# Archived - Retirement Savings Research Program

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27 November 2009
Malcolm Hamilton

Summary
Investment and Longevity Risks Section 1 - Investment Risk
Section 2 – Longevity Risk

## Summary

#### Longevity Risk from Three Perspectives -- by Malcolm Hamilton

This paper presents an analysis of the investment risk and the longevity risk.

On the investment risk, the paper discusses the sensitivity of the contribution rates to different parameters for both a fully funded and a pay-as-you-go pension plan. A benchmark plan targeting a 50 per cent replacement rate (riskless nominal rate of interest is 4 per cent) is used, for which the steady state contribution rates are 23.8 per cent for a fully funded plan and 31.7 per cent for a pay‑as-you-go plan.

It is observed that a fully funded plan is generally less expensive on the long term than a pay‑as‑you‑go plan. However, contribution rates under a pay‑as‑you‑go plan are more stable on the short-to-medium term since the rate of growth on which they rely are less volatile than interest rates (or rates of return). The second observation is that the plan can be made significantly less expensive by increasing the age of retirement or reducing the level of post-retirement indexing. In absence of risk taking, an individual making the maximum 18 per cent RRSP contribution would have to retire at the age of 70 to benefit from a 50 per cent replacement rate and a full inflation protection.

By investing 50 to 70 per cent in risky assets with the objective to increase the rate of return of the fund to 6 per cent, the benchmark contribution rate can be reduced from 23.8 per cent to 13.3 per cent. The cost associated with the risk can be borne by beneficiaries (defined contribution), sponsors (defined benefit), or both (hybrid plans). Since making no risky investment would result in plans that are too expensive, a trade off must be made between stable contributions and stable benefits.

The second part of the paper discusses longevity risk and its implications for the individual, the sponsors, and the society. For retired individuals who must convert their savings into an income for life, longevity is an important risk. Two methods for managing it at the individual level are explored: purchasing annuities and indexing income. Annuities increase a retirement saver's income and confidence in not outliving his savings, although their use has been limited (annuities are illiquid, heirs receive small amount in case of early death, adverse selection increases the price). Encouraging seniors to fully inflation-protect their retirement savings may be unnecessary and unwise since their C/QPP and OAS are already fully indexed. The CPI may also overestimate the rate of increase in spending required to maintain a senior citizen's standard of living.

Another finding is that the longevity risk is often ignored by plan sponsors due to its lack of relative importance, the difficulty in measuring changes in mortality rates and the absence of tools to manage the risk once it is fully appreciated.

Finally, an increase in longevity without a commensurate increase in retirement age will cause the fiscal position of governments to deteriorate. However, some of the issues resulting from linking longevity with retirement age (e.g. women retiring later than men) are highlighted. It is important to distinguish between life expectancies and healthy life expectancies. It is possibly more relevant to link retirement age to healthy longevity instead of increases in life expectancies.

## Investment and Longevity Risks

### Introduction

Retirement savings plans are exposed to significant risks regardless of how they are designed, organized or funded. Funded arrangements1 are exposed to investment risks. Unfunded arrangements2 are exposed to fertility and productivity risks. All are exposed to longevity risk, i.e., the risk that beneficiaries will live longer than expected.

Some risks can be pooled to advantage. Many cannot. The investment risk associated with a large diversified portfolio is proportionally larger than the investment risk associated with smaller diversified portfolios. The risks associated with unexpected increases in longevity are not appreciably diminished by combining small groups into larger ones. The largest pension plans enjoy the advantages of scope and scale, both of which are important; but large funds are exposed to investment and longevity risks commensurate with their size.

Risks that cannot be eliminated through diversification, pooling or hedging must ultimately be borne by individual contributors, beneficiaries, shareholders, creditors3 and/or taxpayers. Losses can be temporarily ignored, shifted from one generation to the next, divided between employers and employees in a variety of ways and/or spread over long periods of time; but ultimately they must be borne by individuals. Defined benefit pension plans can shift the burden of risk bearing from employees to employers. Public sector pension plans can shift risks from today's public sector workers and pensioners to tomorrow's taxpayers. An expanded Canada Pension Plan (CPP) can shift costs and risks to future generations of contributors. Individual retirement savings plans and defined contribution pension plans expect each generation of participants to bear their own costs and their own risks; but no matter how the plan is organized, funded and/or managed, unless the world becomes more predictable the risks will be large.

The challenge, then, is not to eliminate risk. It is to establish a system that can adapt to changing circumstances, manage the risks that can be managed and allocate cost between generations in an equitable way. A retirement system should not strive for timeless perfection. This is not now, and may never be, within our grasp. A fair, efficient and durable system – one that can be sustained with the efforts and support of future generations – would be a good start.

This paper is organized in sections.

• Section 1 looks at investment risk, the largest risk to which funded pension plans are exposed.
• Section 2 looks at longevity risks from three perspectives: individual retirement savers, the sponsors4 of defined benefit pension plans and public policy.

## Section 1 – Investment Risk

Investment risk5 is the largest risk to which funded retirement savings plans are exposed. Plans delivering fully indexed pensions6 struggle when real rates of return are less than expected. Plans delivering fixed pensions struggle when nominal rates of return are less than expected.

In this section we examine the contribution rates required to support retirement savings plans and the sensitivity of these contribution rates to:

• how the plan is funded (fully funded versus pay-as-you-go funding),
• the target benefit as specified by the expected replacement ratio,7 the age at which the pension starts and the level of post retirement inflation protection,
• for fully funded pension plans:
• the rate of return on the pension fund, and
• the rate at which salaries grow, and
• for plans funded on a pay-as-you-go basis:
• the rate of growth in the population, and
• the rate at which salaries grow.

The model is the simplest imaginable. Employees

• enter the plan (or begin to save for retirement) at age 30,
• retire at the age at which unreduced pensions are payable (which depends on the design of the pension plan), and
• die at age 90.8

Unless otherwise indicated:

• the cost of living is assumed to increase by 2% per annum, in line with the Bank of Canada's targets and the experience of the last 15 years;
• wages increase at the rate of 3% per annum9; and
• the target replacement ratio is 50%10 which, when combined with CPP and Old Age Security (OAS), lifts the total replacement ratio above 70% at retirement.

### Benchmark Plans and Benchmark Contribution Rates

For the purposes of this section the benchmark plan will be one which targets a 50% replacement ratio at age 65 with full post-retirement inflation protection. The benchmark plan is more expensive than one typically finds in the private sector, even among private sector employers with defined benefit pension plans, and less expensive than one typically finds in the public sector.

The benchmark contribution rate is the "steady state" contribution rate that would be observed in an environment where

• the plan membership is stable (i.e., 0% population growth), and
• the riskless long- term nominal interest rate is 4% (i.e., the riskless real interest rate is 2%), a rate that is consistent with the yields to maturity recently available on long- term Canada bonds.

The steady state contribution rate is the contribution rate (expressed as a percentage of pay) that is needed to support a fully mature plan in this stable environment.

