CAS Exam 8 IQ Example: LDD vs. Retro
In the CAS Exam 8 Sample IQ (https://www.casact.org/sites/default/files/2021-03/Exam8-IQ.pdf), we're asked to calculate premiums for both an LDD policy and a Retro policy.
In the solutions, the final premiums for both are similar, except that the LDD policy doesn't include the Expected Limited Losses below the $100k deductible in its premium calculation.
Obviously the LDD would only include excess losses (and ALAE on unlimited loss), but why do we include limited losses in the Retro calculation? Stated differently, how do we know that the Per Occurrence Deductible of $100K only applies to the LDD policy?
Thanks!
Comments
It's helpful to think about who is paying for the losses in this situation.
An LDD plan has the insurer paying the losses above the deductible and seeking reimbursement for the deductible losses from the insured. A retro plan has the insurer paying all losses but the premium charged depends on the ratable loss. The ratable loss is essentially the deductible layer loss. The retro premium has its basic premium fixed and that includes a charge for expected losses in excess of the per-occurrence limit (or deductible if we're paralleling an LDD plan). This is then combined with the ratable losses via B+cL.
So a retro plan responds to changes in the ratable loss, just like the final payments by the insured under an LDD plan depends on the deductible layer losses.
Gotcha. So the ratable losses (L) can be subject to a per-occurrence limit and/or an aggregate loss limit - but in this case the per-occurrence limit is just the "per occurrence deductible"? If so, I think I understand. The limit/deductible threw me. I read the per-occurrence deductible as a literal deductible that the insured is responsible for.
Yes, that's the case. Retrospective rating without any limits allows the insurer to potentially bill or reimburse large amounts of premium depending on if the insured has poor or good experience. By including a per-occurrence limit or deductible these swings are limited while the insurer is still covering all of the losses. We can limit the swings further by using a maximum premium which corresponds to some maximum ratable loss amount which is basically an aggregate limit/deductible.