Chapter 11 longevity risk and private pensions

CHAPTER 11 Longevity Risk and Private Pensions Pablo Antolin CONTENTS 11.1 I ntroduction 11.2 Uncertainty Surrounding Mortality and Life Expectancy 11.2.1 The Link between Mortality and Life Expectancy: Life Tables 11.2.2 Uncertainty Surrounding Mortality Outcomes 11.2.3 Approaches to Forecast Mortality and Life Expectancy 11.2.4 Measuring Uncertainty Surrounding Mortality and Longevity Outcomes 11.3 The Impact of Longevity Risk on Defined-Benefit Private Pension Plans 11.3.1 How Does Longevity Risk Affect DB Private Pension Plans? 11.3.2 How Do Private Pension Funds Account for Future Improvements in Mortality and/or Life Expectancy? 11.3.3 The Impact of Longevity Risk on Net Pension Liabilities 25 11.4 P olicy Issues Acknowledgments 26 References 26 238 240 240 243 248 251 256 257 258 262 T his ch a pter e x a mines how uncertainty regarding future mortality and l ife ex pectancy outcomes, i e., longevity r isk, a ffects employerprovided defined benefit (DB) private pension plan liabilities The chapter a rgues t hat t o a ssess u ncertainty a nd a ssociated r isks adeq uately, 237 © 2010 by Taylor and Francis Group, LLC 238 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling a st ochastic a pproach t o m odel m ortality a nd l ife ex pectancy i s p referable bec ause i t per mits t o a ttach p robabilities t o d ifferent f orecasts I n this regard, the chapter provides the results of estimating the Lee–Carter model f or se veral O ECD co untries F urthermore, i t co nveys t he u ncertainty su rrounding f uture m ortality a nd l ife ex pectancy o utcomes b y means of Monte-Carlo simulations of the Lee–Carter model In order to assess the impact of longevity risk on employer-provided DB pens ion p lans, t he c hapter ex amines t he d ifferent app roaches t hat private pens ion p lans f ollow i n p ractice wh en i ncorporating l ongevity risk in their actuarial calculations Unfortunately, most pension funds not fully account for future improvements in mortality and life expectancy The chapter t hen presents estimations of t he range of increase in the net present value of annuity payments for a t heoretical DB pension fund Finally, the chapter discusses several policy issues on how to deal with longevity risk emphasizing the need for a common approach Keywords: Demographic forecast; mortality and life expectancy; life t ables; l ongevity r isk, r etirement; p rivate pens ions; definedbenefit pension plans; Lee–Carter models; Monte-Carlo methods, histograms JEL classifications: J11, J26, J32, G23, C15, C32 11.1 INTRODUCTION The length of time people are expected to live in most OECD countries has increased by 25–30 years during t he last century These gains in life expectancy are good news However, policy makers, insurance companies, and p rivate pens ion ma nagers w orry abo ut t he i mpact t hat t hese g ains may have on retirement finances As long as gains in life expectancy are foreseeable a nd t hey a re t aken i nto acco unt wh en p lanning r etirement, they would have a negligible effect on retirement finances Unfortunately, improvements i n m ortality a nd l ife ex pectancy a re u ncertain I n t his regard, the longevity risk is associated with the risk that the future mortality and the life expectancy outcomes turn out different than expected As a r esult o f t his u ncertainty su rrounding f uture de velopments i n mortality and life expectancy, individuals run the risk of outliving their resources and being forced to reduce their standard of living at old ages Pension funds and life annuity providers (e.g., insurance companies), on the other nd, r un t he r isk t hat t he net present va lue of t heir a nnuity © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 239 payments will turn out higher than expected, as they will have to pay out a periodic sum of income that will last for an uncertain life span In this context, individuals bear the full extent of the longevity risk when this risk is “uncovered.” However, private pension funds and national governments providing defined retirement benefits, as well as financial institutions providing lifetime annuity payments face this longevity risk The ma in p urpose o f t his cha pter i s t o d isentangle h ow u ncertainty regarding f uture m ortality a nd l ife ex pectancy o utcomes w ould a ffect employer-provided defined benefit (DB) private pension plans liabilities In this regard, this chapter first focuses on assessing the uncertainty surrounding f uture de velopments i n m ortality a nd l ife ex pectancy, t hat i s, longevity risk.* Second, it examines the impact that longevity risk could have on employer-provided DB pension plans In order to assess the uncertainty surrounding future mortality and life expectancy outcomes, Section 11.2 first examines t he link between mortality and life expectancy, explaining how life tables are constructed from mortality data Second, it provides an overview of the developments in mortality and life expectancy over the past century The improvements seen in mortality and life expectancy were unanticipated as the consistent underestimation of actual outcomes illustrates Th ird, it focuses on the ma in problem fac ing pens ion f unds, t hat i s, t o f orecast t he f uture path of mortality and life expectancy to ascertain their future liabilities In this context, after discussing the main arguments behind two divergent views as regards the outlook for human longevity, this chapter discusses different approaches available to forecast or project mortality and life expectancy It then argues that a stochastic approach to model mortality and life expectancy is preferable because it permits to attach probabilities to different forecasts and, as a result, uncertainty and risks can be gauged adequately C onsequently, t his chapter presents a st ochastic approach t o m odel u ncertainty su rrounding m ortality a nd l ife ex pectancy In this regard, it provides the results of estimating the Lee–Carter model for several OECD countries However, as the goal is far from providing j ust a nother se t o f f orecasts b ut t o a ssess t he u ncertainty su rrounding different mortality and life expectancy outcomes, Section 11.2 concludes w ith t he Monte-Carlo simulations of t he Lee–Carter model * Throughout this chapter, point forecasts on mortality and life expectancy are not discussed because t he a im of t his c hapter i s to prov ide w ays of e xploring a nd a ssessing u ncertainty instead of providing another set of projections © 2010 by Taylor and Francis Group, LLC 240 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling These randomly generated