CREDIBILITY
FROM THE EYES OF THE CUSTOMER
Michael Round
Rational Systems
August 11, 1999
Rational Systems, formed by Michael Round in 1999, and
located in Overland Park, Kansas, specializes in statistical and
actuarial improvement.
For a copy of “Credibility”, please e-mail me at:
[email protected]
We are now accepting clients.
INTRODUCTION &
BACKGROUND
BACKGROUND
DISRAELI vs. HUCKLEBERRY FINN
Communication /
Presentation of Subject
INTRODUCTION &
BACKGROUND
Well
Poorly
Disraeli
The Quality
Transaction
= win/win
Hack
Huck
Poor Idea
Good Idea
Appropriateness / Relevance of
Idea
THE EXISTENCE OF A
PROBLEM
CONTEXT: the renewal rating process, the pricing actuary, and
the group representative / layperson - all addressing the impending
anniversary date of the group.
THE ACTUARIAL POSITION
goal
We want to have a
reasonably priced
insurance product.
requirements
prerequisite
The pricing
actuary must take
into account claims
variability.
Credibility is used
in the renewal
rating process.
THE GROUPS’ POSITION
goal
requirements
prerequisite
My premium
should reflect my
experience.
Numbers “speak
for themselves”...
no need for
‘credibility’.
We want to have a
reasonably priced
insurance product.
THE CONFLICT
goal
requirements
prerequisite
The pricing
actuary must take
into account claims
variability.
Credibility is used
in the renewal
rating process.
My premium
should reflect my
experience.
Numbers “speak
for themselves”...
no need for
‘credibility’.
We want to have a
reasonably priced
insurance product.
CONFLICT CONSEQUENCES
Credibility may
adjust data to an
“average renewal
rate increase”.
Credibility is used
in the renewal
rating process.
My expectation is a
low renewal rate
increase.
My group has an
empirically low loss
ratio.
Numbers “speak
for themselves”...
no need for
‘credibility’.
UNDESIREABLE EFFECT
Unhappy, angry,
and confused, I go
to the market for
competing quotes.
Credibility may
adjust data to an
“average renewal
rate increase”.
My expectation is a
low renewal rate
increase.
THE ROOT CAUSE
At first glance, we might suggest the root cause of the conflict and the
inevitable action of the group is:
FAILURE OF THE CLIENT TO UNDERSTAND THAT
ADJUSTMENT OF DATA IS NECESSARY IN THE RENEWAL
PROCESS . . . After all, the client has the perception:
THE DATA IS WHAT IT IS!!
However ...
DATA ADJUSTMENTS THAT
ARE UNDERSTOOD
We often adjust the data prior to the application of credibility, and the
group / layperson perfectly understands “the data is NOT what it is” and is comfortable with data adjustments.
For example …
First-Year Cases on a Paid Basis
Late-Year Rapid Contract Growth
DATA ADJUSTMENTS THAT
ARE UNDERSTOOD
Empirical Data
Paid
Paid
Month
Premium Claims
January
$10,000
$0
February
$10,000
$0
March
$10,000
$0
April
$10,000 $7,143
May
$10,000 $10,000
June
$10,000 $14,286
July
$10,000 $5,714
August
$10,000 $2,857
September $10,000 $3,571
October
$10,000 $5,143
Totals
Loss Ratio
Apples-to-Apples
Paid
Paid
Premium Claims
$0
$0
$0
$0
$0
$0
$10,000 $7,143
$10,000 $10,000
$10,000 $14,286
$10,000 $5,714
$10,000 $2,857
$10,000 $3,571
$10,000 $5,143
$100,000 $48,714
$70,000 $48,714
49%
70%
DATA ADJUSTMENTS THAT
ARE UNDERSTOOD
Empirical Data
Paid
Paid
Month
Contracts Premium Claims
January
100
$10,000 $7,143
February
100
$10,000 $10,000
March
100
$10,000 $14,286
April
100
$10,000 $5,714
May
100
$10,000 $2,857
June
100
$10,000 $3,571
July
100
$10,000 $5,143
August
200
$20,000 $6,959
September
200
$20,000 $6,933
October
200
$20,000 $6,495
Apples-to-Apples
Paid
Paid
Premium Claims
$10,000 $7,143
$10,000 $10,000
$10,000 $14,286
$10,000 $5,714
$10,000 $2,857
$10,000 $3,571
$10,000 $5,143
$10,000 $6,959
$10,000 $6,933
$10,000 $6,495
Totals
$130,000 $69,101
$100,000 $69,101
53%
69%
Loss Ratio
THE ROOT PROBLEM
The group often does not
understand the adjustment
of their “good” data when
adjusted via credibility.
