The Risks in Defined Contribution. Pension Schemes: International Evidence

Transcription

1 The Risks in Defined Contribution Pension Schemes: International Evidence By Edmund Cannon* and Ian Tonks** September 24 1

2 The Risk in Defined Contribution Pension Schemes: International Evidence Abstract Using data on the returns on financial assets, the paper simulates replacement ratios, to build up a frequency distribution of the pension replacement ratio for individuals saving in a defined contribution pension plan in different countries. These frequency distributions illustrate the risk in the pension replacement ratio faced by an individual who saves in a typical defined contribution pension scheme. JEL Classification: E62, G14, H55 Keywords: Risks, Defined contribution pension schemes, pension replacement ratio 2

3 I Introduction Around the world there has been a trend away from unfunded pay-as-you-go and funded defined benefit schemes towards funded defined contribution schemes. 1 In a defined contribution scheme an individual builds up his or her own pension fund, and at retirement converts this fund into a life annuity. In return for the capital sum, a life annuity pays out an income stream as a pension until death, and hence insures the individual against insufficient assets to finance consumption due to longevity risk. In this paper we compute the pension income that individuals could have achieved from a variety of different savings schemes, using financial data on equity and bond returns for a number of countries. The computation of the pension income is taken relative to earnings net of savings contributions, and is referred to as the pension replacement ratio. Replacement ratio for each year are calculated for a representative individuals who accumulated savings in a defined contribution pension scheme over the previous forty years using historical returns on financial assets in the respective country to generate a pension fund. At retirement this fund is then decumulated using the effective annuity rates at that time, obtained from our annuity rate series. This computation allows us to examine the time series of pension income from a typical defined contribution pension scheme in a number of countries from 19 to 21, and makes a comparison of replacement ratios across different savings schemes. Of course this actual time series of pension replacement ratios is not independent through time, since the series has been constructed from overlapping financial returns. Therefore, using the same data on annuity returns and the returns on other financial assets, the paper simulates replacement ratio data, to build up a frequency distribution of the replacement ratio for individuals in different countries. These frequency distributions illustrate the risk in the pension replacement ratio faced by an individual who saves in a typical defined contribution pension scheme. 1 James (1997), Poterba, Venti and Wise (1998), Miles and Timmermann (1999). 3

4 The rest of this paper is organised as follows. To relate the decumulation phase of a pension to the accumulation phase, in Section X we conduct an analysis of the relationship of annuity rates and the stock market, and calculate for a hypothetical savings plan, the replacement ratio of pension income to earnings from In Section XX we use simulated data to build up a frequency distribution of the replacement ratio. Concluding comments are discussed in Section VIII. II Pension Replacement Ratios We wish to examine how the value of a defined contribution pension schemes builds up over time during the accumulation phase, and we construct the pension funds of a series of hypothetical individuals who save according to a well-specified rules and use these to calculate the resulting pension. Diamond (1977) introduces the concept of a pension replacement ratio, defined as the ratio of the pension income to labour income (net of pension contributions) in the final year of employment. If the savings rate is 1 per cent and pension income is 6 per cent of labour income, then the pension replacement ratio is 6/9 = 2/3 and Diamond suggests that this replacement ratio might be appropriate. Empirically such replacement ratios are common in UK company pension schemes where employees have completed their full set of contributions. The optimal value of the pension replacement ratio is unclear. In a simple utility maximisation framework where agents only wish to smooth consumption flows, the optimal ratio would be one. However, this result does not follow if agents also obtain utility from leisure and utility is not additively separable in consumption and leisure: because leisure discontinuously increases at the point of retirement we should also expect consumption to discontinuously fall. We might note that there are at least two reasons for consumers expenditure to change upon retirement: the elimination of work-related expenditure (commuting etc) and variation in expenditure on leisure activities. Some of these expenditures may be discrete rather than continuous choice 4