simulations facilitate the task of assessing the uncertainty surrounding those forecasts The second part of this chapter focuses on the impact that the longevity risk may have on employer-provided DB pension plans The longevity risk a ffects t he n et l iabilities o f D B pens ion p lans t hrough t heir l ifetime a nnuity payments a s u nexpected i mprovements i n mortality a nd life expectancy increase the length of the payment period Section 11.3 first ex amines t he d ifferent a pproaches t hat p rivate pens ion p lans f ollow in practice w hen incorporating f uture improvements in mortality and life expectancy in their actuarial calculations While some pension funds account for future improvements in mortality and life expectancy, but o nly pa rtially, o thers u se o nly t he la test a vailable l ife t ables wh en evaluating t heir l iabilities S econd, i t a ssesses t he i mportance o f t he impact of longevity r isk on t he l iabilities of private pension plans For this t ask, t his cha pter presents e stimations o f t he r ange o f i ncrease i n the net present value of annuity payments for a t heoretical DB pension fund The results suggest that the younger the membership structure of a pens ion f und, t he m ore ex posed t o l ongevity r isk t he pens ion f und However, older pension funds have less room for maneuver to deal with the costs associated with the materialization of longevity risk Finally, Section 11.4 discusses several policy issues on how to deal with longevity r isk, w ith a pa rticular emphasis o n i ndexing pens ion ben efits to l ife ex pectancy The first t ask w ould be t o a gree o n a co mmon st ochastic methodology to assess f uture mortality a nd longevity outcomes Governmental agencies are t he best-placed institutions to produce t hese forecasts However, a s t he membership st ructure d iffers a mong pension funds, making assumptions regarding the overall population renders those forecasts less useful for particular pension funds In this regard, pension funds are inclined to use different mortality tables according to socioeconomic status However, this remains controversial Finally, changes in the regulatory framework requiring pension plans to fully account for future improvements in mortality and life expectancy may be required 11.2 UNCERTAINTY SURROUNDING MORTALITY AND LIFE EXPECTANCY 11.2.1 The Link between Mortality and Life Expectancy: Life Tables Life tables provide a summary description of mortality, survivorship, and life expectancy for a specified population They can contain data for every © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 241 single year of age (complete life tables) or by or 10 year intervals (abridged life tables) In its simplest form, a life table can be generated from a set of age-specific death rates (ASDRs) ASDRs are calculated as the ratio of the number of deaths during a y ear (from vital statistics) to the corresponding population size (from censuses and annual population size estimates) They are commonly expressed as per 1000 habitants Mortality rates, on the other hand, are the probability that an individual of a given exact age will die during the period in question (i.e., the probability of dying) In the case of annual probabilities, the denominator is the size of the generation who r each a ge n during t he y ear i n q uestion, a nd t he numerator i s t he number of i ndividuals f rom t his generation who d ie between age n and age n + 1.* The annual probability of dying by age differs from the annual death rate because the latter is the proportion of people of that age who die during the year, while the probability of dying is the proportion of people at that age dying during the age interval.† Therefore, life tables provide a l ink between mortality and life expectancy The final outcome of a life table is the mean number of years still to be lived by a person who has reached that exact age (i.e., the age-specific life expectancies), if subjected throughout the rest of his or her life to the current age-specific probabilities of dy ing Table 11.1 is a n ex ample of a life table for males in France in 2003 It is constructed from the ASDRs, expressed in death rates per 1000 The first column reports different ages x I n t he seco nd co lumn, mx i s t he o bserved per iod A SDRs per c apita (i.e., dividing ASDRs by 1000) The next column contains the age-specific probabilities of dying, qx, computed as (2 ⋅ m ⋅ n)/(2 + m ⋅ n), where n is the width of the age interval In the case of the open-ended age interval 110+, the probability of dying is The fourth column shows the mean number of perso n-years l ived i n t he i nterval b y t hose dy ing i n t he i nterval, ax.‡ People a re assumed to d ie in t he middle of t he age-interval, however, at birth people are assumed to die at the beginning of the interval, while at ages 110+ people are assumed to die late in the interval * Some deaths occur during the year in question, while other deaths occur the following year † For example, a person reaching age 65 in 2000 who dies at age 65 but in 2001 will be counted when c alculating t he pro bability of d ying at 65 i n 000, but it w ill not b e c ounted w hen calculating the death rate at age 65 in 2000 ‡ Th is i s a k ey v ariable W hen u sing 1-year a ge g roups, it i s a ssumed t hat p eople d ie i n t he middle of the age-interval (i.e., a value of 1/2), when using a 5-year age intervals you can also assume the middle of the interval (1/2) or, if data is available, use the single-year age data to build the mean © 2010 by Taylor and Francis Group, LLC 242 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling TABLE 11.1 Life Table, France 2003 Age mx qx ax lx dx Lx Tx ex 20 30 40 50 60 70 80 90 100 109 110+ 0.004 0.000 0.001 0.001 0.002 0.004 0.008 0.017 0.048 0.170 0.447 0.751 0.778 0.00394 0.00038 0.00066 0.00080 0.00170 0.00440 0.00794 0.01673 0.04669 0.15647 0.36562 0.54616 1.00000 0.06 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 1.29 100,000 99,606 99,187 98,530 97,441 94,781 89,416 80,010 60,702 24,949 1,520 394 38 66 78 165 417 710 1,339 2,834 3,904 556 3 99,630 99,587 99,154 98,491 97,358 94,573 89,062 79,341 59,285 22,997 1,242 7,957,453 7,857,823 5,968,537 4,979,901 3,999,349 3,036,208 2,112,789 1,260,628 545,424 106,062 3,069 79.57 78.89 60.17 50.54 41.04 32.03 23.63 15.76 8.99 4.25 2.02 1.31 1.29 Source: Human Mortality Database (http://www.mortality.org/index.html) Notes: Selected ages from table period × (ag e by year), mx is t he per capita annual death rate at age x, qx is the probability of dying at age x, ax is the mean number of person-years lived in the interval by those dying in the interval It indicates when in the interval people dies (e.g., beginning, middle, end), lx is the number of survivors at age x of a hypothetical cohort of 100,000 individuals, dx is the number of deaths in the cohort between two consecutive ages, Lx is the number of personyears lived at age x, Tx is the total person-years remaining at each age x, ex is the life expectancy at age x The next columns compute the number of survivors at each age x of a hypothetical cohort of 100,000 individuals, lx; the number of deaths in the cohort between two consecutive ages, dx; the number of person-years lived by t he cohort, Lx; a nd t he total person-years remaining at each age, Tx.