Fisher.RiskSharing

Reading: Fisher, G. et al, "Individual Risk Study Note," CAS Study Note, Version 3, October 2019. Chapter 2. Sections 1 – 4.

Synopsis: This article introduces the concept of retrospective rating and the components of the retrospective rating formula. There are lots of small testable facts that you may need to use as part of a larger question.

Study Tips

Make sure you know the retrospective rating formula really well and understand how each of the components work. Although the cash flow material is contained in an appendix and barely referred to in the text, it is a key part of the material and has come up on several past exams.

Estimated study time: 2 days (not including subsequent review time)

BattleTable

Based on past exams, the main things you need to know (in rough order of importance) are:

• Retrospective Rating - general background
• Retrospective Rating - cashflows

Questions held out from most recent exam: #X. (Skip these for now to have a fresh exam to practice on later. For links to these questions see Exam Summaries.)

reference	part (a)	part (b)	part (c)	part (d)
E (2018.Fall #14)	Basic Premium - calculate	Net Insurance Charge - calculate	Basic Premium - understanding
E (2017.Fall #13)	Maximum Premium - calculate	Retrospective Rating - understand
E (2017.Fall #15)	Retrospective Rating - cashflows	Retrospective Rating - alternatives	Retrospective Rating - alternatives
E (2015.Fall #13)	Retrospective Rating - cashflows	Retrospective Rating - alternatives
E (2015.Fall #15)	Net Insurance Charge - calculate	Retrospective Rating - understand
E (2015.Fall #17)	Premium Discount - calculate	Retrospective Rating - understand
E (2014.Fall #19)	LDD Premium - calculate	Risk Sharing Plans - why choose	Excess WC Premium - calculate	LDD & Excess WC Policies - profit & taxes

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In Plain English!

Risk Retention and Risk Transfer

A guaranteed cost policy is where the insured's premium is fixed upfront and the insured doesn't share in their own risk except maybe via a small deductible. Private Passenger Automobile bodily injury coverage is a good example of this.

Risk sharing is where the insured's risk tolerance and financial capacity allows them to retain the smaller, more predictable losses but transfer the more volatile and uncertain larger losses to the insurer (the excess losses).

The primary risk retained by the insured is often limited in aggregate to some total. For instance, only the first $1 million of primary losses may be retained. The risk of losses over the aggregate amount is transferred to the insurer.

Rating plans in which the insured shares/retains a (material) portion of the risk are known as loss-sensitive rating plans.

Question: What are four advantages of loss-sensitive rating for the insured?

Solution:

1. Incentive for loss control - affects both direct and indirect costs such as lost productivity.
2. Immediate reflection of good loss experience. Experience rating has lag and is credibility weighted.
3. Cash flow benefits
4. Reductions in premium based taxes and assessments (premiums are lower due to more retention, so taxes and assessments are lower).

Question: What are some disadvantages to the insured when using loss-sensitive rating?

Solution:

1. Uncertain costs compared to fixed premium from guaranteed cost plans.
2. No immediate tax deduction of full guaranteed cost premium.
3. Poor loss experience is reflected immediately.
4. Future financial statements impacts due to cash flows.
5. Higher, ongoing administrative costs.
6. Collateral/security costs for credit risk.
7. Overall higher complexity compared to a guaranteed cost plan.

Question: What are three advantages of loss-sensitive rating for the insurer?

Solution:

1. Insured has loss control incentives which are stronger than those through experience rating.
2. Can write some risks that otherwise the insurer would decline to write on a guaranteed cost basis.
3. Less capital is required to be held for loss-sensitive policies.

Question: What are five disadvantages of loss-sensitive rating for the insurer?

Solution:

1. Higher administrative costs.
2. Credit risk.
3. Less cash flow because the insured is covering the primary losses.
4. Insured may attempt to second guess the claims handling and claims expenses.
5. Insureds may question the profit provision magnitude since they're taking on risk.

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What is Retrospective Rating?

Retrospective rating is using the experience from a policy period to adjust the premium for the same policy period. Adjustments to the policy premium are made after reviewing the actual loss experience in the period. The policyholder pays or receives the difference between the prior premium amount and the newly calculated premium after each adjustment. Retrospective rating plans may be on an "incurred" or a "paid" basis.