• If the plan is funded on a pay-as-you-go basis the steady state contribution rate is the level to which the contribution rate will gradually increase at the end of the 30 to 70 year period typically required for a pension plan to mature,
• if the plan is fully funded and invested in riskless assets,11 the steady state contribution rate is the level contribution rate needed to fully fund the pension plan at the riskless interest rate.12 This contribution rate will not change unless the riskless interest rate changes, and
• if the plan is fully funded and invested in risky assets, the steady state contribution rate is the contribution rate needed to fully fund the plan if, each and every year, it earns the expected rate of return on the plan's investments. This should be interpreted as the middle of the wide range in which contribution rates must move in order to address the gains and losses inevitably produced by risky assets.

For the benchmark plan, the steady state contribution rates are

 Fully funded at riskless (4%) interest rates 23.8% of pay Pay-as-you-go funding 31.7% of pay

### Benchmark Cost – Fully Funded Arrangements

The steady state contribution rate required to support a fully funded benchmark plan is very sensitive to changes in the expected rate of return on the pension fund and somewhat sensitive to changes in the rate at which salaries grow.

Expected Rate of Return on Investment (nominal) Salary Growth 4% 5% 6% 7% 2% 19.8% 14.7% 10.9% 8.0% 5.9% 3% 23.8% 17.8% 13.3% 9.9% 7.4% 4% 28.3% 21.4% 16.1% 12.2% 9.1%

Each 1% change in the rate of return on investment changes the benchmark contribution rate by about 30%. This means that contribution rates will be neither stable nor predictable in a fully-funded pension plan.

• If the pension fund is invested in riskless assets, the cost will fluctuate as riskless interest rates change.13 Between 1992 and 2009 the real yield on Government of Canada real return bonds fluctuated between 1.5% and 5%. The corresponding range for the benchmark contribution rate is 10% to 25% of pay.
• If the pension fund is invested in risky assets there is significant doubt about both the rate of return that can be earned in the future and how this rate will change with the passage of time. The Ontario Teachers' Pension Plan recently valued benefits using a 3.5% assumed real rate of return on investment while CALPERS (the pension plan covering employees of the State of California) recently valued similar benefits using a 6% assumed real rate of return on investment. The corresponding range for the benchmark cost would be 7.5% of pay to 15% of pay. In addition, actual rates of return can differ materially from the expected rate of return over long periods (25 years or more) and contribution rates will need to wander far from the benchmark contribution rate to address gains and losses.

### Benchmark Costs – Pay-as-you-go Funding

Plans funded on a pay-as-you-go basis are not exposed to investment risks but they are exposed to changes in the rate of salary growth14 and in the rate of population growth.

Rate of Population Growth Salary Growth (nominal) 0% 1% 2% 35.7% 26.4% 19.5% 3% 31.7% 23.6% 17.5% 4% 28.3% 21.2% 15.8%

Since rates of population growth are less volatile than interest rates and/or rates of return on investment, plans funded on a pay-as-you-go basis have contribution rates that are more stable and more predictable in the short-to-medium term. In the long term uncertainties about fertility rates, workforce participation rates and productivity growth rates cause pay-as-you-go contribution rates to be highly uncertain.

The benchmark cost is lower on a fully funded basis than on a pay-as-you-go basis provided that

Rate of Return > (1 + population growth) (1 + salary growth) – 1

As this is usually (but not always) the case over long periods, full funding will normally deliver lower long term costs, which is not surprising given the substantially higher investment.15

### Impact of Plan Design on Contribution Rates

With a fully funded riskless cost of 23.8%, the benchmark plan would be viewed as too expensive by most employers and employees. Without changing the 50% target replacement ratio, the plan can be made substantially more or less expensive by changing the retirement age and/or reducing the level of post-retirement indexing.

Retirement Age Level of Post-Retirement Indexing 57 60 62 65 0% (CPI-2%) 30.0% 25.3% 22.7% 19.1% 17.0% 1% (CPI-1%) 34.3% 28.7% 25.5% 21.3% 18.8% 2% (full CPI) 39.5% 32.7% 28.8% 23.8% 20.9%

For example, the cost of the benchmark plan can be reduced from 23.8% of pay to 17% of pay by increasing the retirement age from 65 to 67 and by indexing pensions by CPI-2% instead of providing full inflation protection. Conversely, by reducing the retirement age from 65 to 60 the cost can be increased from 23.8% of pay to 32.7% of pay.

Among other things this means that in the absence of risk taking someone making the maximum 18% RRSP contribution rate from the age of 30 cannot hope for an inflation protected pension replacing 50% of pre-retirement income until approximately the age of 70.17

### Investment Risks and Rewards

To produce a good pension starting at the ages at which most Canadians would like to retire (60 to 65) is very expensive in a world with low real interest rates, slow (or no) population growth and salaries that grow slowly in real terms. Pay-as-you-go funding will generate the equivalent of a 3% return (1% real) if the population is stable and salaries increase by 3% per annum. Long term Canada Bonds do a little better at 4% (2% real), but not much. We are a long way from the 1960s and 1970s when a rapidly growing workforce and rapidly increasing real wages made it possible to offer pay-as-you-go pensions at attractive prices. We are a long way from the 1980s and the 1990s when high real interest rates and a lengthy bull market made fully funded pensions appear inexpensive. While we can always hope for the return of happier times, we cannot rely on this happening in the foreseeable future.

Most of today's retirement plans, defined benefit and defined contribution alike, try to make good pensions affordable by investing 50% to 70% of the fund in risky assets thought to offer higher rates of return in the long term, albeit with commensurately higher risks. The objective is typically to increase the rate of return on the pension fund by about 2% net of fees and to use some combination of risk management, patience,18 fluctuating contribution rates (defined contribution plans), fluctuating benefits (defined benefit plans) or both (hybrid pension plans) to deliver an acceptable compromise between affordability and stability.

Increasing the expected rate of return by 2% reduces the steady state contribution rate by about 40%.

Retirement Age Level of Post Retirement Indexing 57 60 62 65 0% 18.0% 14.9% 13.2% 10.9% 9.6% 1% 20.2% 16.6% 14.6% 12.0% 10.5% 2% 22.9% 18.7% 16.3% 13.3% 11.6%

The 40% reduction in contribution rates comes with a hidden cost. The risk that must be taken to earn an additional 2% per annum net of fees is large in both the short and long terms. Risks of this magnitude are not easily finessed or ignored. Ultimately they must be borne by someone – employees, pensioners, shareholders or taxpayers.

