Actual vs Expected: Curse or Blessing?Cameron Heath & Anthony Wright

Institute of Actuaries TORP Working party

• Alastair Lauder• Alexander Crosby• Anthony Wright• Cameron Heath• Camilla Bennett• Gregory Overton• Jinita Shah

• Joe Ryan• Katherine Laidlar• Keith Taylor• Marios Argyrou• Neil Bruce (Chair)• Sylvie LeDelliou• Tim Jenkins

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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

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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)?

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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

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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

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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?

Start of regular reserve reviewIdentify areas of concern

Identify inappropriate assumptions

End of regular reviewAnalysis of surplusFast close process

Set future expectations

Interim periodsMonitor emerging experience

Leading indicators

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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

Ult

Selected movement

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)Class Description

-

50

100

150

200

250

300

350

400

450

500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

Development Month

£ '0

00

A_2011_03

A_2011_06

A_2011_09

A_2011_12

A_2012_03

A_2012_06

A_2012_09

A_2012_12

A_2013_03

A_2013_06

A_2013_09

A_2013_12

A_2011_03

A_2011_06

A_2011_09

A_2011_12

A_2012_03

A_2012_06

A_2012_09

A_2012_12

A_2013_03

A_2013_06

A_2013_09

A_2013_12

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Example AvE graph (single year)

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£0

£2,000,000

£4,000,000

£6,000,000

£8,000,000

£10,000,000

£12,000,000

£14,000,000

0 1 2 3 4 5 6

Expected

Actual

Ultimate

Example AvE graph (single year)

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£0

£2,000,000

£4,000,000

£6,000,000

£8,000,000

£10,000,000

£12,000,000

£14,000,000

0 1 2 3 4 5 6

Expected

Actual

Ultimate

Example AvE graph (single year)

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£0

£2,000,000

£4,000,000

£6,000,000

£8,000,000

£10,000,000

£12,000,000

£14,000,000

0 1 2 3 4 5 6

Expected

Actual

Ultimate

Example AvE graph (single year)

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£0

£2,000,000

£4,000,000

£6,000,000

£8,000,000

£10,000,000

£12,000,000

£14,000,000

0 1 2 3 4 5 6

Expected

Actual

Ultimate

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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