Kelly

[Examinator]

On page 534 of Kelly’s article, Homeowners Insurance to Value – An Update, he illustrates how increasing coverage amounts provide to generally be profitable for a company. His example assumes that an extra $24 in premium will pay for only an additional $20 in claims, and therefore is a profitable venture for the company. My first impression is that this additional coverage must be inequitably overpriced. Or, should I assume that since the current amount of coverage is apparently too low, that the insured is currently underpriced (for the expected claims the policy will cover), and therefore adding additional coverage (up to the value of the home) will result in additional premium that’s greater than the additional claims assumed, ultimately resulting in a premium that is adequate for the coverage? This is what it seems to me, but it’s not really how it’s worded by Kelly or the All 10. Their presentation simply makes the point that this additional coverage is profitable. Should their point be that this additional coverage returns the company to profitability with respect to this risk? Thanks.

[jk]

As they say in that old CAS standby,

"The answer cannot be determined from the information given."

Kelley's explanation that the higher layer of coverage will be profitable is perhaps too glib. A more precise statement would be,

"If the higher layer of coverage is priced at the same rate per dollar of coverage as lower layers, the higher layer will be more profitable than the lower layers."

[Examinator]

So the assumption is not 1) the insured is currently underpriced (as the insured has underinsured his/her property) so adding coverage in order to arrive at adequate full coverage is more profitable per dollar than the existing coverage, but should be 2) since the price per unit of coverage is the same, regardless of how much coverage there is, so the larger amounts one purchases, the more profitable it is for the company. Once again, isn't that the same thing as saying that the upper tail of a company's coverage amount curve is then overpriced?

[Rice]

I believe that Anderson's paper (which is a rewrite and expansion of Head's paper no longer on the syllabus) states that the higher levels of insurance have lower associated loss costs. This is easy to visualize: if you have a water loss, your first $10,000 or so of coverage will be affected, but your higher amounts are unused. Therefore your lower levels of insurance will cost more than your higher levels because the layer between $80,000 and $90,000 (say) will be used far less often.

What I'm wondering is how they calculate the premium for the extra insurance. Is it just from the AOI curve? If so, the AOI curve is not correct because in a perfect world, losses will equal premium minus expenses, and the operating profit comes from the profit and contingencies factor built into the rates.

[Examinator]

It makes sense that marginal lost costs are lower at the upper reaches of coverage curves, but marginal premiums should follow suit to avoid being excessive, and therefore it shouldn't be any more profitable to write those upper reaches than average coverage amounts.

[jk]

Once again, isn't that the same thing as saying that the upper tail of a company's coverage amount curve is then overpriced?
Yes. Anderson goes into more detail about how to correct for such mis-pricing via premium gradation and coinsurance penalties. But penalties usually zero out after 80%, and Kelley appears to assume that the insurer will not use gradation above that layer. In which case, yes, the upper layers will be overpriced. Or at least, they will be more overpriced (or less underpriced) than the lower layers.

[Rice]

So the question then is why do these inequities exist, if it is not a mathematical phenomenon? Why haven't insurance companies (read: actuaries) corrected this? Inaction on our part has led to several papers being written about it and now we have to study them!

[Examinator]

Exactly.