Matβlas Underwriting and Actuarial Consulting, Training and Research

Matβlas Underwriting and Actuarial Consulting, Training and Research Introduction to insurance rating and claims reserving Presented to The Lloyd s Marine U35 Group by Ana Mata, PhD, ACAS Managing Director and Actuary London, June 2014

Introduction to insurance rating and claims reserving Copyright 2014 by MatBlas Limited. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, without prior written permission by MatBlas Limited. Disclaimer: This presentation has been prepared for educational purpose only. It should only be used for reference purposes for those attending or that have attended the presentation. The content of this note is theoretical in nature and exclusively prepared for training purposes. No part of the content of this course material constitutes actuarial advice for any company or organization. All worked examples shown in this note were derived from hypothetical assumptions only and do not reflect any company s rates, rating factors, benchmark factors, loss experience or reporting processes. Any similarity between these examples and any insurance company is coincidental only.

Agenda What is insurance rating? Technical pricing with UMS Pricing considerations for some marine lines Basics of claims reserving 3

Challenges faced by underwriters Traditional underwriting Look at the policy, rate it and agree to write it or not. Agreed price only record. WHY ME? WHY THIS? WHY NOW? WHAT NOW? Common workflow today Modelling each risk Technical pricing Lloyd s benchmark Loss ratios by policy Rate monitoring (PMD) Business planning Extremely competitive market! 4

What are rating models for? Commercially viable premium? Competitive advantage? Increase or improve profitability? Rating to expect a profit Profit = Premium Claims Commission - Expenses 5

Rating is about forecasting claims costs Product: promise to indemnify the policyholder if An insured event happens Policyholder incurs damages as a result Production cost = cost of actual claims paid Final cost per policy not known in advance Years before known Expected claim costs can be estimated 6

What is the expected claim cost? The expected claim cost of a policy is the average claim cost across all possible future claims and across policyholders Expected claim cost = frequency x severity 7

The expected claim cost: hypothetical example Each vessel 1% chance of a loss Each vessel worth 10M (Insured Value) Assume each loss is total Frequency = 1% Severity = 10M Expected claim cost = 1% x 10M = 100k 8

From claim cost to premium 1. Start by calculating the expected loss cost or risk premium (frequency and severity) This is the amount needed to cover average claims costs 2. Other costs (usually a % of premium): Contingency factor or risk load Operating costs Distribution costs Underwriting profit or ROE 3. Derive the premium rate per unit of exposure 9

Key relationship between premium and claim cost Expected loss ratio (ELR) = loss ratio before claims reported ELR Expected Claim Cost Premium Ultimate loss ratio (ULR) = loss ratio when claims are settled and paid ULR Actual Claims Paid Premium 10

Technical pricing Technical or Benchmark premium Premium that is expected to generate a certain pre-selected expected loss ratio (and thus profits) ELR Expected Claim Cost Technical Premium Technical Premium Expected Claim Cost ELR 11

Technical premium: hypothetical example Each vessel 1% chance of a loss Each vessel worth 10M (Insured Value) Each loss is total Expected claim cost = 1% x 10M = 100k ELR = 65% (10 year average) Technical premium = 100k/65% = 153,846 12

Common approach to comply with underwriting minimum standards (UMS) Technical premium Premium that is expected to support a selected long term ELR Benchmark premium for Lloyd s Premium that is expected to support the business plan (short term) ELR Walk-away or break even premium Premium that covers expected claim costs and expenses without profits (100% combined ratio) Charged premium Premium actually charged for the policy and that appears on the slip 13

Premiums and loss ratios: hypothetical example Expected claim cost = 100k; expenses = 10% of premium Long term ELR = 65% TP = 100k/65% = 153.8k 2014 BP ELR = 80% Lloyd s BP = 100k/80% = 125k Break even ELR = 90% IELR = 100k/140k = 71.4% Walk-away prem. = 100/90% = 111k Agreed premium = 140k 14

The expected claim cost Summary Premiums Loss ratios Technical premium Benchmark premium Walk away premium Charged premium ELR (Long term) BP ELR (Short term) 100% - expenses (break even) IELR (initial expected) 15

