Spring 2015 Exam 5 - Question 5
CY14 EP = 1000
Suppose a rate change of 1.1 occurs on 7/1/14.
30% of policies are written in Q3 every year.
10% of policies are written in Q4 every year
Policies are written uniformly within quarters
What's the % of CY 14 EP is at the new rate level?
One answer that I've seen does the following:
(CY14 Q3 % Written) x (CY14 Q3 % earned in 14) + (CY14 Q4 % Written) x (CY14 Q4 % earned in 14)
30% x (4.5/12) + 10% x (1.5/12)
=.125
1) Can someone mathematically show me how this formula is valid??? Like can someone use real exposure or premium amounts in showing this? I tried mathematically showing this, but I only got .125 via the assumption CY13 WP = CY14 WP = CY14 EP = 1000 as shown below.
2) Does 30% of policies written in Q3 mean 30% of exposures are written in Q3, 30% of premium is written in Q3, or both? Did I even ask the right question by asking "what's the % of CY 14 EP at the new rate level?" Or is it "what's the % of CY 14 earned exposures at the new rate level" or what?
CY14 EP = 1000
Suppose a rate change of 1.1 occurs on 7/1/14.
30% of policies are written in Q3 every year.
10% of policies are written in Q4 every year
Policies are written uniformly within quarters
What's the % of CY 14 EP is at the new rate level?
One answer that I've seen does the following:
(CY14 Q3 % Written) x (CY14 Q3 % earned in 14) + (CY14 Q4 % Written) x (CY14 Q4 % earned in 14)
30% x (4.5/12) + 10% x (1.5/12)
=.125
1) Can someone mathematically show me how this formula is valid??? Like can someone use real exposure or premium amounts in showing this? I tried mathematically showing this, but I only got .125 via the assumption CY13 WP = CY14 WP = CY14 EP = 1000 as shown below.
2) Does 30% of policies written in Q3 mean 30% of exposures are written in Q3, 30% of premium is written in Q3, or both? Did I even ask the right question by asking "what's the % of CY 14 EP at the new rate level?" Or is it "what's the % of CY 14 earned exposures at the new rate level" or what?
Parallelogram Method - Uneven Writings