The group accepts “data
adjustments” they can
understand.
Credibility adjusts data in a
numerical “black box”.
INJECTION TO SOLVE THE
PROBLEM
The group has an understanding of what has
happened to their data - and may not be as
dissatisfied with the perceived gap between the
“expected” and “actual” renewal rate increase.
The group accepts “data
adjustments” they can
understand.
CREDIBILITY - and what
gives rise to its need - ARE
INTUITIVELY presented.
THE SOLUTION TO THE
PROBLEM
CREDIBILITY seeks to quantify the variability, uncertainty,
and predictability of a block of data.
To intuitively present this idea, we need to bridge the gap
between our level of knowledge and that of the group
representative / lay-person - OR PROVIDE A VISUAL
MEANS OF AFFORDING THE LAY-PERSON THE
INTUITIVE KNOWLEDGE OF WHAT VARIABILITY IS.
SIMULATION is an excellent mechanism for
demonstrating variability and uncertainty at an intuitive
level.
SIMULATING VARIABILITY
IF the essence of credibility is “degree of predictability”,
THEN one method of communicating intuitively this concept
is a simple simulation probability distribution for three
different group sizes:
25 Members
250 Members
2500 Members
A ‘25-MEMBER’ GROUP ...
A ‘250-MEMBER’ GROUP ...
A ‘2500-MEMBER’ GROUP ...
CLAIMS: A COMPARISON BY
GROUP SIZE
EXPLAINING CREDIBILITY
IF we have achieved our goal of visually demonstrating the
meaning of “variability”, “uncertainty”, and “predictability”
[all of which CREDIBILITY is addressing], THEN the group
representative / lay-person has some feel why their data is being
adjusted.
WHY NOT USE THE SAME SIMULATION PROCESS THAT
EXPRESSES VARIABILITY VISUALLY TO TABULATE
THE CREDIBILITY FACTORS WE NEED TO ACTUALLY
ADJUST THE DATA?
THE ADVANTAGES
When SIMULATION is used as described here, the advantages
are numerous:
1. The source data [the continuance table] is ours;
2. We can visually and easily explain what the whole process
means;
3. We can quantify ‘credibility’ numerous ways;
4. We can easily make continuance table adjustments to
recognize certain characteristics of a group [e.g., low
specific deductibles, carve-outs, annual maximums];
5. We can operationally define to all parties exactly what is
going on.
TABULATING CREDIBILITY
There are many ways to tabulate credibility when approached
from the perspective defined here. The two basic
categories are:
1. Percentage of simulations falling within +/- x% of the
expected PMPM;
2. Percentage of simulation dollars falling within +/- x% of the
total expected dollars.
CREDIBILITY FOR OUR
PURPOSES
CREDI BI LI TY TABU LAR DATA
CREDI BI LI TY TABU LAR DATA
PROBABI LI T Y M EASU RE: # OF SI M U LAT ED GROU PS
PROBABI LI T Y M EASU RE: AM OU N T OF SI M U LAT ED CLAI M $
Simulated Rates
Group Size in Members
Simulated Rates
in Relation to
Expected Rates
Group Size in Members
in Relation to
10
25
50
100
250
500
10
25
50
100
250
500
0%-5%
0.1%
0.0%
0.0%
0.0%
0.0%
0.0%
1000
0.0%
2500
0.0%
5000
0.0%
Expected Rates
0%-5%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
1000
0.0%
2500
0.0%
5000
0.0%
5%-15%
3.1%
0.1%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
5%-15%
0.4%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
15%-25%
8.6%
