What I've seen done in practice is for a company to look at a sample of
highly rated companies to calculate a probability of surplus declining by
some percentage as a function of how leveraged the companies are, and by the
mean and variance of their after tax return on equity.
Then the company will maximize its expected return by varying its
distribution of assets subject to several constraints. One of the
constraints being its own probability of surplus decline will match that
calculated for the industry. Other constraints will include restrictions on
the percentage of total assets in any one class.
It seems like it could work for any company, not just companies that cover
catastrophe exposures.
>
>Another question about solving for risk tolerance benchmarks that companies
>use. I'd appreciate comments on this approach.
>
>Suppose you're looking at asset allocation strategies and you define risk
in
>a certain way - - let's say probability of surplus declining 50% on a GAAP
>basis while taking no more risk than a peer group of companies on the same
>basis.
>
> Is it possible to calculate reasonably robust results of the peer group's
>implied probability of surplus declining 50% on a GAAP basis using
>historical statutory asset and liability data as the data source?
This certainly can be done in the case of catastrophes. To do this you
need a catastrophe model and the exposure distribution of your peer group
of companies.
I suspect this kind of analysis can be done with the collective risk model.
The big problem with this model is that most current versions do not
recognize correlation between the lines of business -- which can lead to a
significant understatement of the variablity. The CAS Committee on the
Theory of Risk is funding a project to address this problem and I am
hopeful that the results can be posted in the next few months.
-
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