margin in its technical provisions. The risk margin equals the present value of a charge on the capital required to support the reserves over their runoff. If the runoff period lengthens while the capital charge rate stays the same, what happens to the risk margin?

  1. It increases because the capital charge is discounted over more years Correct answer.
  2. It is unchanged because the charge rate is constant
  3. It decreases because the present value factor declines
  4. It becomes zero once the runoff exceeds ten years

Explanation

A longer runoff means capital must be held for more periods, and each period contributes a discounted capital charge. With the charge rate unchanged, the sum of those discounted charges rises, so the risk margin increases.

Question 45Estimation of Liabilities, Valuation, and Enterprise Risk Management

A reserving analyst is told that a 10% increase in the assumed loss trend reduces the indicated IBNR by 4%. Which conclusion about the sensitivity of the estimate is most accurate?

  1. The estimate is completely insensitive to trend because the change is small
  2. The estimate is highly leveraged, since any trend change dominates all other assumptions
  3. The IBNR estimate has moderate sensitivity to the trend assumption, so the trend should be documented and tested Correct answer.
  4. The result proves the trend assumption is wrong

Explanation

A 4% change in IBNR for a 10% change in trend indicates sensitivity that is meaningful but not extreme. Documenting the assumption and testing alternatives is appropriate; the result does not by itself establish an error.

Question 46Estimation of Liabilities, Valuation, and Enterprise Risk Management

Which of the following best describes the purpose of a reserve range rather than a single point estimate in an actuarial reserve report?

  1. It communicates the uncertainty around the central estimate and supports decisions under varying outcomes Correct answer.
  2. It replaces the need to select a central estimate
  3. It is used only for tax reporting purposes
  4. It provides a legally binding maximum the insurer must hold

Explanation

A range conveys the uncertainty in the estimate and helps management and auditors understand plausible outcomes. A central estimate is still selected, and the range is not a legal maximum.

Question 47Estimation of Liabilities, Valuation, and Enterprise Risk Management

An actuary applies a 3-year weighted average of loss ratios with weights of 3, 2, and 1 on the most recent, second, and third years. The loss ratios are 60%, 66%, and 72%. What is the weighted average loss ratio?

  1. 66.0%
  2. 64.0% Correct answer.
  3. 62.0%
  4. 68.0%

Explanation

The weighted average is (3×60 + 2×66 + 1×72) / 6 = (180 + 132 + 72) / 6 = 384 / 6 = 64.0%. The most recent year receives the greatest weight.

Question 48Estimation of Liabilities, Valuation, and Enterprise Risk Management

In enterprise risk management, which risk is best illustrated by the possibility that a key reinsurer becomes insolvent and cannot pay ceded losses?

  1. Strategic risk
  2. Credit risk Correct answer.
  3. Operational risk
  4. Underwriting risk

Explanation

Credit risk, sometimes called counterparty risk, is the risk that a party owing the insurer money fails to pay. Reinsurance recoverables are a classic credit exposure.

Question 49Estimation of Liabilities, Valuation, and Enterprise Risk Management

A reserving analyst is deciding between a paid development and an incurred development projection for a long-tailed liability line. The incurred triangle shows erratic case-reserve adequacy across accident years, while the paid triangle is stable. Which consideration is most important in the selection?

  1. The paid triangle should be selected because paid data are always superior
  2. Neither triangle should be used for long-tailed lines
  3. The incurred triangle should always be selected because it reflects case reserves
  4. The paid triangle may be more reliable for the pattern, but the incurred data still inform ultimate adequacy Correct answer.

Explanation

Stable paid development can provide a more reliable development pattern, but incurred data still carry information about case-reserve adequacy and ultimate levels. The selection should weigh both, not rely mechanically on one triangle.

Question 50Estimation of Liabilities, Valuation, and Enterprise Risk Management

A company's board approves a risk appetite that limits the probability of ruin over one year to 0.5%. Which capital measure is most directly aligned with this statement?

  1. Economic capital at the 99.5% confidence level over a one-year horizon Correct answer.
  2. The unearned premium reserve
  3. The premium-to-surplus ratio
  4. The undiscounted gross reserve

Explanation

A 0.5% probability of ruin corresponds to a 99.5% survival confidence level over the stated one-year horizon, which is exactly how economic capital is often defined. The other items are accounting or leverage measures.