For example, consider the benchmark plan (fully indexed with retirement at 65). The riskless contribution rate is 23.8% of pay. The risky contribution rate is 13.3% of pay. The difference, 10.5% of pay, is a measure of the economic value attached to the risks that must be borne by some combination of beneficiaries (in defined contribution plans), sponsors (in defined benefit plans) or both (in hybrid plans). Both individual retirement savers and pension plan sponsors voluntarily choose to take these risks suggesting that, rightly or wrongly, they believe that the expected reward (10.5% of pay) is ample. However, investment risks were not evident during the long bull markets of the 1980s and the 1990s and this may have engendered a false confidence in the ability of employers and employees to bear these risks. Even those who remembered the more difficult 1960s and 1970s did not fully appreciate the extent to which the maturation of pension plans during the 1980s and the 1990s increased their vulnerability to investment disappointments.20

Looking at the most recent five decades we find

Period Average Real Rate of Return on the Median Canadian Pension Fund1

1960s 3.0%
1970s 0.1%
1980s 7.0%
1990s 8.8%
2000s (9 years) 1.8%

1960 – 2008 4.1%

1 Geometric averages, before expenses Canadian Institute of Actuaries Survey of Economic Statistics - 2009

A 4% real rate of return, net of expenses, is reasonably consistent with the experience of the last half century, but in any one decade the real rate of return can be as high as 9% or as low as 0%. Even for periods as long as 20 years the average real rate of return can differ from the expected value by 3.5% per annum, or more. The pension plan that relies on investment risk to make the average contribution rate affordable (for defined benefit pension plans) or the average retirement benefit adequate (for defined contribution pension plans) must be prepared for periods lasting 20 years or longer with decidedly substandard returns and, as a consequence, very high contribution rates and/or pensions that are well below target.

One advantage frequently cited for defined benefit pension plans is the intergenerational pooling of investment risk – a capability which allegedly allows defined benefit pension plans to take larger risks, earn higher returns and enjoy lower contribution rates. To some extent this is true, but it is not the overwhelming advantage it is sometimes said to be. Contribution rates move in a wide range and the intergenerational differences remain large even after the risk has been pooled. Moreover, the ability to pool risks across generations often leads, in the absence of governance structures that adequately protect the interests of future generations, to a deliberate or inadvertent shifting of cost from today's contributors to tomorrow's contributors.

Returning to the benchmark plan, to lower the steady state contribution rate from the pay-as-you-go level (31.7%) to the fully funded steady state rate (13.3%) the pension plan must maintain a pension fund equal to 6.4 times payroll invested in assets that are sufficiently risky to increase the rate of return on the pension fund by 2% net of expenses. If the fund fails to perform as expected, surpluses and/or deficits arise. These cannot be ignored in the belief that future gains will somehow compensate for past losses.21 If, in a particular year, the pension fund earns -4% instead of the expected 6%, the 10% shortfall will, if the fund earns 6% per annum thereafter, cause the pension fund to run out of money in 80 years unless contribution rates are increased to address the deficiency. The investment gain needed to counteract a 10% loss increases the longer the loss is ignored.

Years Between the Loss and the Subsequent Gain Gain Needed to Counteract a 10% Shortfall at the Start of the Period

1 year 11%
10 years 15%
20 years 22%

If the benchmark plan starts a 20 year period fully funded and earns 4% per annum less than the 4% expected real rate of return (i.e., a 0% real rate of return for 20 years)22 and if this shortfall is ignored,23 the funding shortfall at the end of 20 years would be about 2.8 times payroll and the contribution increase required to address the shortfall would exceed 8% of pay in perpetuity, thereby increasing the contribution rate from 13.3% of pay to 21.3% of pay for all future generations of participants.

The bottom line: based on extensive stochastic modelling, funding with risky investments can reduce the benchmark contribution rate from the 31.7% pay-as-you-go rate to 13.3% of pay, but contribution rates will then move in a wide range bounded by 0% at the low end and by something larger than 31.7% at the high end. Taking investment risk dramatically reduces average contribution rates but not peak contribution rates, i.e. the rates that plan sponsors must be prepared to episodically endure. In fact, peak contribution rates may be significantly increased if funding regulations, such as Canada's solvency funding rules, require deficiencies to be made up over relatively short periods (5 years in the case of solvency deficiencies in Canada).

### Conclusion

The contribution rate required to fund a defined benefit pension plan is unlikely to be stable in the long run regardless of how the plan is funded or how the assets are invested. In a period characterised by low fertility rates, low productivity growth and low interest rates, good pensions will be expensive pensions.

Plan sponsors can pursue high risk investment strategies in the hope that the reward for risk taking will make their pension plans affordable. In normal times this strategy will work, but the sponsor choosing this road must be prepared for challenging periods when contribution rates exceed, perhaps significantly, the pay-as-you-go contribution rate, and do so for an extended period of time. In the current environment, the pay-as-you-go contribution rate can be two to three times the "normal" cost of the plan; so sponsors need to be prepared to endure high contribution rates for long periods if the investment returns disappoint.

Contribution rate risk can be mitigated or eliminated by shifting some or all of the risk to beneficiaries (as is done in hybrid pension plans and defined contribution plans) but the price for stable, predictable contribution rates is unstable, unpredictable pension benefits.

## Section 2 – Longevity Risk

This section examines longevity risk from three perspectives:

• the perspective of individuals trying to determine the income that can safely be drawn from their accumulated savings without running unacceptable risks of outliving their money,
• the perspective of the sponsors of defined benefit pension plans the cost of which depends on the life expectancies of beneficiaries, and
• the perspective of society at large, where the cost of government programs and the sustainability of fiscal policies depends to some extent on the relationship between the age at which citizens retire and the age at which they die.

### 2.1. The Individual Perspective

According to the mortality table most commonly used for valuations of defined benefit pension plans24 in Canada, the life expectancies25 for males and females who have attained the age of 65 are as follows:

Without Provision for Future Mortality Improvement With Provision for Future Mortality Improvement26 (Years) Male Life Expectancy at 65 18.5 19.4 Female Life Expectancy at 65 21.3 21.9

The more we know about individuals the better we can estimate their life expectancies. Women live longer than men. Non-smokers live longer than smokers. University graduates live longer than elementary school graduates. Teachers live longer than forestry workers. Healthy, fit Canadians live longer than those who are overweight and suffering from chronic medical conditions. Still, with the exception of the terminally ill, at age 65 few can accurately predict the age at which they will die.

While averages are useful in estimating the liabilities of pension plans and insurance companies, they are not very useful for individuals trying to determine how much they can prudently withdraw each year from their accumulated retirement savings. Most 65 year old individuals will die well before, or well after, their life expectancy at retirement.

The following table shows the life expectancies, as well as the 50th, 90th, 95th and 99th percentiles for the number of years of remaining life at age 65 based on the UP94 Table and based on a mortality table that was developed for the Ontario Teachers' Pension Plan in 2005.27

The UP94 Mortality Table Ontario Teachers Mortality Table No Allowance for Future Improvement With Allowance for Future Improvement No Allowance for Future Improvement With Allowance for Future Improvement Male Female Male (years) (years) (years) Life Expectancy 18.5 21.3 19.4 21.9 20.7 23.8 21.9 24.9 Median 19.0 22.3 20.0 23.0 21.5 24.9 23.2 26.2 90th Percentile 29.5 32.3 30.6 33.0 30.8 34.6 31.6 35.3 95th Percentile 31.9 34.7 33.0 35.3 33.0 36.8 33.6 37.3 99th Percentile 36.3 38.8 37.1 39.3 36.6 40.4 36.9 40.8

From Table 1 we can see that, for those retiring at the age of 65,

• twenty to twenty-two years is a typical life expectancy,
• women typically live two or three years longer than men,
• allowing for future mortality improvements adds about one year to life expectancies,
• approximately one in ten Canadians will live ten or more years past their normal life expectancy,
• approximately one in one hundred Canadians will live more than fifteen years beyond their normal life expectancy, and
• Ontario's teachers have low mortality rates and these low rates are improving more quickly than suggested by the standard AA improvement scale, particularly for women.

