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 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

© 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

© Taylor Fry Pty Ltd 9 Case study – basic monitoring Is this volatility unusual? Is a change in assumption indicated?

© Taylor Fry Pty Ltd 10 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 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 Accident quarter Development quarter Data used to set assumptions Traditional approach Accident quarter 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!

© 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

© Taylor Fry Pty Ltd 17 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 Step 4 – monitor parameter experience until the next valuation By 2 nd quarter there is a statistically significant difference between the projection and experience. Clear evidence for assumption change Strong SI Projection Inter-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

© Taylor Fry Pty Ltd 20 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 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 Projection Inter-valuation experience

© Taylor Fry Pty Ltd 22 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 Reserving Traditional Vol weighted averages recent diagonals e.g. Excel spreadsheet

© Taylor Fry Pty Ltd 28 Reserving Traditional Vol weighted averages recent diagonals 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

© 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

© Taylor Fry Pty Ltd 34 Conventional view of GLM fit vs 4 qtr avg plus traditional model fit

© Taylor Fry Pty Ltd 35 Conventional view of GLM fit vs 4 qtr avg plus traditional model 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 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