What is the right price for a policy? Accuracy is the degree of closeness of an estimated quantity to that quantity's actual value Precision is the ability of a measurement or estimate to be exactly reproduced Expected Actual Claim cost = 100k 0 or 10M Premium = 153,800 ELR = 65% 0% or 6,500% 16

What is the right price for each year? 100 policies same risk profile, same premium collected Expect 1 claim per year Year Tech. Premium ( M) No. losses Losses ( M) ULR 1 15.38 1 10 65.00% 2 15.38 0 0 0.00% 3 15.38 0 0 0.00% 4 15.38 2 20 130.00% 5 15.38 0 0 0.00% 6 15.38 0 0 0.00% 7 15.38 4 40 260.00% 8 15.38 0 0 0.00% 9 15.38 1 10 65.00% 10 15.38 2 20 130.00% 10 year average loss ratio 65.00% The law of large numbers is about long term averages 17

The expected claim cost in practice Experience rate or burning cost Base on insured own claims experience Rating tables with risk drivers and premium factors Premium factors Origin of tables? Licensed software CAT models 18

Rating tables and risk classification Insurance rating is estimating expected future average claims cost and allocating it to each policy in proportion to its exposure The average claim cost is adjusted up or down to reflect the specific risk profile and potential for claims 19

In an ideal but no utopian world Rating tables should be derived from claim experience Very few are! Rating factors must reflect differences in expected claim costs - risk It can be and has been done Market data can be bought for some lines, e.g. Marine Hull 20

Legal matters Disclaimer: while we (MatBlas) have licensed a database of vessels trading for the last 15+ years together with all casualties and losses recorded, the results presented in the next few slides are for illustration only and are not meant to provide benchmarks to be used for pricing or underwriting purposes. The year of loss has been changed, frequency by type of vessel, age and flag has been randomly re-distributed and the insured loss has been completely changed for this example. The results, as presented, are not real and are inaccurate. While the methodology presented here is overly simplified, it does show typical actuarial methodology used in statistical analysis to derive loss cost rates. 21

Link by vessel ID Rating model for Marine Hull: the data Exposures: list of vessels trading each year worldwide Vessel ID, IMO, Gross weight, dead weight, flag, owner, year built, type of vessel. Losses: list of all incidents, actual and constructive losses with complete details of vessel, location, cause and description of incident. 22

Rating model for Marine Hull: the rating factors Assumptions: Gross weight as proxy for exposure Frequency = number of incidents per vessel Risk drivers for frequency: Type of vessel Age Flag Severity assumed proportional to weight Price of steel as proxy for loss value 23

No. Vessels trading Frequency of incidents Total tonnage trading Losses/Ton Historical frequency and claim cost Frequency of Incidents by Year Loss cost per tonnage 86,000 84,000 82,000 80,000 78,000 76,000 74,000 72,000 70,000 68,000 66,000 64,000 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Year of Incident 0.300% 0.250% 0.200% 0.150% 0.100% 0.050% 0.000% 1,600,000,000 1,400,000,000 1,200,000,000 1,000,000,000 800,000,000 600,000,000 400,000,000 200,000,000-2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Year of Incident 3.5 3 2.5 2 1.5 1 0.5 0 No. Vessels No. Incidents/100 vessels Average frequency Total tonnage across vessels Losses/Ton Average Cost/Ton Year No. Vessels No. Incidents Frequency Total weight Losses (USD) Loss/ton (USD) Avg. cost per incident (USD) 2003 70,750 159 0.225% 1,145,463,046 2,821,662,000 2.463 17,746,302 2004 72,250 180 0.249% 1,177,093,736 2,025,901,500 1.721 11,255,008 2005 73,500 187 0.254% 1,201,534,077 2,538,639,750 2.113 13,575,614 2006 74,000 174 0.235% 1,216,298,656 3,720,723,750 3.059 21,383,470 2007 75,500 171 0.226% 1,235,404,786 1,821,391,500 1.474 10,651,412 2008 76,750 203 0.264% 1,259,177,798 1,429,293,750 1.135 7,040,856 2009 78,850 225 0.285% 1,324,244,309 2,407,461,000 1.818 10,699,827 2010 79,500 205 0.258% 1,332,145,510 1,229,204,250 0.923 5,996,118 2011 81,750 215 0.263% 1,381,926,502 1,922,593,500 1.391 8,942,295 Copyright by Matβlas. All rights 2012reserved 83,250 220 0.264% 1,417,217,800 1,931,509,500 1.363 8,779,589 10 year average 0.253% 24 1.722

