Section D

Question 1

Describe the treatment of covariance under shapley value and covariance share methods

Answer 1

Shapley value: Allocates the mutual covariance equally between accounts
Covariance Share method: Allocates mutual covariance according to weights selected by the user (proportion to loss size)

Mango

Question 2

List the different risks that surplus can protect an insurer from

Answer 2

• Asset risk: chance assets will depreciate
• Pricing risk: chance that losses & expenses are ultimately greater than initially expected
• Reserving risk: risk that reserves are insufficient
• Asset-liability risk: chance that changes in interest rates will affect the market value of assets
  differently to liabilities
• Catastrophe risk
• Reinsurance risk: risk that reinsurance recoverables won’t be collected
• Credit risk: risk that agents/insureds won’t remit premium

Feldblum

Question 3

Explain two ways that u/w profit provisions and what method is preferred by Robbin

Answer 3

• Rate of return approach: rates should be regulated to ensure that companies are able to achieve an adequate return
• Constrained free market theory: the premiums will move to an optimal level, via market forces

Robbin argues that the structure of the insurance industry is greatly different than utility companies: there are a large number of firms, with relatively low market shares.

Robbin_uw

Question 4

What is the objective of the method PVI/PVE

Answer 4

Aims to determine an U/W profit provision which in the ratio of PV of Income to PV of Equity equal to a target rate of return.

Robbin_IRR

Question 5

Briefly describe 2 assumptions made by the insurance IRR model

Answer 5

1. Amount of surplus requirement:
   - Difficult to determine since no foxed relation between premium and surplus
   - Need to be allocated by LOB
2. Timing of surplus commitments/release:
   - Can be related to UEPR, Loss reserve or both

Feldblum

Question 6

Give 3 advantages of using return on sales to assess rate equity

Answer 6

• Achieves true rate equity
• Similar to the concept of markup (understandable to policyholder)
• No need to allocate surplus (artificial)

McClenahan

Question 7

Explain added complication in determining the optimal capital structure for an insurer

Answer 7

• Higher level of reserves implies a higher level of written premium, which could possibly increase diversification. This would partially offset the increase in variability of results. It is not as straightforward as : higher debt = higher risk
• Also, loan interest (u/w loss) is not known until many years

Ferrari

Question 8

Give advantages and disadvantages of the PV CF Return Method

Answer 8

Method advantage:
- The present value of U/W cash flows is what most people think about with regards to U/W profit
Method disadvantage:
- It is not clear what sort of profit is being measured. The cash flows do not have the same timing as GAAP income

Robbin_uw

Question 9

Give a few examples of parameter selection questions

Answer 9

o What discount rate should be used?
o What is the right target return?

Robbin_uw

Question 10

List market characteristics that could affect the company ability to earn a reasonable return

Answer 10

• Size/composition residual market
• Number of insurers (degree of competition)
• Degree of product diversity and innovation

McClenahan

Question 11

Give 3 advantages of calendar year data and a disadvantage

Answer 11

A:

• Data is easily obtained and verified (annual statement)
• Since the figures are reported in filed documents, less manipulable by insurer
• The CY investment portfolio yields are relatively stable

D:
-CY results are prospective, not totally applicable to prospective ratemaking

Robbin_Uw

Question 12

What is the objective of the method IRR on equity flow

Answer 12

Select an U/W profit provision to achieve a target rate of return on the equity flows.

Robbin_IRR

Question 13

What is the interest cost incurred by the insurer to use the reserve?

Answer 13

U/R (in the case of U/W losses) can be thought of as an “interest cost” incurred by the firm to use the reserves, which were contributed by the policyholders.

Ferrari

Question 14

Describe renewal additivity in risk load methodology

Answer 14

Sum of renewal risk loads of each risk is equal to the risk load for the aggregate portfolio.

Mango

Question 15

Describe why insurer’s CF patterns are different than most companies

Answer 15

Insurers collect money at inception (inflow) and pay it out during the policy period (outflow). Most industries have the opposite patterns.