5 variables (especially commuting) and hence provide a further reason for discontinuity at the point of retirement. 2 Consider the pension fund of someone retiring at time t, who has contributed a proportion s of their income y t-i in year t i to a fund for the last R years. Each year t j the entire value of the fund (including previous years returns which are reinvested) earns a rate of return rt j. Then the future value of the fund at retirement at time t is R 1 i= i ( 1+ rt j )/( 1 rt ). FV = s y (1) t t i + j= Where r t is the rate of return on savings and we assume that no return is earned on the last year's contribution. Consider the future value of the pension fund. At the start of the first period the pension scheme member contributes a proportion s of current earnings into the fund, and this contribution will be compounded over the next R-1 years to grow each year by the rate of return on savings to a future value at retirement. At the start of the second year, the same proportion s of the second year s earnings will be paid into the scheme and this will be compounded over the remaining R-2 years to grow to a future value. Adding together each of the compounded pension contributions, will yield the the total value of the pension fund at retirement. With a constant rate of return r and with constant income growth so that s ( g) s y = y 1+, the formula for the value of the fund at retirement in equation (1) simplifies to R 1 i= t i+ R 1 i ( 1+ g) ( 1+ r). FV = s y (2) t Applying the formula for the sum of a geometric progression to the future value of the pension 3 ; Then the future value of the pension fund in equation (2) will be. 3 Remember formula for sum of a geometric progression: Let a=sy(1+g) n (1+r) and x=(1+r)/(1+g). If v = a[1 + x + x + x x ] then n+ 1 a[ x 1] v = ; x 1 5

6 4 4 sy (1 + g) 1+ r FV = 1 (3) r g 1+ g Now consider converting that future value FV into an annuity. Suppose the annuity is P% of final earnings which have grown to y (1+g) 39 and expected life is 2 years, then the annuity value is 4 2 Py (1 + i)(1 + g) 1+ g AV = 1 (4) i g 1+ i If we set the annuity value equal to the future value of the pension fund, FV this will provide the solution to the relationship between the amount of the pension and the required savings necessary to generate this pension. We may calculate the savings rate as a function of the pension rate, given that the future value has to be equal to the annuity. Diamond (1977) calls this ratio the replacement ratio. Combining equations (3) and (4) g 1+ r s = P 1 1 (5) 1+ i 1+ g Assuming r = i = 5 per cent; g = 2 per cent, the term in the pair of square brackets is.167, so that the affordable pension rate is 6 times the savings rate. Hence this pair of equations shows the parameter values that will ensure that a savings rate of 1 per cent will generate a pension of 6 per cent. This forms the basis for the so-called, 6:4:2:1:5:2 rule. This states that to generate a pension of 6 per cent of earnings, if the contributions have been made over 4 years and the pensioner expectes to live for another 2 years, then the required savings rate out of earnings is 1 per cent assuming that the return on savings is 5\% and the growth rate of earnings in 2\%. 6

7 In order to construct our simulations, we assume a representative agent works and saves towards the pension for 4 years; and while working and contributing to the pension fund the contribution rate is 1 per cent. The agent will be retired for exactly 2 years; While it is not suggested that any of these assumptions are true for any particular cohort of savers, they are clearly a reasonable approximation to reality. 4 Perhaps surprisingly, the pension that results is almost exactly 6 per cent of final gross income and hence the replacement ratio is 2/3. From the age of 26 to 65, the representative individual saves 1 per cent of their labour income and invest it in some combination of bonds and equity: all returns are re-invested. To account for charges, we assume that there is a 5 per cent charge for purchasing shares, so that the effective savings rate is 9.5 per cent instead of 1 per cent, that there is a 2 per cent charge every year on the equity investments and 1 per cent per year on bonds, and that the spread is zero. These charges are consistent with the estimates of charges found by Chapman (1999). At 65 the agents purchase an annuity at the prevailing annuity rate. We consider three different investment rules: a) Invest entirely in equity; b) Invest half in equity and half in bonds; c) A life-style scheme whereby everything is invested in equity for the first 28 years of saving. Over the next nine years, gradually reduce the proportion in equity and increase the proportion in bonds until everything is in bonds for the last three years. The life-style suggested rule approximates to the suggested rule of many fund managers, who argue that it is too risky to hold equity towards the end of the accumulation phase. III Data We obtained equity and bond returns for a cross-section of international financial markets, from Dimson, Marsh, and Staunton (22) who present a comprehensive and consistent analysis of investment returns for equities, bonds, bills, currencies and inflation, spanning sixteen countries, from the end of the nineteenth century to the beginning of the twenty-first. The countries covers the U.S., the U.K., Japan, France, 4 An additional consideration is the rôle of taxation, which we do not make any allowance for. 7

