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The next step in performance monitoring – Stochastic monitoring
(and reserving!)
NZ Actuarial Conference
November 2010
© Taylor Fry Pty Ltd 2
Agenda
• Monitoring of claim experience
• Adding some confidence
• Stochastic reserving
• Questions…
© Taylor Fry Pty Ltd 3
Agenda
• Monitoring of claim experience
• Adding some confidence
• Stochastic reserving
• Questions…
© Taylor Fry Pty Ltd 4
What is monitoring?
•Wikipedia definition: – The act of listening, carrying out surveillance
on, and/or– The act of detecting the presence of signals
•Actuarial interpretation:– To identify when experience is contrary to
expected such that appropriate action can be taken when required.
© Taylor Fry Pty Ltd 5
Case study
• Consider a Workers’ Compensation portfolio with periodic income benefits
• Focus on the model of payments per active claim
• Initial model established at December 2008 and monitored quarterly until March 2010
© Taylor Fry Pty Ltd 6
Case study – basic monitoring
Actual versus expected PPAC
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
Mar-09 Jun-09 Sep-09 Dec-09 Mar-10
Payment Qtr
$s
Actual Expected
•Actual has increased rapidly at Dec 09 and Mar 10, but is it significant or simply random variation?
© Taylor Fry Pty Ltd 7
Case study – basic monitoring• Tabulated results • Detailed results
Payment Actual Expected A-E % differenceQuarter
Mar-09 6,514 5,915 599 10.1%Jun-09 6,118 6,071 47 0.8%Sep-09 6,435 6,405 29 0.5%Dec-09 7,399 6,635 764 11.5%Mar-10 8,069 6,773 1,296 19.1%
Accident Payment qtrYear Mar-09 Jun-09 Sep-09 Dec-09 Mar-10
1989/90 1% -14% -22% 0% -3%1990/91 6% -10% -12% 15% 31%1991/92 -13% -35% -21% -9% -2%1992/93 -7% -21% -22% -6% 0%1993/94 24% 1% 46% 12% 32%1994/95 7% 21% -8% 21% 162%1995/96 2% -7% -11% 3% 18%1996/97 33% -8% -20% -2% -4%1997/98 11% 35% 11% 11% 3%1998/99 15% -7% -5% 8% 45%1999/00 2% 52% 36% 78% 25%2000/01 35% -25% -1% 3% 10%2001/02 33% -16% 2% 0% -9%2002/03 38% -20% -5% 35% 38%2003/04 -6% 34% -3% -8% -13%2004/05 20% 4% -2% 29% 3%2005/06 11% 16% 29% -8% 30%2006/07 12% -16% 12% 3% 35%2007/08 -1% -11% -15% 13% 8%2008/09* 12% 11% 3% 25% 4%
Total 10% 1% 0% 12% 19%
*2008/09 is the half year to 31 December 2008
© Taylor Fry Pty Ltd 8
Case study – initial model
Chart shows average of the last 4 payment quarters compared to the selected December 2008 model
PPAC by development quarter
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Development Quarter
$
Dec08 selected
4 qtrs to Dec 08
© Taylor Fry Pty Ltd 9
Case study – basic monitoring
• Is this volatility unusual? Is a change in assumption indicated?
PPAC by development quarter
0
5,000
10,000
15,000
20,000
25,000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Development Quarter
$
Dec08 selected
Mar-09
PPAC by development quarter
0
5,000
10,000
15,000
20,000
25,000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Development Quarter
$
Dec08 selected
Mar-09
Jun-09
PPAC by development quarter
0
5,000
10,000
15,000
20,000
25,000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Development Quarter
$
Dec08 selected
Mar-09
Jun-09
Sep-09
PPAC by development quarter
0
5,000
10,000
15,000
20,000
25,000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Development Quarter
$
Dec08 selected
Mar-09
Jun-09
Sep-09
Dec-09
PPAC by development quarter
0
5,000
10,000
15,000
20,000
25,000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Development Quarter
$
Dec08 selected
Mar-09
Jun-09
Sep-09
Dec-09
Mar-10
© Taylor Fry Pty Ltd 10
PPAC by development quarter
0
2,000
4,000
6,000
8,000
10,000
12,000
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Development Quarter
$
5 qtrs to Mar 10
Dec08 selected
Case study – 5 quarters on
Chart shows average of the 5 payment quarters to Mar 2010 compared to the selected December 2008 model
Significant?
