This paper examines conditions necessary for both Insurer and Reinsurer to be motivated to engage in a quota share reinsurance treaty. The emphasis is on numerical break-evens, and explores capital considerations.

1. Richard
Hartigan
1
21
August
2015
Quota
Share
Reinsurance:
Philosophy,
Theory
and
Practice
Richard
Hartigan,
FIA
FIAA
BEc
MBA
Abstract
This
paper
examines
conditions
necessary
for
both
Insurer
and
Reinsurer
to
be
motivated
to
engage
in
a
quota
share
reinsurance
treaty.
The
emphasis
is
on
numerical
break-­‐evens,
and
explores
capital
considerations.
The
quota
share
reinsurance
treaty
is
the
humblest
form
of
reinsurance,
so
humble
(and
apparently
simple)
that
research
into
the
philosophy,
theory
and
practice
of
the
quota
share
reinsurance
treaty
is
sparse.
This
paper
seeks
to
change
that.
In
its
simplest
form
an
Insurer
agrees
to
cede
X%
of
its
premium
to
a
Reinsurer,
and
in
return
the
Reinsurer
agrees
to
pay
X%
of
the
Insurer’s
losses.
In
practice
the
terms
of
a
quota
share
reinsurance
treaty
are
more
complicated.
For
this
paper
(unless
otherwise
specified)
I
assume
the
following:
• Gross
Loss
Ratio
(GLR)
(Insurer)
(expected):
50%
of
OGP
• Original
Commission
(i.e.
Insurer’s
Acquisition
Expenses):
20%
of
OGP
• Operating
Expenses
(Insurer):
16%
of
OGP
• Reinsurance
Brokerage:
1.5%
of
OGP
(ceded)
• Reinsurance
Brokerage
Rebate:
30%
to
the
Insurer
• Over-­‐rider:
5%
of
OGP
(ceded)
• Profit
Commission:
22.5%
of
Reinsurer’s
Profit
• Reinsurer’s
Expenses
(including
Reinsurance
Brokerage)
for
Profit
Commission
purposes:
10%
of
OGP
(ceded)
• Reinsurer’s
actual
incremental
expenses
(excluding
Reinsurance
Brokerage):
8%
of
OGP
(ceded)
• No
insurance
premium
tax
• No
carry-­‐forward
of
losses
for
Profit
Commission
calculations
• No
contractual
or
gentleman’s
agreement
on
payback
• No
reciprocity
(i.e.
the
reinsurance
treaty
is
not
linked
to
the
purchase,
or
offer,
of
any
other
reinsurance)
• Homogenous
set
of
risks
with
no
individual
risk
dominant
• No
catastrophe
exposure
• Only
one
class
of
business
written
(which
is
the
subject
of
the
reinsurance
treaty)
Several
elements
of
the
above
need
further
explanation.
OGP
=
Original
Gross
Premium.
The
assumptions
with
respect
to
carry-­‐forward
/
gentleman’s
agreement
/
reciprocity
are
made
to
ensure
that
the
particular
quota
share
reinsurance
treaty
stands
on
its
own
(on
a
one
year
basis).
In
practice
all
three
of
these
assumptions
will
usually
be
relaxed
to
some
greater
or
lesser
extent.
The
Reinsurance
Brokerage
Rebate
is
a
feature
of
London
Market
business
and
serves
no
purpose
other
than
to
allow
the
Insurer’s
broker
to
appear
to
receive
higher
brokerage
than
he
is
actually
receiving
(since
he
rebates
some
of
his
brokerage
to
his
client:
the
Insurer).
The
argument,
which
seems
weak
to
your
author
(an
admirer
of
the
Chicago
school
of
economics,
and
believer
generally
in
market
efficiency),
is
that
the
Reinsurer
would
not
give
‘credit’
to
the
Insurer
if
the
brokerage
were
lowered
to
the
net
figure,
thus
the
need
for
the
Reinsurance
Brokerage
Rebate
illusion.

