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Reserve Estimates:The Blended WayThe Blended Way
May 26, 2011
Raunak JhaDeloitte Consulting India Pvt LtdDeloitte Consulting India Pvt. Ltd
Agenda
• Robust Reserving Process
• Popular Methods
• Blended MethodsBornhuetter- Ferguson MethodThe Cape Cod approach
• Q&A
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.1
Robust Reserving Process
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.
An overview of Robust Reserving Process
Company data
Discussions with company
l
Other I d t d t
personnel
Robust Actuarial Process
Other considerations
Industry data
Back-end diagnostics
Pre-analysis diagnostics
VariabilityMultiple
methods and adjustments
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.3
An overview of Robust Reserving Process
Company dataDiscussions
with company l
Other I d t d t
personnel
Other considerations
Industry dataRobust
Actuarial Process
Back-end diagnostics
Pre-analysis diagnostics
VariabilityMultiple
methods and adjustments
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.4
Popular Methods
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.
Popular Methods Used in the Indian Industrys
Paid Loss Development Method
Incurred Loss Development Method
Expected Loss Ratio Technique
• Payment patterns are assumed to be stable
• No change in case reserve adequacy
• Premium is an accurate measure of exposure
Ass
umpt
ions
• Original data used, no i i i l l i
• Uses all the available i f i
• Can be used even if no hi i il blan
tage
s
initial loss estimates information history is available
Adv
as • May generate large,
volatile loss development factors & take longer to develop to ultimate
• Uses case reserves, which are estimates, to develop estimates of ultimate losses
• Pricing inconsistency distorts actual exposure and ignores actual data
Dis
adva
ntag
es
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.6
ultimateD
Blended Methods
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.
Blended Methods
Description
Combines loss development and exposure based information in arriving at Ultimate estimates and increases flexibility to select results based on circumstances
Ad tAdvantages
Reduce prediction errors
Avoid overreaction
Future loss emergence predicted is correlated with an exposure measure
Use of loss information from all the years in order to project any given year
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.8
Example of Blended Method:Bornhuetter-Ferguson(BF) Method
Description
Project IBNR/expected unpaid loss based on expected losses and the percentage of ultimate losses which are currently unreported/unpaid
Ad tAdvantages
Easy to use
Compromises between loss development and expected loss ratio methods – actually the BF Ultimate loss is a weighted average of the LDM Ultimate and ELR Method Ultimate losses
Avoid overreaction - doesn’t apply development factors to an unusual claim occurrence
Suitable for new or volatile lines of business
Can be used for both paid & incurred data
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.9
The Cape Cod approach
DescriptionThe Cape Cod method is a particular case of the Bornhuetter Ferguson method with prior estimators ofThe Cape-Cod method is a particular case of the Bornhuetter-Ferguson method with prior estimators of the expected ultimate cumulative losses which are based on both internal and external information
Formula for Expected Loss ratio for all accident years:
Where;Exp(LR) = Expected loss ratio estimateF = Decay factor (0 <F < 1)Rj = Reported trended losses for accident year jLDF L d l t f t t lti t f id t jLDFj = Loss development factor to ultimate for accident year jEj = Exposures for accident year j.