1.8%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
15%-25%
1.8%
0.4%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
25%-35%
11.2%
5.9%
1.6%
0.1%
0.0%
0.0%
0.0%
0.0%
0.0%
25%-35%
3.4%
1.8%
0.5%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
35%-45%
10.6%
9.3%
5.5%
1.7%
0.0%
0.0%
0.0%
0.0%
0.0%
35%-45%
4.3%
3.8%
2.3%
0.7%
0.0%
0.0%
0.0%
0.0%
0.0%
45%-55%
10.6%
12.3%
11.1%
6.4%
0.8%
0.1%
0.0%
0.0%
0.0%
45%-55%
5.3%
6.3%
5.6%
3.2%
0.4%
0.0%
0.0%
0.0%
0.0%
55%-65%
8.7%
12.5%
14.3%
13.6%
6.9%
1.7%
0.1%
0.0%
0.0%
55%-65%
5.2%
7.7%
8.7%
8.2%
4.3%
1.1%
0.1%
0.0%
0.0%
65%-75%
7.9%
11.1%
14.1%
16.3%
15.7%
9.2%
3.9%
0.3%
0.0%
65%-75%
5.5%
7.9%
10.0%
11.4%
11.1%
6.5%
2.8%
0.2%
0.0%
75%-85%
6.9%
9.1%
11.7%
14.5%
18.3%
20.3%
17.5%
7.7%
2.3%
75%-85%
5.6%
7.4%
9.4%
11.5%
14.8%
16.2%
14.1%
6.3%
1.9%
85%-95%
5.0%
7.8%
9.6%
11.1%
15.8%
20.9%
25.1%
29.4%
27.6%
85%-95%
4.6%
7.2%
8.7%
10.0%
14.3%
18.7%
22.6%
26.7%
25.2%
95%-105%
4.0%
5.3%
6.3%
7.9%
13.1%
15.4%
20.9%
33.2%
44.3%
95%-105%
4.1%
5.4%
6.3%
7.9%
13.1%
15.3%
20.9%
33.2%
44.3%
105%-115%
3.0%
4.2%
4.8%
6.3%
8.1%
10.3%
12.8%
19.3%
21.1%
105%-115%
3.4%
4.8%
5.3%
6.9%
9.0%
11.3%
14.0%
21.1%
23.0%
115%-125%
2.5%
3.5%
3.5%
4.1%
5.1%
6.7%
8.9%
7.2%
4.3%
115%-125%
3.1%
4.3%
4.2%
4.9%
6.1%
8.0%
10.7%
8.6%
5.1%
125%-135%
2.6%
2.5%
2.9%
3.5%
3.4%
4.6%
5.5%
2.2%
0.4%
125%-135%
3.4%
3.4%
3.8%
4.6%
4.5%
5.9%
7.1%
2.9%
0.5%
135%-145%
1.9%
1.7%
2.0%
2.9%
2.9%
3.0%
2.5%
0.5%
0.0%
135%-145%
2.7%
2.5%
2.8%
4.1%
4.1%
4.2%
3.5%
0.7%
0.0%
145%-155%
1.6%
1.4%
1.4%
2.1%
2.2%
2.6%
1.4%
0.1%
0.0%
145%-155%
2.4%
2.2%
2.1%
3.2%
3.3%
3.8%
2.1%
0.2%
0.0%
155%-165%
1.0%
1.2%
1.4%
1.9%
1.8%
2.0%
0.9%
0.0%
0.0%
155%-165%
1.7%
2.0%
2.3%
3.0%
3.0%
3.2%
1.4%
0.0%
0.0%
165%-175%
1.1%
1.1%
1.2%
1.1%
1.2%
1.3%
0.3%
0.0%
0.0%
165%-175%
1.8%
1.9%
2.0%
1.9%
2.0%
2.2%
0.5%
0.0%
0.0%
175%-185%
0.9%
0.9%
1.3%
0.7%
0.8%
0.7%
0.1%
0.0%
0.0%
175%-185%
1.7%
1.6%
2.3%
1.2%
1.4%
1.2%
0.2%
0.0%
0.0%
185%-195%
0.9%
0.8%
0.8%
0.4%
0.4%
0.7%
0.1%
0.0%
0.0%
185%-195%
1.8%
1.6%
1.6%
0.8%
0.8%
1.2%
0.1%
0.0%
0.0%
195%-205%
0.5%
0.6%
0.7%
0.3%
0.5%
0.2%
0.0%
0.0%
0.0%
195%-205%
1.0%
1.3%
1.4%
0.7%
0.9%
0.3%
0.0%
0.0%
0.0%
205%-215%
0.4%
0.7%
0.9%
0.2%
0.6%
0.1%
0.0%
0.0%
0.0%
205%-215%
0.8%
1.4%
1.9%
0.4%
1.2%
0.2%
0.0%
0.0%
0.0%
215%-225%
0.3%
0.4%
0.5%
0.3%
0.6%
0.1%
0.0%
0.0%
0.0%
215%-225%
0.7%
0.9%
1.1%
0.6%
1.3%
0.3%
0.0%
0.0%
0.0%
225%-235%
0.2%
0.3%
0.5%
0.4%
0.6%
0.1%
0.0%
0.0%
0.0%
225%-235%
0.6%
0.8%
1.2%
1.0%
1.5%
0.1%
0.0%
0.0%
0.0%
235%-999%
6.3%
5.4%
3.9%
4.2%
1.2%
0.1%
0.0%
0.0%
0.0%
235%-999%
34.8%
23.6%
16.6%
13.7%
3.1%
0.3%
0.0%
0.0%
0.0%
12.0%
17.3%
20.3%
24.8%
36.4%
45.3%
57.4%
81.0%
92.5%
20.6%
29.0%
33.9%
41.3%
57.2%
69.5%
82.2%
95.9%
99.5%
CREDI BI LI TY
CREDI BI LI TY
as # of Gr oups
with exper ience
as # of Claim $
12.1%
17.3%
20.7%
25.3%
37.0%
46.7%
58.8%
81.9%
93.0%
with exper ience
within +/- 15%
within +/- 15%
of expected r ates
of expected r ates
as # of Gr oups
with exper ience
as # of Claim $
21.5%
29.9%
35.8%
43.9%
60.4%
73.7%
85.2%
96.8%
99.6%
with exper ience
within +/- 25%
within +/- 25%
of expected r ates
of expected r ates
CREDIBILITY FOR OUR
PURPOSES
100%
100%
97%
93%
Credibility Defined in Terms of
"Number of Groups" within
Certain Bounds
85%
82%
74%
75%
60%
50%