Feldblum

Question 16

List and briefly describe 5 types of u/w profit

Answer 16

• Provision included in manual rates/filings to change manual rates
• Corporate target U/W profit provision: generate an expected return similar to that provided by investments with similar risk
• Breakeven U/W profit provision: rate of return to stockholders equal to the rate of return on risk free investments. No compensation for the risk
  borne
• Charged U/W profit provision: the rate achieved after applying experience and schedule rating modifications, as well as other adjustments to the manual rate
• Actual U/W profit: these will differ from the charged provisions, as the provisions for losses and expenses most likely won’t be accurate; and also because the actual catastrophe loss in a year most likely won’t match the provision

Robbin_Uw

Question 17

List regulator’s desired properties of the riskiness leverage ratio

Answer 17

• Be 0 until the capital is seriously impacted
• Not decrease (for excess that significantly exceeds capital) because of the risk to the state guaranty fund

Kreps

Question 18

Explain why insurer’s management has the ability to influence the results in the financial statement

Answer 18

Since there is a lot of uncertainty in the estimation of losses, management can either strengthen (good year, to increase loss and reduce return) or weaken the reserves (reduce u/w loss to increase return).

McClenahan

Question 19

Why should the CY investment income offset procedure requires many iterations

Answer 19

PLR is used in the determinant of profit provision but it also is impacted by the profit provision

Robbin_uw

Question 20

List management’s desired properties of the riskiness leverage ratio

Answer 20

• Be a down side measure
• Be roughly constant for excess that is small compared to capital
• Become much larger for excess that significantly impacts capital
• Reduces to 0 (at least doesn’t increase) for excess that significantly exceeds capital. Once capital is exceeded, bankruptcy so no need to consider past that point.

Kreps

Question 21

Give advantages and disadvantages of the PV Offset Method

Answer 21

Method advantages:
- Accounts for investment income in a simple manner
- Not distorted by rapid growth/decline (uses PLR)
- No need to select a target return, or allocate surplus
Method disadvantages:
- Have to choose discount rate
- Have to choose payment pattern
- Lack of economic theory to support calculation

Robbin_uw

Question 22

List and briefly describe examples of leverage models to determine risk loads

Answer 22

1. Risk neutral: Risk load is 0. Appropriate when in most probable scenarios, liabilities are small compared to available capital.
2. Variance: Whole distribution is relevant
3. TVaR: riskiness leverage ratio is 0 up to a point and then constant
4. VaR: Insurer is only concerned by particular level of losses that threatens its surplus
5. Semi-Variance: Only relevant for bad results (worse than average)
6. Mean downside deviation: Most naive measure. Assigns capital for bad results in proportion to how bad they are.
7. Assigns capital pro-rata to its contribution to the excess over the mean

Kreps

Question 23

What is the main difference between SAP and GAAP accounting frameworks

Answer 23

SAP Incurred expenses are incurred according to a fixed pattern, whereas in GAAP the expenses are incurred as the premium is earned.

Robbin_IRR

Question 24

Name 3 key inputs to which premiums are sensitive

Answer 24

• Surplus (Higher surplus = higher profit, since investors demand higher return for more investment)
• Interest (Higher interest = lower profit margin, since investment income will finance a part of the return)
• Payout pattern (Higher duration = lower profit margin, again more investment income)

Robbin_IRR

Question 25

Describe relation between I/A and U/R in Ferrarri non-equity capital formula in decision to keep writing business or not

Answer 25

- If U/R > 0, the term in parenthesis is positive, so it makes sense for the insurer to keep writing business - If the U/R < 0), but the absolute value is less than I/A, the term in parenthesis is still positive, implying that is still profitable to keep writing business. - Finally, if U/R < 0 and (I/A + U/R) < 0, at this point, it makes sense for the insurer to stop writing business, since writing business will reduce the ROE.

Question 26

Contrast profit and rate of return as a profitability measure

Answer 26

Profit: - Absolute number - Used to pay dividends or grow company - Hard to compare companies Rate of Return - % of a particular base (Equity, Asset and Sales) - Measure of efficiency - Used to compare companies McClenahan

Question 27

List reasons why alternative pricing models have been proposed for the fixed profit margin

Answer 27

- Lack of theoretical justification of the fixed margin - High interest rates (implying the fixed margins may be too low) - Increasing competitiveness of the insurance industry (insurers may therefore have periods of reduced profit margins) Feldblum