2. Richard
Hartigan
2
21
August
2015
The
Over-­‐rider
is
an
over-­‐riding
commission
(over
and
above
the
Original
Commission)
granted
by
the
Reinsurer
to
the
Insurer
in
recognition
of
the
latter’s
operating
expenses.
It
is
strictly
a
pricing
mechanism
of
the
quota
share
reinsurance
treaty
and
rarely
will
there
be
convergence
between
the
Over-­‐rider
and
the
Insurer’s
actual
Operating
Expenses
(as
above:
5%
versus
16%).
Similar
comments
may
be
made
with
respect
to
the
quantum
of
the
Reinsurer’s
Expenses
for
profit
commission
purposes
versus
the
Reinsurer’s
actual
incremental
expenses
(as
above:
10%
versus
8%).
Although
not
uniform
many
quota
share
reinsurance
treaties
feature
a
profit
commission
wherein
the
Reinsurer
agrees
to
reimburse
to
the
Insurer
a
certain
percentage
of
the
Reinsurer’s
profit.
I
use
the
formula:
Profit
Commission
(%
OGP
(ceded))
=
MAX(0,
22.5%
*
[100%
OGP
–
20%
Original
Commission
–
GLR
–
5%
Over-­‐rider
–
10%
Reinsurer’s
Expenses])
For
example,
if
£100
OGP
was
ceded
and
the
losses
payable
by
the
Reinsurer
were
£47
the
Profit
Commission
would
be:
Profit
Commission
=
MAX(0,
22.5%
*
[£100
-­‐
£20
-­‐
£47
-­‐
£5
-­‐
£10])
...
or
£4.05.
Break-­‐even
Insurer’s
GLR
For
a
given
unit
of
premium,
an
Insurer
has
two
choices:
Retain
or
Reinsure.
If
the
Insurer
retains
the
premium
its
profit
will
be
(using
percentages
of
OGP
to
keep
it
clear):
100%
OGP
–
20%
Original
Commission
–
GLR
If
the
Insurer
reinsures
the
premium
its
profit
will
be
(using
percentages
of
OGP
to
keep
it
clear):
5%
Over-­‐rider
+
1.5%*30%
Reinsurance
Brokerage
Rebate
+
MAX(0,
22.5%
*
Reinsurer’s
Profit)
Note
that
in
both
instances
the
whole
of
the
Insurer’s
Operating
Expenses
of
16%
of
OGP
has
been
excluded.
That
is
because
either
way
the
Insurer
will
incur
these
expenses.
This
will
become
more
apparent,
and
the
importance
thereof,
later
in
this
paper.
Thus
the
profit
referred
to
above
is
more-­‐
correctly
‘profit,
pre-­‐
Operating
Expenses’.
Equating
the
two
sides
of
this
equation
and
re-­‐arranging:
Break-­‐even
Insurer’s
GLR
=
100%
OGP
–
20%
Original
Commission
–
5%
Over-­‐rider
–
1.5%*30%
Reinsurance
Brokerage
Rebate
–
MAX(0,
22.5%
*
Reinsurer’s
Profit)
It
turns
out
that
at
the
relevant
GLR
that
MAX(0,
22.5%
*
Reinsurer’s
Profit)
=
0
so
that
term
may
be
discarded,
so
that
generically
the
Break-­‐even
Insurer’s
GLR
=
100%
–
Original
Commission
–
Over-­‐rider
–
Reinsurance
Brokerage
Rebate
which
for
my
example
is
74.55%
(i.e.
100%
-­‐
20%
-­‐
5%
-­‐
1.5%*30%).

3. Richard
Hartigan
3
21
August
2015
This
is
quite
profound
and
requires
amplification:
absent
capital
considerations
(I
shall
address
these
later)
if
the
expected
GLR
is
less
than
the
break-­‐even
Insurer’s
GLR
(e.g.
