math matters how risk managers should use an actuarial report
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MATH Matters How Risk Managers Should Use an Actuarial Report. Norm Hainlen – Director, Alternative Risk Financing Wood Gutmann & Bogart (Coordinator ) Al Rhodes – President and Senior Actuary SIGMA Actuarial Consulting Group, Inc . - PowerPoint PPT PresentationTRANSCRIPT
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MATH MattersHow Risk Managers Should Use an
Actuarial ReportNorm Hainlen – Director, Alternative Risk
Financing Wood Gutmann & Bogart (Coordinator)
Al Rhodes – President and Senior Actuary SIGMA Actuarial Consulting Group, Inc.
Tim East – Director, Risk Management The Walt Disney Company
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MATH Matters
Question…
How do you use the actuarial report?
Do you review the summary?
Do you review the data?
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MATH Matters
Question…
Do you review the calculations?
How do you use the actuarial report?
Do you grab the first number and close the report?
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MATH Matters
Not a bad strategy if:
1. You need a number for a financial statement
2. You need the loss pick for a meeting3. Your broker handles that stuff
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MATH Matters
A bad strategy if:
Actually, that is always a bad strategy – there is a lot more there the MATH is telling you.
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MATH Matters Use the actuarial analysis as part of your
stewardship report to the CFO, Board, …
Use the MATH to show what has happened and what is expected to happen.
The losses are x% of the program, so the MATH to get to that x% is important.
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MATH Matters
- Assumption – You are getting a reserve analysis and a loss projection.
- You need at least two numbers – the estimated reserves and the loss pick.
- How many more are there?
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MATH Matters
LOTS – let’s look at the MATH…
Look at the reserves first:
Reserves = Case Reserves + IBNR
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MATH Matters
o If the IBNR to case reserve ratio has been increasing, then the reserve position MAY be stronger.
o If the ratio is decreasing, then the reserve position MAY be getting weaker.
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MATH Matters
• It is good to know the MATH so you can figure out if a potential problem is looming or if you are now in a stronger position.
• A large claim can give an unusual ratio. Stronger reserving can give an unusual ratio.
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MATH Matters
Still looking at reserves:
What is your range?
• There is one whether it is shown or not!• It should not be large! • It will not give you every possible
outcome.
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MATH Matters
Reserve Range:
The range gives you an opportunity to fund something different, but within a reasonable range.
The MATH will let you know what is reasonable.
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MATH Matters
Let’s look at the loss pick:
Do you get one number? OK Do you get a range? Better Do you get confidence intervals?
Best - MAYBE
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MATH Matters
Loss Pick (Simple Example):
o Pure Loss Rate x Exposures
o Exposures should be easy
o MATH Matters when calculating the pure loss rate
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MATH Matters
For each policy period:
Incurred/paid losses are developed to ultimate
Ultimate losses are trended to a common period
Exposures are trended to a common period
MATH Matters for each step
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MATH Matters
Do you understand how the ultimate losses are calculated?
Are the exposures appropriate and correct?
Are the trend factors reasonable?
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MATH Matters
Pure Loss Rate:Trended Losses / Trended Exposures
A pure loss rate for each policy period. How variable? You need this for TCOR! Is selected rate reasonable?
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MATH Matters
Loss Pick
How is the range calculated?
Does it seem reasonable?
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MATH Matters
Loss Pick
MATH Matters – what is a confidence interval?
The confidence interval tells you the probability an amount will not be exceeded.
What is the “correct” percentile?
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MATH Matters
What do you need to know?
+ Addition
- Subtraction
X Multiplication
÷ Division
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Take Aways… TCOR – use projected losses and
confidence intervals
Metrics – pure loss rate, frequency, severity
Confidence Interval – choice of program
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MATH Matters – The Risk Manager’s View
How to receive and access an actuarial
report
How to use it to drive results within
your business
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The Actuarial Process/Cycle
Advance – Meet and plan before you send the data
Scrub – Make sure the data is screened and vetted before the analysis begins
Draft – Review the draft before the final to understand the assumptions, selections and trends
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Reviewing the Report
Methods – How many methods did the actuary use, and which ones did they rely on?