8 Germany, Canada, Italy, Spain, Switzerland, Australia, the Netherlands, Sweden, Belgium, Ireland, Denmark, and South Africa. The authors analyze total returns, including reinvested income. Mean return for each country in the sample are presented in Table 1. Data on earnings and wage growth for the same countries was obtained from Mitchell (1998) updated by information in ILO yearbooks. We consider a series of hypothetical individuals whose labour income is proportional to their country s average earnings index in each year of their life. Earnings actually vary systematically with age, and Disney and Emmerson (24) estimate the real earnings profile for UK males born between We use this profile and estimates from Miles (1997) for the nineteen nineties. Average wage growth rates for each country are given in Table 2. The UK annuity series are the annual series constructed by Cannon and Tonks (24), based primarily on annuity rates published in the trade magazines Policy and Pensions World. The UK annuity rate for level annuities for 65-year old males is given in Figure 1. Data on US Annuity rates is taken from Mitchell et al (1998), and for Australia from Bateman,.Kingston, and Piggott (21). For other countries estimates of annuities were made from information in James and Vittas, (2), James and Song (21), coupled with data on bond rates. When annuity rates are not available, a synthetic annuity rate is computed from the bond yield. International Evidence on Replacement Ratios Figure 2 shows the UK replacement ratio for the three alternative investment rules. The three graphs show the replacement ratios for a series of individuals who have invested their savings in different portfolios of bonds and equity. So the observations in 1957 are for agents who started saving in 1918 and retired in 1957; and give the replacement ratio for this individual in The observations for 1958 are for different agents who started saving in 1919 and retired in 1958 (and thus faced different wages and rates of return for some of their life. In addition prior to 1957 we do not have UK annuity rates, therefore we construct an additional three graphs of the replacement ratio for each investment strategy, but where we impute an annuity rate from the bond yield. 8

9 These replacement ratios vary throughout the period and lie between.2 and 1.6, with low replacement ratios in the early part of the sample mainly because bond returns were poor. The best strategy was clearly to invest in equity, which earned higher returns, even for most of the 197s. It should also be noted that the steady increase in replacement ratios since 1974 is despite increases in longevity over the last 3 years. Thus individuals retiring in 22 on the same replacement ratio as people 3 years earlier are better off, since they live longer and have a similar or better annual income. Figure 3 shows the Replacement ratio for a series of typical US individuals saving into a pension scheme which annuitised from 1939 onwards. The pattern is very similar to the one for the UK: the equity investment dominates, though at the very end of the sample, the stock market crash of 2 is having a downward effect on the replacement ratio. Figures 4-9 show the actual replacement ratios for a series of countries: 9

10 IV Simulations of Replacement Ratios So far we have calculated replacement ratios from a series of hypothetical individuals retiring between 1972 and 22. We now discuss whether we can use empirical data to say more about replacement ratios. As we have seen in Figure 2, the annuity rate behaves very similarly to the consol rate and we could safely model the annuity rate as the consol rate plus a constant -- in this case 3.21 per cent which is the mean difference over the latter period for which we have data. Having made this assumption about the relationship between the consol rate and the annuity rate, it would be possible to calculate replacement ratio for someone retiring in the last few years so long as we had just three data series: the equity yield, the consol rate and earnings. Using data for 1918 to 2, we estimate the behaviour of the equity yield, the logarithm of the consol rate (using logarithms ensures that this variable is never negative) and the growth rate of earnings in a VAR with a constant but no trend. 5 We use this estimated relationship to conduct two types of simulation. First, we assume that the residuals are normally distributed and use the estimated covariance matrix to generate residuals; second we use a boot-strap style simulation where we randomly sample (with replacement) from the empirical residuals. In each simulation we use 1, replications to calculate the density function of the replacement ratio. Our results for the average of the three different forms of pension saving are shown in table 5. Unsurprisingly the replacement ratio is highest if the pension fund is invested entirely in equity and lowest if invested in half equity and half bonds. Higher replacement ratios, however, are not achieved costlessly: the equity portfolio has the highest risk (measured in terms of standard deviation, not shown here) and the half-and-half 5 None of these variables are obviously trending over the period. Using the Akaike or Schwartz criteria alone we would have chosen only one lag in the VAR, but this model evidenced considerable residual autocorrelation, which was absent in models with two or three lags. Regardless of the number of lags used, there was overwhelming evidence of autoregressive heteroskedasticity and excess kurtosis in the residuals. The latter problem was dealt with individually by using empirical residuals (boot-strapping) in our simulation analysis. Both phenomena are more likely to be due to time-varying risk and a better solution would have been to model the data using a vector-arch process. However, to model a 2-lag VAR whose residuals were ARCH(1) would involve estimating about 5 parameters (depending upon the precise specification) and we had too few observations (8) for this to be a worthwhile exercise. 1