* Life expectancies at age x, ex, are computed by dividing Tx by lx Therefore, given age-specific mortality rates (ASMRs), a life table provides t he associated age-specific life expectancies (Table 11.1) Having a link between mortality and life expectancy, Section 11.2.2 focuses on * The number of deaths, dx, is computed by multiplying the number of survivors of the cohort by the probability of dying The number of survivors, lx, at age x + is the difference between those surviving at x minus those dying at x Computing the number of p erson-years lived, Lx, is a bit more t ricky because we not k now when people dying in the age interval died, at t he b eginning, m iddle, or t he e nd I t i s ge nerally a ssumed i n t he m iddle W hen u sing 1-year intervals this assumption is alright, but when using year intervals it may not be fully accurate The formula is (n (l-(d a) ) Finally, Tx is obtained by accumulating the L column backwards © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 243 reviewing developments in both variables over the last 100 years in several OECD countries 11.2.2 Uncertainty Surrounding Mortality Outcomes Mortality r ates ve decl ined ste adily o ver t he pa st c entury, wh ich s translated into large increases in life expectancy at both birth and age 65 (Figure 11.1 and Table 11.2) These declines stem from substantial reductions in mortality rates at younger ages and, to some extent, improvements at old-ages During the first part of the twentieth century, the decline in mortality wa s ma inly due to a r eduction of i nfectious d iseases a ffecting mainly young ages During the last decades of the twentieth century, the decline in mortality was due to reductions in deaths due to chronic diseases a ffecting primarily older ages.* This is confirmed when looking at the increases in life expectancy at birth and at age 65 during the twentieth century (Table 11.2) Life expectancy at birth increased faster during the first half of the twentieth century while life expectancy at age 65 increased faster d uring t he seco nd lf, a s co mparing t he t op a nd bo ttom pa nels in Table 11.2 confirms Employer-provided DB pension plans are mostly affected by changes in mortality and life expectancy at older ages In this regard, it is important to highlight that for most OECD countries, more than half of the improvement in life expectancy since the 1960s is due to increases in life expectancy at age 65 Past projections have consistently underestimated actual improvements in mortality rates and life expectancy Improvements in mortality rates and life expectancy have increased the number of years that people spend in retirement, bringing in financial troubles for DB pension funds, individuals, a nd social security systems During the past decades governmental agencies, actuaries and academics have tried to project and forecast mortality rates and life expectancy to assess future liabilities However, past projections ve co nsistently u nderestimated i mprovements Table 1.3 shows h ow l ife ex pectancy p rojections b y i nternational o rganizations (e.g., the UN and Eurostat) and actuaries have failed to account for actual improvements A pos itive s ign i ndicates t hat l ife ex pectancy a t birth i n 2003 has already bypassed the UN projected life expectancy for the average of t he per iod 000–2005 (first column) a nd t he E urostat projection * This reduction was mainly due to reduced illnesses from cardiovascular diseases © 2010 by Taylor and Francis Group, LLC 244 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling 81 Life expectancy at birth 78 # Years 75 72 69 66 63 1950 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 60 20 Life expectancy at 65 18 # Years 16 14 12 1950 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 10 0.035 Mortality rate for those aged 65 0.030 Per capita 0.025 0.020 0.015 0.010 0.005 Netherlands France Spain Sweden England and Wales USA 1950 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 0.000 Years FIGURE 11.1 1950–2003 Life expectancy and mortality rates in selected OECD countries, © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 245 TABLE 11.2 Life Expectancy, 1900–2000 Twentieth Century Canada (1921–2002) France (1900–2003) The Netherlands (1900–2003) Italy (1900–2002) Spain (1908–2003) Sweden (1900–2004) United Kingdom (1900–2003) United States (1933–2002) At Birth At 65 2.8 3.3 2.9 3.8 3.9 2.7 3.1 0.7 0.9 0.6 0.9 0.9 0.6 0.7 2.3 0.8 1960–2000 EU15 Averagea OECD Averagea Canada France The Netherlands Germany Italy Spain Sweden United Kingdom United States 2.0 2.2 1.9 2.2 1.3 2.0 2.6 2.5 1.7 1.7 1.8 1.0 1.3 0.7 1.2 1.1 1.0 0.9 0.9 Source: Human M ortality D atabase a nd O ECD Health Data 2005 Note: Increase in the number of years per decade a Unweighted average for 2005.* In the same context, Figure 11.2 shows the U.S Social Security Administration ( SSA) p rojections o f l ife ex pectancy co nsistently bel ow actual outcomes.† Moreover, projections for the next 50 years incorporate a slower improvement in mortality and life expectancy than in the recent past Future projections b y i nternational o rganizations a nd na tional st atistical i nstitutes assume t hat t he p rojected g ains i n l ife ex pectancy a t b irth f or t he n ext * UN pro jections we re pro duced i n 1999 u sing d ata up to 995, w hile Eu rostat pro jections were produced in 2000 using data up to 1999 † Siegel (2005) also reports that the projection by the United States Actuary’s office have been consistently below actual values for most projection years (see Table 10 in his report) © 2010 by Taylor and Francis Group, LLC 246 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling TABLE 11.3 Comparing Realized Gains in Life Expectancy at Birth with Past Projections (Years)a UN OECD average EU15 average Canada France Germany Italy Japan Mexico United Kingdom United States 0.8 0.7 0.2 0.6 0.6 1.1 1.5 1.9 0.5 −0.2 Eurostat 0.4 −0.3 0.3 0.7 −0.1 Source: UN (1999), E urostat (2000), O ECD 2005 Health Data a A p ositive sign me ans t hat lif e exp ectancy in 2003 has already by passed projected life expectancy for the average 2000–2005 (UN) and 2005 (Eurostat) 77 76 75 Actual, SSA data Predicted, Social Security (1992) 74 1980 1989 Data 2000 FIGURE 11.2 Life e xpectancy p rojections b y t he U.S S SA a nd ac tual o utcomes (From L ee a nd M iller 001; L ee, R a nd Tuljapurkar, S , P opulation f orecasting for fiscal p lanning: Is sues a nd i nnovations, i n A uerbach, A a nd L ee, R ( Eds.), Demographic C hange an d F iscal P olicy, C hapter , C ambridge U niversity P ress, Cambridge, U.K., 2001.) © 2010 by Taylor and Francis Group, LLC 252 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling decreases exponentially at each age and at a rate that depends on b(x).