Venter - Experience Rating: Equity and Predictive Accuracy Flashcards
Briefly describe three methods of incorporating actual losses into experience rating.
Pre 1940 plan: no split plan. Actual losses were not split into primary and excess components.
Since 1940, multi-split formula has been used in WC. both actual and expected losses are divided into primary and excess losses.
In particular, the 1961 plan defined any loss 2000, the primary value is determined by multiplying the total loss by a primary factor: 10000/(A+8000)
The 1991 rating formula incorporated two notable differences:
1. B & W values are different
2.Primary-excess split is simplified
primary loss = A if A=5000
Why the change from no-split plan to multi-split plan to a single split plan?
Change from no-split plan to multi-split plan:
due to the heavy tail nature of WC losses. Both primary and excess losses are less heavy tailed than total losses. Eliminating the first small portion from excess loss increase its average value and reduces the probability of losses being a large multiple of average value. This makes the excess loss less heavy tailed and more predictable.
Change from multi-split to single-split:
simplify operation of the plan
Methods for identifying which plan is better.
Method 1: two tests
Group risks by the value of modification.
Test1: the ability to identify differences among risks.
- Higher mods have higher manual LR
- The more disperse the manual loss ratios are, the better.
Test2: How well the plan corrects the differences.
- Review standard loss ratios among various groups of risks. the closer standard LRs are to unity, the better.
- and should not be increasing or decreasing with size of mod
is it necessary to group into 5 groups????
Method2: Gillam’s Quintile Test
Group into 5 groups base on size of Mod.
Calculate: (1) Actual Loss/Expected Loss
(2) Actual Loss/Modified Loss
Test statistic: Var(Modified Ratio)/Var(Actual Ratio)
A low test statistic indicates a plan that hs eliminated much of the between variance or made risks of differing experience more equally desirable.
Method3: Meyers Efficiency Test
Group risks by Size
Calculate Variance (standard LR)/Variance(manual LR)
smaller the value, the better.
What does it mean if LRs increase with size of mode
or decrease with size of mod?
if LR increase with size of mode => credibility is too low
if LR decrease with size of mode => credibility is too high
What are the assumptions behind constant K & B.
Why are these assumptions untrue?
Assumptions behind constant K&B:
- Large risks are more stable than small ones
- The increased stability follows from the law of large numbers
- Variance of LR is inversely proportional to premium
These assumptions are not true:
1. the variance does not decrease that fast with larger risks
2. larger risks display more variation than the law of large numbers would predict
Thus, large risks were given too much credibility and small risks were given too little credibility.
off-balance and rate adequacy
if off-balance is > unity => rates have been inadequate
current yr’s adequacy is better if off-balance decreases, but can’t determine whether rate is adequate or not from state of off-balance.
Two goals of experience rating
- Safety incentive - charging insureds for accidents adds a financial incentive for safety
- Predictive accuracy - allows premiums to be tailored to each insured’s own loss potential
formula for modification factor
mod = (A-E)/E * Z +1
Why debit mod doesn’t mean a risk is not desirable
If experience rating is designed properly, debit and credit risks are equally desirable. Debit mod could just mean risk a poor fit to manual classification. Lastly, any loss is pure chance.
Resulting changes in credibility for large vs small risks after the 1991 NCCI version.
Small risks:
-primary credibility is larger
-excess credibility is a little larger.
even the smallest risks have non-zero excess credibility; before the smallest risks had zero excess credibility
Large risks:
-primary credibility is smaller
[] max primary credibility is