74.55%)
the
Insurer
would
be
unwise
to
contemplate
a
quota
share
reinsurance
treaty,
for
any
quantum.
Conversely,
if
the
expected
GLR
is
greater
than
the
break-­‐even
Insurer’s
GLR
(e.g.
74.55%)
the
Insurer
should
seek
to
reinsure
as
much
as
possible
(up
to
100%
of
OGP,
if
possible).
A
graph
makes
things
clearer:
Note
that
in
my
example
that
at
the
break-­‐even
Insurer’s
GLR
the
Insurer
will
make
a
loss
after
factoring
in
Operating
Expenses.
In
my
example
that
would
be
74.55%
break-­‐even
Insurer’s
GLR
+
20%
Original
Commission
+
16%
Operating
Expenses
=
110.55%
combined
ratio.
It
is
absolutely
critical
to
realise
that
the
correct
response
from
an
Insurer’s
point-­‐of-­‐view
when
faced
with
a
loss-­‐making
class
of
business
is
NOT
to
automatically
“reinsure
as
much
as
possible”.
In
fact,
in
my
example,
expected
combined
ratios
between
100%
and
110.55%
should
not
trigger
that
response,
although
naturally
it
should
trigger
an
intense
review
of
whether
or
not
to
continue
to
underwrite
that
class
of
business.
Note:
if
the
Insurer’s
Operating
Expenses
<
(Over-­‐rider
+
Reinsurance
Brokerage
Rebate),
which
is
NOT
the
case
in
the
example
I
have
constructed,
then
at
the
break-­‐even
Insurer’s
GLR
the
Insurer
will
make
a
profit
(not
loss)
after
factoring
in
Operating
Expenses.
Break-­‐even
Reinsurer’s
GLR
A
Reinsurer’s
break-­‐even
loss
ratio
is
slightly
different.
Here,
the
Reinsurer’s
alternative
is
to
either
write
or
not
write
the
business.
With
respect
to
OGP
ceded,
I
set
the
following
to
equate
to
zero:
100%
OGP
–
20%
Original
Commission
–
GLR
–
5%
Over-­‐rider
–
1.5%
Reinsurance
Brokerage
–
MAX(0,
22.5%
*
Reinsurer’s
Profit)
–
Reinsurer’s
actual
incremental
expenses
(not
the
Reinsurer’s
Expenses
used
in
the
Profit
Commission
calculation;
here:
8%,
not
10%)
Re-­‐arranging
to
make
GLR
the
subject:

4. Richard
Hartigan
4
21
August
2015
Break-­‐even
Reinsurer’s
GLR
=
100%
–
Original
Commission
–
Over-­‐rider
–
Reinsurance
Brokerage
–
MAX(0,
22.5%
*
Reinsurer’s
Profit)
–
Reinsurer’s
actual
incremental
expenses
It
turns
out
that
at
the
relevant
GLR
that
MAX(0,
22.5%
*
Reinsurer’s
Profit)
=
0
so
that
term
may
be
discarded,
so
that
generically
the
Break-­‐even
Reinsurer’s
GLR
=
100%
–
Original
Commission
–
Over-­‐rider
–
Reinsurance
Brokerage
–
Reinsurer’s
actual
incremental
expenses
which
for
my
example
is
65.50%
(i.e.
100%
-­‐
20%
-­‐
5%
-­‐
1.5%
-­‐
8%).
What
is
fascinating
about
this
outcome
is
that
in
all
circumstances
the
break-­‐even
Reinsurer’s
GLR
<
break-­‐even
Insurer’s
GLR,
since
additionally
the
break-­‐even
Reinsurer’s
GLR
has
to
allow
for
the
full
(pre-­‐Rebate)
Reinsurance
Brokerage
and
the
Reinsurer’s
actual
incremental
expenses.
Prima
facie
there
will
be
no
overlap
between
an
Insurer’s
desire
to
cede
premium
and
a
Reinsurer’s
desire
to
underwrite
that
same
premium.
