Feldblum: Pricing Insurance Policies: IRR Model

Question 1

• early procedures to determine premium used fixed profit margins
• several factors encouraged alternative pricing models to be proposed

Answer 1

1. lack of theoretical justification of fixed margin
2. high interest rates (implying the fixed margins may be too low)
3. increased competitiveness of insurance industry (insurers may therefore have periods of reduces profit margins)
   - one example of these new models is the Internal Rate of Return insurance pricing model

Question 2

there are 2 points of view in which to look at insurance transactions

Answer 2

Financial market (shareholders) =expected return is influenced by risk to sharehlolders; IRR model looks at this market

Product market (policyholders) =premium is affected by supply/demand of insurance

Question 3

2 views are interrelated

Answer 3

Financial Market Product Market

Higher cost to obtain capital eg loans -> Lower supply of insurance

Higher returns achievable by investors -> Higher supply of insurance

Product Market Financial Market

Higher demand for insurance -> Better return for investors

Inadequate rates -> Resources pulled from industry

Question 4

these relationships are strong

Answer 4

for the industry but are weak for individual firms

-higher returns achievable in financial market will increase supply of insurance but not all firms will be able to increase the supply by the same degree if at all

Question 5

IRR models focus

Answer 5

cash flows in financial market

-product market is only accounted for through its impact on transactions between company and shareholders via interrelationships

Question 6

companies in various industries can use IRR analysis to help determine whether or not

Answer 6

to take a certain project

Question 7

IRR analysis compares IRR to

Answer 7

opportunity cost of capital, OCOC

Projects are accepted as long as IRR > OCOC

Question 8

Internal rate of return

Answer 8

rate which sets NPV of cashflows to 0

Question 9

Opportunity cost of capital

Answer 9

investment return that providers of capital could earn from an alternate investment (return they are sacrificing by investing in given project)

Question 10

Projects are accepted as long as

Answer 10

IRR > OCOC

calculate difference in cashflows between 2 different projects, calculate IRR (want to focus on incremental cashflows because if you only base IRR off of cashflows from project 2, you ignore change in cashflows from losing project 1), compare IRR to OCOC

Question 11

cashflow patterns for insurers differ from most companies

Answer 11

1. insurers collect money at inception = inflow
2. pay it out during policy period = outflow
   - most industries have the opposite pattern

Question 12

cashflow pattern for equity contributors to insurers is opposite of cashflow pattern for insurers

Answer 12

1. at start of policy, investors need to provide money (surplus) which supports insurer’s policies; this money = outflow
2. as policies expire and losses are paid, this surplus can be returns to investors; this return of surplus = inflow

Question 13

IRR model takes view point of

Answer 13

equity contributors

Question 14

to determine IRR, model needs to make assumptions about

Answer 14

Amount of surplus requirements

Timing of surplus commitments

Timing of surplus release

-1st assumption is difficult to determine because there is not a fixed relationship between premium & surplus

Question 15

companies can not derive the exact amount of surplus needed by

Answer 15

basing it off premiums

Question 16

once surplus requirement is determined

Answer 16

it is allocated to LOB in order to determine IRR by line

-this allocation is often in proportion to reserves and/or premiums

Question 17

this allocation using reserves is going to result

Answer 17

in more surplus being allocated to longer tail lines

Question 18

All being else equal, IRR reduces as amount of

Answer 18

surplus contributed increases

Question 19

if surplus is assumed to be committed once policy is written and no longer needed when it expires

Answer 19

short tail policy will have same commitment/ release timing as long tail since there is no impact from reserves

Question 20

if surplus is committed when UEPR is established and declines as losses are paid

Answer 20

long tail lines will retain the surplus for longer period than short tail line; at any given point in time, long tail lines should have more surplus

higher surplus results in lower IRR

note we should also account for average duration between the loss occurrence and claim payment

Question 21

expense projection is often

& reasons

Answer 21

less accurate than premium and loss projection for several reasons

1. data: companies often do not monitor expense payment patterns as it is not required to populate Schedule P
2. expense levels vary widely by company
3. risk size: unlike losses, not all expenses are proportional to premium
4. policy year: several expenses are higher in 1st policy year than future yrs

Question 22

when calculating equityflows, what you need to calculate/populate

Answer 22

premium

loss paid

expenses

reserves (loss and or UEPR)

investment income

required surplus

contribution by equityholder

total assets pre distribution

distibution to equityholder

total assets post distribution

Question 23

Contribution by Equityholders includes

Answer 23

$$ to cover excess of loss reserve over premium

Contribution to equityholder @t=0: reserves + surplus – (premium – expense)

Question 24

calculating tax

Answer 24

tax on UW income and investment income

UW income is (prem-expenses)@t=i-1 - (paid loss+reserves)@t=i

Investment income is (reserves+surplus)@t=i-1

Question 25

Total assets pre distribution

Answer 25

(Total assets post distribution)@t=i-1 * (1+i)

Question 26

Distribution to equityholder

Answer 26

total assets pre distribution – paid loss – paid tax – total assets post distribution

Question 27

3 ways surplus can be allocated to a line of business & when surplus is committed and when it is released

Answer 27

committed__released

• premium: policy effective date expiration date
• loss reserves: loss occurrence loss payment
• loss reserves & premium: effective date loss payment

*if premium, capital is released at t=1

*timing of surplus commitment and release is different

*surplus required is different

Question 28

Capital allocated by:

premium

reserves

reserves in steady state

Answer 28

Capital allocated by premium = capital *(prem LOB A)/Ʃ(prem LOB i)

