Brehm Ch 2

Question 1

Define decision analysis

Answer 1

using simulation to drive corporate decision making

Question 2

Describe 3 evolutionary steps of decision analysis process

Answer 2

1. Deterministic project analysis
   Uses a single deterministic forecast for project CFs to produce an objective function like PV or internal RoR.
   This analysis may demonstrate some sensitivities to critical variables.
2. Risk analysis
   Forecasts of distributions of critical variables are input into a MC simulation process to produce a distribution of the PV of CFs.
3. Certainty equivalent
   Expands upon risk analysis by quantifying the intuitive risk judgment using a utility function (corporate risk preference).

Question 3

Describe how uncertainty is handled in each step of decision analysis process.

Answer 3

1. Deterministic project analysis: uncertainty is handled judgmentally rather than stochastically.
2. Risk analysis: risk judgment is still applied intuitively.
3. Certainty equivalent: utility function does not replace judgment. Instead, it formalizes judgment to that it can be consistently applied.

Question 4

Explain how efficient market theory removes need for certainty.

Answer 4

Since investors can diversify away firm-specific risk, it does not have a risk premium and should be ignored.

The goal of firm managers is to maximize shareholder value, so they should ignore firm-specific risk as well.

This is why certainty equivalent approach is not appropriate for public companies.

Question 5

Provide 2 counter arguments to the belief that market theory removes need for certainty.

Answer 5

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 affect the stock price and which do not, but results are inconclusive.
2. Market-based risk signals (such as risk-adjusted rate) often lack the refinement needed for manages to mitigate or hedge the risk.
3. Risk-adjusted discount rate (market-based risk signal) reflects risk only if there is a time lag. For many kinds of risks, time aspect is unimportant since risk is instantaneous (jump risk).

Question 6

List the 5 major elements involved in internal risk modelling.

Answer 6

1. Data classification and organizational scheme
2. Capture exposures and loss history
3. Estimate event frequency and severity distribution, Corporate hedging, Correlation and shock scenarios
4. Develop aggregate loss distributions
5. Corporate risk tolerance, CoC allocated, Cost benefit analysis on mitigation and hedging

Question 7

List the 4 objectives of Internal Risk Model (IRM) mechanism

Answer 7

1. Starts with an aggregate loss distribution, with many sources of risk (such as LOBs)
2. Quantifies the impact of the possible aggregate loss outcomes on the corporation
3. Assigns a cost to each amount of impact
4. Attributes cost back to the risk sources

Question 8

Define Corporate Risk Tolerance

Answer 8

Refers to the organization’s:
1. size
2. financial resources
3. ability
4. willingness
to tolerate volatility.

Question 9

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

Answer 9

In order to translate impacts to costs, corporations must define explicit risk preferences.

For example, suppose a firm has identified an efficient frontier of possible insurance portfolios (portfolios that minimize risk for a given RoR).

The firm can plot these portfolios on a standard efficient frontier graph where y-axis is risk and x-axis is return.

The firm can then plot its current portfolio and see how it compares with efficient frontier.

If current portfolio has same return but more risk, then it is suboptimal.

Question 10

List 3 questions a firm should try to answer when selecting one of the efficient portfolios.

Answer 10

1. How much risk is the firm willing to tolerate?
2. How much reward is the firm willing to give up for a given reduction in risk?
3. Are the risk-reward tradeoffs available along the efficient frontier acceptable to the firm?

The 1st question requires an answer to the firm’s risk tolerance.

The second question requires the firm to express its risk preferences explicitely.

Question 11

Describe how RORAC is determined.

Answer 11

Financial firms should rely on allocating the cost of capital (rather than the capital itself).

One way to do so is by allocating risk capital first and then using it to assign the cost of that risk capital to portfolio elements.

The cost is the product of the risk-adjusted capital and a hurdle rate.

This product is known as the Return on Risk-Adjusted Capital (RORAC).

Under RORAC, risk capital for financial intermediary is the amount needed to guarantee the performance of contractual obligations at default-free level.

Question 12

Briefly describe an alternative to RORAC.

Answer 12

The cost of risk capital can be determined directly without allocating risk capital first.