No. Vessels trading Frequency of incidents Historical frequency by age of vessel Frequency of Incidents by Age 160,000 140,000 120,000 100,000 80,000 60,000 40,000 20,000-0-1 2-3 4-5 6-7 8-9 10-14 15-19 20-24 22-29 30+ 0.500% 0.450% 0.400% 0.350% 0.300% 0.250% 0.200% 0.150% 0.100% 0.050% 0.000% Age range No. Vessels No. Incidents Frequency 0-1 40,933 16 0.039% 2-3 39,803 21 0.053% 4-5 39,529 26 0.066% 6-7 41,000 37 0.090% 8-9 44,621 46 0.103% 10-14 127,744 178 0.139% 15-19 139,293 397 0.285% 20-24 115,594 460 0.398% 22-29 73,955 328 0.444% 30+ 103,628 430 0.415% Total 766,100 1,939 0.253% Age of vessel No. Vessels Frequency by age Average frequency 25

No. Vessels trading Frequency of incidents Historical frequency by type of vessel Frequency of Incidents by Type 350,000 300,000 250,000 200,000 150,000 100,000 50,000 0 0.400% 0.350% 0.300% 0.250% 0.200% 0.150% 0.100% 0.050% 0.000% Type No. Vessels No. Incidents Frequency Bulk 59,394 162 0.273% Dredger 9,571 9 0.094% Fishing 115,672 397 0.343% Gas 11,344 20 0.176% General Cargo 288,967 975 0.337% Passenger 40,215 73 0.182% Research 9,604 7 0.073% Tanker 84,226 138 0.164% Tug 103,676 92 0.089% Vehicle 43,431 66 0.152% Total 766,100 1,939 0.253% Type of vessel No. Vessels Frequency by type Average frequency 26

Historical frequency by flag Top ten countries by fleet size Country No. Vessels Frequency United States of America 57,928 0.204% Panama 52,045 0.423% Russian Federation 44,955 0.105% Japan 43,269 0.118% People's Republic of China 23,744 0.126% United Kingdom 20,478 0.259% Indonesia 17,429 0.275% Liberia 17,340 0.202% Norway 16,456 0.140% Greece 16,211 0.339% Top 10 countries by frequency Country No. Vessels Frequency Haiti 34 2.941% Azores 37 2.703% Anguilla 51 1.961% Grenada 52 1.923% The Congo 53 1.887% Syria 1,446 1.176% Barbados 357 1.120% Togo 92 1.087% Sri Lanka 500 1.000% Sierra Leone 302 0.993% 27

A simple marine hull model Average cost/ton = $1.72, Long term ELR = 70% Rate/ton = $2.45 (technical rate) Age range Load/discount 0-1 -84.56% 2-3 -79.15% 4-5 -74.01% 6-7 -64.34% 8-9 -59.27% 10-14 -44.95% 15-19 12.61% 20-24 57.23% 22-29 75.23% 30+ 63.95% Rate for newly built passenger cruise in Greece Type Load/Discount Bulk 7.77% Dredger -62.85% Fishing 35.60% Gas -30.34% General Cargo 33.31% Passenger -28.28% Research -71.20% Tanker -35.26% Tug -64.94% Vehicle -39.96% $0.364/ton 28 Country Load/discount United States of America -19.52% Panama 67.01% Russian Federation -58.69% Japan -53.43% People's Republic of China -50.08% United Kingdom 2.26% Indonesia 8.81% Liberia -20.25% Norway -44.78% Greece 34.05%......

