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Continuous Mortality Investigation User Guide for The CMI Mortality

1. In contrast to mathematical models of mortality fitted directly to relevant data and extrapolated to form a projection the Model requires the user to set parameter values which directly control the projection The Model produces a single deterministic mortality projection for each set of user inputs The structure of the Model allows user input of e Base mortality rates reflecting the estimated current or recent past position e Initial rates of mortality improvement reflecting the current estimate of rates of change e Assumed ultimate long term rates of mortality improvement e An assumed speed and pattern of convergence from initial to long term Initial and long term rates of mortality improvement are each subdivided into two components by age and by cohort These components are projected separately by age and by year of birth cohort respectively and then recombined Convergence from initial to long term rates of mortality improvement is defined separately for by age and by cohort components by user inputs for the convergence time period and the proportion of the total change in rate remaining by the mid point of that period Effectively this approach assumes that in the very short term a good guide as to the likely pace of change in mortality rates is the most recently observed experience In the long term the forces driving mortality change are likely to be v
2. Accordingly users are strongly advised to satisfy themselves of the reasonableness of any projections produced As well as providing information to facilitate comparison of projections the various Model outputs are also intended to support the user in reviewing the reasonableness of the projection It remains the responsibility of any actuary or other person using a projection of future mortality to ensure that it is appropriate for the particular purpose to which it is put regardless of the source of the projection 5 1 5 Saving Parameter Sets The Model only holds a single set of Core parameters defaults and a single set of Advanced parameters user input for each gender Therefore if having completed a projection the user wishes to save the parameter set for future reference this is most easily achieved by saving a copy of the entire Model Alternatively copies of the relevant parameter tables or entire worksheets could be made and stored as a library of parameters ready to be pasted back in to the Model for use when required User Guide for CMI 2011 Mortality Projections Model Page 22 of 33 5 2 Worksheet Structure of the Model The Model contains a series of worksheets These are listed with some summary information in Table II on page 24 A schematic of the Model s worksheet structure outlining the major data and calculation flows between the worksheets is shown in Figure 2 on page 25 Further commentary on the
3. Part One An Outline of the Proposed Approach 2009 CMI Working Paper 39 A Prototype Mortality Projections Model Part Two Detailed Analysis 2009 CMI Working Paper 41 CMI Mortality Projections Model Feedback on Consultation and Issue of CMI 2009 2009 CMI Working Paper 49 The CMI Mortality Projections Model CMI_2010 2010 CMI Working Paper 54 Advancing the release date of the CMI Mortality Projections Model 2011 CMI Working Paper 55 The CMI Mortality Projections Model CMI_2011 2011 User Guide for the CMI Mortality Projections Model Model Name Version CMI 2009 2009 All of the above may be accessed and downloaded from the CMI pages under Research and resources on the UK Actuarial Profession s website in particular e CMI 2011 and its User Guide are located alongside CMI Working Paper 55 e CMI 2010 and its User Guide are located alongside CMI Working Paper 49 e CMI 2009 its User Guide and the spreadsheet of parameter sensitivity tests are located alongside CMI Working Paper 41 Board for Actuarial Standards Technical Actuarial Standard M Modelling April 2010 This document can be found at http www frc org uk bas standards tas cfm User Guide for CMI 2011 Mortality Projections Model Page 33 of 33
4. a is the Long Term Rate of Mortality Improvement value of Core parameter c is the Constant Additional Rate of Mortality Improvement omitted if zero It is permissible to omit the gender extension where the Core Projections being described cover both male and female lives with identical Core Parameters a and c and the gender differentiated defaults applied that is it is sufficient to refer to CMI 2011 a instead of CMI 2011_M a for males and CMI_2011 F a for females 4 1 2 Informal Naming Convention for other Projections produced using the Model The following informal naming convention is applied within the Model It is hoped this will prove helpful for users for example in their documentation as a form of shorthand CMI_2011_x Advanced IR tab_1 LTR tab_2 Conv tab_3 Timing mm dd yyyy c where e CMI refers to the CMI Mortality Projections Model e _2011 is the version number of the Model and reflects the year of its publication e _x specifies the gender and is either _M male or _F female e tab_1 is any short name adopted by the user to represent the tables used for the Initial Rates of Mortality Improvement group of parameters default will be shown here if Core is selected for this parameter group e tab_2 is any short name adopted by the user to represent the tables used for the Long Term Rates of Mortality Improvement group of
5. from age 90 reaching zero at age 120 and to be zero for ages above 120 e The cohort component of the Long Term Rate is set to a default value of zero so the influence of year of birth features is assumed to dissipate completely over the convergence period Further commentary on the rationale for this mapping of the single Core level input parameter to the full parameter set is given in Appendix A section A 2 of the CMI_2009 User Guide Alternatively by selecting the Advanced level for this group of parameters the user may input any table of component Long Term Rates to suit their purpose e Paste the age period and cohort component Long Term Rates into the appropriate cells in the Advanced Parameters worksheet e Enter a short reference name for the user input table in the Inputs worksheet Important Note When the Model is first downloaded from the CMI pages on the UK Actuarial Profession s website the Core Long Term Rate parameter on the Inputs worksheet is set to and no projection is produced Similarly the vectors for the Long Term Rate components in the Advanced Parameters worksheet are also set to The user must therefore enter a numeric value or vectors of values in the appropriate cells in order to produce a projection The choice of a suitable long term rate is clearly subjective but it is intended that the research presented in sections 4 1 to 4 3 of CMI Working Paper 39 may help inform
6. the Advanced level of parameters the user must enter the effective date in the Inputs worksheet 3 3 4 Split of Initial Rates into Age Period Component and Cohort Component The Initial Rates of Mortality Improvement must be split into two components a component influenced by age and period but not year of birth cohort and a component which is solely influenced by year of birth cohort This split is only required for the initial rates that is for the Foundation Year but not for any earlier years The component values may be either positive or negative and vary by age or year of birth and by gender The two components sum to give the Initial Rates of Mortality Improvement at each age for the Foundation Year Where Core has been selected for this group of parameters a default component split is adopted The default component rates have been derived using an age period cohort model developed explicitly for this purpose Further information on the methodology and resulting split is set out in Appendix A section A 1 2 of the CMI 2009 User Guide updated charts reflecting the addition of data for 2010 are contained in section 2 of CMI Working Paper 55 Alternatively by selecting the Advanced level for this group of parameters the user may input any table of component rates to suit their purpose paste the age period and cohort component rates of mortality improvement into the appropriate cells in the Advanced Parameters works
7. 5 2 may also help inform views on likely patterns of convergence and in turn help in setting values for this parameter set 3 6 Constant Additional Rate of Mortality Improvement This parameter allows the user to incorporate a degree of prudence or other appropriate adjustment to a projection The Constant Additional Rate of Mortality Improvement is applied uniformly to all ages and calendar years after the start of the projection The user may enter a value if desired in the Inputs worksheet A negative value may be entered if the user wishes to reduce all projected rates of mortality improvement For the avoidance of doubt e The Constant Addition does not apply to the Foundation year nor to earlier years e In the first year of the projection Foundation Year 1 the annual rates of mortality improvement will be the Initial Rates projected forward one year plus the Constant Addition e In the long term the annual rates of mortality improvement will be the Long Term Rates plus the Constant Addition User Guide for CMI 2011 Mortality Projections Model Page 16 of 33 3 7 Further Parameters for Sample Expectation of Life and Annuity Values Sample expectation of life and annuity values are calculated and presented on the Sample EoL amp Annuities worksheet and these calculations require some additional parameters 3 7 1 Calculation Date The sample values apply as at the effective Calculation Date set by the user on