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.10
XYZ Insurance CompanyCape Cod MethodTrend Rate = 0.0%
Accident Year ExposuresReported Losses
Trend FactorTrended Reported Losses
% of Ultimate Reported
Reported Exposures
Unreported Exposures
(1) (2) (3) (4) (5) (6) (7)2006 7,000 3,600 1.000 3,600 85.0% 5,950 1,050 2007 8,000 4,000 1.000 4,000 75.0% 6,000 2,000 2008 9,000 4,800 1.000 4,800 60.0% 5,400 3,600 2009 10,000 3,600 1.000 3,600 45.0% 4,500 5,500 2010 11,000 2,800 1.000 2,800 25.0% 2,750 8,250
Total 45,000 18,800 18,800 24,600 20,400
Accident YearTrended
Developed Loss Ratio
Expected Ultimate Loss
Ratio
Detrended Expected Loss
RatioIBNR Reserve
Ultimate Losses
(8) (9) (10) (11) (12)2006 60 5% 76 4% 76 4% 802 4 4022006 60.5% 76.4% 76.4% 802 4,402 2007 66.7% 76.4% 76.4% 1,528 5,528 2008 88.9% 76.4% 76.4% 2,751 7,551 2009 80.0% 76.4% 76.4% 4,203 7,803 2010 101.8% 76.4% 76.4% 6,305 9,105
Total 76.4% 15,590 34,390Total 76.4% 15,590 34,390
Notes:(1) Can be premiums,claim counts, ratemaking exposures,etc (7) =(1)X[1.0‐(5)](2) Can also be claim counts,paid losses,ALAE,salvage&subrogation,etc (8) =(4)/(6)(3) Can also reflect other adjustments to losses (9) =Total of(8)Trended to 2010
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.11
(4) =(2)X(3) (10) =(9)/(3)(5) =1.0/(Development factor to ultimate) (11) =(7)X(10)(6) =(1)X(5) (12) =(2)+(11)
XYZ Insurance CompanyCape Cod MethodTrend Rate =7.0%
Accident Year ExposuresReported Losses
Trend FactorTrended Reported Losses
% of Ultimate Reported
Reported Exposures
Unreported Exposures
(1) (2) (3) (4) (5) (6) (7)2006 7,000 3,600 1.311 4,719 85.0% 5,950 1,050 2007 8,000 4,000 1.225 4,900 75.0% 6,000 2,000 2008 9,000 4,800 1.145 5,496 60.0% 5,400 3,600 2009 10,000 3,600 1.070 3,852 45.0% 4,500 5,500 2010 11,000 2,800 1.000 2,800 25.0% 2,750 8,250
Total 45,000 18,800 21,767 24,600 20,400
Accident YearTrended
Developed Loss Ratio
Expected Ultimate Loss
Ratio
Detrended Expected Loss
RatioIBNR Reserve
Ultimate Losses
(8) (9) (10) (11) (12)2006 79 3% 88 5% 67 5% 709 4 3092006 79.3% 88.5% 67.5% 709 4,309 2007 81.7% 88.5% 72.2% 1,445 5,445 2008 101.8% 88.5% 77.3% 2,782 7,582 2009 85.6% 88.5% 82.7% 4,548 8,148 2010 101.8% 88.5% 88.5% 7,300 10,100
Total 88 5% 16 783 35 583Total 88.5% 16,783 35,583
Notes:(1) Can be premiums,claim counts, ratemaking exposures,etc (7) =(1)X[1.0‐(5)](2) Can also be claim counts,paid losses,ALAE,salvage&subrogation,etc (8) =(4)/(6)(3) Can also reflect other adjustments to losses (9) =Total of(8)Trended to 2010
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.12
( ) j ( ) ( )(4) =(2)X(3) (10) =(9)/(3)(5) =1.0/(Development factor to ultimate) (11) =(7)X(10)(6) =(1)X(5) (12) =(2)+(11)
XYZ Insurance CompanyCape Cod Method
Trend Rate = 7.0%Decay Rate = 0.75
Accident Year ExposuresReported Losses
Trend FactorTrended Reported Losses
% of Ultimate Reported
Reported Exposures
Unreported Exposures
(1) (2) (3) (4) (5) (6) (7)
Trend Rate 7.0%
2006 7,000 3,600 1.311 4,719 85.0% 5,950 1,050 2007 8,000 4,000 1.225 4,900 75.0% 6,000 2,000 2008 9,000 4,800 1.145 5,496 60.0% 5,400 3,600 2009 10,000 3,600 1.070 3,852 45.0% 4,500 5,500 2010 11,000 2,800 1.000 2,800 25.0% 2,750 8,250
T t l 45 000 18 800 21 767 24 600 20 400Total 45,000 18,800 21,767 24,600 20,400
Accident YearTrended
Developed Loss Ratio
Expected Ultimate Loss
Ratio
Detrended Expected Loss
RatioIBNR Reserve
Ultimate Losses
(8) (9) (10) (11) (12)(8) (9) (10) (11) (12)2006 79.3% 86.1% 65.7% 690 4,290 2007 81.7% 87.4% 71.3% 1,427 5,427 2008 101.8% 89.7% 78.3% 2,821 7,621 2009 85.6% 89.8% 83.9% 4,616 8,216 2010 101.8% 90.9% 90.9% 7,499 10,299