11 portfolio is the least risky. While we can be confident about the relative size of these replacement ratios, the absolute size depends considerably upon which simulation is used. The deciles for the 3-lag VAR simulation using boot-strapped residuals are shown in Table 6, and as a sensitivity test, deciles for the 2-lag VAR simulation using bootstrapped residuals are shown in Table 7. Figure 6 shows the probability distributions from the 3-lag VAR simulation. It can be seen that the equity:bond portfolio investment strategy appears to dominate the other two. In fact we were not able to demonstrate that any investment strategy stochastically dominated any other, because at low values of the pension replacement ratio the values for the alternative strategies intersect. Although for each strategy there is significant upside potential, according to Table 6 there is a ten per cent probability of getting a replacement ration of less than thirty per cent. Tables 6 and 7 demonstrate that the shape of the pension replacement ratio distributions are similar whichever model for generating the simulated data is used. VIII Conclusions In this paper we have constructed a time series of purchased life annuity prices since This is considerably longer than the only other time series for UK annuities that we know to have been published in Murthi, Orszag and Orszag (1999) which included a graph of the best annuity rate for the period Using this series we are able to answer a number of questions. First, have UK annuity rates been fairly priced over the period ? Second, is there any evidence of adverse selection in annuity markets. Third, given the observed annuity rates, how much pension income would a typical individual have been able to generate? Fourth, what is the risk inherent in a defined contribution pension scheme? In answer to the first question we find no evidence that the average annuity rate in the UK over the period has been unfairly low. Depending on the assumptions we make about future longevity, the present value of an annuity is of the order of between 9 per cent and 12 per cent of the purchase price, and has averaged 98 per cent over the sample period. Compared with the typical costs of buying financial services this figure looks suspiciously good: annuity providers must earn a profit and 11

12 cover the real resource costs of annuity provision. It is possible to turn the question of low annuity rates on its head: are in fact annuity rates too high? James and Song (21) argue that in fact life insurers may be able to earn a higher rate of return than the riskless rate that we have assumed from the term structure and hence such money s worths are consistent with annuity providers making profits and covering resource costs. A possible response to this conclusion is that current annuity rates may appear to provide a good money s worth because the latter is calculated using interest rates which are themselves distorted. Second, we have found some evidence of selection effects in the annuity market, as judged by the difference in the money s worth of annuities calculated using population or annuitants life tables. But the degree of these selection effects is small. In answer to our third question, we find no reason to suggest that individuals are worse off by low annuity rates, since this has been off-set by increases in the value of pension funds over the last forty five years. Even apart from the fact that people retiring today expect to live longer, their pension income (compared to their final salary) looks as good as ever. Finally we have simulated financial market data and calculated pension replacement ratios for a large number of independent economies to build up a frequency distribution of the replacement ratio that would be faced by individuals saving through a defined contribution pension plan. We find that the median pension replacement ratio generated by a typical savings plan of 1 per cent of salary saved over 4 years lies between 6 and 1 per cent. Within this distribution there is a great deal of upside potential, but there is a ten per cent probability of getting a pension that is less than 3 per cent of salary. 12

