CAS C5: 1993 Question 35

[great3981]

(From the All10 manual)

35. You have just calculated that an overall auto liability coverage rate increase of 7.8% is indicated. Current rates, indicated relativities to Class 1, and On-level earned premiums are as follows:

Class....................Current Rate.........Indicated Relativity...Earned Premium
Class 1 (base)............420.....................1.0000.. .................$25.3 M
Class 2......................550.....................1.3 125...................$18.7 M
Class 3......................300......................0. 7530..................$10 M
Class 4......................185......................0. 5000..................$ 8 M

a. Calculate new indicated rates for each class

b. What is the effect on the adequacy of future collected premiums compared to the adequacy of premiums indicated in part a. if:
- The exposure volume for the base class under the new rates is only half what it has been in the past,
- The exposure volume for Classes 2, 3, and 4 remain unchanged, and
- the 7.8% increase is implemented across the board with no change in class relativities

In the answer to part b, the following statement is made:
b. Compare current rate and new rate relativities for classes 2, 3, and 4. The indicated rate relativities are greater than the current rate relativities (550/420 = 1.31, 300/420 = .714, 185/420 = .44). If the exposure volume and class relativities for classes 2, 3 & 4 are unchanged, the adequacy of future premiums collected will decrease.

I don't follow this connection between the indicated relativities and the current relativities with respect to the adequacy of future premiums. Can somone offer insight?

[Been There Done That]

Think of it this way.

First take your statewide increase of 7.8%. After this, current rates are adequate on average (where the weights are the old exposure quantities).

Now look at the relative relativities (like they do). Classes 2, 3, and 4 are underpriced relative to the base class. That means that the base class is subsidizing these other classes. We reduce the number of drivers in the base class and don't change the premium relativities, result: less subsidy and so state-wide rates are now inadequate.

[Garden_Variety]

Someone please correct me if I am wrong but I think I have a mathematical way to answer the question...

What would happen if Exposures for Class 1 (the base class) are half of what they were originally, the rest of exposures remain unchanged, and the +7.8% indicated rate change is applied across the board to the original base rates without a change in relativities?

Divide the original OL EP for class 1 in half then compute the indicated rates as you did for the first half of the problem. Compare those Indicated Rates to the ones you would get if you simply applied the 1.078 to each base rate.

Class....OL EP...Cur Rel..Indic Rel..Adj OL EP....Ind Rates..(1.078 * Cur Rate)
1.........12.65M..1.0000..1.0000...12,650,000....4 37.98.....<.....452.76
2.........18.7M...1.3095...1.3125...18,742,500.... 578.71.....<....592.90
3.........10.0M....0.7143...0.7530..10,542,000.... 332.01......>....323.40
4...........8.0M....0.4405...0.5000...9,081,081... .220.46......>....199.43
Total....49.35M.........................51,015,581

Off Balance Factor = 0.9674 = 49,350,000/51,015,581
Indicated Rate Need = 1.078
Indicated Base Rate Needed = $437.98 = $420 * 1.078 * 0.9674

The base rates for Classes 3 and 4 would be too low and the base rates for Classes 1 and 2 would be too high.