* For ages with high values of the coefficient b(x), mortality rates would change faster If coefficients b(x) were to be equal at all ages, then mortality rates would cha nge a t t he s ame r ate a t a ll a ges Finally, t he er ror ter m ε(x, t) reflects p articular a ge-specific h istorical i nfluences n ot c aptured i n t he model Lee and Carter (1992) assume that the error term is normally distributed with mean zero and variance σ2, that is, ε(x, t) ~ N(0, σ2) The model cannot be i dentified (i.e., estimated uniquely) because b(x) and k(t) appear through their product Therefore, it is often assumed that Σtk(t) = and Σxb(x) = to ensure identifiability of the model Using maximum likelihood techniques and the singular value decomposition (SVD) method (see Lee a nd Carter, 1992), a(x), b(x), a nd k(t) are estimated.† In order to obtain forecasts of mortality rates, Lee and Carter (1992) propose to use a time series model for k(t) The standard choice is an autoregressive model, AR(1), for k(t) k(t ) = α + β⋅ k(t − 1) + e(t ) (11.2) The er ror ter m i s d istributed N(0, 1) D uring t he e stimation p rocedure, dummy variables where used to control for extreme events, for example, the flu epidemic in 1918 or the two world wars Having fitted the model for the time-varying index, k(t) is projected forward Using these forecasts of k(t) and the previously estimated values for a(x) and b(x), one obtains ASMRs for f uture years Finally, u sing t he methodology to produce l ife tables described above, age-specific life expectancies for future years were obtained.‡ However, the purpose of this chapter is far from producing another set of projections but to assess the uncertainty surrounding future mortality and life expectancy prospects With the aim of providing the most useful * The coefficients b(x) can be negative, in particular for old a ges, reflecting an increase in the likelihood of dying at very high ages For negative values of b(x), m(x, t) increases exponentially as k(t) decreases linearly † During the estimation procedure, k(t) is fi rst estimated to minimize errors in the log of death rates rather than the death rates themselves Therefore, in a second step k(t) is re-estimated taking the estimates of a(x) and b(x) from the first step as given The new values of k(t) are found by an iterative search such that for each year, given the actual population age distribution, the implied number of deaths will equal the actual number of deaths ‡ Stata programs to estimate the Lee–Carter model and produce forecast for the period 2005– 2100 are available upon request, as well as Stata programs generating life tables from agespecific mortality rates © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 253 information t o po licy ma kers a nd pens ion f unds, t his cha pter ex plores therefore ways of conveying the degree of uncertainty surrounding those forecasts In this regard, the stochastic method used to obtain forecasts of m ortality r ates a nd l ife ex pectancy per mits t o a ttach probabilities t o these forecasts and thus assess uncertainty around any possible outcome, such as the mean or the central forecast In this context, this chapter conveys t he u ncertainty su rrounding f uture m ortality a nd l ife ex pectancy outcomes (i.e., l ongevity r isk) b y m eans o f f requency d istributions a nd cumulated probabilities generated from 10,000 Monte-Carlo simulations of the Lee–Carter model of mortality.*,† The likelihood that life expectancy in 2050 will turn out lower or higher than a determined forecast value (e.g., the central forecast) measures the risk or uncertainty surrounding that forecast Figure 11.3 shows the histogram and the cumulative probability of 10,000 simulations for life expectancy at age 65 in 2050 using the Lee–Carter model The cumulative probability function provides the probability or likelihood that life expectancy w ill be l ower t han o r eq ual t o t he co rresponding f orecast value In this framework, Figure 11.3 shows that the central forecast lies above the median life expectancy for all countries, that is, the likelihood that life expectancy will turn out higher than the central forecasts is lower than 50% In particular, this likelihood varies from 62% in France to 82% in the United States.‡,§ In other words, there is a 12%–38% chance that life expectancy will turn out higher than the central forecasts, depending on the country examined In addition, the probability of any deviation regarding life expectancy is also easy to determine Ther e is a 5% likelihood that life expectancy at 65 in 2050 will be year higher than the central forecast for each country.¶ * Another way of pre senting t he u ncertainty surrounding forecasts wou ld be to pre sent t he point fore cast a nd t he s tandard d eviation It c ould b e pre sented u sing a f an g raph a s t he inflation report of the Bank of England does (King, 2004) † Monte-Carlo is a technique that involves using random numbers In particular, it produces simulations of t he Lee–Carter model by u sing random number generators for t he random terms i n L ee–Carter E quations 11.1 a nd 11.2 The St ata programs, available upon request, assume that the mean and the variance of ε(x, t) and e(t) are those obtained from the errors of fitting the Lee–Carter model to the historical data ‡ The distribution function is more skew to the right in some countries like the United States This is most likely due to the larger variance of errors when fitting the Lee–Carter model § That is, 0.62 ≤ Pr(LEx ≤ LExc) ≤ 0.82 depending on t he country LEx is life expectancy and LExc is the central forecast ¶ Pr(LEx ≤ LExc+1) = 0.95 © 2010 by Taylor and Francis Group, LLC 254 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling 100% 500 England and Wales 450 400 90% 80% LEx = 23.08 Pr(Lex < 21) = 71.87% 300 Cumulative % 60% 250 50% 200 40% 150 