Most Canadians enter retirement as couples and must plan for an income that continues until the death of the last survivor. If we assume that spouses are the same age and opposite sexes, the life expectancies at age 65 for the last survivor, and the various percentiles, are as shown in Table 2.

The UP94 Mortality Table Ontario Teachers Mortality Table No Allowance for Future Improvement With Allowance for Future Improvement No Allowance for Future Improvement Life Expectancy 25.1 25.9 27.3 28.4 Median 25.5 26.5 27.8 28.9 90 th Percentile 33.5 34.3 35.3 35.9 95 th Percentile 35.6 36.3 37.2 37.7 99 th Percentile 39.4 39.9 40.5 40.9

As can be seen from the table, for a 65 year old opposite-sex couple

• the last survivor is expected to live for about 25 years (to age 90);
• allowing for future mortality improvement adds about one year to the life expectancy:
• approximately one in ten couples will have a last survivor who lives 8 years beyond the normal life expectancy;
• approximately one in one hundred couples will have a last survivor who lives 14 years beyond the normal life expectancy.

### Converting Savings to Life Incomes

Longevity risk becomes relevant when retirement savers devise strategies for converting their accumulated savings into lifetime incomes. The saver can buy an indexed life annuity,28 an unindexed life annuity or adopt a strategy for investing the money and drawing it down gradually over the saver's remaining lifetime. The fact that the length of the remaining lifetime is highly uncertain is a significant complication in devising an effective withdrawal strategy, i.e., a strategy that delivers an adequate post-retirement income without running unacceptable risks of exhausting one's savings before death.

While few Canadians can accurately estimate, at retirement, the age at which they will die, longevity risks are not a serious concern for many.

• Those with below average incomes will typically rely on public pensions (OAS, GIS and the C/QPP) most of which are payable for life.
• Members of generous defined benefit pension plans, in particular those in the public sector, will receive most of their retirement income from private and public pensions that are payable for life.
• Many Canadians retire with more-than-adequate savings, conclude that they are unlikely to outlive their savings (or even to encroach on capital) and realize that their longevity risk is modest and will ultimately be borne by their heirs.

For the remainder of this section we assume that savers can earn a riskless 5% return on investment29 and that the Consumer Price Index (CPI) increases at the rate of 2% per annum. We use the Unisex UP94 Mortality Table30 with provision for future improvements based on scale AA. For a 65 year old individual, the income that can be generated by $1 of retirement savings depends on the withdrawal strategy as follows.  Unindexed Indexed Annual Income from the Purchase of a Life Annuity31 8.2% 6.7% Annual Withdrawal for A Given Probability of Dying Before the Money is Exhausted 50% 7.4% 6.2% 90% 6.1% 4.8% 95% 5.9% 4.6% 99% 5.7% 4.3% As discussed later, the annuity income identified in Table 3 represents a theoretical possibility, not the commercial reality of purchasing an annuity in Canada. We have ignored expenses, profit margins and adverse mortality selection which, taken together, might reduce the annuity income by 10% or more. Returning to Table 3, an individual purchasing an indexed life annuity can, at least in theory, hope to receive an income equal to 6.7% of the annuity premium and can be confident that this income will continue for life and will be fully protected from increases in the CPI. The individual who chooses not to buy an annuity can instead withdraw 4.8% of his retirement savings in the year of retirement and increase the annual withdrawals by the assumed 2% increase in the CPI thereafter with a 90% probability of dying before his or her retirement savings are exhausted. Table 4 is similar to Table 3, but it is constructed for a couple considering the purchase of a joint and 66-2/3% annuity32 or, alternatively, a withdrawal strategy where the amounts withdrawn after the first death are 2/3s of what they were before the first death.  Unindexed Indexed Annual Income from the Purchase of a Joint and 66-2/3% Annuity 7.8% 6.4% Annual Withdrawal for A Given Probability of Dying Before the Money is Exhausted 50% 7.2% 5.9% 90% 6.2% 4.8% 95% 6.0% 4.6% 99% 5.8% 4.3% For example, a couple purchasing an indexed joint and 66-2/3% annuity can, at least in theory, receive in the first year an annual income equal to 6.4% of the annuity premium increasing thereafter at the rate of increase in the CPI. Alternatively, they can invest the money at a riskless 5% interest rate and withdraw 4.8% in the first year with the withdrawals increasing thereafter at the rate of growth in the Consumer Price Index33 with a 90% probability that the last survivor will die before the couple's savings are exhausted. ### The Advantages of Annuitization The advantages of purchasing an annuity are apparent if one compares the withdrawal rates associated with a particular level of confidence that a couple will die before running out of money to the income generated by the corresponding annuity.  Individual Couple34 Probability of Dying Before Running Out of Money Unindexed Indexed Unindexed Indexed 90% 26% 28% 21% 25% 95% 28% 31% 23% 28% 99% 31% 36% 26% 33% Thus, even those who can accept a 90% probability of dying before their savings are exhausted will need to cut their incomes by 20% to 30% relative to the income they theoretically could enjoy by purchasing an annuity. This simplistic analysis exaggerates the advantages of purchasing annuities in two important respects. First, it ignores many of the costs built into annuity prices, including distribution costs, profit margins and differences between the lower rates of mortality built into annuity rates35 and the higher rates of mortality experienced by typical retirement savers. Second, it ignores the source of the annuity's advantage – the ability to use gains from annuitants who die young – gains that would otherwise have gone to their heirs – to support the above-average costs for annuitants who live to advanced ages. Retirement savers can increase their incomes, and their confidence that they will die before running out of money, by buying an annuity. In exchange, they reduce or eliminate the amounts available to those they leave behind. ### Indexed versus Unindexed Incomes Given a choice between an indexed income stream starting from a lower level and an unindexed income stream starting from a higher level, it is unclear which of the two a senior should prefer. Normally it would be prudent to opt for the income that increases with consumer prices, thereby preserving the purchasing power of one's income. However indexed annuities have never been popular, presumably because unindexed annuities deliver higher incomes in the first decade of retirement. It is also possible that seniors believe that their post-retirement expenditures will increase less quickly than increases in the CPI either because • the rate of increase in the price of the basket of goods purchased by seniors is lower than the rate of increase in the price of the basket of goods represented by the CPI or, more probably, • individuals naturally consume less as they age. Without taking a position on the merits of these arguments, if the CPI overestimates the rate of increase in the spending required to maintain a senior's standard of living even slightly, a strong argument can be made for partial inflation protection. For example, suppose a couple retires with a total income that is twice the income generated by government pensions (C/QPP and OAS). Suppose the income generated by their own savings is fixed (or is indexed at CPI -2%). Since half of their income initially comes from fully indexed government pensions (with this percentage increasing each year as their indexed public pensions grow more quickly then their frozen annuity incomes) the real decline in gross family income over 20 years is 17%, about 0.9% per annum. The rate of decline in their after tax income would be even smaller. Seniors need protection from unexpected increases in the cost of living but they do not necessarily need incomes that maintain their purchasing power. Pensions growing by the rate of increase in the CPI minus 2% might provide a reasonable stream of income while protecting seniors in the event that inflation exceeds the Bank of Canada's 2% target. ### Limitations of Annuities and Annuity Markets Table 5 makes the case for annuitization to manage individual longevity risk. This is neither surprising nor new; most experts have long felt that annuitization should play a larger role in the financial plans of seniors than it does. Yet, despite the urging of experts and the efforts of the life insurance industry, Canadians have been reluctant to buy annuities. Indeed, as the requirements to buy annuities with funds in RRSPs and registered pension plans have been relaxed or eliminated, individuals have exhibited a strong preference for RRIF-like withdrawal schedules. There are many reasons for this. • Many retired Canadians rely on government pensions and/or employer sponsored defined benefit pension plans36 for most of their income. They have no longevity risk arising from this income. The risk of not annuitizing the small portion of their income derived from individual savings is of little consequence. • Once purchased, an annuity is illiquid and seldom comes with investment options. Seniors may be understandably reluctant to lose control of their savings. • Annuity prices are not attractive, particularly when interest rates are low. Participants can expect a return comparable to the rate of return on long term Canada bonds. The prices of indexed annuities and annuities for those with substandard mortality are particularly unattractive.37 Since annuities are largely purchased by those with reason to believe that they will live a long life, annuitant mortality is better than population mortality and annuity prices may be unattractive even for those with normal life expectancies. To a limited extent, adverse selection can be addressed through underwriting, medical exams and risk classifications, but trying to separate those with normal life expectancies from those with abnormal life expectancies is a challenge. • Many seniors are uncomfortable with the death benefits in annuity contracts. If the annuitants die young their heirs receive little or nothing. There are options38 that address these concerns, but they also reduce the annuity's principal advantage – the ability to deliver a large guaranteed lifetime income for each$1 of premium.
• It is not easy to persuade seniors to worry about the dangers of long life. Asked to choose between dying young and rich and dying old and poor, most will choose the latter. As a rule, seniors plan for a long life, live frugally, save money throughout their retirement years, spend less as they age and try to preserve their wealth for a variety of reasons. Annuities would let them spend more with confidence – but this may not be their goal.