Question 13

Describe how RORAC can be used to determine if an activity is worth pursuing.

Answer 13

Once we have the Cost of Capital, a good way to determine if an activity is worth pursuing is by calculating the economic value added (EVA).

EVA = NPV Return - CoC

Activities with positive EVA should be pursued.

Question 14

Explain how cost-benefit analysis (CBA) can be used to select risk mitigation strategies.

Answer 14

Once capital allocation is complete, a cost-benefit analysis can be used to determine which mitigation strategies should be pursued.

If we are using EVA approach where the CoC is determined directly, we would implement strategies that produce positive incremental EVA.

If we are using capital allocation approach where we have allocated risk capital, we would pursue activities where the benefit exceeds the costs of implementation.

Question 15

Define economic capital.

Answer 15

Typically, economic capital refers to the VaR (value at risk).

Question 16

Identify 4 advantages of using economic capital for ERM analysis.

Answer 16

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 17

Briefly describe why calculating VaR for all risks combined and then allocated down to individual units is beneficial.

Answer 17

Because it provides a consistent measurement of risk across units.

Question 18

Briefly explain why a rounded number is usually selected for the target level.

Answer 18

Ex: 1-in-3333 VaR instead of 1-in-3467 VaR

The target level is often selected so that the economic capital is slightly less than the actual capital being held.

Question 19

Define Moment-Based Measures and provide 2 examples of such measures.

Answer 19

Use the moment of a random variable, such as the change in capital over an accounting period.

Ex:
1. variance
2. standard deviation

Question 20

Identify 2 disadvantages of using variance or standard deviation as risk measure.

For each, provide an alternative.

Answer 20

1. Favorable deviations are treated the same as unfavourable ones.
   Use semi-standard deviation since it only uses unfavourable deviations.
2. As quadratic measures, they may not adequately capture market attitudes to risk (understated).
   Use skewness since uses higher moment, thus might better capture market attitude.
   OR
   Use exponential moments since they capture the effect of large losses on risk exponentially, the they might better capture market attitude.

Question 21

Describe tail-based measures.

Answer 21

Tail-based measures emphasize large losses only.

Question 22

Describe the 5 types of tail-based measures

Answer 22

1. VaR: percentile of the probability distribution
2. TVaR: expected loss at a specified probability level and beyond
3. XTVaR: calculated as TVaR - mean.
   When mean is financed by other funding, then capital is only needed for losses above the mean.
4. EPD: calculated by multiplying (TVaR - VaR) by the complement of the specified probability level.
   Ex: EPD@96% = (TVaR - VaR)*(1-96%)
5. Value of default put option: when capital and/or reinsurance is exhausted, 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 23

Provide an advantage and disadvantage of using VaR as tail-based risk measure.

Answer 23

Advantage: emphasizes large losses

Disadvantage: only looks at one point in the distribution

Question 24

Provide an advantage and disadvantage of using TVaR as tail-based risk measure.

Answer 24

Advantage: reflects losses that exceed VaR

Disadvantage: losses are reflected linearly in the tail and does not reflect the fact that a risk that is twice as large is more than twice as bad.

Question 25

Define probability transforms

Answer 25

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

Question 26

Provide 1 example of probability transforms

Answer 26

1. Expected loss under transformed probabilities (ex: CAPM and Black-Scholes)
2. Minimum martingale transform
3. Minimum entropy martingale transform
4. Wang transform

Question 27

Provide 3 reasons why probability transforms are useful.

Answer 27

1. Transformed means are useful because they often provide the market value of the risk being measured.
2. Martingale transforms approximate the market prices of reinsurance from application to compound poisson process.
3. Wang transform approximates market prices of standard bonds and CAT bonds.

Question 28

Describe the TVaR criticism and how transformed probabilities can overcome this.

Answer 28

TVaR is often criticized because it is linear in the tail (a loss twice as large is considered twice as bad).

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 29

Describe Generalized Moments.

Answer 29

Expectations of a random variable that are NOT simply powers of that variable.

For example. TVaR at prob level a can be written as E(Y given F(Y) greater than a).

A generalized moment can be used to add weight to losses in the loss distribution around VaR percentile (blurred VaR).