8. A is specified user input or Core default for Initial Rates of Mortality Improvement e Say Date B is specified user input or Core default for Base Rates of Mortality e Say Date C is specified user input as the Calculation Date e The timing definition for cumulative Mortality Reduction Factors follows from Date A that is it takes the exact day and month part of Date A e The timing definition for projected mortality rates follows from Date C that is it takes the exact day and month part of Date C Projected future mortality rates qx are calculated as x t qx X RF gt t gt RF x 0 where xo is the Base Rate of Mortality for age x RF is the cumulative Mortality Reduction Factor for age x and timing consistent with the Calculation Date Date C rolled forwards backwards to year t RF xo is the cumulative Mortality Reduction Factor for age x and timing consistent with the Base Rates of Mortality Date B User Guide for CMI 2011 Mortality Projections Model Page 28 of 33 The RF values are calculated from the table of cumulative Mortality Reduction Factors in the Mortality Reduction Factors worksheet using geometric interpolation to achieve the required timing definition For example using e the Core Projection CMI _2011_M 1 00 e Base Mortality 100 SIPMA Core for life aged x exact on 01 09 2002 and e Calculation Date 01 07 2011 we have e
9. Date A 01 01 2008 e Date B 01 09 2002 e DateC 01 07 2011 RF 5 01 09 02 the Mortality Reduction Factor for age 65 and timing consistent with the Base Mortality Rate is calculated by interpolating between RF 65 01 01 02 and RF 5 01 01 03 RF 5 10902 100 00 x 97 15 100 0 98 10 as 01 09 02 is 0 67 of a year 243 days after 01 01 02 the effective date for the RF RF 65 01 07 2011 the Mortality Reduction Factor for age 65 and timing consistent with the Calculation Date is calculated by interpolating between RF 5 o1o111 and RF6s5 01 01 12 RF 65 010711 76 07 x 73 77 76 07 74 92 as 01 07 11 is 0 50 of a year 181 days after 01 01 11 the effective date for the RF So 65 01 07 11 os 01 09102 X RF 65 010711 RF 65 01 09 02 0 011239 x 74 92 98 10 0 008584 Important Notes The example calculation basis adopted in the CMI Library of Mortality Projections v1 2 User Guide makes two simplifying assumptions e First that all the mortality reduction factor tables published in the Library may be applied to any base mortality table as if their effective timing were aligned The reduction factors are applied as if their timing definition took the exact day and month part of Date B the timing definition for the base mortality rates regardless of the natural timing definition derived from the data or model underlying the reduction factors If desi
10. The Institute and Faculty of Actuaries and the CMI do not accept or assume any responsibility for the use of this document by any party in any context This document does not provide any form of guidance and should not be relied on as such User Guide for CMI 2011 Mortality Projections Model Page 1 of 33 Contents Te Introdtcti n oiin nates ete ee ae a aA tei anata aug 4 2 Overview or the Structure of the Model js ciccrs sass tacnsucagsungtasgy wicuds ahnnge dad euestuusades ade anon tepbadbatas deaseaances 5 2 1 The purpose of the Model iscccc uicascaseasaactdebants seseaustasj eee sepia r sata aves deea sean Llanes 5 2 2 Mod l S CUCU OTe sesiet e e Gna car ital toad lig aeaaeae ae usean 5 2 3 Core and Advanced Parameter layers icv cccvsssieecisasavaceisigenssaapavedsiledeadsasencaeeds devedeadescaasebaceneastes 6 2A COUGIUES src cicetin sich atic ee Shaina aed sede a pea Ice mite Gch Ais eat anc seer a a E Ee 6 2 3 Dimensions of the Models acasciats aplticnie sia daindi anna anda dies aA ae not 7 20s SENSIVIY LESS scien siete te r a te aea aa aa a asra an locates teas aaa e E Sa a 7 3 Parameterisation of the Modelssssrssiinensiiriiiiniii ieee ee ee eee ees 8 Jle Cremer neea e E E A Nh nimi nit mune T E E 8 3 2 Base Rates of Mortality srein nunna n a a E A Laden a AS 8 32k Parameter Develer terstir aa eeuen eigi E aaea EEES AI EESE aS 8 3 2 2 Base Table of Mortality Rates siicaccssccvsssciessateecindsovaiaistg
11. extent Working Papers 49 and 55 also provide further analysis to help inform the setting of parameter values for the Model specific references are given where relevant in the following sections All user input cells are highlighted by a yellow background in the Model In this User Guide e references to worksheets in the Model are indicated by using square brackets worksheet name e references to user selections from dropdown lists are indicated by curly brackets selection 3 1 Gender Although the Model is designed to store parameters for both male and female lives each projection produced by the Model is gender specific The user must therefore select gender Male or Female from the dropdown list on the Inputs worksheet prior to producing a projection The default parameter values accessed through the Core parameter level are differentiated by gender for Base Rates of Mortality and for Initial Rates of Mortality Improvement but not for the other parameter groups Complete mortality projection parameter sets for both genders may be stored in the Model simultaneously but separate projections must be run for Male and Female in order to produce the outputs required to model or value a mixed gender dataset 3 2 Base Rates of Mortality 3 2 1 Parameter Level The user must select the level for this group of parameters Core or Advanced from the dropdown list on the Inputs worksheet prior to produci
12. of 33 Table I Summary of Parameters within CMI_ 2011 Mortality Projections Model Parameter Dimensions amp Format Core Advanced Gender Gender for Mortality Projection User Selection Base Rates of Mortality Parameter Level Choice List Core Advanced User Selection User Selection Mortality Rates Ages 20 to 150 x xxxxxx in range 0 1 Selection sample tables User Input Vector Age Timing Definition Single Date dd mm yyyy Year Yo Default User Input Single Date Initial Rates of Mortality Improvement Parameter Level Choice List Core Advanced User Selection User Selection Initial Rates of Improvement Ages 20 to 150 Years Yo to Y1 x xx pa Default 1991 to 2008 User Input Table Age Year Timing Definition Single Date dd mm yyyy Year Y Default 01 01 2008 User Input Single Date Initial Age Period Component Ages 20 to 150 x xx pa for Y Default for 2008 User Input Vector Age Initial Cohort Component Default for 2008 User Input Vector YoB YoB Y1 20 to Y1 150 x xx pa Y Long Term Rates of Mortality Improvement Parameter Level Choice List Core Advanced User Selection User Selection Long term Age Period Component Ages 20 to 150 x xx pa User Input Single Value User Input Vector Age Long term Cohort Component YoB Y 20 to Y1 150 x xx pa Default zero User Input Vector YoB Convergence Parameter Level Choice List Core Advanced User
13. or F as appropriate to the gender selected Alternatively by selecting the Advanced level for this group of parameters the user may input any table of mortality rates to suit their purpose e Paste the mortality rates into the appropriate cells in the Advanced Parameters worksheet e Enter a short reference name for the user input table in the Inputs worksheet 3 2 3 Timing Definition for Base Rates of Mortality For the purpose of calculating projected mortality rates it is necessary to specify a precise time interval to which the Base Table of Mortality Rates is deemed to apply The Model therefore requires input of the date dd mm yyyy on which the 1 year time interval starts such that qx is the probability that a life attaining age x exact on dd mm yyyy dies before reaching age x 1 exact on dd mm in year yyyyt l Under the Core level of parameters the effective dates are defaulted to those specified in section 3 2 2 for mortality rate tables set by the user under the Advanced level of parameters the user must enter the effective date in the Inputs worksheet If a user does not wish to apply the default timing definition assumed for mortality tables available under the Core level of parameters the user may simply switch to the Advanced parameter level enter the mortality rates for the required table and set the timing definition as they wish User Guide for CMI 2011 Mortality Projections Model Page 9
14. period and blending smoothly into the Long Term Rate However the Model has no regard for the trend in rates of mortality improvement prior to the start of the projection so although the transition from historic to projected rates is continuous it may well not be smooth The worksheets Proj by Age and Proj by Cohort then apply these weights to the Initial and Long Term Rates for each age or year of birth cohort to derive full tables of projected annual rates of mortality improvement for each component Note that as convergence periods are limited to a maximum of 50 years these 4 sheets only operate for the first 50 years of the projection 5 2 6 Proj Mort Imps The Proj Mort Imps worksheet combines the age period and year of birth cohort components to produce a full projection of aggregate annual rates of mortality improvement The table covers the full age attained 20 to 150 and calendar year 1992 to 2130 range of the Model The calculated values feed in to the output Heat Map of mortality improvement rates on the Heat Maps worksheet and may be exported for further use or analysis The timing definition for these improvement rates follows directly from that specified for the Initial Rates of Mortality Improvement That is if the effective date for Initial Rates is dd mm yyyy then the projected rates all relate to movements in mortality rates qx for exact ages on dd mm of each year For Core Projections produced using t