13 Table 1: International Bond and Equity Returns Mean Equity Return StDev Mean Bond Return StDev Australia 9.25% 17.94% 2.9% 13.64% Belgium 4.49% 22.2%.27% 12.51% Canada 7.69% 16.83% 2.22% 1.74% Denmark 6.61% 2.1% 3.56% 12.16% France 6.12% 22.7%.26% 13.45% Germany 9.3% 32.35%.3% 16.1% Ireland 7.% 22.22% 2.3% 15.34% Italy 6.81% 29.55% -.78% 14.69% Japan 9.59% 3.25% 1.36% 21.14% Netherlands 7.84% 21.17% 1.51% 9.72% South Africa 9.25% 22.7% 1.84% 1.59% Spain 5.98% 21.99% 1.95% 12.29% Sweden 1.49% 22.27% 2.98% 12.89% Switzerland 6.44% 19.57% 2.8% 8.4% UK 7.8% 2.8% 2.24% 14.6% USA 9.8% 2.17% 2.8% 9.95% Table 2: International Inflation Rates and Wage Growth Mean Nominal Mean Inflation StDev Wage growth StDev Australia 4.8% 5.51% 5.5% 5.71% Belgium 6.7% 9.37% 3.89% 6.52% Canada 3.27% 4.83% 4.67% 4.85% Denmark 4.29% 6.43% 6.56% 9.55% France 8.49% 12.79% 1.13% 12.77% Germany 2.45% 4.45% 7.56% 8.44% Ireland 4.69% 7.26% 7.9% 6.% Italy 11.8% 36.76% 12.72% 25.78% Japan 11.6% 43.83% 19.99% 57.76% Netherlands 3.14% 4.99% 7.29% 28.89% South Africa 5.9% 7.82% 5.71% 6.49% Spain 6.39% 7.2% 12.71% 7.83% Sweden 4.5% 7.61% 6.7% 7.43% Switzerland 2.6% 5.49% 4.58% 4.48% UK 4.3% 6.91% 5.72% 6.67% USA 3.15% 5.3% 4.6% 5.33% 13

14 Table 3: Simulated Replacement Ratios for Different Investment Styles Equity Half Lifestyle Panel A: UK Mean StDev median Panel B: USA Mean StDev median Panel C: Canada Mean StDev median Panel D: France Mean StDev median Table reports distribution of the pension replacement ratios for simulated data from a 4-lag VAR simulation with bootstrap errors 14

15 References Bateman, H., G.Kingston, and J.Piggott (21) Forced Saving: Mandating Private Retirement Incomes (Cambridge University Press, 21) Brown, Jeffrey R., Mitchell, Olivia S., Poterba, James M. and Warshawsky, Mark J. (21) The Role of Annuity Markets in Financing Retirement (Cambridge: MIT Press). Cannon, Edmund and Tonks, Ian (24) The Construction of UK Annuity Price Series 1957 to 22, Forthcoming Financial History Review Cannon, Edmund and Tonks, Ian (24) UK Annuity Price Series and Pension Replaceement Ratios 1957 to 22, Forthcoming Geneva Papers. Chapman, John (1999) Persistency and charges: exposing the big hitters, Money Management, pp Demery, David, and Duck, Nigel W. (21) Savings Age Profiles in the UK, University of Bristol Working Paper, 1/518. Department for Work and Pensions and Inland Revenue "Modernising Annuities: A Consultative Document", February 22. Diamond, Peter A. (1977) A Framework for Social Security Analysis, Journal of Public Economics, 8, pp Dimson, E., P. Marsh, and M. Staunton (22) Triumph of the Optimists: 11 Years of Global Investment Returns (Princeton University Press). Disney, R. and C. Emmerson, (24) Public Pension Reform in the UK: what effect on the financial well being of current and future pensioners, Paper presented at British Association Festival of Science, University of Exeter, September. Finkelstein, Amy and Poterba, James M. (2) Adverse Selection Insurance Markets: Policyholder Evidence from the UK Annuity Market, NBER Working Paper no. 845 Finkelstein, Amy and Poterba, James M. (22) Selection Effects in the United Kingdom Individual Annuities Market, Economic Journal, 112(476), pp International Labour Office Yearbook of Labour Statistics James, E. (1997) New Systems for Old Age World Bank, Working Paper James, E. and D. Vittas (2) Annuity Markets in Comparative Perspective: Do Consumers Get Their Money s Worth? Development Research Group, World Bank James, E. and Song Xue (21) Annuity Markets Around the World: Money s Worth and Risk Intermediation CeRP Working Paper 16/1. 15