Question 30

How do we determine which measure to use?

Answer 30

If we want to get closer to the market value then a risk measure like WTVaR, minimum entropy transform and exponential moment may be a better decision.

However, these should be weighted against the practicality and simplicity of standard risk measures such VaR and TVaR.

Question 31

The amount of capital an insurance company holds is a function of which 3 things.

Answer 31

1. Customer reaction
2. Capital requirements of rating agencies
3. Comparative profitability of new and renewal business

Question 32

Describe how customer reaction affects amount of capital held. How can it be tracked?

Answer 32

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.

To assess capital needs from this POV requires keeping in touch with customers.

Question 33

Describe how capital requirements of rating agencies affects amount of capital held.

Answer 33

Different rating agencies require different amounts of capital to be held by an insurer.

Modelling may help convince an agency of the adequacy of capital.

Question 34

Describe how comparative profitability of new and renewal business affects the amount of capital held.

Answer 34

Renewal business tends to be more profitable due to more informed pricing and underwriting.

Thus, it is important to retain renewal business.

Question 35

List 2 purposes of capital allocation.

Answer 35

1. Capital allocation shows the contribution of each business unit to overall risk.
2. Capital allocation can be used for calculating risk-adjusted profitability and setting capacity controls by LOBs.

Question 36

Provide the 2 methods for risk allocation.

Answer 36

1. Proportional Capital Allocation
   Allocate the overall risk to individual business units based on their proportion to risk.
2. Risk decomposition
   Estimate contributions of individual business units to overall risk.
   Define risk measure as an average of company results under certain conditions.
   The contributions from each business units is the average of the business unit’s results under same conditions (co-measures).

Question 37

Define co-measures.

Answer 37

In order to create a co-measure, we must express rho(Y) as a conditional expected value:

rho(Y) = E(h(Y)L(Y) given g(Y))

g is dome condition about Y
h is an additive function h(V+W) = h(V)+h(W)
L is any function for which this conditional expected value exists.

Then, the co-measure for such a risk measure is:
r(Xj) = E(h(Xj)L(Y) given g(Y))

Question 38

Explain what it means for a risk decomposition method to be marginal.

Answer 38

It is desirable for a risk decomposition method to be marginal.

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

The marginal property links to the financial theory of pricing proportionality to marginal costs.

This property 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 39

Provide 2 examples of risk measures that can be expressed as marginal decompositions.

Answer 39

1. TVaR
2. Standard deviation

Question 40

Provide the risk measure and co-measure for variance. Can it be decomposed?

Answer 40

rho(Y) = Var(Y) = E(((Y-E(Y))^2)

r(Xj) = Cov(Xj,Y) = E((X-E(Xj))(Y-E(Y)))

Since Var(aY) = a^2Var(Y), the risk measure is not scalable and cannot be decomposed.

Question 41

Provide the risk measure and co-measure for Value-at-Risk (VaR)

Answer 41

rho(Y) = VaR(Y) = E(Y given F(Y)=a)

r(Xj) = Co-VaR(Xj,Y) = E(Xj given F(Y)=a)

Since VaR is scalable, this risk measure can be decomposed.

Question 42

Provide the 2 ways to express standard deviation in co-measures.

Answer 42

Option 1:
h(X) = X
L(Y) = std(Y)/E(Y)
rho(Y) = E((Ystd(Y))/E(Y)) = std(Y)
r(Xj) = E((Xjstd(Y))/E(Y)) = std(Y)*E(Xj)/E(Y)

This spreads the std in proportion to the mean of the components.

Option 2:
h(X) = X - E(X)
L(Y) = (Y-E(Y))/std(Y)
rho(Y) = E((Y-E(Y))^2/std(Y)) = std(Y)
r(Xj) = Cov(Xj,Y)/std(Y)

This decomposes the std in proportion to the covariance of the component of the total.

Question 43

Which option is preferred to express standard deviation as a co-measure.

Answer 43

The second option (proportion to the covariance) is the marginal decomposition of the risk measure.

The total change in std(Y) brought about by a small change in Xj can be attributed to j using this procedure.

Thus, it is the preferred co-measure.