Note:
if
Reinsurer’s
Expenses
<
(Reinsurance
Brokerage
+
Reinsurer’s
actual
incremental
expenses),
which
is
NOT
the
case
in
the
example
I
have
constructed,
then
the
MAX(0,
22.5%
*
Reinsurer’s
Profit)
term
>
0
and
should
not
be
discarded.
Care
will
be
needed
by
the
reader
to
correctly
allow
for
this
in
the
appropriate
circumstances.
In
those
circumstances
the
Break-­‐even
Reinsurer’s
GLR
will
be
slightly
lower.
Capital
Considerations
The
break-­‐even
Insurer’s
GLR
is
a
useful
concept
when
capital
is
not
a
consideration
(i.e.
the
Insurer
has
ample
capital
for
the
class
of
business).
What
happens
if
this
is
not
the
case?
I
start
by
assuming
the
expected
GLR
<
the
break-­‐even
Insurer’s
GLR,
for
if
this
were
not
the
case
the
Insurer’s
path
would
be
clear:
seek
to
reinsure
100%
of
the
premium.
I
assume
the
Insurer
has
a
fixed
(non-­‐changeable)
quantum
of
capital.
I
also
assume
that
an
Insurer
references
the
modelled
1-­‐in-­‐200
year
GLR
(GLR^)
to
assess
risk
(and
that
underwriting
(premium)
risk
is
the
only
risk
the
Insurer
faces,
and
therefore
is
the
only
risk
that
must
be
considered
for
capital
purposes).
The
Insurer
must
scale
the
quota
share
reinsurance
treaty’s
cession
so
that
at
that
modelled
1-­‐in-­‐200
year
GLR
(GLR^)
outcome
the
Insurer’s
loss
leads
to
no
more
than
the
desired
erosion
of
capital.
The
Insurer’s
total
profit
(which
should
be
negative
at
the
modelled
1-­‐in-­‐200
year
GLR
(GLR^)
outcome)
is
as
follows
(using
percentages
of
OGP
to
keep
it
clear):
(100%
-­‐
QS)
*
[100%
OGP
–
20%
Original
Commission
–
GLR^]
PLUS
QS
*
[5%
Over-­‐rider
+
1.5%*30%
Reinsurance
Brokerage
Rebate]
(once
again
recognising
that
at
the
relevant
GLR^
that
MAX(0,
22.5%
*
Reinsurer’s
Profit)
=
0
so
that
term
may
be
discarded)
MINUS

5. Richard
Hartigan
5
21
August
2015
100%
*
16%
Operating
Expenses
and
I
assume
the
Insurer
does
not
wish
to
lose
more
than
Y%
of
OGP
of
its
capital
at
that
modelled
1-­‐in-­‐200
year
GLR
(GLR^)
outcome
(i.e.
the
Insurer’s
risk
appetite).
Re-­‐arranging
to
make
QS
(percentage
of
OGP
ceded)
the
subject:
QS
=
(100%
–
Original
Commission
–
GLR^
+
Y%
–
Operating
Expenses)
(100%
–
Original
Commission
–
GLR^
–
Over-­‐rider
–
Reinsurance
Brokerage
Rebate)
QS
=
(100%
–
20%
–
GLR^
+
Y%
–
16%)
(100%
–
20%
–
GLR^
–
5%
–
1.5%*30%)
Since
this
is
a
two-­‐factor
model
(i.e.