© Taylor Fry Pty Ltd 11
PPAC by development quarter
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Development Quarter
$
5 qtrs to Mar 10
Dec08 selected
4 Qtrs to Dec 08
Case study – combined
Was it ever significant?
© Taylor Fry Pty Ltd 12
Case study
• Difficult to determine “real change” vs random variation
• Often reliant on valuation actuary’s “judgment” in how best to respond
– Impact of judgement is not assessable at the time, and– Generally not subject to hindsight review
© Taylor Fry Pty Ltd 13
Agenda
• Monitoring of claim experience
• Adding some confidence
• Stochastic reserving
• Questions…
© Taylor Fry Pty Ltd 14
Step 1 – use all the data
Acc
iden
t qu
art
er
Development quarter
Data used to set assumptions
Traditional approach
Acc
iden
t qu
art
er
Development quarter
Data used to set assumptions
Stochastic approach
© Taylor Fry Pty Ltd 15
Step 1 – use all the data
• Note– The relative smoothness and sensible shape of the curve, and– The variability of an individual development quarter even using all the data!
Fitted development quarter curve
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Development quarter
Data
Fit
LB_data
UB_data
© Taylor Fry Pty Ltd 16
Step 2 – break development curve into sections
• Each section is controlled by a single parameter allowing it to move up or down over time
Fitted development quarter curve
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Development quarter
Fit
© Taylor Fry Pty Ltd 17
Fitted payment quarter curve for dev qtrs 1 and 2
0%
50%
100%
150%
200%
250%
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82
Payment quarter
Data
Fit
LB_data
UB_data
Step 3 – plot the history of each section over time and project
• The early part of the development curve has moved up and down over time
• The projection of these payment parameters completely determines the valuation
Strong SI
Projection
© Taylor Fry Pty Ltd 18
Fitted payment quarter curve for dev qtrs 1 and 2
0%
50%
100%
150%
200%
250%
300%
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82
Payment quarter
Data
Fit
LB_data
UB_data
Step 4 – monitor parameter experience until the next valuation
• By 2nd quarter there is a statistically significant difference between the projection and experience. Clear evidence for assumption change
Strong SI
ProjectionInter-valuation experience
© Taylor Fry Pty Ltd 19
Another eg – development quarters 20 plus
• Each section is controlled by a single parameter allowing it to move up or down over time
Fitted development quarter curve
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Development quarter
Fit
© Taylor Fry Pty Ltd 20
Fitted payment quarter curve for dev qtrs 20+
0%
50%
100%
150%
200%
250%
20 23 26 29 32 35 38 41 44 47 50 53 56 59 62 65 68 71 74 77 80
Payment quarter
Data
Fit
LB_data
UB_data
Step 3 – again, plot the history of each section over time and project
• Slight upward trend in fitted curve indicates 0.6% p.a. SI consistent across time
• Typically this would be missed by non-stochastic valn methods
Slight SI
Projection
© Taylor Fry Pty Ltd 21
Fitted payment quarter curve for dev qtrs 20+
0%
50%
100%
150%
200%
250%
20 23 26 29 32 35 38 41 44 47 50 53 56 59 62 65 68 71 74 77 80
Payment quarter
Data
Fit
LB_data
UB_data
`
Step 4 – monitor parameter experience until the next valuation
• Combined, the last two quarters show that there is a statistically significant difference between the projection and experience.
