Suppose a $4M liability policy has a $1M SIR. Then essentially the insurance company is insuring the 1M-5M layer. If I wanted to know what that is “worth” I could look at the increased limits table:
100K 1.00
1M 2.11
5M 2.87
It seems the 1M-5M layer would be worth 2.87-2.11=0.76 or 76% of the basic limit, but what about LAE? Do we think that the 1M and 5M ILFs account for the proper amount of LAE and the subtraction is picking up the amount of LAE in the 1M-5M range?
On exam 8 in the Bahnemann paper, it says that it depends on whether LAE is included in the limits. If they are the formula is [(E[X;l] + fixed LAE )(variable LAE)]/[(E[X;b] + fixed LAE )(variable LAE)]
Thanks for directing me to that. That paper wasn’t on the syllabus when I attempted to pass the exam fifteen years ago. Although this paper alludes to it, I need to get straight in my head how ISO is doing it and how this paper suggests I respond. But pages 168-170 did give the impression that the author was reading my mind about what I was wondering.
My recollection is that ALAE is not part of the policy limit, but is in addition to the policy limit. Further, the ISO ILF factor has the same flat dollar amount for ALAE at every policy limit, so a subtraction of ILF’s leaves you with zero ALAE. I have not looked at ISO ILFs in a while, and my recollection could be wrong or outdated, or both.
My recollection is that ALAE generally increases with the amount of loss, but not proportionately.
A $4M liability policy with a $1M SIR may not be an ISO policy.
I was hoping that the ALAE for a $5M limit would be higher than the ALAE for a $1M limit and by subtracting the ILF’s I would retain the 4x1 ALAE in the difference. So as I said I need to get it straight in my head how ISO does it in case I need to create a mechanism to attempt to break down the components. If indeed ISO adds a fixed component then the subtraction gives me the indemnity portion only and LAE needs to be added back in.
The ISO actuarial ILF circular used to be pretty clear on how the ILFs were calculated, if you have access to it.
I used to make use of the ISO actuarial ILF circulars extensively when setting technical premiums on a couple of excess products.
I have access to ISO, not to worry.
Is the ISO treatment of ALAE as the same flat dollar amount for ALAE at every policy limit, or has this changed?
The circular I checked showed ALAE flat for all policy limits (which seems a bit wonky to me, do you really have the same legal costs with a $10M claim as a $100K claim) and it’s only a couple of years old.
Could the theory be that your basic limits policy theoretically covered you for unlimited ALAE, so there is no need to fund more ALAE in higher limits?
That’s the reasoning that ISO gives, but I just don’t buy it on the surface. If you have a $100K or $1M of exposure, I think it the insurer is going to be more motivated to settle at policy limits rather than ring up legal fees. Once they could be on the hook for $10M and they like their chances of winning in court, I think now they are more likely to pay for counsel. Although at my last job $10M was an umbrella claim, so if the limits are more likely to be in the $1M-$2M maybe the difference in ALAE isn’t so wide.
ISO gave the information to explicitly calculate ALAE easily, and from there it’s just a question of how to allocate it if the insured is responsible for the first $1M and you’re on the next $4M.
Ok here’s another question.
Suppose you have a policy with a $1M limit and a $100K deductible. Then from an indemnity point of view your exposure would be $900K XS $100K. Wouldn’t this be equivalent to comparing the $1M ILF to the $100K factor of 1.00? The two methods of quantifying this exposure appear to be miles apart and I’m trying to reconcile the difference.