capital
at
risk
(Y%
of
OGP)
and
the
modelled
1-­‐in-­‐200
year
GLR
(GLR^))
the
result
is
as
follows:
QS
(percentage
of
OGP
ceded)
Y%
of
OGP
5%
10%
15%
20%
25%
30%
Modelled
75%
>100%
>100%
<0%
<0%
<0%
<0%
1-­‐in-­‐200
80%
>100%
>100%
18.3%
<0%
<0%
<0%
Year
85%
>100%
>100%
57.4%
9.6%
<0%
<0%
GLR
90%
>100%
>100%
71.2%
38.8%
6.5%
<0%
(GLR^)
95%
>100%
>100%
78.2%
53.8%
29.3%
4.9%
100%
>100%
>100%
82.5%
62.9%
43.2%
23.6%
Taking
an
example,
if
an
Insurer’s
modelled
1-­‐in-­‐200
year
GLR
(GLR^)
outcome
was
85%
and
the
Insurer
wished
to
lose
no
more
than
20%
of
OGP
in
a
given
year
then
the
Insurer
should
seek
out
a
quota
share
reinsurance
treaty
cession
of
9.6%
of
OGP
(retaining
the
remaining
90.4%
of
OGP).
Since
the
expected
GLR
<
the
break-­‐even
Insurer’s
GLR
this
9.6%
quota
share
reinsurance
treaty
cession
is
sub-­‐optimal
from
the
Insurer’s
expected
profit
point-­‐of-­‐view,
but
wholly
necessary
from
the
Insurer’s
capital
point-­‐of-­‐view.
Raising
Capital
Continuing
on
from
the
previous
section:
how
much
capital
would
the
Insurer
need
to
raise
in
order
to
dispense
with
the
sub-­‐optimal
9.6%
quota
share
reinsurance
treaty
cession
altogether,
and
what
return
could
be
achieved
on
that
incremental
capital?
I
continue
to
assume
the
Insurer’s
modelled
1-­‐in-­‐200
year
GLR
(GLR^)
outcome
is
85%.
QS
(percentage
of
OGP
ceded)
Y%
of
OGP
5%
10%
15%
20%
21%
30%
Modelled
75%
>100%
>100%
<0%
<0%
<0%
<0%
1-­‐in-­‐200
80%
>100%
>100%
18.3%
<0%
<0%
<0%
Year
85%
>100%
>100%
57.4%
9.6%
0.0%
<0%
GLR
90%
>100%
>100%
71.2%
38.8%
32.4%
<0%
(GLR^)
95%
>100%
>100%
78.2%
53.8%
48.9%
4.9%
100%
>100%
>100%
82.5%
62.9%
58.9%
23.6%

6. Richard
Hartigan
6
21
August
2015
If
the
20%
of
OGP
capital
at
risk
is
increased
to
21%
of
OGP
capital
at
risk
one
can
see
that
the
QS
(percentage
of
OGP
ceded)
moves
from
9.6%
to
0.0%.
By
raising
the
equivalent
of
1%
of
OGP
of
capital
(from
20%
to
21%)
the
Insurer
can
dispense
with
the
quota
share
reinsurance
treaty
altogether.
The
expected
profit
re-­‐captured
=
QS
*
(profit
at
expected
GLR
if
retained
-­‐
profit
at
expected
GLR
if
reinsured).
In
my
example
that
would
be:
9.6%
*
(30%
OGP
–
8.83%
OGP)
=
2.03%
of
OGP.
The
expected
Return
On
Equity
(ROE)
>
100%
in
this
case
(2.03%
/
1%)
...
the
Insurer
should
clearly
raise
the
incremental
capital
and
dispense
with
the
quota
share
reinsurance
treaty
altogether.
The
fallacy
of
the
NNLR
The
Net
Net
Loss
Ratio
(NNLR)
is
a
popular
loss
ratio
calculation
used
in
the
London
Market.
The
first
Net
signifies
net
of
Original
Commission;
the
second
Net
signifies
that
only
retained
losses
and
retained
premium
are
used
in
the
loss
ratio
calculation.