Changes in Triangles – Don’t rely on the tables alone; discuss the data
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AccidentYear 1 2 3 4 5 6 7 8 9 10 11 121991 1,782 3,000 6,924 10,167 12,369 14,047 13,577 14,289 13,831 14,419 14,563 14,484 1992 430 2,814 3,557 5,745 9,033 7,884 8,715 8,982 9,048 8,934 8,856 1993 2,234 3,902 10,841 14,262 17,666 19,154 19,411 19,021 18,854 19,085 1994 3,335 12,937 23,694 20,477 19,715 23,689 23,955 25,066 25,269 1995 2,006 5,406 9,802 8,949 10,611 10,623 16,633 16,699 1996 7,640 8,485 12,085 13,515 15,418 18,894 19,029 1997 6,643 13,184 18,530 17,782 20,867 21,358 1998 2,474 9,684 10,636 16,266 16,649 1999 4,229 6,135 5,972 8,613 2000 2,065 2,982 3,384 2001 3,448 4,240 2002 1,736
Age-to-age
1991 1.684 2.308 1.468 1.217 1.136 0.967 1.052 0.968 1.043 1.010 0.9951992 6.544 1.264 1.615 1.572 0.873 1.105 1.031 1.007 0.987 0.9911993 1.747 2.778 1.316 1.239 1.084 1.013 0.980 0.991 1.0121994 3.879 1.831 0.864 0.963 1.202 1.011 1.046 1.0081995 2.695 1.813 0.913 1.186 1.001 1.566 1.0041996 1.111 1.424 1.118 1.141 1.225 1.0071997 1.985 1.405 0.960 1.173 1.0241998 3.914 1.098 1.529 1.0241999 1.451 0.973 1.4422000 1.444 1.1352001 1.230
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AccidentYear 1 2 3 4 5 6 7 8 9 10 11 121991 1,782 3,000 6,924 10,167 12,369 14,047 13,577 14,289 13,831 14,419 14,563 14,484 1992 430 2,814 3,557 5,745 9,033 7,884 8,715 8,982 9,048 8,934 8,856 1993 2,234 3,902 10,841 14,262 17,666 19,154 19,411 19,021 18,854 19,085 1994 3,335 12,937 23,694 20,477 19,715 23,689 23,955 25,066 25,269 1995 2,006 5,406 9,802 8,949 10,611 10,623 16,633 16,699 1996 7,640 8,485 12,085 13,515 15,418 18,894 19,029 1997 6,643 13,184 18,530 17,782 20,867 21,358 1998 2,474 9,684 10,636 16,266 16,649 1999 4,229 6,135 5,972 8,613 2000 2,065 2,982 3,384 2001 3,448 4,240 2002 1,736
Age-to-age
1991 1.684 2.308 1.468 1.217 1.136 0.967 1.052 0.968 1.043 1.010 0.9951992 6.544 1.264 1.615 1.572 0.873 1.105 1.031 1.007 0.987 0.9911993 1.747 2.778 1.316 1.239 1.084 1.013 0.980 0.991 1.0121994 3.879 1.831 0.864 0.963 1.202 1.011 1.046 1.0081995 2.695 1.813 0.913 1.186 1.001 1.566 1.0041996 1.111 1.424 1.118 1.141 1.225 1.0071997 1.985 1.405 0.960 1.173 1.0241998 3.914 1.098 1.529 1.0241999 1.451 0.973 1.4422000 1.444 1.1352001 1.230
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Reviewing the Report Methods – How many methods did the actuary use, and
which ones did they rely on?
Changes in Triangles – Don’t rely on the tables alone; discuss the data
Other Measures:• Case closure rate is a critical metric• Loss-cost per exposure trends • Loss development by reserve category
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Using the Actuarial Report
Translate – Translate the actuarial results into terms that stakeholders can understand
Temper – Actuarial results can be misused or mis-understood; set realistic expectations
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The Nature of Variance…
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Using the Actuarial Report
Translate – Translate the actuarial results into terms that stakeholders can understand
Temper – Actuarial results can be misused or mis-understood; set realistic expectations
Transform – Select outcomes and adopt metrics that can be used to improve the business results
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Take Aways… Dig In – Work with your actuary and those who
supply the underlying data to understand the inputs, assumptions and results
Sort Out – The key metrics that define the true direction of your losses
Present – The results in terms that your organization can understand and act upon
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MATH MattersHow Risk Managers Should Use an
Actuarial Report
Questions & Answers
Thank You!!