A0. Quintile Tests

Question 1

Experience Rating:

How to Quintiles Test / Rating Plan Evaluation

What if too much or too little risk is given to actual experience

Answer 1

Steps
1. Sort risks by their respective mods in increasing order
2. Group in quintiles of equal exposure
3. Calculate wtd avg manual and standard LRs

Evaluation
* See maximum dispersion in manual LRs. This means the plan does a good job of identifying risk differences
* See flat standard LRs. This means the plan corrects for the risks differences
* If too much risks was given to actual experience, we would credit too much for good risks and debit too much for bad risks. Standard LRs would be too high would good risks and too low for bad risks (downwards trend)
* Vice Versa

Question 2

Experience Rating

How to Efficiency Test on a Quintiles Test

Answer 2

Efficiency statistic = Var(Standard LR) / Var(Manual LR)
Lower means plan is more effective

Question 3

How to Create Simple Quantile Plot / Evaluation of Model

Answer 3

Steps:
1. Sort dataset based on model’s predicted loss cost
2. Bucket data into quantiles with equal exposures (# of risks)
3. Calculate and plot avg predicted and actual loss within each quantile

Evaluation:
* Predictive accuracy - difference between actual vs predicted in each quantile
* Monotonicity - actual loss cost (pure prem) should consistently increase across quantiles
* Lift from 1st to last quantile - greater distance between actual loss cost indiciates better distinction between best and worst risks

Question 4

How to Create Double Lift Chart / Evaluation of Model

Answer 4

Steps:
1. For each risk, calculate sort ratio = model 1 predicted loss cost / model 2 predicted loss cost
2. Sort the dataset by sort ratio
3. Bucket the data into quantiles with equal exposures (# of risks)
4. Calculate and plot avg predicted loss cost for each model and avg actual loss costs
5. (Alternative) Calculate % error from actual = (predicted - actual) / actual

Evaluation:
* Which model’s curve more closely resembles the avg actual loss cost curve
* Which model’s curve has lower % error from actual

Question 5

How to Create LR Chart / Evaluation of Model

Answer 5

Steps:
1. Sort the dataset based on model’s predicted LR
2. Bucket the data into quantiles with equal exposures 9# of risks)
3. Calculate and plot the avg actual LR for each quantile

Evaluation of Model
* The greater the vertical distance between the best and worst LR, the greater the model does at identifying further segmentation opportunities not present in current rate plan

Advantage
* LR charts are easier to explain and understand as LRs are a very common metric in insurance

Question 6

Lorenz Curve / Gini Index / Model Evaluation

Formula, what is it, how to plot?

Answer 6

Steps:
1. Sort the data by model’s predicted actual loss
2. Calculate and plot cumulative % actual loss cost and cumulative % of exposures

Plotting Lorenz Curve:
* X-axis = % of cumulative exposures (ex. 0%, 20%, …, 100%)
* Y-axis = % of cumulative actual losses (sorted by predicted losses)
* Line of equality = straight line (0%, 0%) –> (100%, 100%)

Evaluation:
* Gini Index = 2 * (Area between line of equality and Lorenz Curve)
* Gini Index quantifies how well a model identifies best and worst risks. Higher the better