30% 100 20% 50 10% 0% 22.1 22.1 22.2 22.2 22.3 22.3 22.4 22.4 22.5 22.5 22.6 22.6 22.7 22.7 22.8 22.8 22.9 22.9 23.0 23.0 23.1 23.1 23.2 23.2 23.3 23.4 23.4 23.5 23.5 23.6 23.6 23.7 23.7 23.8 Frequency Frequency Cumulative (%) 70% 350 100% 500 90% 80% 400 70% 300 Frequency Cumulative % 250 60% Lex = 18.03; Pr(Lex < 21) = 61.65% 200 50% 40% 150 30% 100 20% 50 10% 0% 16.7 16.8 16.8 16.9 16.9 17.0 17.0 17.1 17.1 17.2 17.2 17.2 17.3 17.3 17.4 17.4 17.5 17.5 17.6 17.6 17.7 17.7 17.7 17.8 17.8 17.9 17.9 18.0 18.0 18.1 18.1 18.2 18.2 18.2 18.3 18.3 18.4 18.4 18.5 18.5 18.6 18.6 18.7 18.7 18.7 18.8 18.8 18.9 18.9 19.0 More Frequency 350 Cumulative (%) 450 France (a) FIGURE 11.3 Histogram and cumulative probability of life expectancy at birth and at age 65 in 2050, selected OECD countries (a through c) Life expectancy at age 65 in 2050, 10,000 Monte-Carlo simulations Notes: Lex stands for life expectancy at age 65 in 2050 Consequently, t he r isk o r u ncertainty su rrounding t he f orecasts i s large, but the magnitude of the likely deviation is relatively small.* Thanks to using a stochastic approach to model mortality and life expectancy, the * This deviation depends on t he variance used in the random number generators to pro duce Monte-Carlo simulations This exercise uses the variance of the fitted errors, which depend on whether dummies are used or not i n the estimation of t he Lee–Carter model to c ontrol for extreme events like the flu epidemic or the two world wars © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 255 100% 500 Spain 450 90% Lex = 21.04; Pr(Lex < 21.04) = 76.69% 400 80% Cumulative % 300 60% 250 50% 200 40% 150 30% 100 20% 50 10% 0% 19.5 19.6 19.7 19.8 19.8 19.9 20.0 20.0 20.1 20.2 20.3 20.3 20.4 20.5 20.5 20.6 20.7 20.7 20.8 20.9 21.0 21.0 21.1 21.2 21.2 21.3 21.4 21.4 21.5 21.6 21.7 21.7 21.8 21.9 Frequency Frequency Cumulative (%) 70% 350 100% 500 The Netherlands 90% 450 80% 400 Cumulative % 60% 300 50% 250 Lex = 16.74; Pr(Lex < 21) = 66.43 200 40% 150 30% 100 20% 50 10% 0% Cumulative (%) 70% 15.61 15.67 15.73 15.78 15.84 15.90 15.96 16.02 16.08 16.13 16.19 16.25 16.31 16.37 16.42 16.48 16.54 16.60 16.66 16.71 16.77 16.83 16.89 16.95 17.00 17.06 17.12 17.18 17.24 17.29 17.35 17.41 17.47 17.53 Frequency 350 Frequency (b) FIGURE 11.3 (continued) (continued) uncertainty su rrounding l ife ex pectancy c an be m easured b y a ttaching probabilities to a range of future mortality and life expectancy outcomes The next step is therefore to evaluate how this uncertainty affects pension fund liabilities In this regard, Section 11.3 calculates the increase in the net present va lue of a nnuity payments a s m ortality a nd l ife ex pectancy changes © 2010 by Taylor and Francis Group, LLC 256 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling 100% 500 90% 80% 400 70% 350 Cumulative % 60% 300 Lex = 20.5; Pr(Lex < 21) = 76.20% 250 50% 200 40% 150 30% 100 20% 50 10% 0% 19.1 19.2 19.2 19.3 19.4 19.5 19.5 19.6 19.7 19.7 19.8 19.9 20.0 20.0 20.1 20.2 20.2 20.3 20.4 20.5 20.5 20.6 20.7 20.7 20.8 20.9 20.9 21.0 21.1 21.2 21.2 21.3 21.4 21.4 Frequency Frequency Cumulative (%) 450 Sweden 500 90% 400 80% 350 70% 300 Cumulative % Lex = 24.9; Pr(Lex < 24.9) = 81.48% 60% 250 50% 200 40% 150 30% 100 20% 50 10% 0% 15.2 15.5 15.9 16.2 16.6 17.0 17.3 17.7 18.0 18.4 18.7 19.1 19.4 19.8 20.1 20.5 20.8 21.2 21.5 21.9 22.2 22.6 22.9 23.3 23.6 24.0 24.4 24.7 25.1 25.4 25.8 26.1 26.5 26.8 Frequency Frequency Cumulative (%) 450 100% United States (c) FIGURE 11.3 (continued) 11.3 THE IMPACT OF LONGEVITY RISK ON DEFINED-BENEFIT PRIVATE PENSION PLANS This section examines the impact of longevity risk on employer-provided DB p rivate pens ion p lans Section 1.2 sh owed t hat u sing a st ochastic approach to forecast mortality and life expectancy permits to attach probabilities to a r ange of d ifferent forecasts a nd t hus assess t he u ncertainty surrounding f uture m ortality a nd l ife ex pectancy o utcomes H owever, private pens ion f unds a re co ncerned w ith t he effect o f t his u ncertainty © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 257 on their pension liabilities As the main impact of this longevity risk on net pension liabilities is through their guarantee annuity payments, this section evaluates the changes in the net present value of annuity payments as mortality and life expectancy evolves These changes are evaluated for pension fund members at different ages, and for pension funds with different age-membership structure 11.3.1 How Does Longevity Risk Affect DB Private Pension Plans? The main impact of longevity risk on the net pension liabilities of employerprovided DB private pension plans is through their annuity payments An annuity is an agreement for one person or organization to pay another (the annuitant) a stream or series of payments (annuity payments) Annuities are i ntended t o p rovide t he a nnuitant w ith a ste ady st ream o f i ncome over a n umber o f y ears, wh ich c an st art i mmediately o r i n t he f uture The capital and investment proceeds are generally tax-deferred Ther e are many categories of annuities They ca n be classified i n several ways, for example: (1) according to the underlying investment into fi xed or variable; (2) according to t he primary purpose, t hat i s, acc umulation or pay-out, into deferred or immediate; (3) according to the nature of pay-out commitment into fi xed period, fi xed amount, or lifetime; and (4) according to the premium payment arrangement into single or flexible premium In a fixed annuity, the insurance company or pension fund guarantees the principal and a minimum rate of interests, while in a variable annuity the annuity payment depends on the investment performance of the underlying portfolio An immediate annuity is designed to pay an income one-time or an income stream immediately after the immediate annuity is bought, while in a deferred annuity, the annuitant receives the payment(s) at a later time Fixed period annuities pay an income for a specified period of time (e.g., 10 years), while lifetime annuities provide income for the remaining life of the annuitant A single premium annuity is an annuity funded by a single payment, while a flexible premium is an annuity intended to be funded by a series of payments Flexible annuities are only deferred As employer-provided DB private pensions g uarantee a fi xed f uture stream of payments at retirement to their members for the rest of their life, the analysis throughout focuses on the impact of longevity risk on fixed, deferred, lifetime, and flexible premium annuities The longevity risk would have its la rger ef fect on a nnuities t hat a re f ixed, deferred, and