Feldblum: Pricing Insurance Policies: IRR Model Flashcards
- early procedures to determine premium used fixed profit margins
- several factors encouraged alternative pricing models to be proposed
- lack of theoretical justification of fixed margin
- high interest rates (implying the fixed margins may be too low)
- 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
there are 2 points of view in which to look at insurance transactions
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
2 views are interrelated
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
these relationships are strong
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
IRR models focus
cash flows in financial market
-product market is only accounted for through its impact on transactions between company and shareholders via interrelationships
companies in various industries can use IRR analysis to help determine whether or not
to take a certain project
IRR analysis compares IRR to
opportunity cost of capital, OCOC
Projects are accepted as long as IRR > OCOC
Internal rate of return
rate which sets NPV of cashflows to 0
Opportunity cost of capital
investment return that providers of capital could earn from an alternate investment (return they are sacrificing by investing in given project)
Projects are accepted as long as
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
cashflow patterns for insurers differ from most companies
- insurers collect money at inception = inflow
- pay it out during policy period = outflow
- most industries have the opposite pattern
cashflow pattern for equity contributors to insurers is opposite of cashflow pattern for insurers
- at start of policy, investors need to provide money (surplus) which supports insurer’s policies; this money = outflow
- as policies expire and losses are paid, this surplus can be returns to investors; this return of surplus = inflow
IRR model takes view point of
equity contributors
to determine IRR, model needs to make assumptions about
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
companies can not derive the exact amount of surplus needed by
basing it off premiums
once surplus requirement is determined
it is allocated to LOB in order to determine IRR by line
-this allocation is often in proportion to reserves and/or premiums
this allocation using reserves is going to result
in more surplus being allocated to longer tail lines
All being else equal, IRR reduces as amount of
surplus contributed increases
if surplus is assumed to be committed once policy is written and no longer needed when it expires
short tail policy will have same commitment/ release timing as long tail since there is no impact from reserves
if surplus is committed when UEPR is established and declines as losses are paid
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
expense projection is often
& reasons
less accurate than premium and loss projection for several reasons
- data: companies often do not monitor expense payment patterns as it is not required to populate Schedule P
- expense levels vary widely by company
- risk size: unlike losses, not all expenses are proportional to premium
- policy year: several expenses are higher in 1st policy year than future yrs
when calculating equityflows, what you need to calculate/populate
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
Contribution by Equityholders includes
$$ to cover excess of loss reserve over premium
Contribution to equityholder @t=0: reserves + surplus – (premium – expense)
calculating tax
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
Total assets pre distribution
(Total assets post distribution)@t=i-1 * (1+i)
Distribution to equityholder
total assets pre distribution – paid loss – paid tax – total assets post distribution
3 ways surplus can be allocated to a line of business & when surplus is committed and when it is released
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
Capital allocated by:
premium
reserves
reserves in steady state
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)
NPV analysis
discounts all future cashflows to present date at OCOC
Projects with positive NPVs may be accepted
most of the time, NPV and IRR will produce the same accept/reject decision
there are situations where they may differ
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
regarding cashflow, most projects involve a series of outflows followed by a series of inflows
- 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
if oversimplifications are corrected
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
projects are sometimes mutually exclusive
-NPV and IRR do not necessarily result in the same ranking of these projects
IRR analysis assumes that
revenues are reinvested at IRR which is not the case most of the time
-NPV is preferable since it does not make this assumption
problem with mutually exclusive projects usually applies to certain capital budgeting decisions
- 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
insurer can have problems with regulators if following conditions apply
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
-insurers are more likely than utility companies to run into problem of positive IRRs which are less than COC
- for utility companies, capital is fixed, known amount which does not depend on projections of this model
- 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
because insurers are more likely to have positive IRRs which are less than COC and regulators may potentially find these returns adequate
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
insurer needs surplus to protect itself against various risks
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
amount of surplus required often depends on policy form
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
IRR models will differ in their treatment of various policy forms
- 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 - 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
firms use assets to produce output just as insurers use
surplus to write policies
there are differences between fixed assets of a manufacturer and surplus of an insurer
- manufacturer can objectively measure needed assets whereas for an insurer the needed surplus is an estimate based on expected future development
- 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
in terms of amount of surplus held, approach of insurers differs from firms in other industries
- 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
Briefly describe two items that should be considered when allocating surplus to auto liability vs. workers compensation insurance.
variability of potential losses: higher volatility requires more surplus
length of the payment pattern: longer tail lines may require more surplus