NNLR
=
(100%
-­‐
QS)
*
Gross
Loss
–
QS
*
Profit
Commission
(100%
-­‐
QS)
*
(100%
OGP
–
20%
Original
Commission)
+
QS
*
(Over-­‐rider
+
Reinsurance
Brokerage
Rebate)
Note:
the
decision
whether
to
include
the
Profit
Commission,
the
Over-­‐rider,
and
the
Reinsurance
Brokerage
Rebate
as
either
a
negative
in
the
numerator
or
a
positive
in
the
denominator
is
largely
a
matter
of
choice.
I
have
chosen
to
allocate
these
as
I
believe
is
market
standard.
For
reference
the
Gross
Net
Loss
Ratio
(GNLR)
and
the
GLR
calculations
are
shown:
GNLR
=
Gross
Loss
100%
OGP
–
20%
Original
Commission
GLR
=
Gross
Loss
100%
OGP
I
start
by
assuming
the
expected
GLR
is
50%
(and
note
this
is
lower
than
the
break-­‐even
Insurer’s
GLR
of
74.55%),
and
I
vary
the
QS
(percentage
of
OGP
ceded).
For
this
example
only
OGP
=
£300,000.

7. Richard
Hartigan
7
21
August
2015
At
0.0%
QS
the
Insurer
Gross
Profit
(no
QS)
(LHS)
=
the
Insurer
Net
Profit
(post
QS)
(LHS)
=
£42,000,
the
expected
GLR
(RHS)
=
50%
(given),
and
the
GNLR
(RHS)
=
the
NNLR
(RHS)
=
62.5%.
As
the
QS
increases
the
expected
GLR
(RHS),
and
the
GNLR
(RHS)
are
held
constant,
and
(of
course)
the
Insurer
Gross
Profit
(no
QS)
(LHS)
remains
constant.
What
seems
incongruent
though
is
that
at
the
same
time
the
Insurer
Net
Profit
(post
QS)
(LHS)
is
declining
the
NNLR
(RHS)
is
also
declining.
How
can
this
be?
The
reason
the
Insurer
Net
Profit
(post
QS)
is
declining
is
simple:
the
expected
GLR
(RHS)
at
50%
is
lower
than
the
break-­‐even
Insurer’s
GLR
(74.55%).
Absent
capital
constraints
the
quota
share
reinsurance
treaty
is
not
in
the
Insurer’s
interest
(for
any
quantum),
and
the
net
result
to
the
Insurer
becomes
poorer
and
poorer
as
the
QS
percentage
increases
(e.g.
at
a
70.0%
QS
the
Insurer
Net
Profit
(post
QS)
is
negative).
But
this
still
leaves
the
conundrum:
why
is
the
NNLR
(RHS)
also
declining
(thus
falsely
indicating
that
the
quota
share
reinsurance
treaty
is
favourable)?
The
net
premium
retained
decreases
linearly
as
the
QS
increases
and
is
flattered
by
the
Over-­‐rider
and
the
Reinsurance
Brokerage
Rebate
which
are
modest
in
absolute
terms
but
become
bigger-­‐and-­‐bigger
in
relative
terms.
The
net
loss
retained
decreases
linearly
as
the
QS
decreases
and
is
flattered
by
the
off-­‐setting
Profit
Commission.
The
result
is
progressively
falling
NNLRs.
What
is
missing,
and
what
is
absolutely
critical
to
realise,
is
that
the
smaller-­‐and-­‐smaller
net
premium
retained
(modestly
bolstered
by
the
Profit
Commission,
the
Over-­‐rider,
and
the
Reinsurance
Brokerage
Rebate)
must
wholly
support
the
Insurer’s
Operating
Expenses
(16%
of
OGP
in
my
example).
At
a
certain
point
(somewhere
between
60%
QS
and
70%
QS
in
my
example)
the
Insurer’s
Operating
Expenses
completely
swamp
the
net
premium
retained
and
a
negative
profit
(i.e.
loss)
results.
The
NNLR
is
a
terrible
measure
of
the
success
(or
otherwise)
of
a
quota
share
reinsurance
treaty.
