Brehm 2 CF Only

Question 1

Describe the 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 present value or internal rate of return. Uncertainty is handled judgmentally 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 present value of cash flows. Risk judgment is still applied intuitively
⇧ Certainty equivalent – expands upon risk analysis by quantifying the intuitive risk judgment using a utility function (i.e. corporate risk preference). The utility function does not replace judgment. Instead, it formalizes judgment so that it can be consistently applied

Question 2

a) Explain how the efficient market theory removes the need for the certainty equivalent step of the decision analysis
b) Provide two counterarguments to this theory.

Answer 2

Part a:
⇧ 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
Part b:
⇧ It is difficult to determine which risks are firm-specific and which risks are systematic. Attempts have been made to determine which corporate decisions a↵ected the stock price and which did not, but the results are inconclusive
⇧ 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

Briefly explain corporate risk tolerance.

Answer 3

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

Question 4

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

Answer 4

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 one 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 vice versa)

Question 5

a) Briefly describe how return on risk-adjusted capital (RAROC) is determined.
b) Explain how RAROC can be used to determine if an activity is worth pursuing.

Answer 5

Part a:
⇧ 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
Part b:
⇧ 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 6

a) Assuming risk capital itself has been allocated, explain how cost-benefit analysis can be used to determine which risk mitigation strategies should be pursued.
b) 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 6

Part a:
⇧ Pursue activities where the benefit (i.e. decrease in required capital) exceeds the costs of implementation
Part b:
⇧ Pursue activities that produce positive incremental EVA

Question 7

Provide four advantages of using economic capital for an ERM analysis.

Answer 7

⇧ Provides a 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 8

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 8

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 9

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 9

Part a:
⇧ Favorable deviations are treated the same as unfavorable ones
⇧ As a quadratic measure (i.e. based on the second moment), it may not adequately capture market attitudes to risk
Part b:
⇧ Semistandard deviation – only uses unfavorable deviations
⇧ Skewness – since this uses a higher moment, it might better capture market attitudes

Question 10

Briefly describe five types of tail-based risk measures.

Answer 10

⇧ 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 11

a) Briefly describe probability transforms.
b) 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 11

Part a:
⇧ Probability transforms measure risk by shifting the probability towards the unfavorable outcomes and then computing a risk measure with the transformed probabilities
Part b:
⇧ 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 12

Briefly describe generalized moments.

Answer 12

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

Question 13

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 13

⇧ 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 14

a) Briefly describe what it means for a risk decomposition method to be “marginal.”
b) Provide two reasons why the marginal property is desirable.
c) Describe two required conditions for a marginal decomposition.

Answer 14

Part a:
⇧ 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
Part b:
⇧ 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
Part c:
⇧ 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 15

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 15

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 16

Provide two disadvantages of leverage ratios.

Answer 16

⇧ They do not distinguish among business classes

⇧ They do not incorporate risks other than underwriting risks

Question 17

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

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 considered to be at risk and warrant regulatory scrutiny

Question 18

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 18

Part a:
⇧ Unlike leverage ratios, risk-based capital (RBC) models combine measures of different aspects of risk into a single number
Part b:
⇧ Invested asset risk
⇧ Credit risk
⇧ Premium risk
⇧ 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 19

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 19

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 20

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

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

Answer 20

Part a:
⇧ Static scenarios are pre-defined scenarios (defined by the firm). Stochastic scenarios are generated through a stochastic process
Part b:
⇧ The projection model should include correlations among the various moving parts (for example, how do stock returns move with a shock event)
⇧ The projection model should include reflections of management responses to adverse financial results

Question 21

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 21

⇧ 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 – In this case, 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 is unknown. A model incorporating asset and liability fluctuations would be needed at this point to determine the optimal
investment portfolio

Question 22

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 22

⇧ 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 23

Briefly describe three paradigms for measuring the value of reinsurance.

Answer 23

⇧ 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. 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
⇧ Reinsurance adds market value to the firm

Question 24

a) Explain why it is misleading to analyze the distribution of the differences in underwriting results between two reinsurance programs.
b) Briefly describe a more useful way to compare the distributions of two reinsurance programs.

Answer 24

Part a:
⇧ 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
Part b:
⇧ It is more useful to analyze the differences in the individual probability distributions

Question 25

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

Answer 25

⇧ 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 26

Briefly describe two classes for required capital.

Answer 26

⇧ 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 (ex. BCAR, S&P CAR), regulatory requirements (ex. RBC, ICAR), or actual capital

Question 27

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

Answer 27

Part 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
Part 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 28

a) Explain how accumulation risk is created. Provide an example of something that produces accumulation risk.
b) Briefly describe the concept of as-if loss reserves and explain how it can be used to approximate accumulation risk.
c) Provide two advantages of as-if loss reserves
d) Briefly describe how the tails of the distribution of underwriting results changes when including accumulation risk.

Answer 28

Part a:
⇧ 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
Part b:
⇧ 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
Part c:
⇧ 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
Part d:
⇧ By including accumulated risk, the distribution of underwriting results is less compressed and has bigger tailson risk