Actual vs Expected: Curse or Blessing?
Cameron Heath & Anthony Wright
Institute of Actuaries TORP Working party
• Alastair Lauder
• Joe Ryan
• Alexander Crosby
• Katherine Laidlar
• Anthony Wright
• Keith Taylor
• Cameron Heath
• Marios Argyrou
• Camilla Bennett
• Neil Bruce (Chair)
• Gregory Overton
• Sylvie LeDelliou
• Jinita Shah
• Tim Jenkins
2
Background
• Part of the “Towards the Optimal Reserving Process” (TORP)
working party
• Long term aim is to identify areas where the reserving process
can be made more efficient
• The working party has noted the extremely broad potential
scope of the “reserving process”
• Idea is to focus on particular areas in series, whilst also having
an eye on efficiencies to be gained in the wider process
• Feedback suggested AvE is an area many people are thinking
of as a step towards optimal reserving
3
Quick survey:
• Do you think you know what AvE is?
• Do you use one or more types of AvE within your reserving
process?
• If so, are they used as a direct input into the setting of
reserves at any point?
• Is it a mechanical process (rather than judgement being
applied)?
4
Agenda
• What is AvE?
• Types of Expected
• Why use AvE and who is interested in it?
• What methods are used?
• How can AvE be displayed?
• Pros and cons of using AvE
5
Definition
• We think AvE is:
– Develop a (series of) expectations of the behaviour of an observable
quantity over a period of time in the future based on assumptions at a
particular point in time
– Compare observed experience during that period against those
expectations
– Use the results to complete a task and/or come to a conclusion
6
Types of Expected
• Written & Signed Premium
• Number of claims reported & settled
– small vs. large
• Paid
• Incurred
• Average cost per claim
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What methods are used?
• Extremely long list possible but 2 overarching types:
– Comparing movements in development data in a period
• Expected paid in the period vs actual paid in the period
• Eyeballing graphically
– Comparing previous ultimate to a new ultimate
• Re-apply previous models to fresh data
• Apply pre-selected models to fresh data
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Why use AvE and who is interested in it?
Interim periods
Monitor emerging experience
Leading indicators
Start of regular reserve review
Identify areas of concern
Identify inappropriate assumptions
End of regular review
Analysis of surplus
Fast close process
Set future expectations
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How can AvE be displayed?
• Tables vs. charts
• Split by class or year
• Single AvE period or multiple periods
Different exhibits are suited to different analyses
Multiple exhibits are likely to be needed for a particular “use”
Good ones can assist in interpretation, bad ones can make results impossible
to identify
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How can AvE be displayed? - Tables
Reserving
class
Origin
year
Actual
incurred
move
Expected
incurred
move
Delta
Inc’d
Previous
ultimate
Updated
mechanical
ultimate
Delta
Calc
Selected
movement
Ult
Class 1
2011
1,032
965
67
14,692
13,347
(1,345)
0
…
…
Class 2
2013
7,963
8,100
(137)
25,693
21,325
(4,368)
6,500
…
…
Class n
2012
10,586
8,400
2,186
40,346
38,200
2,146
2,000
Total
All
32,500
30,100
2,400
n/a
n/a
(1,596)
10,000
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How can AvE be displayed? - Tables
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Example AvE graph (eyeballing)
•Plot of incurred
development as a
percentage of last selected
ultimate claims (dotted line =
100%)
•Looking for signs of obvious
over/under reserving to
assist in targetting resources
•Requires some prior
knowledge for efficient
interpretation
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Example AvE graph (multiple years)
A_2011_03
Class Description
A_2011_06
500
A_2011_09
A_2011_12
450
A_2012_03
A_2012_06
400
A_2012_09
A_2012_12
350
A_2013_03
A_2013_06
£ '000
300
A_2013_09
A_2013_12
250
A_2011_03
A_2011_06
200
A_2011_09
A_2011_12
150
A_2012_03
A_2012_06
A_2012_09
100
A_2012_12
A_2013_03
50
A_2013_06
A_2013_09
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
A_2013_12
Development Month
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Example AvE graph (single year)
£14,000,000
£12,000,000
£10,000,000
£8,000,000
Expected
Actual
£6,000,000
Ultimate
£4,000,000
£2,000,000
£0
0
1
2
3
4
5
6
15
Example AvE graph (single year)
£14,000,000
£12,000,000
£10,000,000
£8,000,000
Expected
Actual
£6,000,000
Ultimate
£4,000,000
£2,000,000
£0
0
1
2
3
4
5
6
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Example AvE graph (single year)
£14,000,000
£12,000,000
£10,000,000
£8,000,000
Expected
Actual
£6,000,000
Ultimate
£4,000,000
£2,000,000
£0
0
1
2
3
4
5
6
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Example AvE graph (single year)
£14,000,000
£12,000,000
£10,000,000
£8,000,000
Expected
Actual
£6,000,000
Ultimate
£4,000,000
£2,000,000
£0
0
1
2
3
4
5
6
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Example AvE graph (multiple years)
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Example AvE graph (“banana chart”)
Format derived
by Lloyd’s of
London as way
to feed back
development for
each class
against
expectations
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Example AvE graph (range indication)
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Pros and cons of using AvE…
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Conclusion
• Good thing - can be very useful in your reserving process
• Used with care – eyes wide open
• Next steps for WP
– Paper and presentation at GIRO
– Consider other areas for focus next year
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