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:
roundml@ix.netcom.com
We are now accepting clients.
INTRODUCTION &
BACKGROUND
BACKGROUND
DISRAELI vs. HUCKLEBERRY FINN
INTRODUCTION &
BACKGROUND
The Quality
Presentation of Subject
Well Disraeli Transaction
Communication /
= win/win
Poorly 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 requirements prerequisite
The pricing Credibility is used
actuary must take in the renewal
into account claims rating process.
variability.
We want to have a
reasonably priced
insurance product.
THE GROUPS’ POSITION
goal requirements prerequisite
We want to have a
reasonably priced
insurance product.
My premium Numbers “speak
should reflect my for themselves”...
experience. no need for
„credibility‟.
THE CONFLICT
goal requirements prerequisite
The pricing Credibility is used
actuary must take in the renewal
into account claims rating process.
variability.
We want to have a
reasonably priced
insurance product.
My premium Numbers “speak
should reflect my for themselves”...
experience. no need for
„credibility‟.
CONFLICT CONSEQUENCES
Credibility may My expectation is a
adjust data to an low renewal rate
“average renewal increase.
rate increase”.
Credibility is used My group has an Numbers “speak
in the renewal empirically low loss for themselves”...
rating process. ratio. no need for
„credibility‟.
UNDESIREABLE EFFECT
Unhappy, angry,
and confused, I go
to the market for
competing quotes.
Credibility may My expectation is a
adjust data to an low renewal rate
“average renewal increase.
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 Apples-to-Apples
Paid Paid Paid Paid
Month Premium Claims Premium Claims
January $10,000 $0 $0 $0
February $10,000 $0 $0 $0
March $10,000 $0 $0 $0
April $10,000 $7,143 $10,000 $7,143
May $10,000 $10,000 $10,000 $10,000
June $10,000 $14,286 $10,000 $14,286
July $10,000 $5,714 $10,000 $5,714
August $10,000 $2,857 $10,000 $2,857
September $10,000 $3,571 $10,000 $3,571
October $10,000 $5,143 $10,000 $5,143
Totals $100,000 $48,714 $70,000 $48,714
Loss Ratio 49% 70%
DATA ADJUSTMENTS THAT
ARE UNDERSTOOD
Empirical Data Apples-to-Apples
Paid Paid Paid Paid
Month Contracts Premium Claims Premium Claims
January 100 $10,000 $7,143 $10,000 $7,143
February 100 $10,000 $10,000 $10,000 $10,000
March 100 $10,000 $14,286 $10,000 $14,286
April 100 $10,000 $5,714 $10,000 $5,714
May 100 $10,000 $2,857 $10,000 $2,857
June 100 $10,000 $3,571 $10,000 $3,571
July 100 $10,000 $5,143 $10,000 $5,143
August 200 $20,000 $6,959 $10,000 $6,959
September 200 $20,000 $6,933 $10,000 $6,933
October 200 $20,000 $6,495 $10,000 $6,495
Totals $130,000 $69,101 $100,000 $69,101
Loss Ratio 53% 69%
THE ROOT PROBLEM
The group often does not
understand the adjustment
of their “good” data when
adjusted via credibility.
The group accepts “data Credibility adjusts data in a
adjustments” they can numerical “black box”.
understand.
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 CREDIBILITY - and what
adjustments” they can gives rise to its need - ARE
understand. 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 Group Size in Members
in Relation to in Relation to
Expected Rates 10 25 50 100 250 500 1000 2500 5000 Expected Rates 10 25 50 100 250 500 1000 2500 5000
0%-5% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0%-5% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 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%
CREDI BI LI TY CREDI BI LI TY
as # of Gr oups as # of Claim $
with exper ience 12.1% 17.3% 20.7% 25.3% 37.0% 46.7% 58.8% 81.9% 93.0% with exper ience 12.0% 17.3% 20.3% 24.8% 36.4% 45.3% 57.4% 81.0% 92.5%
within +/- 15% within +/- 15%
of expected r ates of expected r ates
as # of Gr oups as # of Claim $
with exper ience 21.5% 29.9% 35.8% 43.9% 60.4% 73.7% 85.2% 96.8% 99.6% with exper ience 20.6% 29.0% 33.9% 41.3% 57.2% 69.5% 82.2% 95.9% 99.5%
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 85%
82%
Certain Bounds 74%
75%
60% 59%
50% 47%
44%
36% 37%
30%
25%
25% 22% 21%
17%
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 93%
"Amount of Claim $" within 82% 81%
Certain Bounds
75% 70%
57% 57%
50% 45%
41%
36%
34%
29%
25%
25% 21% 20%
17%
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?
The control limits of his charts are
Dr. Walter Shewhart, the not solely statistical in nature, but
founder of the Statistical PRACTICAL…that is, Dr.
Process Control Chart, is Shewhart addressed the question
perhaps the best source to “WHAT MAKES ECONOMIC
consult to address this AND PRACTICAL SENSE?” and
question. 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?