FW: More comments on D'Arcy/Doherty
D'Arcy, Stephen ( (no email) )
Thu, 30 Apr 1998 16:22:30 -0500
> -----Original Message-----
> From: D'Arcy, Stephen
> Sent: Wednesday, April 29, 1998 9:46 AM
> To: 'Snaps99999'
> Subject: RE: More comments on D'Arcy/Doherty
> See below.
> -----Original Message-----
> From: Snaps99999 [SMTP:Snaps99999@aol.com]
> Sent: Tuesday, April 28, 1998 6:36 PM
> To: email@example.com
> Subject: More comments on D'Arcy/Doherty
> There are a couple of additional points regarding the underwriting
> margin per D'Arcy/Doherty that have come to mind that I'd like to add
> to my
> earlier message.
> Point #1
> First, the D'Arcy/Doherty expected underwriting profit margin does not
> at all on the insurer's surplus. This eliminates the questionable
> practice of
> allocating surplus to line of business or state.
> Various commonly used methods start with an ROE target and then
> determine the
> underwriting return needed to produce that ROE. For example, an
> Internal Rate
> of Return method (1) starts with an allocation of surplus, (2)
> determines the
> income generated from the cash flows, (3) pays the income to the
> investor as
> it is earned, and (4) repays the surplus to the investor using some
> pattern or rationale. The surplus repayment pattern generally depends
> on the
> preferences of the person who sets up the model. Also, the formula or
> rationale for surplus repayment may or may not be consistent with the
> rationale for allocating the surplus in the first place.
> Other approaches modify the recognition of income, but still rely on
> an IRR
> method. If I recall correctly, Bender recently proposed an approach
> where the
> definition of income was revised so that it matched the repayment
> pattern for
> surplus. I believe Bender's suggestion was intended to eliminate
> discrepancies between various methods for determining the return on
> Suppose the D'Arcy/Doherty formula can be used to determine the proper
> underwriting profit margin. What does that imply about the "cost of
> issue? Capital doesn't come into this formula.
> [D'Arcy, Stephen]
> I assume you are referring to the CAPM without taxes. The tax version
> requires an allocation of surplus. The downplaying of the role of
> surplus is a distinguishing feature of the CAPM model, which is both a
> benefit and drawback. This is not a cost of capital model.
> Point #2
> A second point is in regard to the Beta of investments. My earlier
> mentioned that the insurer isn't free to raise its Beta as high as it
> because the insurer needs to be conservative due to its underwriting
> risk. It
> also seems that there should be a practical lower limit to Beta as
> well. That
> limit is based on the requirement that the actual dollar amount of
> income to
> an insurer must be greater than the dollar amount of income to a pure
> with a Beta of 1.00.
> A pure investor would expect a return equal to the expected market
> times the invested amount (i.e., the surplus). In comparison, an
> insurer with
> the same amount of surplus should earn at least this amount of income,
> otherwise it wouldn't write insurance. So, the expected ROE of the
> times its equity should equal or exceed the expected market return
> times the
> E(roe) * equity >= E(market return) * surplus
> This limits the insurer from investing only in risk-free bonds. If an
> did this, the return on equity would be so low that the owners would
> sell or close the insurer and invest the surplus on their own.
> [D'Arcy, Stephen] Allstate recently decided to hold a large portion
> of its investment assets in risk frees. Let's see what the market
> does to them.
> Point #3
> Should I interpret the D'Arcy/Doherty formula as basically a statement
> Income = Revenue - Cost, where Revenue is the investment return and
> Cost is
> the underwriting loss?
> On that basis, shouldn't the maximum profit be earned when marginal
> cost =
> marginal revenue? Couldn't this then be solved for the appropriate
> amount of
> premium needed to maximize profit?
> [D'Arcy, Stephen] Revenue is revenue from all sources, including
> premiums, and cost is losses, taxes and expenses. Basic economics
> indicates how to maximize profits. However, that applies to a
> monopoly. In competition, in theory, the industry cannot earn excess
> profits because [D'Arcy, Stephen] excess profits are bid away and
> companies must charge a price that just covers average costs. That's
> the theory at least.
> Frank Schnapp
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