for t he l ifetime of t he a nnuitant once r etirement a ge i s r eached © 2010 by Taylor and Francis Group, LLC 258 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling The impact of longevity risk on fi xed period annuities, on the other hand, is less clear-cut Moreover, the magnitude of the impact of longevity risk on a nnuity pa yments w ould depen d n ot o nly o n t he t ype o f a nnuity guarantees but also on how pension funds account for improvements in mortality and life expectancy when calculating the net present value of annuity payments 11.3.2 How Do Private Pension Funds Account for Future Improvements in Mortality and/or Life Expectancy? Unfortunately, pens ion f unds d o n ot se em t o f ully acco unt f or f uture improvements in mortality and life expectancy Recent studies, in particular, the research by the Actuarial Profession and Cass Business School (2005), f ound t hat c urrent p ractice va ries co nsiderably ac ross t he E U Pension funds in some countries incorporate an allowance for expected future improvements in mortality, while others use tables that relate to mortality o bserved o ver a per iod i n t he pa st, w ithout a llowing f or t he fact that life expectancy may continue to increase (Belgium, Denmark, Norway, S weden, a nd S witzerland) O f t hose co untries i ncorporating an allowance for future improvements in mortality, Austria, France, Germany (for o nly 25 y ears a nd u sing 996 a s t he ba se y ear), I reland (improvements i ncorporated o nly u ntil 010), I taly, t he N etherlands, Spain, a nd t he United K ingdom u se f orecasts; wh ile C anada, F inland, and t he U nited S tates, de spite o f ving m ortality t ables w ith b uilt-in mechanisms to take into account future changes in mortality, generally not use them Furthermore, t here i s n ot a co nsistent o r st andard m ethodology t o incorporate future improvements in mortality and life expectancy In this regard, there is a big problem with tracking longevity risk because the lack of a st andard m ethodology ma kes m ortality c alculations a rbitrary a nd difficult to compare across pension funds and, let alone, countries.* Moreover, i n m ost co untries pens ion f unds a re r estricted a s r egard the demographic assumptions they can incorporate in their assessments The study by the Groupe Consultatif Actuariel Europeen (2001) on actuarial methods and assumptions used in the valuation of retirement benefits in the EU and other European countries, suggests that only in a * The C ass Bu siness S chool (2005) re ports a l arge v ariety of appro aches u sed by t hose p ension f unds adjusting partially t heir l iability c alculations for mor tality a nd l ife e xpectancy improvements © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 259 few countries ( Ireland, Italy, t he Netherlands, Portugal, a nd t he United Kingdom) demographic assumptions a re chosen by t he ac tuary w ithout any direct restrictions from the supervisory or taxation authorities.* Rigid regulation regarding demographic assumptions can be i nadequate when restricting pens ion f unds f rom u sing a lternative m ortality t ables t hat incorporate improvements in mortality and life expectancy, as they may not result in a better assessment of longevity risk Therefore, as a result, the impact of longevity risk is compounded The impact of t he u ncertainty su rrounding f uture i mprovements i n mortality and life expectancy (i.e., longevity risk) on employer-provided DB private pension plans is compounded as few actuaries and pension schemes account f or f uture i mprovements i n m ortality a nd l ife ex pectancy, a nd those that account for improvements generally it only partially In addition, t he ba se t ables u sed f or dem ographic a ssumptions, e ven i f ad justments f or f uture i mprovements i n m ortality a re i ncluded, a re a lmost 10 years old, from the early to mid-1990s Furthermore, the lack of standard methods to forecast mortality and life expectancy, and the fact that these methods are generally far from being fully stochastic complicate any comparative analysis and make the task of examining the impact of longevity risk on pension fund liabilities fuzzier 11.3.3 The Impact of Longevity Risk on Net Pension Liabilities This section focuses on the impact of unexpected improvements in mortality a nd life ex pectancy on t he net present va lue of a nnuity payments of a n employer-provided DB f und.† First, it presents t he results of calculating t he increase in the net present value in 2005 of annuity payments due to a pension f und memb er at d ifferent a ges The pension benefit i s a fixed amount of 10,000€ at 2005 values, and it is paid over the lifetime of a m ember after reaching retirement age at 65 Second, this section discusses the results of calculating the increase in the net present value in 2005 of annuity payments of * In a ddition, t he s tudy by t he G roup C onsultatif Ac tuariel Eu ropeen not es t hat on ly i n Ireland, Cyprus, France, Italy, and the United Kingdom an allowance for i mprovements in mortality is part of the demographic assumptions † In this section, this chapter does not prov ide a w hole range of p ossible outcomes The next step in the current project is to provide this range using Monte-Carlo simulations and thus be able to assess uncertainty In this case, random number generators can also be incorporated i n i nterest r ates, d iscount r ates, a nd wage a ssumptions, a llowing t herefore a ssessing the whole range of risks affecting annuity payments © 2010 by Taylor and Francis Group, LLC 260 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling TABLE 11.5 The Increase in the Net Present Value of Annuity Paymentsa Hypothetical Pension Fund Age in 2005 25 23.6 40 15.3 55 7.3 65 3.3 70 2.4 (1) 10.4 (2) 9.6 (3) 8.2 Source: O ECD calculations Note: P ercentage increase a Increase r esulting f rom co mparing t he net p resent value of annuity payments at 2005 from 2005 till 2090 when life expectancy at birth improves by 1.2 years per decade a nd lif e exp ectancy a t 65 b y 0.8 y ears p er decade, with the net p resent value (NPV) o f annuity payments at 2005 w hen the latest available mortality tables (2005) a re used without allowing for improvements in mortality Membership str ucture in 2005: 65% ag ed 25–49; 20% aged 50–59; 10% ag ed 60–69; and 5% aged 70 or more Membership str ucture in 2005: 60% ag ed 25–49; 20% aged 50–59; 15% ag ed 60–69; a nd 5% ag ed 70 or more Membership str ucture in 2005: 50% ag ed 25–49; 20% aged 50–59; 20% aged 60–69; and 10% aged 70 or more a hypothetical DB pension fund given different age-membership structures For simplicity, the pension fund is assumed to be closed to new members.