Converting from a Gross to Net Quota Share

Quota Share contracts generally deal with acquisition costs in one of two ways - premium is either ceded to the reinsurer on a ‘gross of acquisition cost’ basis and the reinsurer then pays a large ceding commission to cover acquisition costs and expenses, or premium is ceded on a ‘net of acquisition’ costs basis, in which case the reinsurer pays a smaller commission to the insurer, referred to as an overriding commission or ‘overrider’, which is intended to just cover internal expenses.

Another way of saying this is that premium is either ceded based on gross gross written premium, or gross net written premium.

I’ve been asked a few times over the years how to convert from a gross commission basis to the equivalent net commission basis, and vice versa. I've written up an explanation with the accompanying formulas  below.

Source: @ Kuhnmi, Zurich

​Demonstration

Let’s work from the insurer’s perspective; the position net of cede on a gross quota share will be :

$$\textrm{Gross Written Premium}*\textrm{QS %}*\textrm{Ceding Commission Gross} - \textrm{Gross Written Premium}*\textrm{QS %} $$

And the position net of cede on a net quota share basis will be:

$$ \textrm{Gross Written Premium} * ( 1 - \textrm{Acquisition costs} ) * \textrm{QS %} * \textrm{Ceding Commission Net} - \textrm{Gross Written Premium}*\textrm{QS %}*(1- \textrm{Acquisition costs})$$

Equating the two formulas, and removing the common terms gives:

$$\textrm{Ceding Commission Gross} - 1 =  (1- \textrm{Acquisition costs})*\textrm{Ceding Commission Net} - (1- \textrm{Acquisition costs})$$

Solving for Ceding Commissions Gross gives:

$$\textrm{Ceding Commission Gross} =  (1- \textrm{Acquisition costs})*\textrm{Ceding Commission Net} + \textrm{Acquisition costs}$$

Or solving for Ceding Commissions Net gives:

$$\textrm{Ceding Commission Net} =  \frac{\textrm{Ceding Commission Gross}}{(1- \textrm{Acquisition costs)}}$$

​Note that above use of gross and net should not be confused with a given quota share being gross or net of Reinsurance, which is a completely separate concept.

For a Spreadsheet version of the above, see the following:
​github.com/Lewis-Walsh/Excel-Gross-to-Net_Quota-Share