59%
47%
44%
37%
36%
30%
25%
22%
25%
17%
21%
12%
0%
10
25
50
100
250
500
1000
2500
5000
Group Size: Members
Number of Groups with +/- 15% of Expected Rates
Number of Groups within +/- 25% of Expected Rates
CREDIBILITY FOR OUR
PURPOSES
100%
100%
96%
Credibility Defined in Terms of
"Amount of Claim $" within
Certain Bounds
93%
82%
75%
81%
70%
57%
50%
57%
45%
41%
36%
34%
29%
25%
21%
25%
17%
20%
12%
0%
10
25
50
100
250
500
1000
2500
5000
Group Size: Members
Amount of Claim $ with +/- 15% of Expected Rates
Amount of Claim $ within +/- 25% of Expected Rates
WHICH METHOD TO USE?
We can obviously choose from a number of
tabular formulations to use as our
“credibility” factors . . . Which one is best?
Dr. Walter Shewhart, the
founder of the Statistical
Process Control Chart, is
perhaps the best source to
consult to address this
question.
The control limits of his charts are
not solely statistical in nature, but
PRACTICAL…that is, Dr.
Shewhart addressed the question
“WHAT MAKES ECONOMIC
AND PRACTICAL SENSE?” and
he developed a process from that
perspective.
THE ANSWER?
What tabular selection is best? Which should be used in
the adjustment of data?
WHICHEVER METHOD IS BEST FOR YOU IN
YOUR MARKET DEALING WITH THE PEOPLE IN
YOUR MARKET AND THE COMPETITION IN YOUR
MARKET.`
CONCLUSION
Have I convinced you there is a problem?
Have I addressed the reason for this problem?
Have I developed the cause of the problem?
Have I solved the problem?
Have I quantified in practical terms what “solution” means?
Have I shown numerous advantages to such a solution, while not
introducing negative consequences?
CONCLUSION
Have I convinced you there is a problem?
Have I addressed the reason for this problem?
Have I developed the cause of the problem?
Have I solved the problem?
Have I quantified in practical terms what “solution” means?
Have I shown numerous advantages to such a solution, while not
introducing negative consequences?
CONCLUSION
Have I convinced you there is a problem?
Have I addressed the reason for this problem?
Have I developed the cause of the problem?
Have I solved the problem?
Have I quantified in practical terms what “solution” means?
Have I shown numerous advantages to such a solution, while not
introducing negative consequences?
CONCLUSION
Have I convinced you there is a problem?
Have I addressed the reason for this problem?
Have I developed the cause of the problem?
Have I solved the problem?
Have I quantified in practical terms what “solution” means?
Have I shown numerous advantages to such a solution, while not
introducing negative consequences?
CONCLUSION
Have I convinced you there is a problem?
Have I addressed the reason for this problem?
Have I developed the cause of the problem?
Have I solved the problem?
Have I quantified in practical terms what
“solution” means?
Have I shown numerous advantages to such a solution, while not
introducing negative consequences?
CONCLUSION
Have I convinced you there is a problem?
Have I addressed the reason for this problem?
Have I developed the cause of the problem?
Have I solved the problem?
Have I quantified in practical terms what “solution” means?
Have I shown numerous advantages to such a
solution, while not introducing negative
consequences?