* Results show that the gap in the net present value of annuity payments between taking into account mortality and life expectancy improvements or not is inversely related with the age of pension fund members Table 11.5 reports the increase in the net present value of annuity payments for several a ges This i ncrease i s t he result of comparing t he net present va lue of annuity payments when using the latest available mortality tables and when u sing m ortality t ables t hat acco unt f or i mprovements i n m ortality and life expectancy In this particular case, the calculations reported assume t hat l ife ex pectancy a t b irth a nd a t a ge i ncreases b y 1.2 a nd 0.8 years per decade, respectively As a result of taking into account these improvements in mortality and life expectancy, benefit payments to a * Additionally, wages are assumed to grow at 3.5% nominally in line with productivity growth of 1.75% and inflation of 1.75% The discount rate is set at 3.5% offsetting therefore any impact due to differences between discounting and the growth of payments Hence, the changes in annuity payments are only due to changes in life expectancy © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 261 25 year old member in 2005 increased by almost one-fourth with respect to t he c ase when no account for i mprovements a re t aken This increase drops to 3.3% for a year old member This inverse relationship stems from the fact that the exposure of the pension fund to improvements in life expectancy is larger the younger the individual is today Therefore, pens ion f unds w ith a n o lder a ge-membership st ructure will ex perience a s maller i mpact f rom longevity r isk on t heir l iabilities However, they may have less room for maneuver to correct for changes in longevity risk The age composition of the pension fund members is quite important to determine the overall impact of unexpected improvements in mortality and life expectancy The right hand side panel of Table 11.5 shows t he i ncrease i n t he n et p resent va lue o f a nnuity pa yments f or a “theoretical pens ion f und” acco rding t o i ts m embership st ructure This increase is smaller a s t he membership a ges Table 11.5 i ndicates t hat a n unexpected improvement in life expectancy at birth of year per decade could i ncrease pension f und l iabilities by a s much a s 10%.* Taking i nto account that funding regulations of pension funds suggest that a deviation in liability calculations of more than 5% is over the acceptable margins of risk, the impact of longevity risk needs to be reckoned with.† Furthermore, following the results in Section 11.2, there is a 10%–30% chance that the net present value of annuity payment increases by as much as 10%.‡ Additionally, t he i mpact o f l ongevity r isk o n pens ion f und l iabilities is reinforced by reductions in interest rates Pension funds have recently experienced sharp increases in their liabilities as interest rates fell Lower interest rates result in lower discount rates, giving a relatively higher weight to the future As longevity risk is back-loaded, reductions in interest rates increase t he i mpact o f l ongevity r isk o n t he n et p resent va lue o f a nnuity payments In t his regard, Table 11.6 compares t he change in annuity * It is important to recall here that the difference between the projections of life expectancy for 2050 prepared by n ational statistical institutes a nd t he simple extrapolation of p ast trends (Table 11.4) is year per decade † A re cent s tudy by C ass Bu siness S chool ( 2005) c ompares mor tality a ssumptions u sed in c orporate p ension l iability c alculations a cross EU c ountries, C anada, a nd t he United States C onsidering a p ension s cheme w ith a n a ctuarial d eficit £ 200 m (e.g., w ith a ssets of £ 800 m a nd l iabilities of £ 1000 m), c alculated u sing U K’s mor tality a ssumptions, t hey fi nd an increase in the net liabilities of £ 63 m when using French mortality assumptions, but a reduction in net liabilities of £131 m (i.e., net liabilities of £69 m) when using Dutch mortality assumptions ‡ Section 11.2 showed that there is a 10%–30% uncertainty surrounding the likelihood that life expectancy at 65 in 2050 would be year higher than the central forecasts © 2010 by Taylor and Francis Group, LLC 262 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling TABLE 11.6 Impact of Longevity Improvements and Changes in Interest Rates on Annuity Payments Interest Rates Improvements in Life Expectancy 3.5 4.5 5.5 No improvements, latest available mortality table used (2005) Individual aged 65 in 2005 118.6 108.6 100.0 Individual aged 25 in 2005 254.6 158.9 100.0 Life expectancy improves by 1.2 years per decade Individual aged 65 in 2005 122.3 111.6 Individual aged 25 in 2005 312.7 192.6 102.4 119.8 Source: O ECD Note: Percentage c hange in t he net p resent val ue o f a nnuity payments, 2005–2090 payments stemming from different interest rates (i.e., discount rates) with the change due to improvements in life expectancy A 2% point reduction in interest rates increases annuity payments by around 18%–20% points, while a n i mprovement i n t he l ife ex pectancy o f y ears per dec ade increases annuity payments by only 2.4% for a 65 year old individual, and almost 20% for a 25 y ear old individual The combination of both effects can lead to an increase in the net present value of annuity payments of as much a s 213% Hence, l ife i nsurance co mpanies a nd pens ion f unds a re strongly affected by the interest rate-longevity correlation risk.* 11.4 POLICY ISSUES This chapter has shown that the longevity risk, defi ned as the uncertainty surrounding future developments in mortality and life expectancy, has a nonnegligible impact on the liabilities of employer-provided DB pension plans t hrough t heir l ifetime a nnuity payments as t hey depend on the length of t ime people a re ex pected to l ive Section 11.3 provided a measure o f t his i mpact o n t he n et p resent va lue o f a nnuity pa yments for a “t heoretical pens ion f und.” It showed t hat t he ma gnitude of t his impact depends on the age structure of the pension fund membership * The ECB (2005) reports t hat a 0% improvement in longevity leads to a n increase by 5.4 % of t he net present value of t he immediate a nnuity—an immediate a nnuity being a re gular income payable t hroughout life, which is usually secured in exchange for a l ump sum—to meet an annual payment of 10,000€ over 25 years, based on a 3% interest rate With interest rates equal to 5% and 10% respectively, this figure would fall to 4.2% and 