Loss Sensitive Rating (Fisher Chap 2)

Question 1

Define Loss-sensitive rating plans

Answer 1

LSRSPs are plans in which insured retains a greater portion of risk compared to typical policy.

Insured’s costs are significantly dependent on actual losses of insured during policy term.

Question 2

Who usually buy LSRSPs

Answer 2

Due to significant amount of risk retained, these plans are usually only available to large commercial risks.

Question 3

Briefly explain the main types of LSRSPs

Answer 3

1. Retrospective Rating Plans
   Plans in which insured’s premiums will develop based on their losses during policy term.
2. Large deductible plans
   Insurer indemnifies all losses in XS of per-occ deductible and all primary losses in XS of optional aggregate deductible limit
   Insurer provides services equivalent to full coverage
3. Self-Insured Retentions with XS policy
   Insurer indemnifies all losses in XS of per-occ retention and all primary losses in XS of optional aggregate retained limit
   Insurer only becomes involved with claims that exceed retention

Question 4

List 4 advantages of LSRPs from insured’s perspective

Answer 4

1. Financial incentive for loss control
2. Opportunity to save money in short-term with good experience
3. Possible CF benefits compared to traditional insurance policy (lower premiums)
4. Possible savings from reduced premiums-based taxes and assessments

Question 5

List 4 disadvantages of LSRPs from insured’s perspective

Answer 5

1. Uncertain costs compared to traditional insurance plan
2. Loss of immediate tax deductibility of traditional insurance premium
3. Possibility of high costs in short-term with bad experience
4. Impact on future financial statements as losses develop
5. Ongoing administrative costs as losses develop
6. Need to post security as collateral against credit risk
7. Additional complexity compared to traditional insurance plan

Question 6

List 3 advantages of LSRPs from insurer’s perspective

Answer 6

1. Insured’s immediate incentive for loss control
2. Greater willingness to write risks insurer would not otherwise (reduces uncertainty)
3. Less capital required to write policies under which insured shares risk

Question 7

List 3 disadvantages of LSRPs from insurer’s perspective

Answer 7

1. Higher administrative costs (more bills)
2. Existence of credit risk for some plans when need to collect from insured
3. Possible CF disadvantages compared to traditional policy (lower premium)
4. Insured’s tendency to second-guess claims handling & ALAE costs
5. Insured’s tendency to question profit provisions since insured is taking on significant risk

Question 8

Explain the cashflows in a retrospective plan

Answer 8

Insured pays initial premium at start of policy

Within a few months after policy expires, exposures are audited and premium is recalculated

Insured will be billed or refunded for any differences in premium

Premium is recalculated multiple times using actual loss experience of individual policy as it develops

Question 9

How do we calculate initial premium for retrospective policy

Answer 9

Common choice is premium as if policy was prospectively rated

Choice of initial premium is important because it can lead to CF advantage for either insured or insurer

Question 10

Calculate retrospective premium

Answer 10

R = (B + cL)T

B is basic premium

c is Loss conversion factor
c = 1 + E(LAE)/E(Loss)

L is Loss amount (retable losses)

T is Tax multiplier
T = 1/(1 - tax rate - v)

Question 11

Describe basic premium (B)

Answer 11

Reflects fixed charges such as: profit, and underwriting expenses not included in T (comm $, UW profit provision)

B is fixed during policy term, but changes due to premium audit

Question 12

What are the lower and upper bound of R

Answer 12

H < R < G

H = (B + cLH)T

G = (B + cLG)T

Question 13

Briefly describe why an iterative procedure is needed to obtain net insurance charge

Answer 13

Net instance charge in B depends on G & H, but G & H also depends on B

Question 14

Briefly explain the balance principle

Answer 14

Expected losses for a retro-rated policy would be equal to expected losses from that insured for a guaranteed-cost policy (GCP)

For some plans in US, it is a requirement that expected premium for retro rating plan equal premium under GCP

Question 15

Define GCP

Answer 15

GCP = policy where premium is fixed upfront and insured does not share their own risk (except small deductible)

Question 16

Why is the balance principle flawed

Answer 16

Because there is a difference in risk transfer and capital needed to support retro plan vs GCP

Question 17

Describe what common features can be utilized for very large risks

Answer 17

Depending on regulation, retro plan parameters may have to be filed with regulators.

Those parameters include ELR, e, LER for per-occ limits, table of insurance charges for age limits and T

Plans such as NCCI & ISO in US include provision called LRARO that allows flexibility in plan design for very large risks

Question 18

Explain LRARO

Answer 18

Large Risk Alternative Rating Option

Assumes large risks are knowledgeable consumers that can negotiate parameters with insurers directly.