15. to experiment with a model of convergence to see the effect varying the parameters has on the path of convergence The data underlying the charts is manipulated in the worksheet Input Tables 5 2 10 Output Charts The Output Charts worksheet contains a series of charts to illustrate the results of the projection e Charts showing projected annual rates of mortality improvement Chart_O_01 by calendar year for selected ages Chart_O_02 by age attained for selected calendar years Chart_O_03 by calendar year for selected year of birth cohorts Chart_O_04 by year of birth cohort for selected calendar years e Charts showing projected mortality rates Chart_O_05 qx by age attained x for selected calendar years t Chart_O_06 logit m by age attained x for selected calendar years t e Charts showing projected life expectancies Chart_O_07 Cohort expectation of life by calendar year for selected ages Chart_O_08 Period expectation of life by calendar year for selected ages e Further charts showing the projected annual increase in life expectancies by calendar year for selected ages Chart_O_09 For cohort expectation of life by calendar year for selected ages Chart_O_10 For period expectation of life by calendar year for selected ages e Charts showing projected survival probabilities between selected ages by calendar year Chart_O_11 On a cohort life projection basis Chart_O_12 Ona period life pro
16. values which are applied when the Core level of parameters is selected There are separate tables for each of the four main parameter groups each covering the Model s full range of individual ages or year of birth cohorts and gender The colour coding applied to separately identify the parameters for males and females is followed through depending on the user s selections to the Parameters Used by CPM worksheet User Guide for CMI 2011 Mortality Projections Model Page 23 of 33 Table II Summary of Worksheets within CMI_ 2011 Mortality Projections Model Worksheet Name Description Type Rank Inputs User Home page primary control of the projection User Input Primary Proj Mor Imps Primary Sample EoL amp Annuities Tables of expectation of life and annuity values for sample ages Output Primary The worksheets Inputs gt gt Outputs gt gt and Mechanics gt gt are used purely as signposts and play no active part in the Model The worksheet Notices provides general information and plays no active part in the Model User Guide for CMI 2011 Mortality Projections Model Page 24 of 33 Figure 2 Schematic of Model Structure Outline of major Data and Calculation flows between Worksheets Userinput Mechanics CCC ie Results l Inputs l l l Advanced Parameters Sample q x t User Guide for CMI 2011 Mortality Projections Model Core Parameters Tre
17. worksheets is given in the following sections In the Model for example one of the worksheet names and User Guide the acronym CPM is still used to refer generically to the CMI Mortality Projections Model This acronym has been deliberately retained rather than replaced by the current Model version name CMI 2011 in order to avoid the potential need for further updates to such references for each future version of the Model 5 2 1 Model Inputs The Inputs worksheet is the Home sheet for users of the Model Using the input cells on this sheet users e Select the level Core or Advanced for each of the four main parameter groups Where Core is selected additional parameter inputs on this sheet fully specify the projection Where Advanced is selected the user is required to input dates to specify the timing definition of the user input tables of parameters and is invited to input short names by which to refer to the tables e Select gender for the projection this determines whether the calculations in the Model work from the parameters stored for male lives or those for female lives e Set any Constant Additional Rate of Mortality Improvement A shorthand description of the projection using the naming conventions set out in section 4 and driven by the user s parameter choices is also shown on this worksheet 5 2 2 Core Parameters The Core Parameters worksheet contains the full tables of default
18. 3 of 33 1 Introduction In November 2009 the CMI published a new mortality projections model denoted CMI 2009 The Model was released in response to the continuation of significant year on year increases in life expectancy and to concerns over the continued widespread use albeit with modifications of the Interim Cohort Projections which inevitably became increasingly out of date The release of the CMI_2009 Model followed a consultation on the prototype Model CPMv0 0 which was issued alongside two Working Papers CMI Working Paper 38 provided an overview of the Model and set out specific questions for the consultation CMI Working Paper 39 detailed further analysis to help inform the setting of parameter values for the Model CMI Working Paper 41 summarised the responses to this consultation outlined the changes between the prototype Model and CMI_2009 and provided a quantification of the effect of updating the default parameter values in the CMI 2009 Model to reflect the publication of England amp Wales population data for calendar year 2008 In November 2010 an updated version of the Model CMI_2010 was published alongside CMI Working Paper 49 The structure of the CMI_2010 Model was identical to that of CMI_2009 however the default parameters were updated to reflect the publication of population mortality data for calendar year 2009 The Model has now been updated once again The principal purpose of this annual u
19. Continuous Mortality Investigation User Guide for The CMI Mortality Projections Model Model Name Version CMI 2011 It remains the responsibility of any actuary or other person using a projection of future mortality to ensure that it is appropriate for the particular purpose to which it is put regardless of the source of the projection The CMI has produced this Model in compliance with the principles in the Technical Actuarial Standard M Modelling April 2010 published by the Board for Actuarial Standards regarding its construction checking and documentation Documentation of the Model in addition to that in the Model itself is contained in this User Guide and further information is detailed in the Working Papers referenced herein Extensive checking has been undertaken during the development of the Model and the CMI is confident that it correctly produces projections from the various inputs in the manner described in this User Guide However the Institute and Faculty of Actuaries and the CMI do not warrant the accuracy of the Model and do not accept or assume any liability for its use September 2011 2011 Institute and Faculty of Actuaries The text in this document may be reproduced free of charge in any format or medium providing that it is reproduced accurately and not used in a misleading context The material must be acknowledged as Institute and Faculty of Actuaries copyright and the title of the document specified
20. E ARAS TEESE 21 5 1 4 Constraints amp Reasonableness of Model Outputs ssesssseseseesseesseesseessseeesseessresseesseresseee 22 5 1 3 Saving Parameter Sets ena eii E EE E E A a EEES 22 5 2 Worksheet Structure of the Model seeseeeeeseeeseseessessresressessresresstssrestessesstesresseeseesereseeseseeesee 23 5 2 Model AN PWS oee rernu ea e e e EE E AEE Hd EEES 23 5 22 Core ParameterSs sssini ease ose anaE eldest hate a EES Sa aa ni esa aa 23 5 2 3 Advanced Par metetS Scorte e a A a E a ol aac oem ose cin 26 5 2 4 Parameters Used by CPM sivaccisiscaseseciavscaissestanascageets nosine e ae i iE 26 5 2 5 Calculation of Projection over Period of Convergence eeseesseeseesereseereeseesseseresresseseresee 26 5 2 6 lt Ptoj Mort IMPS erer n E E A A S REE AE TEEN 27 5 2 1 Mortality Reduction BACIOIS senasis a a a a aa 27 5 2 8 Calculation of Summary Projection Outputs ssseseesseeeseeeesseessresseesseeesseeesseesseesseesseesseee 28 J2 Tnp t MALS cscsasienssasacctgvastenvepasstbngsesascGosndaceaeanenee uaa tangeed aa eouensaeetennavige eaten ansseusea pase 30 5 2 10 Output Charts aeiee E e E Ea e EEEE AEE SATE CETATE 30 Dad ts Heat Mapsen a E a a a a a E e a EEE aN 31 5 212 Sample EoL amp Annuities sienna a a Aae aE E ER ES 31 6 Changes from the CMI 2010 Model leones ee itere e e ain e rte e anh 32 E E E E EEE T calaee e hentia ae scta 33 User Guide for CMI 2011 Mortality Projections Model Page
21. Selection User Selection Period of Convergence e Age Period Component Ages 20 to 150 x years Default User Input Vector Age e Cohort Components YoB Yj 20 to Y1 150 x years Default User Input Vector YoB Change after mid point of Period e Age Period Component Ages 20 to 150 x Default 50 User Input Vector Age e Cohort Components YoB Y 20 to Y1 150 x Default 50 User Input Vector YoB Constant Addition to Rates of Mortality Improvement Constant Single Value x xx User Input Single Value User Input Single Value User Guide for CMI 2011 Mortality Projections Model Page 10 of 33 3 3 Initial Rates of Mortality Improvement 3 3 1 Parameter Level The user must select the level for this group of parameters Core or Advanced from the dropdown list on the Inputs worksheet prior to producing a projection 3 3 2 Table of Initial Rates of Mortality Improvement The mortality improvement rate for age x and year t rx is defined as Txt 1 qx gt qxt 1 A table of initial rates of mortality improvement by age and gender is required for the Foundation Year of the projection that is the last year for which improvement rates are known estimated or assumed and accordingly which forms the start point for the projection In addition rates of mortality improvement for earlier years are required to cover any time interval between the effective dates for the Base Rates of Mortal
