Brehem Chapter 2

Question 1

Three evolutionary steps of the decision analysis process

Answer 1

• Deterministic project analysis: uses a single deterministic forecast for project cash flows to produce an objective function like PV or IRR. Uncertainty is handled judgementally rather than stochastically. This analysis may demonstrate some sensitivities to critical variables
• Risk Analysis: forecasts of distributions of critical variables are input into a Monte Carlo simulation process to produce a distribution of the PV of cash flows. Risk judgement is still applied intuitively
• Certainty equivalent: expands upon risk analysis by quantifying the intuitive risk judgement using a utility function (i.e. corporate risk preference). Utility doesn’t replace judgement. Instead formalizes judgement so that it can consistently applied

Question 2

Explain how efficient market theory removes the need for the certainty equivalent step of the decision analysis and provide two counterarguements

Answer 2

• 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 it should ignore firm-specific risk as well
• Counter: difficult to determine which risks are firm-specific and which are systematic.
• Counter: Market-based risk signals (such as the risk-adjusted rate) often lack the refinement needed for managers to mitigate or hedge the risk

Question 3

Explain corporate risk tolerance

Answer 3

• refers to the organizations’s size, financial resources, ability and willingness to tolerate volatility

Question 4

Describe efficiency frontier

Answer 4

• graphs the portfolios that maximize return for a given risk level (Risk on the x-axis and reward on the y-axis)
• if current portfolio has the same return as one of the efficient portfolios but more risk, it is sub-optimal
• to select one of the efficient portfolios, firm 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

Question 5

Describe how return on risk-adjusted capital (RAROC) is determined and how it can be used to determine if an activity is worth pursuing

Answer 5

• allocate risk capital to portfolio elements. Then multiply the allocated risk capital by a hurdle rate to determine RAROC for each portfolio element
• economic value added (EVA) is NPV of activity’s cash flows minus RAROC. If EVA is positive, activity is worth pursuing

Question 6

Four advantages of using economic capital for ERM analysis

Answer 6

• provides unifying measure for all risks across an organization
• more meaningful to management than risk-based capital or capital adequacy ratios
• forces the firm to quantify the risks it faces and combine them into a probability distribution
• provides a framework for setting acceptable risk levels for the organization as a whole and for individual business units

Question 7

Two disadvantages of using std deviation to measure risk and give alternative risk measure that addresses the disadvantage

Answer 7

• favourable deviations are treated the same as unfavourable ones (use semistandard deviation- only uses unfavourable std dev)
• as a quadratic measure (ie. based on the second moment), it may not adequately capture market attitudes to risk (use skewness - since this uses a higher moment it might better capture market attitudes)

Question 8

Five type of tail-based risk measures

Answer 8

• VaR: percentile of probability distribution (limitation is that it only looks at one point in the loss distribution)
• TVaR: expected loss at a specified probability level and beyond (limitation is that it treats all large losses in the tail linearly)
• XTVaR: TVaR minus mean
• EPD: (TVaR minus Var)* (1 - probability level)
• 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 MV of this risk is the value of the default put option. Usually estimated using option pricing methods

Question 9

Describe probability transforms

Answer 9

• shift probability towards the unfavourable outcomes and then computing a risk measure with the transformed probabilities
• TVaR becomes WTVaR and this is not linear in the tail and considers a loss that is twice as large more than twice as bad

Question 10

Describe generalized moments

Answer 10

• expectations of a random variable that are not simply powers of that variable
• can be used to add weight to the losses in the loss distribution around the VaR percentile, using higher weights nearer to the percentile. This is the blurred VaR.

Question 11

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 11

• customer reaction: some customers care deeply about the amount of capital being held by insurers and/or financial rating of an insurer. Declines in financial ratings can lead to declines in business
• capital requirements of rating agencies: different rating agencies require different amounts 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. Important to retain renewal business. eg. if renewals are 80% of book, 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 12

What does it mean for a risk decomposition to be “marginal”. Why the marginal property is desirable. Describe two required conditions for a marginal decomposition.