Pricing must still comply with regulatory principles and golden rule of actuarial rating: rates shall not be inadequate, excessive or unfairly discriminatory

Question 19

List 3 common LRARO customizations

Answer 19

1. Allow NCCI plan to be on paid basis
2. Allow LH and LG to be set directly instead of indirectly through H & G
3. Allow B, LH & LG to be based on exposures instead of P

Question 20

Describe the difference between incurred basis retro plans and paid basis

Answer 20

Incurred basis:
Cumulative incurred losses evaluates starting 6m after expiration and 12m thereafter

Paid basis:
Cumulative paid losses are evaluated monthly starting 1st month of policy term.
Those are often converted to incurred basis after pre-determined amount of time (ex: 5y)

Question 21

Why do retro plans have credit risk

Answer 21

As losses develop, evaluation increases, premium increases so there is credit risk

Question 22

How is premium for large deductible plan calculated?

Answer 22

LDD are often written as full coverage policies with extra endorsement specifying insured will reimburse insurer for losses below per-occ deductible up to aggregate limit.

Because of d, policy premium will be much lower

LDD can be priced using the same methods as retro-rated plans

Policy per-occ d of $250K and agg limit of $600K = retro rated policy with $250K per-occ limit and $600K agg limit.

LDD P = (Fixed expenses + E(Loss)u + XS Losses above d + charge)T

XS ratio = k = E(X) - E(X;l) / E(X)
E(Prim) = E(Loss)*(1-k)
E(XS) = E(Loss) - E(Prim)

Question 23

Identify 4 similarities between LDD and retro plans

Answer 23

1. Losses may or may not include ALAE
2. Losses may or may not be capped by aggregate limit
3. Risk transfer is same if retro has per-occurrence limit & LG but no LH
4. Net P covers expected per-occ XS losses, aggregate expected XS losses, expenses and UW Profit provision.
5. Comm may be % of GCP, flat allowance or 0.

Question 24

Identify 4 differences between LDD and Retro Plans

Answer 24

1. Losses subject to d reimbursement must be subject to per-occ limit
2. No analogy to min eatable loss (no d reimbursement min)
3. P does not cover E(loss) below per-occ d and agg d limit
4. Net LDD P lower so premium-based taxes/assessments/commissions are also lower

Question 25

Calculate E(Loss for insurer) for LDD

Answer 25

E(Insurer Loss) = E(Loss Cost) = E(XS) + Charge*E(Prim)

r for charge is Agg limit / E(Prim)

Question 26

Identify 4 differences between LDD and SIRs with XS policy

Answer 26

1. For required coverage such as WC & Auto Liability in US, regulator approval is required for SIR with XS Policy.
2. In SIR, insured is responsible for adjusting & paying claims, so insurer only reimburses insured for losses in XS of SIR.
3. Retention applies to pure loss (no ALAE) only; ALAE is generally shared pro-rata
4. ULAE charges are minimal because insurer does less claim-handling so lower premium-based expenses
5. No credit risk in waiting for insured to reimburse losses below retention
6. Policy limit is not eroded by SIR because specification is different in order to provide same loss coverage

Question 27

Briefly describe dividend plans

Answer 27

Regular policies allowing some profit to be returned to insureds if losses are lower than expected

Subject to BoD approval

Money returned is considered expense for insurer, not a premium, thus not considered credit for accounting purposes (no savings in taxes and assessments)

Credit risk: if insured losses develop upward after dividend is paid, some of the dividend may need to be paid back to insurer

Question 28

Briefly describe clash coverage

Answer 28

Protects insureds from single occurrences impacting multiple loss-sensitive policies, each with separate per-occ retention.

A single class deductible (aka class aggregate) will represent the aggregate amount insured will retain from occurrence and insurer cover loss above that amount.

Can be difficult to estimate E(Loss) and may require simulations and assumptions about frequency, severity and correlations between LOBs

Question 29

Briefly describe basket aggregate coverage (aka Account Aggregate)

Answer 29

Policies cap insured aggregate reimbursement or retable losses across multiple loss-sensitive policies at single aggregate retention, up to specified limit.

Insured reimbursed for losses above aggregate retention retention up to limit.

Underlying loss-sensitive insured policies are usually written without aggregate limits on d losses or LR so basket aggregate coverage provides main source of aggregate loss protection.

Question 30

Briefly describe the adjustments needed on multi-year plan

Answer 30

The longer the time period, the more stable are expected losses (good and bad offset) so reduced insurance charge.

Multi-year plans get popular during soft market since insured want to lock in lower rates.

Adjustments required:
1. Per-off and agg XS charges need to account for longer loss trend
2. Contract wording should allow for significant changes in exposures during policy term
3. Credit risk increases since insured financial condition can deteriorate over longer period.

