Thanks for your responses. I appreciate getting such clear (and brief)
answers. I do have a few more questions to ask.
First, even if this model is not used to set underwriting profit margins, do
you think it would still be appropriate in establishing relative underwriting
profit margins? That is, if there are two lines of business (or two companies
writing the same line of business) with losses of different durations, then
should the difference in the underwriting profit margins be proportional to
the difference in durations? I was wondering whether Florida doesn't do
something like this.
In algebraic terms,
E(underwriting return on A) = constant - duration of A * risk-free rate, and
E(underwriting return on B) = constant - duration of B * risk-free rate,
where the constant is an extra profit loading needed because of other forms of
risk not included in the CAPM approach. Then the difference between the two
expected underwriting profit margins equals the difference in durations times
the risk-free rate.
Second, you stated that "this model ignores any risk that is not correlated
with the market." Should risk that is not correlated with the market be
considered in pricing? CAPM says that it shouldn't. However, I know that the
practical answer to that question is yes, we want to include a charge for
risk. But why isn't the CAPM rationale valid? Why should methods that don't
consider the market risk and instead use techniques such as options pricing
theory, be superior? If this requires a longer response than can be given
here, could you direct me to a source I can review?
Third, you also stated that the high target combined ratios were "why this
method is rarely used by companies, although some regulators propose it at
times." Even though actuaries include a larger underwriting profit margin
than (-duration * risk-free rate) in most of our pricing work, does the
industry actually achieve a result that is more in line with this formula than
with the profit loadings the actuaries build into their pricing? Underwriters
might offset the actuarial pricing margin through schedule credits to
counteract the perceived conservatism of the actuaries. In brief, my question
is whether you think that the high target combined ratios give the proper
underwriting profit margins.
Finally, I was wondering about the meaning of the CAPM formula. It appears
that the expected total return, E(r), represents the inverse of the expected
value of the price/earnings ratio for a stock. This suggests that CAPM's
original purpose was to provide an estimate of the price to earnings ratios
for a stock based on the stock's volatility (Beta), so that the appropriate
market price could be determined based on the stock's earnings. Now that I
think about it, it is called a Price Model, not a rate of return model.
This leads to my question. Ordinary, the way in which actuaries establish
underwriting profit margins by methods such as the Internal Rate of Return
technique is to work backwards from a preselected ROE. However, doesn't the
CAPM really mean that investors in the successful companies are rewarded not
by high ROE's but by high market values? A company that achieves a Beta of 0
has an expected ROE equal to the risk-free rate of return. Its market value
would be bid up until its ROE reaches this level. In this case, it wouldn't
make sense to develop an underwriting profit margin using an IRR model with a
target ROE equal to the market return. If so, is the IRR model based on the
false premise that the objective is a high ROE? Or, am I misunderstanding
If I were to summarize my questions, it would be this: what's the right way to
determine the underwriting profit margins, and why?
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