• Incurred Loss Basis: The first evaluation is six months after the policy expires and then every 12 months afterwards.
• Paid Loss Basis: The first evaluation is after the first month of the policy and then every month onwards.

It is normal to switch from a paid basis to an incurred basis after a period of time (such as five years) which was agreed at policy inception.

Generally a primary layer of loss is used to retrospectively adjust the policy premium. Primary losses may be capped at a maximum ratable loss amount to protect the insured from volatility. The cap may be either a maximum loss amount or a maximum premium. There may also be a minimum loss amount or minimum premium.

Retrospective Rating Formula

The retrospective premium, R, is calculated as [math]R=(B+cL)\cdot T[/math], where

B	basic premium amount
c	loss conversion factor (LCF)
L	loss amount used in the calculation (the ratable loss - see below)
T	Tax multiplier

B accounts for fixed charges that won't vary with losses. Some examples are:

• Underwriting expenses and commissions not included in the tax multiplier.
• Expected per-occurrence excess losses assuming losses are subject to a per-occurrence limit. Generally, this includes a provision for associated loss adjustment expenses. The NCCI and ISO retrospective rating plans have a separate component in the formula for the charge per-occurrence excess losses.
• Expected aggregate excess losses or insurance charge if there is a maximum ratable loss amount. This generally includes an provision for loss adjustment expenses.
• A credit if losses which influence the premium are subject to a minimum ratable loss amount, or if the retrospective premium is subject to a minimum premium. This is often called the insurance savings or just savings.
• Underwriting profit provision.

The combination of the insurance charge and insurance savings is called the net insurance charge. The basic premium, B, will only change as the result of a premium audit.

c accounts for expenses which vary with the actual loss experience, such as loss adjustment expenses and loss based assessments. It is fixed at policy inception. It is possible to switch expenses between B and c but if you charge fixed expenses in c and the losses are lower than expected then you won't get those expenses back...

To switch expenses between the basic premium and the loss conversion factor, use the following formula: [math]e-(c-1)E[/math] to calculate the expense portion of the basic premium. Here

e	is the expense ratio for the guaranteed cost premium. It includes loss adjustment expenses and reflects the premium discount (expenses are a lower percentage of premium for large accounts).
c	is the selected loss conversion factor.
E	is the expected loss ratio for the guaranteed cost premium policy.

Note that as c increases the expense portion of the basic premium decreases.

Alice: "Can you use the above information to calculate the expense portion of the basic premium in the following problem?"

Determine the expense portion of the basic premium

L represents ratable losses, i.e. those used to calculate the retrospectively rated premium. The ratable loss is the amount of loss in the primary layer, that is it is the loss amounts the insured is responsible for. However, it's important to note there are several ways in which the actual losses may be modified in order to arrive at the ratable loss.

L may or may not include ALAE [the ISO plans for commercial auto liability, general liability, and hospital professional liability must include ALAE].

If L includes ALAE then c covers ULAE and the expense ratio e includes ULAE but not ALAE. The expected loss ratio E would be an expected loss and ALAE ratio.

If L excludes ALAE then c and e both cover ALAE and ULAE. The expected loss ratio E is then an expected loss only ratio.

Observe if there are no ratable losses then we get the minimum premium formula, [math]R=B\cdot T[/math].

Ratable losses may or may not be subject to a per-occurrence limit [this is required under ISO rating plans but is optional under NCCI rating plans]. If they are subject to a per-occurrence limit then the charge for expected losses over the per-occurrence loss limit may either be included in the basic premium amount or kept separate. The charge for expected losses above the per-occurrence loss limit needs to have the loss conversion factor c applied to it.

Ratable losses may or may not be subject to an aggregate loss limit. If losses are subject to an aggregate limit then the charge for the expected losses above the aggregate loss limit is typically included in the basic premium amount. The charge must have the loss conversion factor, c, applied to it.

Note there is an interaction between the occurrence limit and aggregate limit because if the occurrence limit is small relative to the aggregate limit then it will take a lot longer to reach the aggregate limit than if the occurrence limit is comparatively large.