Finally, annuities are of little interest to families who retire with more money than they need. These families conclude early in their retired lives that they are unlikely to consume their savings no matter how long they live. The risks they take in their twilight years, including longevity risk, will ultimately be borne by their heirs.

### Variable Withdrawal Strategies

Rather than purchasing an annuity, many Canadians choose to withdraw funds from their RRSPs on an "as needed" basis or according to some withdrawal schedule. Those drawing most of their retirement income from public or workplace pensions will often draw their RRIF down using the minimum withdrawal schedule imposed by the Income Tax Act while reserving the right to withdraw larger amounts for special purchases or special occasions.

One of the most difficult tasks facing a retiring couple is deciding how to manage their RRSP/RRIF withdrawals to provide the right amount of money as and when it is needed.

• Focussing on the simplest case, suppose a couple has all of its money in the RRSP of one spouse and that the objective is to use this money to supplement their public pensions. This might be done in a number of ways.39
• They might withdraw only their investment income (including realized gains) without encroaching on capital.40
• They might withdraw a fixed amount from the RRSP each year, choosing the amount in such a way that there is a high probability that they won't run out of money.
• They might withdraw a fixed percentage of the amount of the RRSP each year (say 4% or 5%) with the percentage chosen in such a way that the purchasing power of the withdrawals is unlikely to decline rapidly.
• They might withdraw according to a pre-determined schedule (like the RRIF minimum withdrawal schedule) calling for a gradually increasing percentage of the remaining funds to be withdrawn each year.

Of these options, variable withdrawal schedules do the best job of adapting to the couple's changing circumstances. In particular, variable withdrawal schedules guarantee that the couple's savings are never fully depleted (because the withdrawals are a percentage of what remains) but they do not prevent a sizable decline in the purchasing power of withdrawals as the couple grows old.

There are many different ways to construct withdrawal schedules. The faster money is withdrawn from the RRSP/RRIF the better the standard of living in the early years but the faster the purchasing power will decline later in life and/or if the investment returns disappoint. There is no optimal withdrawal schedule. Those with ambitious spending plans who are relatively unconcerned about the income they will have in their 90 s will prefer schedules that allow larger withdrawals in the early years. Those who attach great importance to having money later in life will favour a schedule with small withdrawals in the early years.

Suppose, for example, an individual retires at age 65 and invests entirely in riskless investments earning 5%. Suppose each year the individual draws the amount that would be payable if he or she purchased an indexed life annuity at the beginning of the year based on the UP94 generational mortality table41 without any provision for expenses, profit or adverse selection. The withdrawal schedule would then be as follows with the factors increasing as the individual ages and the annuities become progressively less expensive.

Age % of Remaining Balance to be Withdrawn

65 6.6%
75 9.3%
85 15.6%
95 30.7%

If the individual starts down this road, invests in riskless assets earning a 5% rate of return and withdraws the scheduled percentages of the remaining balances, the annual withdrawals decline in real terms with the passage of time because, as the individual grows older, the age at which he or she is expected to die increases as well, albeit at a slower rate. For example, at 65 the life expectancy is 20.7 years and the expected age at death is 85.7 years. If the individual is still alive at age 66, the life expectancy is 19.9 years and the expected age at death increases to 85.9 years. Consequently, the amount that can be withdrawn at age 66 is less, in real terms, than it was at age 65. The extent to which the purchasing power of the withdrawals declines is shown in the second column of the following table.

Age Purchase Power as a % of the First Year Withdrawal Probability of Survival

65 100% 100%
75 86% 85%
85 57% 56%
95 14% 16%

This particular withdrawal strategy causes the withdrawals to lose 43% of their purchasing power by age 85, an average rate of decline of 2.8% per annum. As mentioned earlier, the rate of decline in income from all sources would be smaller because public pensions are fully indexed. The reduction would be smaller still after tax.

The individual prepared to accept smaller withdrawals in the earlier years in exchange for larger withdrawals later in life might reduce the rates of withdrawal by 10% or 20%, with the following results.

Reduction in Scheduled Withdrawals 0% 10% 20% Age Purchasing Power Average Rate of Decline Purchasing Power 65 100 N/A 90 N/A 80 N/A 100% 75 86 1.5% 84 0.7% 81 -0.1% 85% 85 57 2.8% 63 1.8% 69 0.7% 56% 95 14 6.3% 20 4.9% 29 3.3% 16%

As can be seen from the table, by cutting 20% off the scheduled withdrawals, an individual can avert a serious decline in real income prior to age 85, the life expectancy of a 65 year old. However, the reduction in purchasing power between the ages of 85 and 95 is still significant.