22. ameters to suit their purpose e Paste the Age Period and Cohort Component Proportions Remaining into the appropriate cells in the Advanced Parameters worksheet e Enter a short reference name for the user input table in the Inputs worksheet A great variety of transitions may be modelled in this way Input values are not restricted to the range 0 to 100 as other scenarios are plausible For example where the Initial Rate is above the Long Term Rate selecting a relatively high proportion say in the range 75 to 125 can generate projected rates of mortality improvement that initially increase before falling towards the assumed Long Term Rates Users therefore have the flexibility for example to generate scenarios in which the rate of change accelerates in the short term before decelerating in the longer term User Guide for CMI 2011 Mortality Projections Model Page 15 of 33 Figure 1 illustrates how the shape of the convergence path can be altered in practice with a 2 0 p a initial rate converging towards a 1 0 p a long term rate in 40 years time 3 00 2 50 2 00 1 50 1 00 0 50 Rate of Mortality Improvement op a 0 00 0 5 10 1 LA 20 25 30 35 40 45 50 Year of Projection Figure 1 Illustration of the operation of the convergence algorithm over a 40 year period with various Proportions of Convergence Remaining at Mid Point The research material noted in section 3
23. ases e The second has certain elements of the basis fixed so as to be consistent with the basis adopted for calculation of the expectation of life and annuity values illustrated in the CMI Library of Mortality Projections v1 2 User Guide Base Mortality is set to 100 PCxA00 for life aged x exact on 01 07 2007 not 2000 The timing definition for Initial Rates of Mortality Improvement is deemed to be 01 07 yyyy Calculation Date is set to 01 07 2007 Annuity discount rate is set to 5 0 pa These results tables are fed by two Excel Data Tables calculation of the Data Tables must be forced by pressing the F9 key to update the sample results table Table_02 allows the user to select a larger grid of 119 model points Results calculated on the full projection basis specified by the user are shown in e Table 02 ona cohort life projection basis and e Table 03 ona period life projection basis These results tables are fed by four further Excel Data Tables calculation of the Data Tables must be forced by pressing the F9 key to update the sample results table User Guide for CMI 2011 Mortality Projections Model Page 31 of 33 6 Changes from the CMI_2010 Model A relatively small number of changes have been made between the CMI_2010 Model and the current version CMI_2011 These are detailed below The principal change in CMI_2011 has been to update the default parameter values supplied in the Core param
24. del for each projection are e A table of projected annual rates of mortality improvement by age and calendar year e A table of projected cumulative mortality reduction factors by age and calendar year The Model also produces a variety of charts and tables to illustrate the projection As well as providing information to facilitate comparison of projections these outputs are also designed to support the user in reviewing the reasonableness of the projection Specifically the following outputs are generated e A heat map of annual rates of mortality improvement by age attained and calendar year e A heat map of cumulative mortality reduction factors by age attained and calendar year e Sample expectation of life and annuity values User Guide for CMI 2011 Mortality Projections Model Page 6 of 33 e Charts showing projected rates of mortality improvement by age attained and calendar year by year of birth cohort and calendar year e Charts showing projected mortality rates qx by age x and calendar year t logit m In m 1 mxo by age x and calendar year t e Charts showing projected life expectancies on both period and cohort calculation bases life expectancy at selected ages by calendar year annual increase in life expectancies at selected ages by calendar year e Charts showing projected survival probabilities on both period and cohort calculation bases between selected ages by ca
25. each age and each year of birth cohort and also by gender Where Core has been selected for this group of parameters a default table of convergence parameters is adopted e The default convergence period for Age Period Components of improvement rates is fixed at 10 years for ages up to 50 then increasing by one year for each year of age up to 60 fixed at 20 years for all ages 60 to 80 then decreasing by one year for each year of age up to 95 and fixed at 5 years for all ages 95 and above e The default convergence period for Cohort Components of improvements is fixed at 5 years for year of birth cohorts 1913 and earlier then increasing by one year for each year of birth cohort up to 1948 and fixed at 40 years for all year of birth cohorts 1948 and later that is the convergence periods for the Cohort Components run to age 100 subject to a minimum of 5 years and a maximum of 40 years The default convergence periods are not differentiated by gender The default parameter values for the periods of convergence for Age Period Components are unchanged from those used in both CMI_2009 and CMI_2010 The approach taken to setting the default values for the periods of convergence for Cohort Components is also unchanged i e they again run to age 100 subject to a minimum of 5 years and a maximum of 40 years as a result the default periods of convergence for the Cohort Components have reduced by one year compared to CMI_2010
26. eesseeesseeessresseesseesseresseee 16 3 7 Further Parameters for Sample Expectation of Life and Annuity Values eeeeeeseeeees 17 3 7 1 Calculation Date scvcccscst ceca ites cedesdastees eesi esci apocrine pE tee aaa eludes hag eve 17 3 62 lt ANMWILY DISCOURE KALE osese ienai ea Wee dacgdule Seedy o E a SE 17 31 34 Model POMtSecsnseneniniuosnenetananinn nh nanii hae aa s aSa 17 4 Projection Naming Conventio iietra ete e a s eeii ees toot ss 18 4 1 1 Formal Naming Convention for Projections produced using Core Parameters 18 4 1 2 Informal Naming Convention for other Projections produced using the Model 18 4 1 3 Description of Base Rates of Mortality 0 00 cee ceescecssneeceeceecsseeeceeeeeceeeecsceecseeeecseeeeenaeees 19 4 1 4 Changes to the Model s Calculations cccccccecsscceseceseceescecaeceseeseeeeeacecsaeceseeeeneeeaeeesaeees 19 5 Mechanics of the Model vc cess gecesscvnsereiedsdece teat cataes Godeas capac lebidaee Ha dated eiiiai a aE dade nee 20 DLs HEMEL AL cates sl galets crag E E A E A E oe aeedua ns ganten ens E 20 Plate SOWAS a teal actos aadcsiue cadences tau E deta lartekist Ea 20 User Guide for CMI 2011 Mortality Projections Model Page 2 of 33 Sele2 Open Soiree Code iiisdisishea iarccdais eecadeicsihndiahpeaands saad a haa Waseda ENE aes E o RE 20 5 1 3 Excel Calculation Opus sscscsseasessevesosseiveyeel aese eote E an eas tyasster ghey TE
27. en cinch ovaass eoeed teres seeaaidees aa etadeutioeseentes 8 3 2 3 Timing Definition for Base Rates of Mortality 00 ceeeeeseeesceceneceeeeeseeesseecnaeeneeseeeeenees 9 3 3 Initial Rates of Mortality Improvement i i siicis scccsacigeacsssagacdevsssdeatscostaacs deneceds sacseassasedantausseezens 11 33ks Parameter Levels bch 26 oh cacea biel cabanas a e tack locas plen Satara ts ass aE ek Gm ns 11 3 3 2 Table of Initial Rates of Mortality Improvement 0 0 0 0 cee cceeceeceeeeeceeeeeceeeeeceeeeeceeeeeseeeeees 11 3 3 3 Timing Definition for Rates of Mortality Improvement ssssssesssessseessseeessresseessesseresseee 12 3 3 4 Split of Initial Rates into Age Period Component and Cohort Component 0 12 3 4 Long Term Rates of Mortality Improvement ssssesesssesesseeesseesseesseesseesssetessresseesseesseeesseee 12 3 4 1 Parameter Leyelsusnsiisenssiietora esines Bayete asi in a E each eles Je eee 12 3 4 2 Long Term Rates of Mortality Improvement sesesssesesseessseesseesseesseesseessseessresseesseeesseee 13 B D MCOMVETSENCE apnena a a A sed aa es 13 Sioa lt P tameter Lee Viel 5 6 ee Gane acs teh TG a eet outta aces etek esac acti Eretas aea Gets Gat at ae 13 3 5 2 Period of Conver Bence onnsa i o a E AE AE AREE A A R S 14 3 5 3 Proportion of Convergence Remaining at Mid point of Convergence Period 5 15 3 6 Constant Additional Rate of Mortality Improvement ss sssssssesseess
28. ent via e mail to projections cmib org uk or in writing to CMI Cheapside House 138 Cheapside London EC2V 6BW Such comments will be considered for future reviews and updates of the Model User Guide for CMI 2011 Mortality Projections Model Page 4 of 33 2 Overview of the Structure of the Model 2 1 The purpose of the Model The purpose of the CMI Mortality Projections Model is to allow users to produce projections of annual rates of mortality improvement in particular in the context of UK pension and annuity portfolios Specifically the Model e reflects the latest experience on trends in mortality and e allows users the flexibility to modify projections tailored to their own views and purpose The CMI intends to update the Model regularly to reflect emerging experience 2 2 Model Structure The structure of the Model is based on the projection of annual rates of mortality improvement i e the pace of change in mortality rates Specifically the Model assumes that current i e recently observed rates of change blend over time into a long term rate of change specified by the user This approach has been adopted by practitioners in a number of countries In the UK the mortality projections that have formed part of the population projections now produced by the Office for National Statistics ONS and formerly by the Government Actuary s Department GAD have utilised this methodology for a number of years