I
also
note
that
in
all
circumstances
the
NNLR
<
the
GNLR
(another
false
indication
that
the
quota
share
reinsurance
treaty
is
favourable).

8. Richard
Hartigan
8
21
August
2015
Catastrophe-­‐exposed
classes
of
business
For
the
purposes
of
this
section
I
assume
that
the
class
of
business
now
has
catastrophe
exposure.
Since
I
have
already
demonstrated
that
an
Insurer
should
only
contemplate
a
quota
share
reinsurance
treaty
if
the
Insurer
was
capital
constrained,
I
must
conclude
that
is
the
case
here
too.
I
further
assume
that
the
quota
share
reinsurance
treaty
has
no
Event
Limit.
An
Event
Limit
limits
the
quantum
of
losses
an
Insurer
can
cede
to
the
Reinsurer
in
the
event
of
a
catastrophic
loss.
The
idea
is
that
the
Reinsurer
wants
to
avoid
offering
‘cheap’
catastrophe
cover.
Often
the
opposite
problem
occurs.
Looking
again
at
a
previous
graph,
slightly
augmented:
At
a
50%
expected
GLR
the
profit
ceded
to
the
Reinsurer
is
21.17%
(indicated
by
{
)
of
OGP
ceded
(i.e.
30%
-­‐
8.83%).
This
figure
is,
in
effect,
how
much
the
Insurer
is
paying
the
Reinsurer
due
to
the
Insurer’s
capital
constraints.
It
is
compensation
for
both
catastrophe
exposure
and
attritional
exposure.
Is
the
Insurer
paying
the
Reinsurer
too
much
for
the
catastrophe
exposure
element?
Until
one
benchmarks
the
cost
of
buying
a
catastrophe
excess
of
loss
reinsurance
programme
with
an
appropriate
attachment
and
limit
at
market
rates
it
is
impossible
to
know.
The
relative
contribution
of
the
catastrophe
exposure
element
and
the
attritional
exposure
element
to
the
Insurer’s
capital
inadequacy
will
also
need
to
be
determined.
It
may
be
that
the
Insurer
can
shed
the
catastrophe
exposure
element
cheaply
via
a
catastrophe
excess
of
loss
reinsurance
programme
and
that
the
residual
attritional
exposure
element
is
within
the
Insurer’s
existing
capital
capacity.
In
that
case
the
correct
course
is
clear.
Note,
however,
that
if
the
Insurer
has
ample
capital
and
that
quantum
of
capital
is
fixed
(non-­‐
changeable)
then
reinsurance
of
any
type
is
moot
(at
the
assumed
expected
GLR).
Investment
Income
I
will
be
criticised
by
purists
for
not
allowing
for
investment
income.
Quota
share
reinsurance
treaties
generally
result
in
significant
transfer
of
premium
and
so
investment
income
may
be
significant.
However,
in
the
current
environment
of
near-­‐zero
interest
rates
I
prefer
to
leave
investment
income
as
the
tie-­‐breaker
if
an
Insurer’s
reinsurance
decision
is
marginal.
In
that
case
the
Insurer
should
not
reinsure:
by
reinsuring
the
Insurer
is
forgoing
investment
income
on
OGP
ceded
(less
Original
Commissions).

9. Richard
Hartigan
9
21
August
2015
Reinsurer
Credit
Risk
That
significant
transfer
of
premium
will
also
invoke
reinsurer
credit
risk,
another
element
for
which
I
have
made
no
allowance.
Again,
I
prefer
to
leave
reinsurer
credit
risk
as
the
tie-­‐breaker
if
an
Insurer’s
reinsurance
decision
is
marginal.
Again,
in
that
case
the
Insurer
should
not
reinsure:
by
reinsuring
the
Insurer
is
accepting
that
reinsurer
credit
risk.
Conclusions
Some
fairly
profound
conclusions
emerge.