Question 31

Briefly describe captives

Answer 31

Very large insureds can create their own insurance called captives to insure their own exposures.

Often accomplished by typical insurer providing a policy to the insured and then ceding most of exposure to captive (acting as reinsurer).

Question 32

Discuss which loss sensitive plans contain credit risk and its source

Answer 32

Credit risk in retro-rating (premiums), LDD (d amounts) and Dividend plans (return of dividends)

Credit risk is especially relevant for long-tail LOBs and when higher amounts are involved.

Question 33

Describe 3 ways insurers can protect themselves agains credit risk

Answer 33

1. Security: insurer can hold collateral for expected future insured payments
2. LDFs: for retro and dividend plans, insurers can use LDFs to estimate ultimate losses instead of basing retro premium or dividend formula on actual losses to date.
   Not available for LDD and not done in paid retro since intended to mimic CFs of LDD.
3. Holdbacks: insurers and insureds can delay retro premium adjustment or dividend payments until later maturity.
   Not done for paid retro plans.

Question 34

List 4 considerations when deciding upon retention levels

Answer 34

1. Insured should retain the higher frequency predictable working layer of occurrence losses and insurer should cover less predictable losses above that level
2. Insured should be comfortable with risk implied by retention (depends on risk tolerance and financial capacity)
3. Insurer should be comfortable with credit risk implied by retention level
4. Retentions should increase over time due to loss trend

Question 35

Describe how profit provision compares to traditional policies

Answer 35

Since LSRPs (except dividend plans) have insured retaining most of the risk for primary losses, capital needed by insurers to support is lower than capital needed in GCP.

However, since insurer is keeping riskier portion of losses, profit provision is larger % of insured loss (Profit % increases, Profit $ decreases)

Question 36

Discuss how LSRPs can be closed

Answer 36

Since LSRPs can continue to develop over many years, at some point, insured and insurer will agree to close plan.

Retro-rating are closed by closeouts: apply LDFs to losses to determine final premium amount.

LDD are closed using either:
1. Buyout: for a fee, insurer assumes liabilities related to d layer of loss
2. Portfolio transfer: insured’s remaining loss obligations are ceded to insurer or reinsurer though separate policy

SIRs are closed using loss portfolio transfers.

Question 37

List 4 reasons for dissolution of LSRPs

Answer 37

1. Insured wants to free up BS from liabilities under plan (ex: wants to sell)
2. Insured wants to eliminate need to post collateral
3. Insurer wants to eliminate admin costs
4. Insured going bankrupt or reorganization

Question 38

Contrast CFs of Incurred Retro and LDD for both insurer and insured

Answer 38

Incurred Retro:
Insurer: P collected - Losses - Expenses
Insured: - P collected

LDD:
Insurer: P + d reimbursements collected - Losses - Expenses
Insured: P + d reimbursements

Question 39

Can we use the same diagram of charges by entry ratio for both large and small accounts

Answer 39

No, the diagram will look different for small and large accounts

Even if individual losses come from same distribution, aggregate distribution will look different.

Question 40

True or False?
Retrospective premium can be reduced by selecting a higher per occurrence limit.

Answer 40

False

If per occ limit is higher, the charge for it is lower, but losses that enter calculation are higher

If plan is balanced E(R) = GCP

Changing per occ limit does not change GCP, thus E(R) stays the same

Question 41

Contrast LDD and XS WC in terms of profit provision and tax rate

Answer 41

Since insurer keeps riskier portion of losses in LDD, profit provision is larger in %.

LDD uses WC tax rate, while XS WC uses GL tax rates. LDD has higher tax rate.

Question 42

Which type of LSRPs is least attractive in terms of credit risk

Answer 42

LDD since insurer handling claims in full an seek reimbursement for losses below deductible

Question 43

Which type of LSRPs is least attractive in terms of interest rate risk

Answer 43

Excess policy since it has the longest payout period, thus most subject to interest rate risk.

Question 44

Explain why profit loads can be higher for LDD policies compares to SIR XS policies.

Answer 44

For LDD, insurer services claims in deductible layer.

For XS policy, service is handled by TPA.

Because LDD insurers compete on both service and profit, profit can be higher versus SIR XS insurers who only compete on price.

Question 45

Name 2 changes that can be done to an incurred retro plan to make it more attractive to insured.

Answer 45

1. Changing retro to be based on paid losses would give an additional CF advantage to the insured since premiums at early maturities will be lower.
2. Adding holdbacks to the retro plan would defer retrospective premium adjustments to a later date when losses have reached more maturity and would result in more predictable CFs for insured
3. Use of retrospective development option would allow for more predictable CFs for insured