Slight SI
ProjectionInter-valuation experience
© Taylor Fry Pty Ltd 22
Fitted payment quarter curve for dev qtrs 20+
0%
20%
40%
60%
80%
100%
120%
140%
160%
180%
200%
68 70 72 74 76 78 80 82 84
Payment quarter
Data
Fit
LB_data
UB_data
`
Step 4 – last 2 quarters combined
• Having combined last 2 estimates, giving a narrower confidence interval we see that the fit clearly falls outside the 95% CI
• Ie, a 5% level of significance hypothesis test concludes that the experience has altered
Fitted falls outside the confidence
interval
© Taylor Fry Pty Ltd 23
Agenda
• Monitoring of claim experience
• Adding some confidence
• Stochastic reserving
• Questions…
© Taylor Fry Pty Ltd 24
Why use stochastic (GLM) reserving models?
• Allows stochastic monitoring to be carried out– ...which improves understanding of underlying trends– ...and gives earlier warning of changes
• More likely to produce more accurate valuations– ...less prone to bias– ...able to find underlying trends not readily observable by the
human eye
• It’s easier and faster (except the first time)!
© Taylor Fry Pty Ltd 25
Dealing with some common misconceptions
• Fantasy– Time consuming– Black box and difficult to understand – The results are not transparent– Can’t apply judgement
• Reality– Like all modelling significant upfront establishment required. Once established
more efficient than traditional methods– Output provides additional insights– Professional judgement remains a key feature– Stochastic reserving follows exactly the same path with the same input and
output as traditional models– Help is available!– Don’t have to licence additional software to do it (most organisations have sas)
© Taylor Fry Pty Ltd 26
Reserving
© Taylor Fry Pty Ltd 27
ReservingTraditional
Vol weighted averages
recent diagonals
e.g. Excel spreadsheet
e.g. Excel spreadsheet
e.g. Excel spreadsheet
e.g. Excel spreadsheet
© Taylor Fry Pty Ltd 28
ReservingTraditional
Vol weighted averages
recent diagonals
e.g. Excel spreadsheet
e.g. Excel spreadsheet
e.g. Excel spreadsheet
e.g. Excel spreadsheet
Stochastic
Fit GLM using SAS or other statistical
software
e.g. Excel to SAS, convert to columns
e.g. SAS output to Excel
e.g. Excel spreadsheet
e.g. Excel spreadsheet
© Taylor Fry Pty Ltd 29
First time GLM fitting procedure
• Identify model structure
• Fit saturated model
• Simplify development curve shape
• Simplify payment or accident year trends
• Add seasonal patterns
• Search for interactions
• Review output and fit diagnostics– Triangles of fitted values and comparison of actual v fitted– AvE summaries by development period, payment period and accident
period
© Taylor Fry Pty Ltd 30
Simplify development curve shape
© Taylor Fry Pty Ltd 31
Some standard diagnostics
© Taylor Fry Pty Ltd 32
Second and subsequent valuations
• Run previous model on updated data set
• Review diagnostics on updated model
• Adjust model when necessary
© Taylor Fry Pty Ltd 33
Back to the case study...Conventional view of GLM fit vs 4 qtr
avg
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
Development Qtr
Avg last 4
GLM fit
© Taylor Fry Pty Ltd 34
Conventional view of GLM fit vs 4 qtr avg plus traditional model fit
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
Development Qtr
Avg last 4
GLM fit
Traditional fit
© Taylor Fry Pty Ltd 35
Conventional view of GLM fit vs 4 qtr avg plus traditional model fit
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
Development Qtr
Avg last 4
GLM fit
Traditional fit
Traditional methodology has underestimated the
trends
© Taylor Fry Pty Ltd 36
Conventional view of GLM fit vs 4 qtr avg plus traditional model fit
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
Development Qtr
Avg last 4
GLM fit
Traditional fit
The traditional fit under-estimated the tail by about 5% (excl SI)
© Taylor Fry Pty Ltd 37
Agenda
• Monitoring of claim experience
• Adding some confidence
• Stochastic reserving
• Questions…
© Taylor Fry Pty Ltd 38
Key points
• Stochastic monitoring enables the user to readily determine changes in experience Earlier warning than traditional model Identify when response required
• Stochastic models for reserving readily identify trends over the entire triangle of experience Less prone to bias Better able to capture underlying trends in experience Ability to analyse the data by numerous variables to check the model
fit