Question 28

List some risk sources than can generate surplus need

Answer 28

- Risk of not making plan - Risk of serious deviation from plan - Risk of not meeting the investor analysts’ expectations - Risk of a downgrade from the rating agencies - Risk of triggering a regulatory notice - Risk of going into receivership - Risk of not getting a bonus Kreps

Question 29

List factors that will influence the amount of capital allocated to a new member of the group in the game theory

Answer 29

- Stability/incentive to split from the group - Bargaining power - Marginal impact to the group’s characteristic function value Mango

Question 30

List a few features of cooperative games with tranferablw utilities

Answer 30

- Participants that have benefits or costs to share - Opportunity to share the benefits/costs due to the cooperation of all the participants - Ability of the players to enter into negotiations - Conflicting player objectives, where each wants to maximize his/her share of the benefits Mango

Question 31

Describe how the financial market impacts the product market in insurance transactions

Answer 31

- Higher cost to obtain capital will lower the supply of insurance - Higher returns achievable will increase the supply of insurance Feldblum

Question 32

Why is the opportunity cost calculated at risk free rate?

Answer 32

Policyholder is not exposed to any of the risk of the insurer’s investment: if the insurer speculates and loses money, the policyholders do not have to provide for this shortfall. McClenahan

Question 33

Describe 2 factors that drives the relation between P/S and I/A

Answer 33

- A higher portion of the surplus is from current business, and is therefore in the form of uninvestable balances. - A higher ratio of P/S results in more risk to Owners Equity. To compensate, insurers will need to follow more conservative investment policies. Ferrari

Question 34

Contrast the possible options of rate to discount losses in the PV Offset method

Answer 34

There are a few options of rates at which to discount the losses: - Portfolio yield from a recent year - Estimated portfolio yield for the year in which the rates will be in effect - New money yield New money yields are more suited to the prospective nature of ratemaking. However, historical prospective yields are more stable & verifiable. Robbin_uw

Question 35

Give advantages and disadvantages of the Risk-adjusted discounted CF method

Answer 35

Method advantages: - Great intuitive appeal - Grounded in modern financial theory (CAPM) - Not necessary to determine a target rate of return Method disadvantage: - It is hard to determine beta for liabilities: no active market where liabilities are traded and little data exists from which to calculate parameters Robbin_uw

Question 36

Give reasons why expense projection less accurate than premium and losses projection

Answer 36

- Data: companies often do not monitor the expense payment patterns - Vary widely by company - Risk size: unlike losses, not all expenses are proportional to premium - Policy year: several expenses are higher in the first policy year than future years Feldblum

Question 37

Give a few examples of model construction questions

Answer 37

o Should surplus be included in the model? o How should the surplus requirement be determined? o How should risk be incorporated into the model? o It is better to use cash flows or incomes flows? o How to reflect income taxes? Robbin_uw

Question 38

Give advantages and disadvantages of the CY investment income offset procedure

Answer 38

A: - Easy to get the numbers - Calculation is short & relatively straight forward D: - Lack of economic theory supporting the calculation - Results distorted if large change in volume or reserve adequacy (based on retro numbers) Robbin_uw

Question 39

Explain one problem with the IRR assumption and reasons why it is rarely an issue in pricing

Answer 39

IRR assumes that revenues are reinvested at IRR, which is rarely the case. - If IRR > cost of capital, insurers can write more policies and grow at IRR. The “reinvestment rate” of revenue is equal to the IRR, and therefore assumption holds. - Policies are usually priced using an underwriting profit provision which sets the IRR equal to the cost of capital. Again this would mean that the assumptions hold, since IRR = CC = Reinv Rate. Feldblum

Question 40

List 2 factors affecting current underwriting results

Answer 40

- Current reserving decisions - Amortization of past reserving decisions McClenahan

Question 41

Name 2 factors influencing the opportunity cost

Answer 41

1. Line of business: Payment pattern 2. Cash needed to support the infrastructure: This cannot be invested McClenahan

Question 42

List 2 situations where NPV and IRR analysis results could differ

Answer 42

- Projects with unusual cash flows - Projects with budget constraints/mutually exclusive projects Feldblum

Question 43

Describe how the product market impacts the financial market in insurance transactions

Answer 43

- Higher demand for insurance will increase the return to investors - Inadequate rates will pull ressources from the industry Feldblum