29. eriod The pattern of convergence for each Age Period Component and each year of birth Cohort Component may be altered to influence the initial trajectory of the projected mortality improvement rates over time This is achieved by specifying the proportion of the change between the Initial Rate and the Long Term Rate that remains to be covered at the mid point of the Period of Convergence The convergence process operates separately for Age Period Components and year of birth Cohort Components of improvement rates so that different tracks may be set for each age and each year of birth cohort and also by gender by varying the Proportion Remaining parameters Where Core has been selected for this group of parameters a default table of convergence parameters is adopted e The default Proportion of Convergence Remaining at Mid point of Convergence Period is set at 50 for both Age Period and Cohort Components and for all ages and years of birth e Therefore the projected rates of mortality improvement half way through the periods of convergence will be the average of the relevant Initial and Long Term Rates This default parameter value is unchanged from that used in both CMI_2009 and CMI_2010 further commentary on the rationale for the value is set out in Appendix A section A 3 2 of the CMI_2009 User Guide Alternatively by selecting the Advanced level for this group of parameters the user may input any table of convergence par
30. ery different from those currently influencing patterns of improvement Therefore the long term rate is better informed by expert opinion and analysis of long term patterns of change and the causes driving them Over time the relative weight placed on the recently observed past versus the more subjective longer term view can shift appropriately Such a model structure could be achieved through a suitably parameterised statistical model However at the heart of the Model design is the desire to produce a tool which is easy to understand User Guide for CMI 2011 Mortality Projections Model Page 5 of 33 intuitive in structure and capable of widespread application by users with varying degrees of expertise in this field of actuarial work 2 3 Core and Advanced Parameter layers The Model may be operated at different levels of complexity reflecting the needs and resources of different users and uses By selecting the Advanced parameter level for a group of inputs users obtain unrestricted access with considerable flexibility to set each of the parameters as tables or vectors varying if desired by individual age or year of birth cohort where relevant year and gender However when the Core parameter level is selected for a group of inputs either a set of default parameter values is applied or users are required to set the value for a single simplified parameter from which a full set of parameter values for the gr
31. eter layer for Initial Rates of Mortality Improvement to reflect the publication of England amp Wales population data for calendar year 2010 the CMI_2010 Model used data up to 2009 To allow earlier release of CMI_2011 the CMI has changed its process of working with the population data published by the ONS In previous years the ONS has provided a consolidated dataset of death registrations and population estimates by single year of age from 0 to 104 and grouped for ages 105 and by calendar year from 1961 to 2009 To construct the required dataset for use in parameterising CMI_2011 the CMI has extended and updated that dataset by using two separate component datasets issued by the ONS e 2010 death registrations data for England and Wales ages 0 to 104 105 e Mid 2010 population estimates for England and Wales ages 0 to 89 90 To complete the dataset the CMI has sought to mirror the calculation algorithm used by the ONS to produce high age 90 population estimates rather than waiting for the ONS to publish that part of the required data Any loss of accuracy from this approach is expected to be minimal in the context of using the estimates in the Model Further details of this change of process are set out in CMI Working Paper 54 The methodology used for deriving smoothed estimates of mortality improvement rates for the previous Models has been reapplied to the updated data similarly the APC Model used to separate aggregate rate
32. f the assumed day and month elements of timing are only made when the mortality reduction factors are applied to calculate projected mortality rates as described in the next section 5 2 8 Calculation of Summary Projection Outputs The worksheet Sample q x t calculates projected mortality rates for selected calendar years for all ages via an Excel Data Table The results feed into Chart_O_05 and Chart_O_06 The worksheets EoL amp Annuity Calcs 1 and EoL amp Annuity Calcs 2 calculate projected expectation of life and annuity values for sample model points via Excel Data Tables The results feed into the worksheet Sample EoL amp Annuities Results are produced on both period and cohort life projection bases The worksheet EoL amp Survival Trends calculates projected expectation of life values and survival rates by calendar year for selected ages again via Excel Data Tables The results feed into charts Chart_O_07 to Chart_O_12 Results are produced on both period and cohort life projection bases In calculating projected mortality rates qx1 as building blocks for each of the outputs noted above the Model takes account of the timing definitions set for Base Rates of Mortality Initial Rates of Mortality Improvement and the Calculation Date For this Model timing definitions are specified in terms of the start date for the one year time interval for which the relevant qx applies e Say Date
33. for download from the CMI pages on the UK Actuarial Profession s website the Excel Calculation Option is set to Automatic Except for Data Tables This is intended to optimise the performance of the Model for most users and uses By setting the Excel Calculation Option to Automatic Except for Data Tables e Most worksheets calculate automatically and quickly in particular Inputs worksheet reacts quickly to choice of Core or Advanced The output tables of Projected Annual Rates of Mortality Improvement and Projected Cumulative Mortality Reduction Factors update automatically and quickly The Heat Maps Input Charts and some of the Output Charts update automatically and quickly e However those Charts and Tables fed by Excel Data Tables will not update until the user forces the Data Table calculations to be updated Press the F9 key to calculate the Excel Data Tables and wait for the outputs to update Warning messages are in place for the Charts and Tables which need to be updated in this way Alternative Excel Calculations Options are e Automatic All calculations and Data Tables will automatically update after any change to parameter values or formulae This removes the risk that Output Charts are out of line with the parameter values set but will slow down the basic operation of the Model e Manual This option is NOT recommended It allows parameters to be set without any calculation time delays but the user mu
34. for year of birth cohorts from 1913 to 1947 The approach taken to updating the convergence periods in response to moving the Initial Rates of Mortality Improvement forward by one is the same as was used for the update from CMI_2009 to CMI_2010 and is discussed along with alternative approaches in section 2 2 of CMI Working Paper 49 and section 2 11 of CMI Working Paper 41 Further commentary on the rationale for the original selection of the default values is set out in Appendix A section A 3 1 of the CMI_2009 User Guide Alternatively by selecting the Advanced level for this group of parameters the user may input any table of convergence parameters to suit their purpose e Paste the Age Period and Cohort Component Convergence Periods into the appropriate cells in the Advanced Parameters worksheet Convergence Periods are limited to a maximum of 50 years e Enter a short reference name for the user input table in the Inputs worksheet The choice of a suitable pattern of convergence periods is clearly subjective Some insight may be gleaned from the study of features evident in past patterns of mortality improvement rates and through study of mortality trends by cause of death Additional research and analysis on these topics is presented in sections 5 1 and 5 2 of CMI Working Paper 39 User Guide for CMI 2011 Mortality Projections Model Page 14 of 33 3 5 3 Proportion of Convergence Remaining at Mid point of Convergence P
