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Individual Risk Rating

1. Experience Rating

  • Be able to briefly describe the purpose of experience rating.
  • Be able to calculate an experience mod using the ISO CGL experience rating formula.
  • Be able to calculate an experience mod using the NCCI experience rating formula.
  • Be able to understand the purpose of each calculation in the experience rating formulas.

Purpose

🧮 ISO CGL Experience Mod

Commercial General Liability Insurance

Expected Dev

Possible assumptions to make: If only premium is given, assume its at basic limits.

  • BLEL = ELR \(\times\) BLEP
  • BLEL detrended = CSLC
    • if trend = 0, CSLC = BLEL cause already comparable
  • Use B-F technique to find the expected development. CLSL \(\times\) \%unreported
  • Then limit this by MSL, CLSL \(\times\) \%unreported \(\times\) EER (portion when limited by MSL1
    • Apply EER only when estimating the unreported losses (If unreported losses are already given to you, no need to apply EER)

Actual Losses

  • Cap each loss at basic limits
  • Cap loss & ALAE at MSL
  • Call it \(\text{L\_Basic\_ALAE\_MSL}\)

Mod

  • AER = \(\dfrac{\text{L\_Basic\_ALAE\_MSL}+\text{Expected Dev}}{\text{CSLC}}\)
  • Mod, credibility weighted %chg = \(\dfrac{\text{AER} - \text{EER}}{\text{EER}}\)

🧮 NCCI Experience Mod

Workers Compensation

  • Only Losses (not ALAE)
  • Split into primary & excess
    • \(A_{e} + A_{p}= \hat{A}\)
    • \(E_{e}+E_{p} = E\)

Formulae

\[ \text{Mod} = \dfrac{\text{Cred}(Z_{p},A_{p}, E_{p}) + \text{cred}(Z_{e},A_{e}, E_{e})}{E} = \dfrac{A_{p} + \text{cred}(W,A_{e},E_{e}) + B}{E+B} \]
  • \(W:\) Weights for excess (Actual & Expected)
  • \(B:\) Ballast (off-set numerator & Denominator)
  • \(Z_{p} = \dfrac{E}{E+B}\)
  • \(Z_{e}=WZ_{p}\) (What portion of credibility of primary is excess?)

Expected Loss component

Given,

  • \(ELR_{i}\)
  • \(D-\)ratios\(_{i} = \dfrac{\text{Primary Portion (under \textbf{D}eductible)}}{\text{Total Expected Loss}}\), there is no deductible… just for us to remember D-ratio better.

Calculation,

  • \(E = \sum E_{i}\) where \(E_{i} = \dfrac{\text{Payroll}_{i}}{1000} \times ELR_{i}\)
  • \(E_{p} = \sum D_{i}E_{i}\)
  • \(E_{e} = E - E_{p}\)

2. Schedule Rating

Credit is good, discount, keep up the good work!

Schedule mod = sum of all schedule rates.

Purpose

  • A pricing mechanism
  • Subjectively adjust premium for individual risk
  • risk characteristics that are not otherwise reflected in premium calculation

Max credit and debit for each category allowed

When should you (not) apply a schedule Credit/Debit?

  • Avoid reflecting any risk characteristics that are already fully reflected in experience rating
  • Let's take an example, there are two risk categories in the Schedule rating plan
    1. Level of training of employees
    2. Condition of all equipment
  • Training program was placed 10 years ago. All brand new equipment installed this year.
    • Training program been in place for the entire experience period that would be used in experience rating \(\implies\) it's benefits are fully reflected in insured's experience \(\implies\)Don't apply schedule credit
    • Equipment is new \(\implies\) Won't yet be reflected in experience period for experience rating \(\implies\) Can apply schedule credit
      • In a few years, when benefit of new equipment is reflected in experience period \(\implies\) Don't apply schedule credit

3. ISO Composite Rating Plan for Loss-Rated Risks

  • Rate multiple coverages using a single exposure base instead of each separately \(\implies\) Composition
  • Loss rated = Priced entirely based on their own experience

Calculation of composite rate

Trending

The most important nuance: We are trending data for an individual. Meaning we don't have to assume uniformly written policies and stuff, because there is only one policy per year. Hence,

  • Each policy is written at 1/1/20xx (Written date)
  • Avg Earned & Avg Accident date = 7/1/20xx
  • Trended (from-to avg accident dates) Ult. loss & ALAE by coverage for last 5 completed years of xp \(\implies\) sum
  • Measure trended (from-to avg earned dates) exposures for each year \(\implies\) sum
  • Adjusted Premium \(= \dfrac{\text{Ult. Loss \& ALAE}}{ELR}\)
  • Composite Rate \(= \dfrac{\text{Adjusted Premium}}{\text{Exposures}}\)