Question 44

According to game theory, what are a few rules for allocation

Answer 44

- The allocation methods must be renewal additive - Coalition should be stable (Fair). There should be no possibilities where a subgroup is better on its own. Mango

Question 45

Define the insurance leverage factor

Answer 45

It looks at the relationship between the money borrowed from the policyholders (reserve) and the owner investment in the company (surplus). Ferrari

Question 46

Describe the factor that drives the relation between U/P and I/A

Answer 46

- Higher U/W profit means that the insurer can engage in more aggressive investments - More money to invest from the additional premiums Ferrari

Question 47

Explain why both marginal surplus and marginal variance methods are not renewal additive

Answer 47

- In the MS method, Σ Renewals Risk Loads < Risk Load for the portfolio. Accounts will be undercharged due to sub-additivity of square root. - On the other hand, the MV method will overcharge the accounts, as Σ Renewal Risk Loads > Risk Load for Portfolio due to double counting the Covariance. Mango

Question 48

Give advantages and disadvantages of pricing method IRR on equity flow

Answer 48

A: -Simple to interpret: Expected interest earned on shareholders loan of surplus to the company - Nicely captures the impact that accounting rules and regulatory capital restrictions directly impacts shareholders D: -Need to assume a particular surplus requirement which may not make sense on a LOB/policy basis - Need to identify a target IRR - Assumes reinvestment rate = IRR Robbin_IRR

Question 49

List 2 factors that affect the value of the firm

Answer 49

- Expected Earnings stream - Rate at which this stream is discounted by the market Ferrari

Question 50

What are Robbin's 2 general goals for price of policies?

Answer 50

- Should be consistent & sensitive to risk. - Should reflect management’s risk return preferences. Robbin_IRR

Question 51

What will be the consequences on the market if insurer perceive rates as inadequate (unreasonable rate of return)

Answer 51

- Increasing size of residual market - Reducing degree of product diversity - Reduced innovation McClenahan

Question 52

List the different desired qualities for an allocatable risk load

Answer 52

- It can be able to be allocated down to any level - The risk load of any sum of random variables should equal the sum of the risk loads allocated individually - The same additive formula can be used to calculate the risk load for any subgroup or group of groups Kreps

Question 53

List and briefly describe the 3 problems with using ROE in regulation

Answer 53

1. Focuses on return on equity instead of rate equity 2. Surplus allocation is artificial since 100% of surplus is available to support each risk. Regulation based on ROE requires surplus allocation. 3. ROE regulation is a complicated method of regulating ROS, because of the usage of target ratios of premium to surplus to assign surplus McClenahan

Question 54

Describe opportunity cost

Answer 54

Lost investment income because premiums are paid by the policyholder before the losses and expenses are paid by the insurer. McClenahan

Question 55

Why should investment income from surplus be excluded from the opportunity cost?

Answer 55

- Surplus is not owned by the policyholders, but rather the owners of the insurer - Including surplus will penalize high surplus insurers, as they will need to charge lower premiums McClenahan

Question 56

List the different parties involved in insurance industry and which metric interests them

Answer 56

1. Investors are interested in ROE - Which company to invest in - Prefer companies that generate a higher return from a given equity investment 2. Society is interested in ROA - Which companies are best using resources - Prefers that companies use the assets efficiently 3. Regulators/Actuaries are interested in ROS - Make sure rates are not excessive, inadequate, unfairly discriminatory Ferrari

Question 57

Describe a practical criticism of the IRR model in relation to regulation and a reason why insurers are more likely to run into this problem

Answer 57

Regulators may believe that insurer is profitable if IRR is greater than investment yield or even only positive. Having IRR lower than cost of capital is a clear sign of unprofitability. Insurer's capital is not fixed (based on reserves for example). This means that fluctuating results will make surplus requirement move as well (investment income on surplus), offsetting u/w results. Feldblum

Question 58

Describe the riskiness leverage ratio

Answer 58

Arbitrary selection by management, allowing their views towards risk to be incorporated Kreps

Question 59

Explain what may explain cash flow reversal in IRR analysis

Answer 59

In many cases, these sign reversals are not true reversals, but instead result from oversimplifications in the analysis Feldblum