Answer 12

• 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
• it links to the financial theory of “pricing proportionally 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
• 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. This is also known as homogenous of degree 1

Question 13

Describe how firm can allocate the cost of capital

Answer 13

• set the min. profit target of a business unit equal to the value of its right to call upon the capital of the firm. Then, excess of the unit’s profits over this cost of capital is the added value for the firm. We are allocating the overall firm value (rather than the cost of capital) to each business unit

Question 14

Explain how a business unit’s right to access capital can be viewed as a stop-loss agreement

Answer 14

• 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

Question 15

Provide one approach for calculating the value of the stop-loss agreement

Answer 15

• calculated the expected value of a stop-loss for the business unit at the break-even point

Question 16

Two disadvantages of leverage ratios

Answer 16

• don’t distinguish among business classes

- do not incorporate risks other than u/w risks

Question 17

Describe IRIS ratios

Answer 17

• 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 considred to be at risk and warrant regulatory scutiny

Question 18

How do risk-based capital (RBC) models differ from leverage ratios.

Answer 18

• RBC models combine measures of different aspects of risk into a single number

Question 19

Four main sources of risk in RBC models. how RBC models quantify these sources of risk

Answer 19

• invested asset risk, credit risk, premium risk, reserve risk
• each of these risks is measured by multiplying factors by accounting values. The magnitude of the vector varies by the quality and type of asset or the line of business

Question 20

Why could regulatory RBC models differ significantly from a rating agency RBC model. why could two rating agency models differ significantly

Answer 20

• Use of models: rating agency 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 -> rating agency models should have higher factors
• 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 21

Describe the difference between static and stochastic scenarios

Answer 21

• static scenarios are pre-defined scenarios. Stochastic scenarios are generated through a stochastic process

Question 22

Two critical features an actuary’s projection model must include:

Answer 22

• correlations among the various moving parts (eg. how do stock returns move with a shock event)
• include reflections of management responses to adverse financial results

Question 23

How does investment risk differ in each of the following asset/liability mixtures:

• asset portfolio with no liabilities
• asset portfolio with fixed duration liabilities
• asset portfolio with variable duration liabilites

Answer 23

• Asset portfolio with no liabilities: 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 introduce risk if depressed assets have to be liquidated to find liabilities. Duration matching would be good strategy to neutralize interest rate changes
• Asset portfolio with variable duration liabilities: duration matching is no longer possible because the duration of the liabilities is unknown. A model incorporating asset and liability fluctuations would be needed at this point to determine the optimal investment portfolio

Question 24

For each account system, explain how bonds and liabilities are valued and state whether assets successfully hedge against liabilities:

• statutory accounting
• GAAP accounting
• economic accounting

Answer 24

• statutory 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 25

Describe asset- liability modeling approach

Answer 25

• start with models of asset classes, existing liabilities, and current business operations
• define risk metrics: either income-based or balance-sheet based. depending on risk metric chosen, different risk measures may be appropriate eg. VaR and TVaR are better for b/s items such as surplus
• define return (eg return on equity or earnings): when defining return, the accounting system used should be consistent with the system used for defining risk
• define the timing or analysis: over single period (might not fully capture true nature of a business) or multi-period (may be too complicated to implement
• Define constraints: eg. which asset classes are not allowed by state regulators? which investments would drive RBC too high?
• model should be run for a variety of investment strategies, u/w strategies and reinsurance options: each combination of scenarios, thousands of simulations are created. the selected risk and return metrics should be calculated for each simulation
• create efficient frontier across various portfolio scenarios: plot current portfolio and the efficient frontier. find portfolios on the efficient frontier that can decrease risk without sacrificing return or increase return without increasing risk

Question 26

three paradigms for measuring the value of reinsurance

Answer 26

• 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
• reinsurance frees up capital: by purchasing reinsurance, insurers are able to hold less capital. 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 ROE number. as long as this ROE is less than the firm’s target return, the purchase was a good choice
• reinsurance adds market value to the firm

