Switch expenses between the basic premium and the loss conversion factor
What does the formula do? How do B an d c change if we switch the ALAE from c to B?
The example has us calculate portion of B as a % of guaranteed premium. Is the c in the formula 𝑒 − (𝑐 − 1)E , the one with or without the ALAE?
How does c change?
Comments
To apply this formula we first need to know the expenses associated with the guaranteed cost plan. These include ALAE, ULAE, general expenses, other acquisition expenses etc.
We then express these expenses as a percent of the guaranteed cost premium. This is the expense ratio, e. If we were pricing a guaranteed cost plan then we'd load this in as the expense provision.
The goal is to cover all our expenses and we have a choice of where to do it. Either via the basic premium, B, or the loss conversion factor. If we cover all our expenses in B then if losses come in lower than expected we may overcharge. If we try to cover all our expenses in c then if losses come in lower than expected we may not receive enough to cover the expenses.
Therefore, we set c to be the ratio of expenses that vary with losses to the GCP. This means as the ratable losses increase then we recoup the associated expected increase in expenses. The formula e - (c-1)E removes the part of the expense ratio which varies with ratable losses, leaving the "fixed" expense ratio that then goes into the calculation of the basic premium, B.
The insurer has to choose which expenses they believe vary with ratable losses. Usually this means both ALAE and ULAE would be incorporated in the loss conversion factor, c. However, they could decide to say only include ALAE in c.