4. Large Deductible Policies

Remember Deductible applies to LOSS & ALAE

Unique Considerations

  • Who will handle claims & how?
    • Insurer/Insured?
    • Insured \(\implies\) TPA, take caution since less incentive to play safe
    • Insurer \(\implies\) Higher ULAE
  • Apply deductible
  • Deductible processing & Credit risk
    • Pay all loss & seek reimbursement
    • Extra cost to bill and process these amounts
    • Credit risk for not being able to pay
  • Risk margin
    • Losses above, difficult to estimate
    • higher profit margin to reflect higher level of risk

🧮 Premium for Large Deductible Policy

  • Standard
    • Experience ground-up losses
    • ALAE (% of ground-up losses) (if ALAE is not subject to deductible…)
    • Variable Expenses
    • Fixed Expenses
    • Profit [ + risk premium] (% of net premium)
  • Specific
    • Excess ratio $250k
    • Deductible processing cost (% below deductible)
    • Credit Risk (% below deductible)
    • Additional risk load (make an assumption3)
  • Expected above, expected below, expected ALAE
  • Deductible processing & risk charge
\[ \text{Premium} = \dfrac{\text{Loss Above} + ALAE + \text{Processing \& Credit Risk} + \text{FE}}{1-V-Q_{t}} \]

5. Retrospective Rating

Basic Idea
- At every stage of loss development, re-estimate retrospective premium
- Bill or refund the insured at each re-estimation for:

\[ \text{New Re-estimated Prem} - \text{Last estimated Prem} \]

Prospective vs Retrospective

FACTOR RETROSPECTIVE PROSPECTIVE (EXPERIENCE & SCHEDULE RATING)
Responsiveness to changes in experience period More responsive. Losses during the policy period impact premiums during the same policy period. Less responsive. Impact premiums only on policy renewal
Stability of costs Less stable. Ratings change during the policy period as losses develop. Change from one policy period to next as actual loss changes. More stable. Premiums don't change within a given policy term
Less stable. Uses a single policy term More stable. Experience rating uses multiple years of experience.
Incentive for risk control More financial incentive. Reduced losses results in lower premium immediately. Less of an incentive. Takes some time before loss control changes will impact premium.
Timing of Payments from Insured Payments over many years as losses develop and change the retrospective premium. Full payment in advance for a policy term (except premium audits)

🧮 NCCI Retrospective Premium

Formulae & Notation

\[ R = (b + CA)T \]
  • \(H \leq R \leq G\)
  • \(b:\) Basic premium covers for
    • profit
    • net insurance charge (for min, max)
  • \(A:\) Reported Loss
    • with or without ALAE
  • \(C:\) Loss Conversion Factor \(\implies\) Apply to \(A\) \(\implies\) Loss + (total) LAE
    • consistent with the definition of \(A\)
    • if \(A\) with ALAE: \(C = (1+\dfrac{\text{ULAE}}{A})\)
    • if \(A\) without ALAE: \(C = (1+\dfrac{\text{Total LAE}}{A})\)
  • \(T:\) Tax multiplier

Working

  • \(b\), \(C\) and \(T\) are fixed at inception. Thus, \(\Delta A \implies\Delta R\), retrospective premium change over time as losses develop.
  • If rating plan is balanced,
    • Retrospective premium = prospective premium (if the same risk group was prospectively rated)
    • In such a case, \(b = \text{Total Expense} - \text{Expected LAE} + \text{Net Insurance charge}\)2
    • Again, \(b\) covers for UW expenses, UW profit and net insurance charge
  • Total expenses denoted by \(e\)

So the basic premium is given by,

\[ b = e - (C-1)E[A] + CI \]
  • Net insurance charge, \(CI\) is calculated as
    • \(I = (\text{Insurance Charge} - \text{Insurance Savings})\times E[A]\)
    • where,
      • Insurance charge = \(\dfrac{E[\text{Loss above }A_{G}]}{E[A]}\), portion of expected losses which were eliminated by the limit.
      • Insurance savings = \(\dfrac{E[\text{Loss below }A_{H}]}{E[A]}\), portion of losses which the insured had to pay for.
  • The ratios might be given as a ratio to Standard Premium (see Workers Compensation)

Last step! Ensure that you have checked premium limits and have charge him based on the minimum and maximum, state that in the answer!

  1. A single, multi-million dollar loss can be a random, fortuitous event. It does not necessarily mean the insured is more likely than any other similar business to have another such catastrophic event in the near future. Thus we limit by MSL (Maximum Single Loss) ↩

  2. Expense doesn't include tax, but includes LAE which gets subtracted. ↩

  3. Usually load is loaded in the numerator, in this case like ULAE. ↩