Sharing Longevity Risk: Why Governments Should Issue Longevity Bonds

Abstract

Government-issued longevity bonds would allow longevity risk to be shared efficiently and fairly between generations. In exchange for paying a longevity risk premium, the current generation of retirees can look to future generations to hedge their systematic longevity risk. Longevity bonds will lead to a more secure pension savings market, together with a more efficient annuity market. By issuing longevity bonds, governments can aid the establishment of reliable longevity indices and key price points on the longevity risk term structure and help the emerging capital market in longevity-linked instruments to build on this term structure with liquid longevity derivatives.

Notes

The mortality rate for a given age measures the frequency of occurrence of deaths of people of the given age in a defined population during a specified time interval, typically one year. Mortality rates are derived from crude death rates, which are calculated as the ratio of deaths to the exposed population, i.e., the number of lives at the start of the period exposed to the risk of dying during a specified time interval, typically one year. A survivor (or survival) rate for a given age measures the proportion of people of the given age surviving a specified time interval. The survivor rate at age 65 equals (1 – mortality rate at age 65). Life expectancy measures the average number of years a person of a given age would live under a given set of mortality conditions. Life expectancy is usually computed on the basis of a life table showing the probability of dying at each age for a given population according to the age-specific death rates prevailing during a specified period. For example, life expectancy at 65 = 0.5 + (1 − q(65)) + (1 − q(65)) × (1 − q(66)) + (1 − q(65)) × (1 − q(66)) × (1 − q(67)) + ^… + (1 − q(65)) × ^… × (1 − q(120)) and q(120) is typically set to unity and q(65) is the mortality rate at age 65, etc. We also need to distinguish between period life expectancy that makes no allowance for future improvements in mortality rates—and so assumes, for example, that q(67) in the above formula will equal the mortality rate of today's 67-year-olds—and cohort life expectancy that makes such an allowance—and hence will involve a lower q(67) than used to calculate period life expectancy.

Factors such as obesity and environmental degradation could eventually lead to a trend decline in life expectancy.

Milevsky et al. (2006) prove this result.

See Appendix A for more details about Solvency II.

OECD (2011) and Life and Longevity Market Association

Levy (2012) and Association of British Insurers; the figures are for year-end 2010.

Pension Protection Fund and the Pensions Regulator (2006, Table 5.6).

Hobbs (2012); the figures are for year-end 2010.

The U.K. government has linked the social security pension age to increases in life expectancy and is planning to do the same for public-sector employees, so this figure is not expected to increase in future as it has in the past.

Bulk buyouts transfer the pension liabilities in corporate pension plans to insurance companies. This market began in earnest in the United Kingdom in 1999, when the Prudential Assurance Company did £1 billion of business. There is also an increasing use of longevity swaps provided by both insurance companies and investment banks (Hymans Robertson, Buy-outs, Buy-ins and Longevity Hedging (various issues)). A longevity swap exchanges fixed for floating survivor rates over the tenor of the swap. The fixed rates might be set equal to the expected rates in Figure 2 plus the longevity risk premium. The floating rates are the realized rates that could be above or below the fixed rate. Each year, the pension plan or annuity provider pays the fixed rate and receives the floating rate and thereby locks in the cost of the pension or annuity payments. The first suggestion for longevity swaps—or survivor swaps—was made in Dowd et al. (2006).

For example, the loss of upfront allowances for the liquidity premium and for credit risk.

Tully (2011). Of this 10%, industry insiders estimate that 7% is accounted for by the lost allowances for the liquidity premium and for credit risk, with the remaining 3% due to the absence of a longevity risk hedge. With £12 billion annual sales of annuities in the United Kingdom, this implies a cost to every new annual cohort of retirees in the United Kingdom alone of £360 million.

Blake et al. (2008).

Cairns et al. (2006). This model is briefly explained in Appendix B.

The CBD model was estimated using data between 1991 and 2006. The historical period over which a stochastic mortality model such as the CBD model is estimated is certainly important for getting a good fix both on the future trend improvements in mortality rates and on their volatility around this trend. However, this does not necessarily mean that a longer data period is better. If there has been a significant change in the trend, then this suggests the model should be estimated over a short period for the purpose of getting a reliable estimate of the latest trend. On the other hand, a longer period might be used to get an estimate of long-run volatility. This is a matter of experimentation. The results we present here are purely illustrative, although they were compared for consistency with the official Office for National Statistics 2008 projections. Much more analytical work would have to be done using a wider range of models before a real-world longevity bond could be issued.

This is the risk that the “underlying”—in this case, the survivor rates of the particular population being hedged—does not move in line with the hedging instrument, which, in this case, depends on the survivor rates of the national population.

Willets (2004); Richards et al. (2006).

This is an index based on the mortality experience of the national population.

See the discussion in section 8 of Blake et al. (2006).