Aggregate loss limits are often set in one of two ways:

1. A multiple of the expected losses subject to the aggregate limit.
   • For example, if the expected limited losses are $300k then the aggregate loss limit might be $600k or $750k (2x or 2.5x the expected limited losses respectively).
2. The maximum premium under the retrospective rating plan is a multiple of the guaranteed-cost premium.
   • For example, if the guaranteed-cost premium is $1million and the selected multiple is 1.25 then the aggregate loss limit is set so the maximum retrospectively rated premium is $1.25m.
   • This gives rise to an iterative approach: The implied maximum ratable loss increases the basic premium by adding a charge for expected losses above the maximum ratable loss amount. This reduces the implied maximum ratable loss and thus increases the insurance charge which reduces the maximum ratable loss further.

The second approach automatically varies with exposure changes as premium audits reflect the exposure change in the guaranteed-cost premium. The first approach has to be translated to a rate per exposure to be able to scale with exposure changes.

Ratable losses may or may not be subject to a minimum ratable loss amount. If subject to such a limit then the basic premium typically includes a credit. Even if there is no minimum ratable loss amount there's still a minimum premium amount that would be charged.

For Workers' Compensation or Auto Liability there is no aggregate policy limit. If there is a per-occurrence loss limit and no aggregate loss limit then the insured technically retains unlimited loss exposure.

If there is an aggregate loss limit but no per-occurrence loss limit then a low aggregate loss limit could remove the insured's loss control incentive because a few losses could use up the limit.

There must be either a per-occurrence limit, or an aggregate loss limit, or both in order for the insured to transfer risk to the insurer.

Ratable losses may be paid or incurred. If paid losses are used then we have a paid loss retrospective plan, whereas if incurred losses are used then we have an incurred loss retrospective plan. Paid plans are often converted to incurred at a predetermined point in time, say 5-years after policy inception.

Incurred retrospective rating plans typically have a one-year policy period and are first evaluated at 18-months (six months after the policy expires) and then annually afterwards. Losses are typically estimated much lower at 18-months than they will ultimately be, so the insured often receives a partial refund of premium and then at later evaluations is required to pay additional premiums. This creates credit risk for the insurer.

Paid retrospective rating plans are usually evaluated monthly from the first month of the policy period. The retrospective premium amounts increase as the paid losses increase. Again, this creates credit risk for the insurer.

T is the tax multiplier, [math]T=\frac{1}{1-\mbox{tax rate}}[/math]. The tax rate may include residual market and premium-based assessments. If commission is a percentage of net premium (net of retrospective rating adjustments) then commission is included in the tax rate and not the basic premium. T is fixed at policy inception.

Alice: "Now you're familiar with the basics of retrospective rating, try applying it alongside your Exam 5 knowledge to solve the following problems."

Determine the retrospective rating premium

Alice: "You're doing great - now try piecing together the policyholder and insurer cash flows for an incurred retrospective rating plan. This type of problem is well-suited to an online exam but is tedious to set up by hand."

Construct the cash flows for an incurred retrospective rating plan

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The Balance Principle

Some US retrospective rating plans require the expected premium under the retrospective rating plan to equal the (expected) premium, P, under a guaranteed-cost plan, i.e. [math]P=E[R][/math]. This is known as the balance principal.

According to Fisher et al, this doesn't make sense due to differences in the risk transfer mechanism and capital required to support each type of rating plan.

Regulatory Approval and Large Risk Alternative Rating Option (LRARO)

In the US, retrospective rating plans are typically filed and approved by regulators. The filings include both the methodology and parameters such as expected loss ratio, expense ratio, loss elimination ratios for per-occurrence limits, tax multiplier, tables of insurance charges for aggregate limits, etc.

Both the ISO and NCCI retrospective rating plans have Large Risk Alternative Rating Options (LRARO). These allow large insureds to be retrospectively rated as "mutually agreed upon by carrier with insured". Large normally refers to the standard premium for the line or lines of business.

A key assumption of an LRARO is large risks are knowledgeable and sophisticated enough to negotiate with insurers. LRAROs give pricing flexibility but must comply with regulations and not be inadequate, excessive, or unfairly discriminatory

Examples:

• The NCCI standard retrospective rating plan uses incurred loss. We need an LRARO to give pricing flexibility to price a paid loss plan.
  • This allows the insurer to adequately reflect the lower investment income associated with a paid loss plan.
• Under an LRARO the maximum and minimum ratable loss amounts can be set directly rather than via the minimum and maximum premiums.
• An LRARO allows for exposure based pricing instead of using the standard premium.

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