16 Miles, David (1997) A Household Level Study of the Determinants of Income and Consumption, Economic Journal, 17(44), pp Miles, D. and A. Timmerman (1999) Costing pension reform: Risk sharing and transition costs in the reform of pension systems in Europe, Economic Policy, Mitchell, Brian R. (1988) British Historical Statistics (Cambridge University Press). Mitchell, Brian R. (1998) International Historical Statistics: Europe; The Americas; Africa, Asiana and Oceania; 175- (Basingstoke: Macmillan) Mitchell, Olivia S., Poterba, James M., Warshawsky, Mark J. and Brown Jeffrey R. (1999) New Evidence on the Money s Worth of Individual Annuities, American Economic Review, 89, pp This article is reprinted in Brown et al (21). Murthi, Mamta, Orszag, J.Michael and Orszag, Peter R. (1999) The Value for Money of Annuities in the UK: Theory, Experience and Policy, Birkbeck College, London. Discussion Paper. Poterba, J. M. (21) Annuity Markets and Retirement Security, Fiscal Studies vol. 22, no. 3, Poterba, J.M., S.F. Venti and D.A. Wise (1998), 41(k) plans and future patterns of retirement savings, American Economic Review, vol. 88, no. 2, Stark, J. (22) Annuities: the consumer experience, ABI Research Report, (ISBN ) Warshawsky, Mark J. (1988) Private Annuity Markets in the United States: , Journal of Risk and Insurance, 55 (3), pp This article is reprinted in Brown et al (21) Yaari, M. (1965) Uncertain lifetime, life assurance, and the theory of the consumer, Review of Economic Studies, vol. 32, no. 2,

17 Figure 1: UK Annuity Rate, Male 65, level 18% 16% 14% 12% 1% 8% 6% 4% 2% Mean annuity rate, gtd 5 years, no stale prices Consols (2½% until 1992, then 3½% War loan) Median Annuity Rate, no gtee % q1 Figure 2: UK Replacement Ratio Annuity: Equity Fund Bond Yld + 3.5%: Equity Fund Annuity: Bond Fund Bond Yld + 3.5%: Bond Fund Annuity: Lifestyle Fund Bond Yld + 3.5%: Lifestyle Fund

18 Figure 3: USA Replacement Ratio Annuity: Equity Fund Bond Yld + 3.5%: Equity Fund Annuity: Bond Fund Bond Yld + 3.5%: Bond Fund Annuity: Lifestyle Fund Bond Yld + 3.5%: Lifestyle Fund Figure 4: Japan Replacement Ratio nb only make sense after 1966, since no wages before Bond Yld + 3.5%: Equity Fund Bond Yld + 3.5%: Bond Fund Bond Yld + 3.5%: Lifestyle Fund

19 Figure 5: Canada Replacement Ratio Bond Yld + 3.5%: Equity Fund Bond Yld + 3.5%: Bond Fund Bond Yld + 3.5%: Lifestyle Fund Figure 6: France Replacement Ratio Bond Yld + 3.5%: Equity Fund Bond Yld + 3.5%: Bond Fund Bond Yld + 3.5%: Lifestyle Fund

20 Figure 7: Germany Replacement Ratio Bond Yld + 3.5%: Equity Fund Bond Yld + 3.5%: Bond Fund Bond Yld + 3.5%: Lifestyle Fund Figure 8: Australia Replacement Ratio Annuity: Equity Fund Bond Yld + 3.5%: Equity Fund Annuity: Bond Fund Bond Yld + 3.5%: Bond Fund Annuity: Lifestyle Fund Bond Yld + 3.5%: Lifestyle Fund

21 Figure 9: Replacement Ratios (Equity Fund) Maxima, minima and mean Australia Canada France Germany Italy Japan UK USA Figure 1: Frequency Distribution UK Replacement Ratio Equity Half Equity, Half Bonds "Lifestyle"

22 Figure 11: Frequency Distribution US Replacement Ratio Equity Half Equity, Half Bonds "Lifestyle" Figure 12: Frequency Distribution France Replacement Ratio Equity Half Equity, Half Bonds "Lifestyle"

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