Question 44

Provide 3 advantages of marginal allocation.

Answer 44

1. Marginal allocation produces co-measures.
2. Marginal allocation sum to the total risk measure
3. Marginal allocation leads to consistent strategic implications

Question 45

Explain how to obtain a scalable form of EPD.

Answer 45

Let B = Fy^-1(a)
rho(Y) = (1-a)E(Y-B given F(Y) greater than a)
r(Xj) = (1-a)E(Xj given Y greater than b) = (1-a)*(co-TVaR - co-VaR)

Question 46

Interpret the risk-adjusted profitability ratio.

Answer 46

Using decomposition of a risk measure to measure risk-adjusted profitability of business units works best if the risk measure is proportional to the market value of the risk.

The ratio of a unit’s profit to its risk measure would be proportional to the ratio of the profit to the market value.

Thus, business units with higher ratios yield more profit.

Question 47

Describe how to allocate the Cost of Capital.

Answer 47

Set minimum profit target of a business unit equal to the value of its to call upon the capital of the firm.

The XS of the unit’s profits over this cost of capital is added value for the firm.

This right is a cost to the firm because the company is carrying the risk of the unit’s right to access insurer’s entire capital.

Question 48

Provide 2 disadvantages of allocating capital (instead of CoC)

Answer 48

1. It is arbitrary because different risk measures allocate capital differently.
2. It is artificial because each business unit has access to the entire capital.

Question 49

Explain why allocation of CoC can be viewed as a stop-loss agreement.

Answer 49

The right to call upon the capital of the firm is a cost to the firm because the company is carrying the risk of the unit’s right to access entire capital.

This is an implicit stop-loss agreement where a business unit can either make money or break even.

The economic value of implicit stop-loss is more than its expected value.

Incorporating full distribution of profit results for each business units to obtain a better measure of the true economic value.

Question 50

Provide 2 examples of leverage ratios to evaluate capital adequacy.

Give 2 advantages of those ratios.

Answer 50

1. Premium to Surplus ratio
2. Reserve to Surplus ratio

They are easy to calculate and easy to monitor

Question 51

Provide 2 disadvantages of leverage ratios to evaluate capital adequacy

Answer 51

1. They do not distinguish among business classes
2. They do not incorporate risks other than UW risks

Question 52

List 4 IRIS ratios

Answer 52

1. Gross WP to Surplus
2. Net WP to Surplus
3. Change in writtings
4. Surplus aid to Surplus
5. 2y operation ratio
6. Investment yield
7. Liabilities to liquid assets
8. Change in surplus
9. Agents balances to surplus
10. 1y reserves development to surplus
11. 2y reserves development to surplus
12. Estimated current reserve deficiency to surplus

Question 53

Explain how IRIS ratios are used to measure firm health

Answer 53

For each ratio, a range of reasonable values was determined.

Any company that had 4 or more ratios that did not fall within their corresponding reasonable ranges was considered to be at risk and warranted regulatory scrutiny.

IRIS ratios are still used today but are given less weight than other capital adequacy measures.

Question 54

Contrast leverage ratios and risk-based capital (RBC)

Answer 54

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

Question 55

Briefly explain how the risks in RBC are quantified.

Answer 55

Each risk is measured by multiplying factors by accounting values.

The magnitude of the factors varies by the quality and type of asset or the line of business.

Question 56

Define accumulation risk

Answer 56

Exposure to catastrophic events affecting a large number of insureds.

Many RBC models include recognition of accumulation risk.

Question 57

Explain 2 ways to quantify accumulation risk

Answer 57

1. Through stress testing of the impact of a second severe event
2. Through the use of annual aggregate loss amounts rather than per-occurrence losses

Question 58

Explain the reasoning behind different factors between different RBC models (2).

Answer 58

1. Different model uses
   Rating agency models (AM Best, S&P) focus on long-term viability
   Regulatory models (US RBC) focus on 1y solvency, thus use lower factors.
2. Covariance adjustment
   Models with a covariance adjustment (AM Best) will have relatively higher factors than models without it (S&P).
   The covariance adjustment will reflect independence between risks so that overall capital is less than sum of individual risks.