Capital allocation by reserves = capital *(reserves LOB A)/Ʃ(reserves LOB i)

Capital allocated by reserves in steady state = capital * (prem * LR * reserve duration)

Question 29

NPV analysis

Answer 29

discounts all future cashflows to present date at OCOC

Projects with positive NPVs may be accepted

Question 30

most of the time, NPV and IRR will produce the same accept/reject decision

there are situations where they may differ

Answer 30

Projects with unusual cashflows

Projects with budget constraints/mutually exclusive projects

**due to issues described later, we can conclude that NPV analysis is preferable to IRR analysis

Question 31

regarding cashflow, most projects involve a series of outflows followed by a series of inflows

Answer 31

• if patterns change more than once ie outflow followed by an inflow followed by another outflow, there may be 2 positive roots to IRR
• in many cases, the sign reversals are not true reversals but instead result from oversimplifications in the analysis
• insurer often simplifies recognition of certain revenues/expenses by recognizing them at single point in time, instead of uniformly -> may cause reversal due to large magnitude of recognizing a series of payments at one point in time

Question 32

if oversimplifications are corrected

Answer 32

can be seen that in insurance industry expected cashflows rarely show reversals

-there may be reversals in actual cashflows

-IRR analysis can be used for expected cashflows whereas NPV can be used on actual

Question 33

projects are sometimes mutually exclusive

Answer 33

-NPV and IRR do not necessarily result in the same ranking of these projects

Question 34

IRR analysis assumes that

Answer 34

revenues are reinvested at IRR which is not the case most of the time

-NPV is preferable since it does not make this assumption

Question 35

problem with mutually exclusive projects usually applies to certain capital budgeting decisions

Answer 35

• problem is rarely an issue for this IRR pricing model for following reasons:
  1. if pricing model produces an IRR which is greater than cost of capital, insurers can use this extra revenue to write more policies and can effectively grow at IRR rate; as long as it maintains its current UW standards, reinvestment rate of revenue = IRR and IRR assumptions hold
  2. policies are usually priced using UW profit provision which sets the IRR = cost of capital; this would mean that the assumptions hold since IRR = cost of capital = reinvestment rate

Question 36

insurer can have problems with regulators if following conditions apply

Answer 36

0 < IRR < COC

Investment yield < IRR < COC

• company is clearly unprofitable as shown by the fact that IRR < COC
• some regulators may believe that this is sufficient if it is positive as it implies that the insurer is making money
• they may believe that is more than sufficient if it is also exceeding the investment yield

Question 37

-insurers are more likely than utility companies to run into problem of positive IRRs which are less than COC

Answer 37

1. for utility companies, capital is fixed, known amount which does not depend on projections of this model
2. for insurers, required surplus is an assumption which could be based off of reserves of the company; deteriorating results usually result from increasing reserves which means that the assumed required surplus level would also increase; this increased surplus level would produce increased investment income which would offset some of the UW loss and keep IRR > 0

Question 38

because insurers are more likely to have positive IRRs which are less than COC and regulators may potentially find these returns adequate

Answer 38

it is important to present filings in such way that regulators do not get false impression that a company is profitable when it indeed is not

• NPV analyses may be appropriate in these scenarios because they discount cashflows at COC and therefore would produce a negative number in case that return on investment is less than COC
• this is clear demonstration that project is not profitable unlike demonstration from IRR analysis

Question 39

insurer needs surplus to protect itself against various risks

Answer 39

Asset risk: chance assets will depreciate

Pricing risk: chance that losses and 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

Cat risk

Reinsurance risk: risk that reinsurance recoverables won’t be collected

Credit risk: risk that agents/insureds won’t remit premium

Question 40

amount of surplus required often depends on policy form

Answer 40

Claims made contracts eliminate pure IBNR and therefore uncertainty of reserves; less uncertainty means that less surplus is needed

Service contracts involves no insurance risk and therefore no surplus is required for insurance risk

Retrospective contracts share risk between insurer and insured; surplus required is between surplus

Question 41

IRR models will differ in their treatment of various policy forms

Answer 41

1. some models will make no distinction
   - this will overstate risk on retro policies because it neglects the fact that the insured is sharing the risk
   - this will understate risk for excess policies because insurer is bearing all risk above the limit
2. others may allocate surplus only in proportion to true insurance risk
   - this will understate risk for retro, excess, and large deductible policies; these all have less insurance risk due to lower amount of coverage but there is a lot more volatility involved than a standard prospective policy

Question 42

firms use assets to produce output just as insurers use

Answer 42

surplus to write policies

Question 43

there are differences between fixed assets of a manufacturer and surplus of an insurer

Answer 43

1. manufacturer can objectively measure needed assets whereas for an insurer the needed surplus is an estimate based on expected future development
2. manufacturer can divide the assets into product as different products would use different types of assets; surplus for an insurer can not really be divided into LOB

Question 44

in terms of amount of surplus held, approach of insurers differs from firms in other industries

Answer 44

• firms in other industries choose a strategic amount of investments by conducting analysis of potential returns; if returns are favorable, they will invest more funds
• for an insurer amount of surplus often isn’t a deliberate amount but rather heavily dependent on past profits of firm ie insurers with high profits in past would have strong levels of surplus

Question 45

Briefly describe two items that should be considered when allocating surplus to auto liability vs. workers compensation insurance.

Answer 45

variability of potential losses: higher volatility requires more surplus

length of the payment pattern: longer tail lines may require more surplus