Spring 2019 Q8 a)
in W-13-Other
We want a 0.7 PLR for the total book. In the sample answer, we see that implementing 10% for territory A and 8.57% for territory B gives us 0.7. However, why can we multiply, for example, 1.1*2700000 in the denominator? Don't we have to account for the number of policies renewed by implementing the 10% change and could that give us an ultimate loss ratio that is not 0.7? (i.e. if there are less policies renewed, the current premium would be lower than 2,700,000 due to less policies renewed and multiplied to 1.1 would give us a lower value in the denominator). Thank you.
Comments
Your observation is spot-on: the assumption that the total premium for territory A will simply increase to 1.1×2,700,000 with a 10% rate change overlooks the potential impact on policy renewals. Typically, rate changes could affect customer behavior, either increasing or decreasing the number of policies renewed, which in turn affects the denominator when calculating the loss ratio.
Since this question is worth only 1.5 points, you were not expected to take that into account, and what the solution did is a necessary simplification to make the problem solvable in an exam setting. This makes the calculation easier but less reflective of real-world complexity.
If you're working in a more sophisticated ratemaking model, you would indeed consider the elasticity of demand and how changes in rates might affect the number of policies renewed, among other factors.