Question 59

Provide the largest component of credit risk in RBC models.

Answer 59

Comes from reinsurance recoverables.

Several models use risk factors that vary with credit quality of reinsurer.

A.M. Best model also increases credit risk charge for companies that are heavily dependent reinsurance (as determined by ratio of reinsurance recoverable to surplus).

Question 60

Briefly explain the difference between static scenarios (DCAT) and stochastic scenarios.

Answer 60

Stochastic scenarios are generated using a stochastic process.

Static scenarios are taken from a predefined list.

Question 61

Summarize the 3 best practices used by regulators in terms of scenarios testing.

Answer 61

1. RBC model is used as a base metric.
2. Each insurer performs its own assessment of its risk-based capital needs.
   Internal assessment includes scenario testing and/or stochastic modelling.
3. Regulator reviews company’s analysis and has the right to provide alternative capital requirements.

Question 62

Provide 2 critical features the actuary’s projection must include in scenario testing.

Answer 62

1. Correlations among risks
2. Reflection of management responses to adverse financial results (for multi years models)

Model should includes 1 to 5 y of financial projections and incorporation of probability distributions for as many sources of uncertainty as can be modelled.

Question 63

Provide 2 uses of RBC models

Answer 63

1. Issue surplus notes
2. Purchase reinsurance

Question 64

Define Asset-Liability Matching

Answer 64

Setting investment portfolio to have the same duration as the duration of the liability portfolio to protect the firm against changing interest rates.

Question 65

Provide 3 additional factors (in addition to interest rate risk) considered in asset-liability management.

Answer 65

1. Inflation risk
2. Credit risk
3. Market risk

Question 66

Describe 3 asset/liability mixtures. How does investment risk differ in each mixture.

Answer 66

1. Standalone asset portfolio with no liabilities
   Short-term treasuries are considered risk-free while high-yield assets are considered risky.
2. Add fixed duration liabilities
   Short-term treasuries have duration shorter than liabilities and introduce reinvestment risk.
   If interest rates drop, total investment income may not be sufficient.
   If interest rates rise, longer-term investments 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.
3. Add liabilities with variable timing and amount.
   Duration matching is no longer possible because duration of liabilities is unknown.
   Model incorporating asset and liability fluctuations would be needed to determine optimal investment portfolio.
4. Consider underwriting income

Question 67

How does a company’s choice of risk-return metrics impact the optimal investment strategy under the following:
1. SAP
2. GAAP
3. Economic accounting

Answer 67

1. Under statutory accounting, bonds are amortized and liabilities are not discounted.
   Assets provide little hedging to liabilities from duration matching.
2. Under GAAP, bonds are marked to market and liabilities are not discounted. Assets provide little hedging to liabilities.
3. Under economic accounting, assets are marked to market and liabilities are discounted.
   Hedging does occur.
   Short term investment portfolios increase risk and decrease return.
   Long-term investment portfolios increase risk and increase return.
   Choice of investment portfolio becomes a judgment call by company.

Question 68

Describe the 9 steps in asset-liability modelling.

Answer 68

1. Start with models of assets classes (stocks, bonds), existing liabilities (loss reserves, receivables) and current business operations (premium incomes, incurred losses, expenses)
2. Define risk metrics
   Can either be income-based or balance-sheet-based.
   Potential ones include: std, VaR, TVaR
   VaR and TVaR are better suited for BS items such as surplus.
3. Define return (ROE, earnings)
   Accounting system used should be consistent with system used for defining risk.
4. Define timing of analysis.
   Single period models may not fully capture true nature of business, but multi-period models may be too complex to implement.
5. Define constraints
   Prohibited asset classes and investments that would drive RBC numbers too high.
6. Run the model with different investment, underwriting and reinsurance strategies.
7. Construct an efficient frontier across various portfolio scenarios.
   Plot current portfolio against efficient frontier.
   Find portfolios on frontier that can decrease risk without sacrificing return ON increase return without increasing risk.
8. Test the effects of different reinsurance structures.
9. Review simulations where portfolios performed poorly.

Question 69

List 2 areas of future research in terms of optimal investment portfolio. Explain how they could be handled.