2.1% © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 263 As a r esult, pens ion f unds w ith a y ounger m embership st ructure w ill experience a larger impact from longevity risk because the pension fund is ex posed for longer to u ncertain i mprovements i n mortality a nd l ife expectancy Unfortunately, the impact of longevity risk is compounded as few pension p lans acco unt f or f uture cha nges i n m ortality a nd l ife ex pectancy, and those funds that account for improvements only partially Adding t o t he p roblem, pens ion f unds u se m ortality t ables t hat a re almost a dec ade old i n most c ases Moreover, t he t ask of a ssessing t he best way to account for improvements in mortality and life expectancy is complicated by the lack of a common methodology to account for longevity risk In this respect, there is a clear advantage from using a common methodology to forecast mortality rates and life expectancy In this regard, this chapter s a rgued f or u sing a st ochastic m odel a s i t per mits t o a ttach probabilities and thus assess the degree of uncertainty surrounding future mortality and life expectancy outcomes.* Unfortunately, many small and medium-size pension f unds may not have t he financial resources or t he technical c apability t o p roduce f orecasts u sing a co mmon m ethodology Insofar as governmental agencies (e.g., national statistical institutes) have t he resources a nd tech nical c apabilities, t hey could produce t hem However, assumptions regarding the overall populations rather than the specific membership populations of private pension plans may not be o f much use to them Governmental agencies could produce forecasts for the entire po pulation a nd f or d ifferent subg roups acco rding t o g ender, a ge, income, and educational level Hence, different pension f unds could use the co rresponding sub population t hat ma tches i ts c urrent m embership structure more closely However, using mortality tables differentiating according to socioeconomic status and gender has its own problems as it could give rise to problems of d iscrimination A rguments i n favor of d ifferentiating tables in clude t hat u sing a n a verage lif e e xpectancy in dex p enalizes people with higher life expectancy (e.g., women, highly educated and high-income p eople) favoring p eople w ith lower l ife e xpectancy (e.g., men, less educated and low-income people) Moreover, private pension plans need to hedge against t heir own longevity risk, t hat is, t he risk * CMI ( 2005, 006) a nd L ee ( 1998) a lso a rgue for u sing a s tochastic appro ach to fore cast mortality and life expectancy © 2010 by Taylor and Francis Group, LLC 264 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling attached to their own membership structure, instead of an average longevity risk Furthermore, there may be a need for a change in the regulatory framework requiring pension f unds to f ully account for f uture i mprovements in mortality and life expectancy as well as guiding pension funds regarding the type of approaches best suited to forecast those improvements and assess its associated uncertainty Finally, in addition to incorporating improvements in mortality with the help of a common methodology and the use of average or differentiated mortality t ables, t he i mpact of longevity r isk on employer-provided DB plans can be partly offset by indexing pension benefits to life expectancy.* However, indexing benefits to life expectancy shifts part of the longevity risk back to individuals, removing one of the main incentives individuals have to acquire annuities In this regard, differentiating between individual and aggregate or cohort longevity risk can be of help Individual risk is associated to each individual, and it can be easily offset by pooling risks Therefore, it would be more efficiently undertaken if assumed by pension funds, as they are best placed to pool individual specific risks The aggregate or cohort risk, on the other hand, is more difficult to address or hedge against Therefore, this risk is more open to be shared by pension funds and individuals by indexing benefits to cohort longevity changes.† ACKNOWLEDGMENTS The author would like to t hank A ndé Laboul, Fionna Stewart, a nd Juan Yermo f or co mments o n e arlier d rafts He al so th anks d elegates to the Working Party on Private Pensions of t he OECD Insurance and Private Pensions C ommittee f or u seful d iscussions, a nd pa rticipants a t t he OECD/IOPS Gl obal F orum o n Pr ivate P ensions h eld i n Ist anbul o n November –8, 006; t he C hatham H ouse S eminar o n Red istributing the R isk: P ublic a nd Pr ivate A pproaches t o Re tirement Pr ovision h eld in L ondon o n Oc tober –10, 006; t he fift h C onference o n Re gulation and Supervision of Pension Funds held i n L isbon on t he June 22 , 006; * Yet, indexing also brings up the previous discussion related to using average or differentiated mortality tables † Antolin and Blommestein (2007) deal with this issue in the context of whether government should issue longevity bonds to hedge against longevity risk OECD (2005) provides further discussions on t he issue of lon gevity bonds and government involvement Th is issue could be addressed further at the following Working Party in Debt Management (WPDM) and the Financial Markets Committee (CMF) © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 265 the 2006 European Pensions and Investment Submit held in Montreux, Switzerland; as well as participants at ASSAL XVII Annual Meeting held in Lisbon in May 2006 The views expressed herein are those of the author and not necessarily reflect those of the OECD or the governments of its member countries The author is solely responsible of any errors REFERENCES Antolin, P and H Blommestein (2007), Governments and markets in addressing aggregate longevity risk, Forum Financier, Revenue Bancaire et Financier 71, 2007/2 Continuous Mortality Investigation, CMI (2004), Projecting future mortality: A discussion paper, Mortality Committee, Working Paper Continuous M ortality I 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Years FIGURE 11. 1 1950–2003 Life expectancy and mortality rates in selected OECD countries, © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 245 TABLE 11. 2 Life Expectancy,... collection of 26 countries © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 251 11. 2.4 Measuring Uncertainty Surrounding Mortality and Longevity Outcomes The u ncertainty... diseases, and diabetes These are chronic and progressive, and more difficult to treat © 2010 by Taylor and Francis Group, LLC Longevity Risk and Private Pensions ◾ 249 approaches that employ a