I received one additional response to my three messages regarding the
D'Arcy/Doherty publication on the Part 10 syllabus. Several of you requested
copies of the responses I received in order to post them on the Part 10 study
site. I apologize for not sending this prior to the exam. This (slightly
edited, as marked by "...") response is from David Ruhm:
His message follows:
==================
Subj: Underwriting Margins Theory & Practice
Date: 98-04-30 14:29:21 EDT
From: David.Ruhm@aig.com (Ruhm, David)
Frank,
....
It does appear that the "-k(1-x)i + Beta" formula yields about -11.5% U/W
profit for a line of 2.3 years' duration, if Beta = 0.
The perspective that the owners are borrowing funds from policyholders at the
risk-free rate ("rfr" for short) and reinvesting at possibly higher rates is
an accurate interpretation of the formula, in my view. This is not unique to
insurance - the original CAPM model assumes an investor can take the same sort
of leveraged investing position by borrowing funds at the risk-free rate (an
assumption I personally have trouble with from a risk vs. assets perspective).
Insurers freedom to invest in risky securities vis a vis underwriting risk is
discussed in several Part 10 articles, notably Ferrari. Beta actually can be
>1.0, depending on how much risk the owners are willing to take -
unfortunately, owners are pretty free to assume such risks. Even if investing
risks had to be curbed to compensate for underwriting risk, this is not an
additional cost of borrowing under the CAPM theory, because CAPM says there's
no value difference between riskier, higher return investments and less risky,
lower return investments (if the return difference is exactly offset by the
risk difference).
Your argument that Beta should be negative based on the cash-flow-
underwriting argument seems right on target to me, and is consistent with
industry history and also with other papers suggesting that Beta is negative.
....
On the cost of capital issue: The authors are trying to determine a market
equilibrium U/W profit. A corporation is usually trying to meet ROE goals,
and is pricing to those goals (more on this below). It can be argued that a
regulator should be more accepting of the first criterion than the second when
reviewing a submission, but regulators have not taken this stand as far as I
know.
Re the Beta lower limit: Some investors invest in bonds, for safety. Again,
if you believe CAPM, the central point is that there's no cost to being
restricted to low-Beta investments, or not obtaining a market yield, as long
as risk is commensurately reduced. For what it's worth, I hold a different
point of view: 1) CAPM's assumptions are generally invalid, and therefore so
is the model; 2) risk and return only go together in the absence of
intelligent investing, because there is imperfect use of information
("unintelligent capital"); 3) restrictions on investing can create an
opportunity cost.
If you want to maximize profit for a company, you would set Marginal Cost =
Marginal Revenue, but you'd also need to account for volume changes due to
supply and demand. D'Arcy & Doherty are going in a different direction with
their formula, attempting to get equilibrium conditions for the whole market.
...The places to look for flaws are (as you already know at least as well as
I do) the model assumptions, and the algebra leading to te formula. The
thought-logic behind the algebra almost always contains hidden assumptions,
often in the form of missing relevant parameters (e.g., supply / demand
factors).
The question about compensating non-market-correlated risk in some models but
not others is outstanding, and I have no good answer for it, except that maybe
the only insurance risk that should be compensated in any return-based-on-
risk/volatility model is non-diversifiable risk (since it's arguably the
insurer's job to achieve diversification, just as it's an investor's job in
the CAPM world).
Market returns: A company with Beta = 0 would (according to CAPM) establish
a corresponding market price immediately at the IPO, so no reward would be
available to investors from appreciation.
The point of setting ROE (possibly as measured by IRR) at a certain level and
then solving for U/W profit is to answer the question, "Given that the
Corporate ROE Target is 15.0%, what does the Combined Ratio Target have to be
to hit that goal?". The idea is to translate Corp. Financial Goals
(determined from stockholder assumptions) into more directly controllable
Production Goals (market level). It's to get firmer control of ROE via
production control. An economist might show that: a) Insurance market
equilibrium prevents such production control, and/or b) regulators shouldn't
allow prices based on ROE goals higher than a specific (formula-driven)
floating benchmark.
I hope this was useful and entertaining - it has been for me. If you don't
think it inappropriate, I'd be interested in your further correspondence on
this (if any), and in Dr. D'Arcy's comments.
....
David Ruhm
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