Answer 69

1. Better understand correlations between LOBs and assets/liabilities over time.
   Correlation can materially alter one’s view of optional portfolio.
2. Better understand the link between inflation and future loss payments.
   AY and CY trends are not usually based on historical economic data nor are they projected using economic scenario generators.

One way to handle the issues above is by treating correlations and inflation sensitivity as random variables within the model.

Question 70

Provide 3 paradigms for measuring reinsurance value.

Answer 70

1. Reinsurance provides stability
   Protecting of surplus, improved predictability of earnings and customer’s assured recovery of their insured losses.
   Cost of stability is:
   Ceded premium - Losses - Expense recoveries
2. Reinsurance frees up capital
   Insurers are able to hold less capital.
   ROE = Reinsurance Cost / Capital Freed
   As long as ROE is less than firm’s target return, purchase of reinsurance is a good decision.
3. Reinsurance adds market value to the firm
   Can be measured by incremental increase in market value to the company.

Question 71

Briefly explain why it is misleading to analyze distribution of difference in UW results between 2 reinsurance programs. Provide a more useful way to compare distribution.

Answer 71

It is misleading because the percentiles of the individual distributions do not line up.

Comparing probability distributions of each reinsurance program is more useful than examining distribution of different between 2 programs.

Question 72

Briefly explain why it is misleading to compare standard deviation between 2 reinsurance programs

Answer 72

The standard deviation is misleading because it can be reduced by eliminating favorable deviations (compressing distribution).

Question 73

Briefly explain why it is misleading to use CR to compare 2 reinsurance programs.

Answer 73

If a reinsurance program has slightly stronger UW results but far more ceded premium, then CR will be worse (even though the absolute UW income is better).

Question 74

Briefly explain how interpretation of ROE differs when releasing capital vs when consuming capital.

Answer 74

When releasing capital (ex: purchasing reinsurance to reduce capital needs), reinsurance programs with low marginal ROEs are preferred.

When consuming capital (ex: changing reinsurance programs to a less expensive option requiring a bit more capital), programs with higher ROEs are preferred.

Question 75

When looking at probability distributions for comparing reinsurance options, provide 3 things you should look at.

Answer 75

1. Which option protects best against worst losses
2. Which option does not limit profitable scenarios too much
3. Which option produces better results in different areas of prob distribution

Question 76

When looking at Box/Space Needle View for comparing reinsurance options, provide 2 things you should look at.

Answer 76

1. Which program protects from most unfavourable scenarios
2. Which sacrifices profitable good years

Question 77

When looking at Cost-Benefit Diagram for Reviewing Reinsurance Options, name 2 things you should look at.

Answer 77

1. Which option performs best at different probability levels
2. If a program is more costly but has worse loss outcomes at each prob level, it is inefficient and should not be considered.

X-axis: cost of reinsurance
Y-axis: Loss amount

Question 78

Describe 2 classes of models for measuring change in capital due to reinsurance.

Answer 78

1. Theoretical models
   Required capital is calculated with risk measures using ERM.
2. Practical models
   Required capital is calculated using rating agency or regulatory models (ex: 175% of BCAR)

Question 79

Provide 1 advantage of theoretical models.

Answer 79

Required capital is more consistent with management’s view of risk.

Question 80

Provide 1 advantage and 1 disadvantage of practical models. How can we overcome?

Answer 80

Advantage: Easier to implement

Disadvantage: Uses proxies for risk (ex: premium) to measure capital instead of modelling risks directly.

We can compensate for this disadvantage by building rating agency and regulatory models into ERM.
A capital score can be calculated for each scenario and prob distribution of capital scores can be produced.
Required capital can then be set at different prob levels.

Question 81

Calculate the Marginal ROE and use it to decide which reinsurance option is best.

Answer 81

1. Calculate NPV(Ceded P - Ceded L) compared to current program
   Negative = cost of buying more
   Positive = benefit of buying less

This should release capital if negative and consume capital if positive.

Marginal ROE = delta(Ceded P - Ceded L)/delta(capital)

If marginal ROE is less than CoC, buying reinsurance is a good deal.

If marginal ROE is greater than CoC, buying LESS reinsurance is a good deal.