One way to deal with the decline in purchasing power would be to invest some of the savings in equities in an attempt to improve the rate of return. Investing in equities increases the expected rate of return but it also increases the risk of disappointing returns and the related reductions in income. To illustrate, suppose an individual retires at age 65 and invests 25% of his or her accumulated savings42 in equities.43 Suppose the withdrawal rates are as before, based on the 5% riskless rate, and not the higher rate of return that the portfolio is now expected to earn.

Reduction in Scheduled Withdrawals 0% 10% Purchasing Power Purchasing Power Age 65 100 100 90 90 100% 75 92 76 94 64 85% 85 65 49 80 46 56% 95 17 12 29 14 16%

The addition of a relatively small equity component improves the median outcome and, in conjunction with a 10% reduction in the withdrawal schedule, does a good job of preserving the purchasing power of withdrawals during the first 20 years of retirement. However, the expected loss in purchasing power beyond the normal life expectancy is still large as is the exposure to a sizable loss in purchasing power at younger ages if equity returns are disappointing.

To conclude on the point, variable withdrawal schedules are useful for helping retired individuals budget their withdrawals and expenditures. By cutting back the scheduled withdrawals by 10% or 20% and by adding a small equity component, individuals give themselves a good chance of preserving the purchasing power of their withdrawals right up to the normal life expectancy at retirement. However they have longevity and investment exposures and individuals who are uncomfortable with these exposures will need to further reduce their withdrawals in the early years and/or purchase annuities.

### Opportunities for Innovation in Insurance Markets

Those Canadians whose post retirement incomes are primarily supported by their retirement savings (as opposed to public or workplace pensions) are exposed to several large risks:

• the risk that inflation will exceed expectations;
• the risk that the rate of return on their savings will be disappointing due to low interest rates or poor stock markets; and
• the risk that they will live well beyond the normal life expectancy of a retiring Canadian.

These are long term risks. If the couple live a few years longer than expected and if inflation and/or investment returns are slightly disappointing, they can adjust. It is the extreme events from which they need protection: the twenty year bear market; living into their late 90's; 20 years of 4% inflation, etc. Products that address these exposures at reasonable prices would be welcome.

To some extent this is beginning to happen:

• products that allow investors to hold balanced portfolios with a guaranteed lifetime withdrawal rate can simultaneously address investment and longevity risks, and
• long deferred annuities (with payments commencing at 85 or 90) allow the recently retired to insure longevity risks without committing a large part of their savings.

Still, more could be done. If the federal and provincial governments issued more indexed bonds it would be easier for insurers to offer inflation protected annuities at a reasonable price. If Canadians were required to annuitize part of their savings, adverse selection would be less of a concern and the reward for product innovation and aggressive pricing would be larger. If annuities and guaranteed withdrawals were standard products purchased in bulk by knowledgeable institutions rather than custom products sold by sophisticated sales forces to poorly-informed individuals, distribution costs could be reduced. But without a catalyst it is difficult to see how today's annuity market can become the market that Canadians need and it is hard to see how individual retirement savings plans can fully realize their potential.

### Conclusion

From the perspective of individuals who must convert their retirement savings into lifetime incomes, longevity is an important risk. This is particularly true of those with above-average incomes who are not members of defined benefit pension plans. It is prudent for these individuals to draw down their savings on the assumption that they will live at least 10 years beyond the normal life expectancy, thereby reducing their annual withdrawals by 20% to 30%. Alternatively they can use some or all of their savings to purchase life annuities, although this prospect would be more attractive if Canada had a larger, more innovative and more competitive annuity market. Despite the many theoretical advantages of buying annuities to manage longevity risk, the practical disadvantages have limited their appeal.

## 2.2. The Plan Sponsor's Perspective

Many large employers still provide defined benefit pension plans to their employees. In the private sector these plans are becoming less common. In the public sector they are not.

The employer who offers a defined benefit pension plan effectively underwrites the risk that the cost of the plan will exceed expectations. Sometimes this risk is shared with employees through formal cost or risk sharing arrangements; sometimes the risk is fully transferred to employees, as it is in multi-employer pension plans where benefits are adjusted to address surpluses and deficits; but often the employer bears, at least directly,44 most of the risk.

Pension plans are exposed to longevity risk; the longer employees live, the longer they collect pensions. If retired employees live much longer than the plan sponsor expected at the time the obligations were assumed, the plan will cost more than the sponsor expected to pay. If the sponsor becomes insolvent for this or other reasons, retired employees will typically lose the unfunded, uninsured portion of their pension benefits.

Longevity risks have, at least until recently, been largely ignored. There are several reasons for this.

• Longevity is seldom the largest risk to which a pension plan is exposed; in some instances it is hardly even material. Pension plans have much larger exposures to investment risk than to improving mortality rates. While it is difficult to generalize, the investment risks voluntarily taken by pension plans might be five to ten times larger than the longevity risks.
• Most plan sponsors do not have enough experience to accurately measure mortality levels; very few have the information needed to accurately measure changes in the rate of mortality improvement. Consequently, longevity gains and losses cannot be accurately determined other than in the very long term.
• Tools to manage investment and interest rate risks have been developed but tools to manage longevity risk45 are not yet available in a form, or at a price, that interests plan sponsors.

From the plan sponsor's perspective longevity risk has several distinct elements:

• incorrect assumptions about current mortality levels,
• incorrect assumptions about the rates at which mortality rates have been improving, and
• the inability to predict how future rates of improvement will differ from past rates.

Actuarial valuations of pension liabilities are typically based on standard mortality tables, such as the UP94 Table with or without provision for mortality improvements between 1994 and the valuation date, and with or without provision for mortality improvements between the valuation date and the future dates on which benefits will be paid.46 Where provision is made for post-1994 mortality improvement, the AA scale released with the UP94 Table will almost always be used.

As a guide to the importance of past and future mortality improvement, the present value47 of an indexed pension of $1 per annum depends on the mortality assumption as follows.  Individual(1) Couple(2) Using the UP94 Table$14.04 $15.05 Using the UP94 Table projected to 2009$14.63 $15.62 Using the UP94 Table with provision for past and future mortality improvement$15.03 \$16.03

(1) based on a 50/50 unisex table
(2) a joint and 66-2/3% survivor pension
(3) using a 5% interest rate and 2% inflation

Thus, allowing for mortality improvement between 1994 and 2009 (which most pension plans do) adds about 4% to the present value. Allowing for future mortality improvement, which is increasingly common, adds an additional 3%.

Both the UP94 Table and the AA scale were developed in the early 1990s from American (not Canadian) experience. At best, the UP94 Table provides a reasonable approximation to the mortality that a typical Canadian pension plan will experience; but many plans are atypical and will experience mortality that differs materially from the UP94 Table.

Large employers with mature pension plans usually perform regular studies of the plan's mortality experience to develop, where necessary, modifications to the UP94 Table that conform more closely to the plan's recent experience. While there is always some doubt about the mortality rates that best approximate the plan's recent experience, the larger the plan, the smaller the estimation errors.