Total 88.5% 17,052 35,852
Notes:(1) Can be premiums,claim counts, ratemaking exposures,etc (7) =(1)X[1.0‐(5)](2) Can also be claim counts,paid losses,ALAE,salvage&subrogation,etc (8) =(4)/(6)(3) C l fl h dj l (9) T l f(8)T d d 2010
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.13
(3) Can also reflect other adjustments to losses (9) =Total of(8)Trended to 2010(4) =(2)X(3) (10) =(9)/(3)(5) =1.0/(Development factor to ultimate) (11) =(7)X(10)(6) =(1)X(5) (12) =(2)+(11)
XYZ Insurance CompanyCape Cod Method
Calculation of a‐priori loss ratio for 2007(b) Calculation of a‐priori loss ratio for 2010(b)
Decay Rate = 0.75(a)
Accident Year
Reported Exposures Lag
Trend Factor
based on lag
Weighted Exposure
Trended Ultimate Loss Ratio
Accident Year
Reported Exposures Lag
Trend Factor
based on lag
Weighted Exposure
Trended Ultimate Loss Ratio
(1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6)(1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6)2006 5,950 1 0.750 4,463 79.3% 2006 5,950 4 0.316 1,883 79.3%2007 6,000 0 1.000 6,000 81.7% 2007 6,000 3 0.422 2,531 81.7%2008 5,400 1 0.750 4,050 101.8% 2008 5,400 2 0.563 3,038 101.8%2009 4,500 2 0.563 2,531 85.6% 2009 4,500 1 0.750 3,375 85.6%2010 2,750 3 0.422 1,160 101.8% 2010 2,750 0 1.000 2,750 101.8%Total 24,600 18,204 87.4% Total 24,600 13,576 90.9%
Notes:(2) From earlier exhibit(3) =absolute value of difference between (b) and (1)(4) =(a) raised to power of (3)(5) =(4)X(2)
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.14
( ) ( ) ( )(6)(a) Selected judgementally, based on observed diagnostic tests results
From earlier exhibit, Column 8 for Individual years. Total is
Points to consider
• Whenever an appropriate exposure base has been identified, the actuary could rely on a loss reserving method that mixes loss development methods with exposure-based expected loss methods
When should loss development methods be used? When should exposure-based methods be used?
• The expected ultimate loss ratio could be determined using the Generalized Cape Cod (GCC) method described. The expected ultimate loss ratio is based on a combination of factors namely:
What is an appropriate way to determine the expected ultimate ultimate loss ratio is based on a combination of factors, namely:
(a) maturity of data, (b) volume of data and (c) decayde e e e e pec ed u a eloss ratio?
f• The exposure base should be a leading indicator for the quantity being projected
• The exposure base requiring a fewer adjustments would be preferred
What items should be considered when selecting the exposure base for the GCC method?
• As long as there is a stable environment, ultimate reported claim counts are generally used as exposure base when projecting ultimate losses using the GCC method
What exposure base is generally used for projecting ultimate losses in the GCC method?
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.15
ultimate losses using the GCC methodin the GCC method?
References
Applying a Robust Actuarial Reserve Analysis to Long-Tailed General Insurance Coverage (by Charles Cicci, Debashish Banerjee and Raunak Jha, Deloitte Consulting)Using Best practices to Determine a Best Reserve Estimate (by Paul J Struzzieri and Paul R HussainUsing Best practices to Determine a Best Reserve Estimate (by Paul J. Struzzieri and Paul R. Hussain,Milliman & Robertson Inc.)Balancing Development and Trend in Loss Reserve Analyses (by Gluck, Spencer)
©2010 Deloitte Touche Tohmatsu India Pvt. Ltd. All rights reserved.16
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