35. he CMI_2011 Model the effective date for Initial Rates is 01 01 2008 so that the projected rates for Core Projections all relate to movements in mortality rates qx for exact ages on 1 January of each year The choice of table for Base Rates of Mortality plays no part in these calculations Accordingly the table of actual and projected annual rates of mortality improvement is invariant to the assumed effective timing for Base Rates of Mortality 5 2 7 Mortality Reduction Factors The Mortality Reduction Factors worksheet shows cumulative mortality reduction factors The timing definition for these factors matches that stated above for projected annual rates of mortality improvement The factors start at 100 for the mortality improvement rate year which contains the effective date for the Base Rates of Mortality User Guide for CMI 2011 Mortality Projections Model Page 27 of 33 The table covers the full age attained 20 to 150 range of the Model and runs to 2130 The calculated values feed in to the output Heat Map of cumulative mortality reductions on the Heat Maps worksheet and may be exported for further use or analysis The choice of table for Base Rates of Mortality determines the start year for the table of actual and projected mortality reduction factors However only the year element of the assumed effective timing for Base Rates of Mortality is taken into account here Adjustments to take account o
36. heet The worksheet contains a check that the two components do sum to the input aggregate Initial Rates of Mortality Improvement for the Foundation Year The subdivision of aggregate rates of mortality improvement into age period and cohort components is at least partly subjective Some insight may be gleaned from the study of patterns in the emerging observations of mortality improvement rates and through study of recent changes in mortality rates by cause of death Additional research and analysis on these topics is presented in sections 3 3 5 1 and 5 2 of CMI Working Paper 39 3 4 Long Term Rates of Mortality Improvement 3 4 1 Parameter Level The user must select the level for this group of parameters Core or Advanced from the dropdown list on the Inputs worksheet prior to producing a projection User Guide for CMI 2011 Mortality Projections Model Page 12 of 33 3 4 2 Long Term Rates of Mortality Improvement The Model requires a table of long term rates of mortality improvement by age and gender split into age period and year of birth cohort components Where Core has been selected for this group of parameters e The user is required to set a value for the age period component of the Long Term Rate Enter the value in the Inputs worksheet The input value applies uniformly for ages 20 to 90 and to both genders For higher ages the age period component of the Long Term Rate is assumed to reduce linearly
37. ity Improvement with the weights varying over the Period of Convergence The worksheets Convergence Fn by Age and Convergence Fn by Cohort take the convergence group of parameters and create tables of weighting factors reflecting the selected pattern and duration of convergence by age and by year of birth cohort for the respective components of mortality improvement rates The proportion of the weight to be placed on the Initial Rate is determined independently for each individual age and year of birth by fitting cubic polynomials in time f t such that f 0 1 where t O at the start Foundation Year of the projection f T 0 where T is the length of the Period of Convergence in whole years f T P the Proportion Remaining at the Mid Point The first derivative of f t at T is zero that is f T 0 Let t t T sothat t 1 at the end of the Period of Convergence and f t at br ct d The four criteria above lead to four simultaneous equations e d 1 e a b c d 0 e at ab Ycx d P e 3a 2b c 0 User Guide for CMI 2011 Mortality Projections Model Page 26 of 33 These may be solved to give e a 8P 2 e b 5 16P e c 8P 4 e d l This gives full weight to the Initial Rates of Mortality Improvement at the start of the projection and to the Long Term Rates at the end of the Period s of Convergence The convergence path is smooth passing through the selected level at the mid point of the convergence
38. ity and the Initial Rates of Mortality Improvement Where Core has been selected for this group of parameters a default table of rates of mortality improvement is adopted This default table contains estimated improvement rates for individual ages separately for males and females for calendar years 1991 to 2008 derived using a P spline age cohort model fitted to ONS data for the population of England amp Wales for ages 18 to 102 and the period 1961 to 2010 The default Initial Rates of Mortality Improvement are taken as those for calendar year 2008 the first year of the projection is therefore assumed to be 2009 This approach of stepping back two years from the final year for which raw experience data is available 2010 is taken in order to derive sufficiently reliable estimates of the rates of mortality improvement as it avoids much of the distortion of edge effects which are a common danger with smoothing algorithms including P spline models Further information on the derivation of the default table of rates of mortality improvement is set out in Appendix A section A 1 1 of the CMI 2009 User Guide updated charts reflecting the addition of data for 2010 are contained in section 2 of CMI Working Paper 55 A general commentary on the approach taken to reduce edge effects is given in section 3 1 2 of CMI Working Paper 39 Alternatively by selecting the Advanced level for this group of parameters the user
39. jection basis The user may select data series to show on the charts using the input cells highlighted by a yellow background to the left of each chart On a number of charts the user may also select the range for the User Guide for CMI 2011 Mortality Projections Model Page 30 of 33 X axis using the start and end parameters also highlighted by a yellow background in the titles line at the top of the worksheet The data underlying the charts is manipulated in the worksheet Output Tables Charts Chart_O_05 to Chart_O_12 are fed by Excel Data Tables calculation of these Data Tables must be forced by pressing the F9 key to update the charts 5 2 11 Heat Maps The Heat Maps worksheet shows the patterns of projected mortality across two dimensions age attained and calendar years e Chart_H_01 Projected Annual Rates of Mortality Improvement pa e Chart_H_02 Projected Rates of Mortality qx 1 as of Base Rates qx that is cumulative mortality reduction factors 5 2 12 Sample EoL amp Annuities The Sample EoL amp Annuities worksheet shows tables of expectation of life and annuity values calculated for sample model points selected by the user Table _01 allows the user to select a small set of 6 model points Two sets of results are produced and shown within Table_01 e The first is on the full projection basis specified by the user showing values on both period and cohort life projection b
40. lendar year 2 5 Dimensions of the Model The data and the projection range together cover 1992 to 2130 in line with the CMI Library of Mortality Projections and an age range of 20 to 150 the Library range is 20 to 120 2 6 Sensitivity Tests This User Guide does not illustrate the sensitivity of results from the Model to the various parameters however users can refer to Appendix B of the CMI 2009 User Guide which contains the results of a large range of sensitivity tests illustrated relative to the Medium Interim Cohort Projection A spreadsheet containing the results of a wider range of sensitivity tests for the CMI_2009 Model Section 4 of CMI Working Paper 55 which illustrates the sensitivity of results from CMI 2011 to changes in the Long Term Rate of Mortality Improvement User Guide for CMI 2011 Mortality Projections Model Page 7 of 33 3 Parameterisation of the Model The Model parameters are listed with some summary information in Table I on page 10 Further description of the parameters is given in sections 3 1 to 3 7 together with notes on their use and a brief statement of the defaults provided through the Core parameter level Additional commentary on the rationale for the default parameter values is set out in Appendix A of the CMI 2009 User Guide and notes on the derivation of updated parameter values for CMI_2011 are set out in CMI Working Paper 55 Working Papers 38 39 and 41 and to a lesser
41. may input any table of rates of mortality improvement to suit their purpose e Paste the improvement rates into the appropriate cells in the Advanced Parameters worksheet Cell highlighting is used in the worksheet to indicate the years for which data input is mandatory further data may optionally be entered for earlier years to give additional history for the projection outputs for example the heat map of mortality improvements e Enter a short reference name for the user input table in the Inputs worksheet Additional research and analysis of observed rates of mortality improvement for population insured lives and pensioner datasets is presented in sections 3 1 to 3 3 of CMI Working Paper 39 User Guide for CMI 2011 Mortality Projections Model Page 11 of 33 3 3 3 Timing Definition for Rates of Mortality Improvement For the projection it is necessary to specify a precise time interval to which the Initial Rates of Mortality Improvement are deemed to apply The Model therefore requires input of the date dd mm year t on which the 1 year time interval for qx using the notation set out in 3 3 2 starts Note in particular that year t specifies the Foundation Year for the projection of improvement rates Under the Core level of parameters the effective date is defaulted to 01 01 2008 reflecting the data and methodology used to derive the rates For mortality improvement rate tables set by the user under