Trying to predict current and future mortality improvements is more problematic. With the exception of the Ontario Teachers Pension Plan and the plan covering the federal public service, few Canadian pension plans have sufficient data to study rates of mortality improvement. The Ontario Teachers Pension Plan retained the University of Waterloo to examine 35 years of pensioner mortality experience and to construct plan specific mortality tables and improvement rates. The study concluded that the rates of improvement had been larger than predicted by the AA scale, particularly for women.48 Even though the plan was using a modified UP94 Table with full provision for future mortality improvement according to the AA scale, the adoption of custom mortality tables and custom improvement rates increased the liabilities by about 4%. While significant, this increase is equivalent to reducing the valuation interest rate by less than 0.25% and is small compared to 2008's investment loss, which was close to 25% of liabilities.

Even if pension plans could be confident that their current mortality assumptions were consistent with recent experience and with recent rates of improvement, there would still be significant uncertainty about the rates at which mortality will improve in the future.

• To the extent that improvements are the product of medical advances, public health improvements and changing lifestyles (e.g., fewer smokers) there is no reason to believe that the pace of future improvement will resemble past experience.
• Mortality rates improve at different rates for different ages. Not all of the ages are equally important. Improvements below the age of 70 have little impact on pension liabilities because few are assumed to die at these ages. Improvements after the age of 100 are also unimportant because most members will die before they attain these ages. Improvements in the 80s and early 90s are particularly important because these are the ages at which large numbers of plan members are expected to die. The statistical foundation for the currently assumed rates of improvement for people in their 80s and early 90s, particularly women, is not very solid; hence surprises are to be expected.
• Finally, while studies of past improvements might provide some guidance about the rates of improvements that might reasonably be expected in the future if we gradually improve our ability to treat cancer, cardiovascular disease, Alzheimer's, etc., they do not prepare us for game-changing breakthroughs for which there is no historical precedent. For example, if scientists were to discover a way to slow, arrest or reverse aging, mortality rates could collapse at the older ages. The financial consequences for pension plans would be catastrophic. I am not saying that such a scientific breakthrough is imminent, likely or even possible. I am simply pointing out that past rates of mortality improvement cannot be relied upon to accurately predict future rates.

### Conclusion

The sponsors of defined benefit pension plans are exposed to longevity risk in the sense that those entitled to benefits may collect them for longer than the sponsors expect, with a commensurate increase in cost.

While important, longevity risk is not one of the larger risks to which pension plans are exposed. It is often ignored given its lack of relative importance, the difficulty in measuring changes in mortality rates and the absence of tools to manage the risk once it is fully appreciated.

Finally, to the extent that future discoveries might alter the aging process itself, pension plans are exposed to catastrophic cost increases that are difficult to quantify.

## 2.3. The Public Policy Perspective

Longer lives increase the cost of retirement plans. Defined benefit pension plans become more expensive as do government programs like CPP/QPP and OAS. To the extent that working Canadians are net payers of tax (i.e., they pay more tax than they collect in government benefits) and retired Canadians are net recipients of government benefits (i.e., they receive more in government benefits than they pay in taxes), an increase in longevity without a commensurate increase in retirement age will cause the fiscal position of government to deteriorate.

It would be convenient if the age at which people retired could be tied in some clever way to longevity so that the cost of retirement programs and the fiscal positions of governments were insulated from increases in longevity. Some countries have already increased the ages at which public pensions become payable and others are considering it. Some countries have established links between longevity and the size of public pensions for those who retire in the future.

Change comes more slowly to defined benefit pension plans because, while governments can legally roll back benefits that have already (in a sense) been earned, employers are usually prevented by collective agreements, statutes and/or employment law from rolling back pensions that have already been earned or from increasing the age at which accrued pensions become payable. An employer wishing to increase the age at which employees can collect unreduced pensions can make the change for those hired in the future, or for pensions to be earned in respect of future service or, in some instances, for employees who are not yet eligible to retire. These changes are never popular and usually take decades to implement fully. One way for employers to limit their exposure to longevity risk is to wind up or wind down their defined benefit pension plans and replace them with defined contribution plans where longevity (and other risks) are borne by employees.

While it is convenient to tie retirement ages and/or benefits to longevity, the decision to do so is usually influenced more by affordability considerations than by benefit adequacy considerations. The advocates of direct linkage act as if the age up to which people should reasonably be expected to work can be scientifically linked to the age at which people die. So far, little has been offered in support of such a link.

In 1850 the life expectancy (at birth) of an American citizen was 38 years; yet over 75% of senior citizens worked. By 2000 the life expectancy of Americans had increased to 75 years but the percentage of seniors working had dropped below 18%. During the last century retirement ages declined despite significant increases in life expectancies and despite significant increases in the cost of public and private pensions. Retirement age is, and has always been, a lifestyle preference not a physical necessity. Workers prefer to retire in their 50s and 60s even though they are able to work longer. They are prepared to pay for the right to retire early through contributions, forgone wages and taxes. Unions attach great importance to the early retirement provisions in their defined benefit pension plans. Employers and financial institutions have long appreciated that the ability to retire early is valued by employees and by retirement savers.

In this sense early retirement, like the five day work week and the seven hour work day, is a choice that an increasingly affluent society made to improve the lives of employees. To the extent that increasing longevity and declining fertility rates increase the costs of these choices, their wisdom should be questioned. This happens naturally in individual retirement savings plans, where people can decide to save more, work longer or spend less after retirement in response to increasing longevity. The process of adjustment is more difficult in government programs and in employer-sponsored programs, but no less important.

To the extent that cost increases induced by increasing longevity can be easily addressed by gradually increasing retirement ages, longevity risk might be viewed as important risk, but one that is easily managed. Ultimately, the success of these policies will rest on the correctness of the underlying premise; that increasing longevity means axiomatically that people should be expected to work longer. If longevity and retirement age are inextricably linked then

• women should retire later than men,
• those with low incomes and little education should retire earlier than those with good incomes and advanced educations, and
• those with health problems should retire earlier than those who are healthy.

Demographers are beginning to study healthy life expectancies, i.e. the number of years that people of different ages can be expected to live before ceasing to be healthy. Healthy life expectancies are difficult to define and measure but the objective – distinguishing the age of death from the earlier age at which people cease to be healthy, is worthwhile. Unless we expect the unhealthy to remain on the job, changes in healthy life expectancies should provide better support for changes in the retirement age than changes in traditional life expectancies.

Unfortunately, not much is known about the rate at which healthy life expectancies increase. One U.K. study produced the following results.

Men Women (years) Increase in Life Expectancy 4.6 3.6 Increase in Healthy Life Expectance 2.6 2.1

In this study, healthy life expectancies increased at slightly more than half the rate of increase in traditional life expectancies.

Before tying retirement ages and/or benefits to life expectancies we need to know more about the reasons for increasing longevity and the implications, if any, for retirement ages. Some medical advances increase productive working lifetimes without increasing longevity. Some increase longevity without increasing productive working lifetimes. Some do both. Some do neither.