Why is not everyone doing this? Commonly heard excuses I am happy with my model rates Back tested? Downloading from websites to cut and paste too much work Websites can transfer data to Excel Data in pdf Tools can convert to Excel Large fleets too much work Pre-rate and search by insured name (owner) 29

Typical approach 1 st choice would be NOT to model Often an admin after binding But UMS not optional Models built from underwriters anecdotal experience and class performance Back into an expected loss cost from premium and ELR Expected claim cost = Model premium x ELR 30

Is not that simple! True! Models are tools not decision makers Some classes difficult or impossible to rate War and terrorism Consistent models can streamline inefficient workflows 31

Basics of claims reserving

Pricing and reserving Start YOA with business plan ELR for class For each unit of premium set aside ELR% as reserve Each individual policy priced with IELR Aggregate IELR across policies Allows to validate business plan 33

Comparing losses by year Reported claims to date Year 31/12/2013 2008 16,160 2009 21,378 2010 46,147 2011 50,008 2012 9,640 2013 4,256 Maturity = Months since start of year Reported claims by "maturity" Year 12 24 36 48 60 72 2008 16,160 2009 21,378 2010 46,147 2011 50,008 2012 9,640 2013 4,256 34

Basic definitions Paid = amount paid to or on behalf of policy holder Outstanding or case reserve = amount allocated to specific claim and held as reserve (not yet paid) Incurred = paid + case reserve IBNR = Incurred but not reported (held as reserve) IBNER = incurred but not enough reported (held as reserve) 35

Actuarial estimates of future claims movements Reported claims to date Year 31/12/2013 2008 16,160 2009 21,378 2010 46,147 2011 50,008 2012 9,640 2013 4,256 Reported claims by "maturity" Year 12 24 36 48 60 72 2008 1,688 6,340 13,472 13,203 15,117 16,160 2009 1,165 7,527 15,038 21,926 21,378 2010 2,549 8,814 27,816 46,147 2011 3,565 16,747 50,008 2012 3,760 9,640 2013 4,256 36

The chain ladder method Reported claims by "maturity" Year 12 24 36 48 60 72 2008 1,688 6,340 13,472 13,203 15,117 16,160 2009 1,165 7,527 15,038 21,926 21,378 2010 2,549 8,814 27,816 46,147 2011 3,565 16,747 50,008 2012 3,760 9,640 2013 4,256 2011 estimate at 48 months = 50,008 x 1.443 = 72,161 Total claim movement (36 to 48 months) 13,203 13,472 21,926 15,038 46,147 27,816 1.443 37

Squaring the triangle Incurred claims by maturity Premium Plan ELR YOA 12 24 36 48 60 Actuarial ULR 10,000,000 70% 2009 2,525,253 13,888,889 16,666,667 12,500,000 7,500,000 75.00% 10,000,000 75% 2010 2,551,020 12,500,000 14,375,000 11,500,000 6,900,000 69.00% 10,000,000 72% 2011 2,518,986 13,098,729 14,408,602 11,166,667 6,700,000 67.00% 10,000,000 74% 2012 3,183,034 14,960,262 17,204,301 13,333,333 8,000,000 80.00% 10,000,000 67% 2013 2,763,595 14,025,245 16,129,032 12,500,000 7,500,000 75.00% x 5.08 x 1.15 x 0.78 x 0.60 Year on year relative claims movement ("link ratios") YOA 12 to 24 24 to 36 36 to 48 48 to 60 2009 5.50 1.20 0.75 0.60 2010 4.90 1.15 0.80 2011 5.20 1.10 2012 4.70 Actuary's selection 5.08 1.15 0.78 0.60 38

Practical issues with claims reserving Historic claims emerging patterns Consistent case reserve setting Changes in patterns may cause distortion Large or CAT losses separate treatment Some classes ULR is pegged Long tail lines: what happens after 60 months? ULRs starting point of plan loss ratio Reserving Pricing 39

Wrap Up Underwriting minimum standards does not mean minimum effort Consistent rating helps achieve efficiency Rating models are tools and should not replace Underwriting Portfolio management Risk selection Diversification Common sense! 40