42. meter level or directly entered as mortality rates under the Advanced parameter level Therefore to use a different percentage of a published table the actual mortality rates required must be entered using the Advanced parameter level 4 1 4 Changes to the Model s Calculations Where a user chooses to modify the Model s calculations the proposed naming conventions for projections should not be used without a clear statement of the changes made User Guide for CMI 2011 Mortality Projections Model Page 19 of 33 5 Mechanics of the Model 5 1 General 5 1 1 Software The Model has been constructed as a Microsoft Office Excel 2007 Workbook but saved in Excel 97 2003 compatible file format It is intended and believed that the Model is fully compatible with Excel 97 2003 versions of the software although it is not practical for the CMI to undertake exhaustive testing in this regard 5 1 2 Open Source Code The Model is transparent in the sense that its mechanics are open for users to view and indeed alter if they wish Extensive checking has been undertaken during the development of the Model and the CMI is confident that it correctly produces projections from the various inputs in the manner described in this User Guide However the Institute and Faculty of Actuaries and the CMI do not warrant the accuracy of the Model and do not accept or assume any liability for its use Users must satisfy themselves that the parameter
43. mple this can be used to calculate sample expectation of life and annuity values for ages from 20 to 100 in 5 year intervals for calculation dates in say 2011 to 2041 in 5 year intervals The grid of model points is specified by setting e The 17 ages age exact on the calculation dates that is age exact in whole years there is no facility for part years of age e The7 calculation dates specify 7 calendar years The calculation dates take the day and month from the main Calculation Date see 3 7 1 e The minimum vesting age for the annuities if the age specified for a model point is less than the minimum vesting age annuity payment for that model point is deferred to the minimum vesting age otherwise annuity payments are assumed to begin at the age specified for the model point User Guide for CMI 2011 Mortality Projections Model Page 17 of 33 4 Projection Naming Convention 4 1 1 Formal Naming Convention for Projections produced using Core Parameters It is recommended that Core Projections that is those produced when the parameter level is set to Core for all parameter groups should be referred to by using the following prescribed naming convention CMI_2011_x a c where e CMI refers to the CMI Mortality Projections Model 2011 is the version number of the Model and reflects the year of its publication _x specifies the gender and is either _M male or _F female
44. nds EoL amp Annuity Calcs 1 EoL amp Survival EoL amp Annuity Calcs 2 Output Tables Page 25 of 33 Heat Maps Sample EoL amp Annuities Output Charts 5 2 3 Advanced Parameters The Advanced Parameters worksheet contains the cells into which user input tables may be pasted when the Advanced level of parameters is selected There are separate tables for each of the four main parameter groups each covering the Model s full range of individual ages or year of birth cohorts and gender that is the layout is identical in most respects to that for the Core Parameters worksheet Cell highlighting bright yellow for mandatory pale yellow for optional and driven by user selections for parameter levels is used to indicate the areas of the Advanced Parameters worksheet open for user input The colour coding applied to separately identify the parameters for males and females is followed through depending on the user s selections to the Parameters Used by CPM worksheet 5 2 4 Parameters Used by CPM The Parameters Used by CPM worksheet simply holds the final selected set of parameter tables which drive the projection This sheet only contains parameters for the gender the user has chosen to model 5 2 5 Calculation of Projection over Period of Convergence The algorithm for the convergence process operates by calculating a weighted average of the Initial and Long Term Rates of Mortal
45. ng a projection 3 2 2 Base Table of Mortality Rates A base table of initial mortality rates qx by age and gender is required so that the Model can calculate projected mortality rates and summary statistics such as life expectancies and annuity values The base rates of mortality do not influence the projected rates of mortality improvement generated by the Model so their function is purely to aid the illustration of the projection by providing a base level from which future mortality rates may be calculated User Guide for CMI 2011 Mortality Projections Model Page 8 of 33 Where Core has been selected for this group of parameters the user may select a base table of mortality rates from the dropdown list on the Inputs worksheet The options are e 100 PCxA00 published by CMI assumed timing 01 07 2000 e 100 SIPxA published by CMI assumed timing 01 09 2002 e 100 Ax00 Ult published by CMI assumed timing 01 07 2000 e 100 ILTO7 09x E amp W published by ONS assumed timing 01 01 2008 This is unofficial shorthand for the Interim Life Tables 2007 2009 published by ONS based on ONS population estimates and death counts for the population of England amp Wales Separate ILTs are published for male and female lives The published ILT mortality rates are not graduated and only cover ages up to 100 a simple extrapolation beyond age 100 by reference to the AxC00 tables is built into the Model where x M
46. oup is derived via a default mapping In this way users may choose to operate the Model at a much simpler level The default values are intended to be reasonable assumptions but should not necessarily be interpreted as best estimates Users need to consider whether or not the default values included in the Model are appropriate to the purpose for which they are using the Model If the Core parameter level is selected for all groups of inputs the user needs to set values for just two parameters representing the most critical inputs e A single rate x xx pa to define long term rates of mortality improvement x xx for ages 20 90 falling linearly to 0 at age 120 0 for age gt 120 e A constant additional rate of mortality improvement z zz pa this constant which may take a negative value applies to the entire projection At the Core parameter level all other inputs are given default values or restricted choice e Initial rates of improvement default to rates derived from England amp Wales population data e Convergence parameters default to a pattern and values set by the CMI Working Party e Base mortality rates are restricted to a selection of published tables Projections produced using the Core parameter level for all groups of inputs are referred to as Core Projections and are subject to a formal naming convention which is described in section 4 1 1 2 4 Outputs The main outputs provided by the Mo
47. parameters the Core Long Term Rate parameter akin to a in 4 1 1 will be shown here if Core is selected for this parameter group e tab_3 is any short name adopted by the user to represent the tables used for the Convergence group of parameters default will be shown if Core is selected for this parameter group e Timing shows the user input date for the timing definition for Initial Rates of Mortality Improvement e c is the Constant Additional Rate of Mortality Improvement omitted if zero User Guide for CMI 2011 Mortality Projections Model Page 18 of 33 4 1 3 Description of Base Rates of Mortality The naming conventions above only describe the basis for projection of mortality improvement rates Base Rates of Mortality must be described separately The following convention is applied within the Model and is recommended for adoption by users 100 TABLE level for life aged x exact on dd mm yyyy where e TABLE is a short name adopted to represent the table of mortality rates this may be a published table name for example PCMA00 or a name adopted by the user for a bespoke table e level is Core or Advanced showing the parameter level selected for Base Rates of Mortality e dd mm yyyy specifies the timing definition of the mortality rates described Important Note The Model always uses 100 of the input mortality table whether selected from the dropdown list of options available under the Core para
48. pdate of the Model is to incorporate 2010 population mortality data into the default Core parameters for the Initial Rates of Mortality Improvement other changes have been kept to a minimum This User Guide is intended to describe the mechanics of the updated Model CMI_2011 The structure of CMI_2011 is identical to that of the previous two versions of the Model so much of the content of this User Guide is unchanged from those associated with CMI_2009 and CMI_2010 The changes made between the CMI_2010 Model and the CMI_2011 Model are detailed in section 6 of this User Guide CMI Working Paper 55 has been published alongside CMI_2011 to document the update The Paper illustrates the impact of incorporating data for 2010 the change in the estimates of the annual rates of mortality improvement resulting from extending the dataset is discussed and the overall results of projections from CMI_2011 expressed in terms of expectations of life are compared with those from CMI 2010 The CMI_2011 Model CMI Working Paper 55 and this User Guide as well as the earlier material may be accessed and downloaded from the CMI pages under Research and resources on the UK Actuarial Profession s website As the changes made in the latest version of the Model are limited the CMI is not undertaking a consultation exercise on the CMI_2011 version of the Model Feedback on the CMI Mortality Projections Model is always welcome though and can be s