If scientists find an economically viable way to slow, arrest or reverse human aging, existing retirement programs might suddenly become unaffordable and unsustainable. Luckily, this is a problem with an obvious solution; the elimination of retirement programs for those who remain forever young and healthy.

However, if medical science and public health programs extend lives by allowing dependent elderly Canadians to survive longer as dependent elderly Canadians, there is no easy way to address the increase in the cost of retirement plans. Cost increases could be mitigated by increasing retirement ages but if those expected to work longer are unable to work effectively or if they are unable to find and hold jobs, increasing the retirement age may prove to be an ineffective, inconsiderate and insensitive way to address rising costs.

1 Arrangements where funds are set aside as benefits are earned and invested until they are needed (usually several decades later) to pay benefits.

2 Arrangements where the benefits earned today are paid for by future generations of participants as they fall due – often called pay-as-you-go funding because contributions are collected as and when they are needed to pay benefits.

3 To the extent that unfunded pension liabilities take precedence to the claims of other creditors in bankruptcy, as is sometimes advocated.

4 The sponsor of a defined benefit pension plan means the party or parties who directly or indirectly bear the cost of the plan. Usually the employer is the plan sponsor but sometimes employees (in multi-employer pension plans or "target benefit" pension plans) or both employers and employees (in risk shared plans such as the jointly sponsored pension plans found in Ontario's public sector) can be considered the sponsors of a pension plan.

5 The extent to which the rate of return on the plan's investments might be less than expected, thereby increasing the cost of the arrangement or reducing the pensions that can be paid. In this section investment risk is construed broadly to include inflation risk (which affects real rates of return on retirement savings) interest rate risks (which affect rates of return on fixed income investments) and demographic factors, such as population growth and real wage growth, which affect the cost of unfunded arrangements and the ability of funded defined benefit plans to bear risk.

6 Pensions that are fully protected from increases in the Consumer Price Index, i.e. indexed to increases in the CPI.

7 The pension at the point of retirement expressed as a percentage of the salary immediately preceding retirement.

8 90 is a reasonable approximation to the expected age of death for the last survivor of a couple retiring in their early 60s – the assumption being that the full pension is payable until the death of the last survivor. This overstates the cost of a pension reducing on first death, or on the death of the member, but not by enough to warrant the use of a more sophisticated model.

9 A common actuarial assumption for the valuation of pension liabilities; there have been long periods where real wages have grown more quickly and more slowly than this.

10 Chosen to conform to the traditional 70% total replacement target, not because the author believes that this is needed to maintain the standard of living of retired Canadians.

11 i.e. as benefits accrue the pension plan assembles a matching portfolio of riskless bonds to minimize the risk to which the plan is exposed.

12 i.e. the level percentage of salary needed to fund the target pension over the period starting at age 30 and ending at the retirement age, assuming that the funding instrument is tax-sheltered.

13 There will be no gains or losses associated with the accrued benefits because the pension fund is invested in assets that will fluctuate in value to match changes in the liabilities. However, the cost of newly earned benefits will fluctuate with changes in the riskless interest rate.

14 Rates of salary growth will be influenced by inflation rates, productivity improvements and other factors.

15 In a fully funded benchmark plan, the pension fund will typically be 6 to 8 times payroll.

16 Assuming a 4% riskless interest rate and 2% inflation and a pension fund that earns the assumed 4% riskless rate of return.

17 Unless real interest rates increase from the low levels of the last 5 years.

18 i.e. use the fact the pension plan or the retirement saver can ignore, at least in the short-to-medium term, fluctuations in asset values.

19 Approximately 4% real.

20 As pension plans mature, the size of the pension fund increases as a multiple of payroll, as do the gains and losses produced by fluctuating capital markets.

21 A mature pension fund will have benefit payments that exceed contributions most of the time, i.e. there is a net operating cash outflow. Even if the plan continues forever it does not have an infinite investment horizon. Twenty years would be more typical.

22 A plausible shortfall based on the last 50 years.

23 Assuming for the moment that the plan is permitted to ignore it.

24 The 1994 Uninsured Pension Mortality Table (the "UP94 Table"), projected to 2009, with or without provision for future mortality improvements using scale AA.

25 Since the probability of working Canadians living to age 65 is very high, longevity risk arises primarily from the possibility that mortality rates will decline after age 65. Consequently this paper focuses on life expectancies at age 65, not life expectancies at birth.

26 The provision for future mortality improvement takes the form of a set of age and sex specific improvement rates representing the rates of which future age and sex specific mortality rates will decline (geometrically) with the passage of time.

27 This mortality table is perhaps the only table recently constructed from the experience of a group of Canadian pensioners that was large enough and had experience covering a sufficiently long period (35 years) to construct a plan-specific set of mortality improvement factors.

28 An annuity where the payments increase in line with increases in the Consumer Price Index, thereby preserving the purchasing power of the income.

29 This exceeds the interest rates currently available on long term Canada bonds but is representative of the spread one might more typically see between a 2% inflation expectation and long term interest rates.

30 With a 50/50 weighting of male and female mortality rates.

31 A life annuity is a contract issued to an individual (the annuitant) by a life insurance company paying a monthly, quarterly or annual income for life.

32 An annuity where the payments are reduced by 1/3 on first death.

33 And reducing by one third after the first death.

34 Assuming a one third reduction in the income on the first death.

35 Due to adverse selection, i.e. annuities are (and should be) priced for the population that purchases them, a population consisting largely of people who expect to live a long time.

36 Including all low income seniors and most public sector employees.

37 Due to the scarcity of indexed bonds and mortgages other than low-yielding real return bonds issued by the federal government and due to the absence of a viable market for annuitants with chronic health problems.

38 Such as adding lengthy guarantee periods.

39 In each case, the withdrawal must be at least the minimum prescribed by the ITA. If this exceeds the amount that the couple wants to spend, the after tax excess withdrawal might be saved in a TFSA, or outside a tax shelter.

40 Although inflation will slowly erode the purchasing power of their capital.

41 For the remainder of Section 2.1, we use the UP94 Table with a 50/50 weighting of male and female mortality and full provision for future mortality improvement based on scale AA.

42 With annual rebalancing.

43 With an expected annual return of 8% and a 15% standard deviation.

44 Some believe that employers transfer pension risks to employees by adjusting other compensation elements in response to fluctuating pension costs. While it seems reasonable that this should happen, there is little evidence to suggest that it does.

45 Longevity bonds and swaps have been offered primarily in the U.K. and the U.S., where there is greater demand. While there is some interest in hedging longevity risk, particularly among closed defined benefit plans that have chosen to eliminate or significantly reduce their exposure to investment risk, there have not been many transactions to date.

46 At the present time, most large plans make some provision for mortality improvement in their liabilities. For these plans the risk is not that life expectancies improve, as provision has already been made for improvements at the expected rates. The risk is that the rates of improvement have been underestimated and that the provision will prove inadequate.

47 Using 5% interest and 2% inflation.

48 The CPP's studies of the rates at which mortality has been improving are generally consistent with this observation.