Scenario
1:
an
Insurer
has
ample
capital
and
that
quantum
of
capital
is
fixed
(non-­‐changeable):
• where
expected
GLR
<
break-­‐even
Reinsurer’s
GLR
o Reinsurer
should
be
keen
to
reinsure
o Insurer
should
not
be
keen
to
reinsure
• where
break-­‐even
Reinsurer’s
GLR
<
expected
GLR
<
break-­‐even
Insurer’s
GLR
o Reinsurer
should
not
be
keen
to
reinsure
o Insurer
should
not
be
keen
to
reinsure
• where
break-­‐even
Insurer’s
GLR
<
expected
GLR
o Reinsurer
should
not
be
keen
to
reinsure
o Insurer
should
be
keen
to
reinsure
i.e.
there
is
no
commonality
of
interest
to
reinsure.
Where
an
Insurer
has
ample
capital
and
that
quantum
of
capital
is
fixed
(non-­‐changeable)
quota
share
reinsurance
treaties
are
inappropriate
in
all
circumstances.
Scenario
2:
an
Insurer
has
inadequate
capital
and
that
quantum
of
capital
is
fixed
(non-­‐changeable):
• where
expected
GLR
<
break-­‐even
Reinsurer’s
GLR
o Reinsurer
should
be
keen
to
reinsure
o Insurer
should
be
keen
to
reinsure
• where
break-­‐even
Reinsurer’s
GLR
<
expected
GLR
<
break-­‐even
Insurer’s
GLR
o Reinsurer
should
not
be
keen
to
reinsure
o Insurer
should
be
keen
to
reinsure
• where
break-­‐even
Insurer’s
GLR
<
expected
GLR
o Reinsurer
should
not
be
keen
to
reinsure
o Insurer
should
be
keen
to
reinsure
i.e.
there
is
a
commonality
of
interest
to
reinsure
only
where
the
expected
GLR
<
break-­‐even
Reinsurer’s
GLR.
Since
the
Insurer
must
reinsure
from
a
capital
point-­‐of-­‐view
(i.e.
the
Insurer
has
no
choice)
then
in
all
other
circumstances
a
method
must
be
found
to
raise
the
break-­‐even
Reinsurer’s
GLR
above
the
expected
GLR,
typically
by
reducing
demands
with
respect
to
the
Over-­‐rider
and/or
the
Reinsurance
Brokerage.
Should
a
commonality
of
interest
to
reinsure
be
found
and
a
quota
share
reinsurance
treaty
be
contemplated
the
Insurer
must
then
determine
if
catastrophe
exposure
(if
any)
can
be
better
shed
via
a
catastrophe
excess
of
loss
reinsurance
programme.
Scenario
3:
an
Insurer
has
inadequate
capital
but
the
Insurer
could
raise
capital
if
economically
sensible:
• firstly,
determine
the
quantum
of
capital
that
must
be
raised
• secondly,
determine
the
profit
re-­‐captured
at
the
expected
GLR
• thirdly,
determine
if
the
profit
re-­‐captured
can
adequately
service
(expected
ROE)
the
quantum
of
capital
that
must
be
raised

10. Richard
Hartigan
10
21
August
2015
Summary
The
circumstances
in
which
a
quota
share
reinsurance
treaty
should
be
agreed
are
limited
(broadly)
to
Insurers
with
inadequate
capital
where
the
expected
GLR
<
break-­‐even
Reinsurer’s
GLR.
In
that
circumstance
the
quota
share
reinsurance
treaty
will
be
sub-­‐optimal
from
the
Insurer’s
expected
profit
point-­‐of-­‐view,
but
wholly
necessary
from
the
Insurer’s
capital
point-­‐of-­‐view.
In
all
other
circumstances
the
use
of
a
quota
share
reinsurance
treaty
will
be
of
doubtful
value
to
an
Insurer.
Editing
Notes
Version
1:
30
July
2015,
original
Version
2:
21
August
2015,
various
typographical
corrections
(especially
formulae
on
Page
5)