49. red users of the Model may follow these timing assumptions rather than the Model s Core defaults by using the Advanced parameter facility e Second that projections only run up to age 120 Expectation of life and annuity values are truncated after age 120 effectively assuming all remaining lives die at the end of their 120 year The Model allows projections to run up to age 150 but if desired users of the Model may apply this lower limit by ensuring that qi29 1 in all years of the projection using the Advanced parameter facility where necessary The differences between the Model and the Library are discussed in section 6 of CMI Working Paper 49 User Guide for CMI 2011 Mortality Projections Model Page 29 of 33 5 2 9 Input Charts The Input Charts worksheet contains a series of charts to illustrate the parameters set for the projection Comparison is given where relevant against the defaults available for the Core level of parameters Chart_I_01 Initial Rates of Mortality Improvement Aggregate Chart_I_02 Initial Rates of Mortality Improvement Cohort component Chart_I_03 Initial Rates of Mortality Improvement Age Period component Chart_I_04 Period of Convergence Chart_I_05 Proportion of Convergence Remaining at Mid point of Convergence Period Chart_I_06 Base Mortality Rates log qx Chart_I_07 Base Mortality Rates as of selected published tables A further chart Chart_I_08 allows users
50. s calculations and outputs of the Model are suitable for whatever application they make of the Model The Model has been developed with a general philosophy of keeping the formulae relatively simple so that most actuarial users of Excel should be able to follow the calculations and methodology It is acknowledged that there is some cost in this approach in terms of slower calculation speeds and larger file size than could have been obtained The worksheet structure of the Model is covered in section 5 2 With the intention of simplifying the presentation of the Model to users especially those who prefer to operate it at the Core level of parameters the worksheets are presented in three groups rather than in their natural order of calculation e Inputs the points for data parameter entry and control of the projections e Outputs the presentation of the results of the projection e Mechanics the workings of the Model The Inputs and Outputs groups are the worksheets required for operation of the Model and so should be regarded as the Primary worksheets The Mechanics group should be regarded as Secondary worksheets users only need to study these sheets if they wish to follow through the detailed workings of the Model or view the full default parameter tables available through the Core parameter level If desired the Secondary worksheets could easily be hidden from view by using
51. s into Age Period and Cohort Components has also been reapplied The following changes result in the Model e Core Parameters The aggregate Initial Rates of Mortality Improvement have been updated based on the extended ONS dataset giving revised estimates for 1991 to 2007 plus a first estimate for 2008 e Core Parameters Similarly the Component Split of Initial Rates of Mortality Improvement has been updated and now refers to 2008 rather than 2007 e Inputs The timing definition for the Core parameter default Initial Rates of Mortality Improvement has been changed from 01 01 2007 to 01 01 2008 e Advanced Parameters The initial values that is those in place when the Model is first accessed via the CMI pages on the UK Actuarial Profession s website have been updated in line with the changes in the Core Parameters worksheet A quantification of the effect of updating the default parameter values in the Model is presented in section 3 of CMI Working Paper 55 The following minor changes have also been made e The naming convention for Core Projections has been updated to refer to CMI 2011 e The default Calculation Date on the Sample EoL amp Annuities worksheet has been changed to 31 12 2011 User Guide for CMI 2011 Mortality Projections Model Page 32 of 33 References CMI Library of Mortality Projections v1 2 User Guide 2011 CMI Working Paper 38 A Prototype Mortality Projections Model
52. st then force the calculations to run by pressing the F9 key Important Note The Inputs worksheet will not automatically update for example for a change from Core to Advanced parameter level if this option is selected The Excel Calculation Option may easily be changed if desired by using the commands e Excel 2007 Formulas Calculations Options and then selecting the desired option e Excel 97 2003 Tools Options Calculation and then selecting the desired option User Guide for CMI 2011 Mortality Projections Model Page 21 of 33 5 1 4 Constraints amp Reasonableness of Model Outputs No constraints have been placed on parameter values other than basic input validation on the range of possible values for example Base Rates of Mortality must lie in the range 0 1 Only a few constraints have been placed on the projection notably e Projected mortality rates are restricted to the range 0 1 e Projections only run up to age 150 expectation of life and annuity values are truncated after age 150 effectively assuming all remaining lives die at the end of their 150 year e Projections only run up to calendar year 2130 expectation of life and annuity values are shown as 44N A where mortality rates would need to be calculated beyond 2130 Users should therefore be aware that the Model may generate projections with unusual properties or even errors particularly if extreme parameter values are entered
53. the Sample EoL amp Annuities worksheet 3 7 2 Annuity Discount Rate An interest discount rate is required for the annuity value calculations This may be set on the Sample EoL amp Annuities worksheet This single parameter is intended to reflect the net combined effect of pension benefit escalation and allowance for future expected investment returns 3 7 3 Model Points The Model supports two independent sets of model points for sample expectation of life and annuity values A small set of 6 model points may be selected via Table_01 on the Sample EoL amp Annuities worksheet The corresponding sample values are then also shown in Table_01 These model points are specified by setting e The age exact on the Calculation Date that is age exact in whole years there is no facility for part years of age e The deferment period for annuities this specifies the period in whole years before the annuity commences payment for expectation of life this specifies the delay in whole years before the remaining expectation of life is calculated for example to calculate e as at n years after the Calculation Date enter age as x n and deferment period as n years A larger grid of model points may be selected via Table _02 on the Sample EoL amp Annuities worksheet The corresponding sample values are then shown in Table_02 and Table_03 The grid has 119 model points 17 ages by 7 calendar years For exa
54. the commands e Excel 2007 Home Format Hide amp Unhide Hide Unhide Sheet or e Excel 97 2003 Format Sheet Hide Unhide and selecting the required sheet if unhiding User Guide for CMI 2011 Mortality Projections Model Page 20 of 33 All the worksheets have the Excel worksheet protection facility enabled apart from user input cells in order to protect the Model from accidental change and corruption However this protection may easily be turned off if desired by using the commands e Excel 2007 Home Format Unprotect Sheet no password is set or required e Excel 97 2003 Tools Protection Unprotect Sheet no password is set or required Where a user chooses to modify the Model s calculations the proposed naming conventions for projections should not be used without a clear statement of the changes made 5 1 3 Excel Calculation Options When the Model is run to produce a projection and full set of outputs the calculation time is typically of the order of 5 to 30 seconds depending on the speed of the computer processor used and the demands of any other software running simultaneously with the Model Excel Data Tables are used in the Model to populate some of the charts and also the sample Expectation of Life and Annuity Values Some of these Data Tables have a heavy workload and so account for a very large proportion of the calculation time In the version of the Model available
55. the selection of suitable parameter values In addition the Appendix to CMI Working Paper 38 contains a description of future scenarios in terms of different causes of death consistent with projections using alternative long term rates of change Mortality models that decompose trends into constituent causes either cause of death models or disease based approaches may provide users with insights into appropriate future rates of change Moreover the views of experts in different fields are likely to be especially valuable and the CMI welcomes attempts to build links with other professions as evidenced for example by the Joining Forces on Mortality and Longevity multidisciplinary conference held in October 2009 and the Emerging Trends in Mortality and Longevity Symposium in September 2011 3 5 Convergence 3 5 1 Parameter Level The user must select the level for this group of parameters Core or Advanced from the dropdown list on the Inputs worksheet prior to producing a projection User Guide for CMI 2011 Mortality Projections Model Page 13 of 33 3 5 2 Period of Convergence The Model assumes that Initial Rates of Mortality Improvement converge smoothly towards Long Term Rates of Mortality Improvement over a specified period The convergence process operates separately for Age Period Components and Cohort Components of improvement rates so that different convergence periods may be set in whole years for

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