>Can anyone make sense of the numerical example on p. 546-7 of Kelley?
>Here's how I solve Kelley's peculiarly worded example. What's wrong with
>it?
>Wrong Solution:
>Last year, the avg loss was $150.
>Last year there were 1000 policyholders (presumably all with losses.)
>100 policyholders had unrepaired roofs and incurred 30% of the losses
>$45,000 in
>total or $450 each
>So, the other 900 incurred $105,000 or $117 each.
>If we nonrenew the 100 with the unrepaired roofs we can expect $105,000 of
>losses.
>So, the average claim cost goes from 150 to 117. a 22% improvement.
The problem here is that the given information isn't stated very clearly.
I don't think Kelley is saying that 30% of total loss dollars are
attributable to the 100 houses with unrepaired roofs, while 70% of total
loss dollars are attributable to the other 900 houses.
I think he's saying that, for the 100 houses with unrepaired roofs, 30% of
claims are are made worse by the pre-existing roof damage, whereas the
other 70% of claims for these 100 houses are normal claims for which the
roof damage was irrelevant.
(I could be wrong, but this interpretation seems to fit with his math.)
The 70% "normal" claims are assumed to be at the overall average size of
claims for all 1000 houses. It is estimated that the average size of the
other 30% is 1.4 times the overall average. This gives Kelley the $168
figure for the average loss per policy for the 100 damaged houses, and his
calculation proceeds from there.
Note that total losses for the 100 pre-damaged houses will be $168 * 100 =
$16,800 and not $45,000.
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