Question 82

Explain why accumulated risk must be considered when evaluating the value of reinsurance for LT LOBs.

Answer 82

Loss reserves absorb capital over multiple periods. Thus, loss reserves create accumulated risks.

Marginal ROEs for measuring reinsurance value are based on capital for a single year.

Thus, we must consider accumulated risk for LT LOBs.

Question 83

Define As-If Loss Reserves and explain how they are used.

Answer 83

Loss reserves that would exist at the beginning of a new AY if that business had been written in a steady state for all prior years.

We can approximate the PV of required capital for an AY over time by modelling the capital needed for both:
1. Current year for CAY
2. As-If Loss Reserves

Question 84

Provide 2 advantages of using As-If Loss Reserves.

Answer 84

1. It can measure the impact of accumulated risk caused by correlated risk factors across accident years.
2. It can fully measure the impact of reinsurance by applying reinsurance to AY and As-If Reserves.

Question 85

Explain how accumulated risks impact the distribution of underwriting loss and required capital for insurer.

Answer 85

Results of analysis of accumulated risks are highly dependent upon underlying projection risk model because reserves are exposed to trend risk.

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

Capital consumed is also greater.

Question 86

True or False?
The effect of accumulated risk on required capital is greater for Home insurer in a hurricane-prone area than a Work Comp insurer.

Answer 86

False,

Home insurer in a CAT prone area is a ST line.
Capital is needed more for CAY underwriting losses.
There is less accumulation of loss reserves.
Therefore less accumulated risk then WC.

So the effect of accumulated risk on required capital would be smaller.

Question 87

Justify an asset management that could reduce company’s earnings volatility during soft market.

Discuss a risk if strategy was implemented.

Answer 87

During a soft market, the company has deteriorating UW performance, thus reduce market share.

The company should shift assets to equities that provide higher investment yields to offset a poor underwriting performance.

Shifting to equities results in a higher investment risk due to increased reliance on stock market.

Question 88

Justify an asset management that could reduce company’s earnings volatility during hard market.

Answer 88

During a hard market, the company has improved UW performance, thus expand market share.

The company should shift assets to bonds that provide lower (but more stable) investment yields.

Question 89

Calculate the CF from a surplus note

Answer 89

CF = Note Amount*(coupon rate - bond yield)

Question 90

Discuss the modelling challenges that exist for economic capital.

Answer 90

ERM models are not reliable at such remote probabilities because of the approximations, assumptions and lack of data in the tail.

The prob level close to 100% (1-in-3000 is 99.97%) is impractical to model.

Question 91

Recommend an approach to using an enterprise risk model to set capital requirements that overcomes modelling challenges with economic capital.

Answer 91

The company can use impairment, rather than insolvency, as the reference point for the probability level.

Example: if the company wants capital level to be adequate so that an average of 1-in-100 year result destroys no more than 25% of its capital, then it would set its minimum capital requirements at 4 times TVaR@99.

Question 92

Discuss a risk of holding short-term assets and a risk of holding long-term assets, relative to liability duration.

Propose an approach that would reduce risk to surplus.

Answer 92

Short-term treasuries have durations shorter than liabilities and introduce reinvestment risk.

If interest rates drop, total investment income may not be sufficient to cover the liabilities.

If interest rates rise, longer-term investments 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.

Question 93

Briefly discuss three additional considerations that should be included in the asset-liability analysis to make it more realistic.

Answer 93

1. Add liabilities with variable timing and amount.
   In this case, duration matching is no longer possible because duration of liabilities is unknown.
2. Consider underwriting income in addition to investment income.
   This requires even more model complexity because we now need a model of the current business operation in addition to asset and liability models.
3. Consider accounting system
   Under SAP, bonds are amortized and liabilities are not discounted. Assets provide little hedging to liabilities.
   Under GAAP, bonds are marked to market and liabilities are not discounted. Once again, assets provide little hedging to liabilities.
   Under economic accounting, assets are marked to market and liabilities are discounted, hedging does occur.
   In this case, short investment portfolios increase risk and decrease return.
   Long-term investment portfolios increase risk and increase return.
   Choice of portfolio becomes a judgment call.