Question 27

why is it misleading to analyze the distribution of the differences in u/w results b/t two reinsurance program. What is a more useful way to compare the distributions of two reinsurance programs

Answer 27

• misleading since it assumes that the percentiles of each individual distribution relate to the same loss event. eg. 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
  more useful to analyze the differences in the individual probability distributions

Question 28

why using a combined ratio to compare reinsurance programs is misleading

Answer 28

• reinsurance program with stronger u/w results but more ceded premium would have a worse combined ratio (since we divide by net premium) even though the absolute u/w income is better

Question 29

Two classes for require capital

Answer 29

• 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)
• practical models: those that derive required capital based on rating agencies ( eg. BCAR), regulatory requirements (eg, RBC, ICAR) or actual capital

Question 30

Identify and briefly describe one disadvantage of using practical models for required capital. How can this disadvantage be overcome

Answer 30

• 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
• can compensate by building the practical models into the ERM. 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 31

how is accumulated risk created. provide an example

Answer 31

• result from elements of an insurer’s business that absorb capital over multiple periods. eg. loss reserves

Question 32

describe as-if loss reserves and explain how it can be used to approximate accumulated risk

Answer 32

• for AY of new business, the as-iff loss reserves are the reserves that would exist at the beginning of the AY, if that business had been written in a steady state in all prior years. This acts as a proxy of the accumulated risk from the prior years of reserves

Question 33

provide two advantages of as-if loss reserves

Answer 33

• can measure the impact of accumulated risk caused by correlated risk factors across accident years
• reinsurance being considered can by applied to the AY and as-if reserves, providing more valid measure of the impact of reinsurance on accumulated risk and on capital absorbed over the full life of the accident year

Question 34

briefly describe how the tails of the distribution of U/W results changes when including accumulated risk

Answer 34

• distribution of u/w results is less compressed and has bigger tails

Question 35

Discuss the modeling challenges that exist for economic capital. Recommend and approach to using an enterprise risk model to set capital requirements that overcomes the modeling challenges with economic capital

Answer 35

• ERM models aren’t reliable at such remote probabilities because of the approximations, assumptions and lack of data in the tail. (eg. probability level of 99.97 would be impractical to model)
• can use impairment rather than insolvency as the reference point for the probability level (if company wants the capital level to be adequate so that an average 1-in-100 year result destroys no more than 25% of its capital then it would set its min capital requirement at 4 times TVaR at 99%

Question 36

Discuss two different methods the company can use to allocate capital

Answer 36

• Proportional allocation: calculate the risk measure for the insurer and each line of business unit separately, allocate the total risk measure for the insurer proportionally using the individual risk measure
• marginal decomposition: calculate the overall risk measure for the insurer. Then, calculate the marginal co-measures for each business unit. The marginal co-measures sum to the company risk measure

Question 37

For RBC model, other than invested asset risk, credit risk, premium risk, reserve risk, identify an additional risk the rating agency should consider for the model and briefly discuss why it should be included

Answer 37

• accumulation risk (not to be confused with accumulated risk in sect 2.5): this is the exposure to cats that impact a large number of insureds. This is typically measured through stress testing of the impact of a second severe event as well as through the use of annual aggregate loss amounts rather than per occurrence losses.
• can pose a significant risk to an insurer and should be included, otherwise the required capital won’t distinguish between insurers with different cat risks

Question 38

Describe asset-liability matching and asset-liability management and discuss the differences

Answer 38

• asset-liability matching: establishing and maintaining an investment portfolio with the same duration as the liability portfolio
• Asset-liability management: comprehensive analysis and management of the asset portfolio with respect to the current liabilities and future cash flows from asset/liability portfolios and future premiums
• asset-liability matching just looks at interest rate risk, but ALM incorporates other risks (inflation, credit, market). ALM also considers the impact of hedges such as equities for inflation or reinsurance.