Since annuity providers buy bonds to make the annuity payments, annuities are subject to interest-rate risk. If interest rates fall, bond prices rise and this will reduce the amount of the annuity that can be paid from a given lump sum.

If longevity improves at a higher rate than that expected along the glide path, this too will reduce the amount of the annuity that can be paid from a given lump sum.

Dowd (2003).

The first suggestion for governments to do this was made in Blake and Burrows (2001).

See Appendix D for a critique of this view.

See Bohn (2012) for a formal model of intergenerational risk sharing in the face of shocks to labor productivity, return on capital, and longevity. Bohn recommends governments should issue both wage- and longevity-indexed bonds, since these would help to reduce both the mismatch between pension assets and liabilities and the pension fund's dependence on corporate sponsors.

Many of the people buying annuities in the United Kingdom are also on means-tested benefits. Any reduction in annuity payments arising from more onerous capital requirements resulting from insurers being unable to hedge longevity risk will immediately increase means-tested benefits.

The government will always have more refined information than the private sector as a result of data protection legislation. This legislation prevents the release of information that would allow an individual—even one who has died—to be identified. Mortality data will be published only in a sufficiently aggregated form—in terms of date and location of death—that makes it impossible for specific individuals to be identified.

For an examination of longevity hedging using longevity indices, see Coughlan et al. (2011).

The longevity risk premium is paid by the longevity bond's buyer to the bond's issuer to remove systematic longevity risk. It therefore results in a lower coupon that the bond's issuer has to pay the bond's buyer for purchasing the bond, thereby lowering the effective yield on the bond.

Currently the survivor rates for future years are based on model projections, such as the CDB model. Figure 2 illustrates this for males aged 65 at the end of 2006. The theoretically fair price of a longevity bond could therefore be determined using the CBD model. However, with a traded market in longevity bonds, a market view of future survival rates would replace model projections and the resulting price points would be used in determining the market price of the bonds. Pricing-to-market would replace pricing-to-model.

If a strips market in longevity bonds develops—as happens with fixed-income and index-linked bonds—then hedgers could buy the subset of the coupon payments that most closely meets their hedging requirements, rather than having to buy the whole bond. In addition, if the individual coupons in Figure 4 are traded separately, this will allow more accurate determination of the price points for longevity risk along the diagonals of the longevity risk term structure.

It will also be related to the extent of the basis risk that remains unhedged and potentially the size of any liquidity premium contained in the price of longevity bonds. If longevity bonds are not actively traded, investors will demand a liquidity premium to hold them and the regulator might be reluctant to accept that the bonds’ prices can be used for mark-to-market pricing for capital release purposes.

The Joint Forum of the Basel Committee on Banking Supervision, the International Organization of Securities Commissions, and the International Association of Insurance Supervisors.

In the private sector, long-term contracts can involve significant credit risk as mentioned above and collateralization can introduce significant frictional costs.

Pension plans and annuity providers might still be willing to invest in government-issued longevity bonds covering the age range 65–90 if they are competitively priced compared with capital market hedges.

LBM(65,75) is a longevity bond for males aged 65, with the first coupon paid at age 75.

Total U.K. government bond issuance will exceed £700 billion over five years as a consequence of the fallout from the 2008 financial crisis.

Chief Risk Officers Forum (2008). See Appendix C for an explanation.

The desired survival probability could be higher if required.

Notice that the PV(65,90) bond is more volatile than the PV(65,75) bond, which, in turn, is more volatile than the PV(65,65) bond. This is for precisely the same reason that a zero-coupon bond is more volatile than a coupon-paying bond with the same maturity: Because the zero's cash flows are more heavily concentrated toward the end of its maturity than a bond paying regular coupons, it has greater duration.

The explanation for the choice of a fixed risk-free discount rate of 4% is given in Appendix C. A more sophisticated approach would stochastically model the risk-free term structure.

An alternative would have been to use the discounted mean term or duration of the bond. This, however, has the effect that it changes when the discount rate changes. This is inappropriate because the potential dispersion of projected cash flows, and hence the risk against which capital is being held, does not depend on interest rates. We did, however, examine the effect of using the discounted mean term with a fixed discount rate of 4%, and it made very little difference to the final estimate of the longevity risk premium.

As the age 65 and 75 cohorts grow older, the range of possible outcomes narrows.

This follows because 0.9995 raised to the power of a lower mean term produces a higher quantile than 0.9995 raised to the power of a higher mean term as Table 2 shows.

Chief Risk Officers Forum (2008, pp. 16–18).

Chief Risk Officers Forum (2008, p. 8). See Appendix C for an explanation.

Chief Risk Officers Forum (2008, Figure1, p. 30).

This would include an allowance for model risk, e.g., in the model used to project future mortality rates. An alternative approach to the cost-of-capital method used in this article is the “percentile method,” which determines the level of capital needed to ensure that all payments can be met for a set percentage of all the scenarios. In the context of Solvency II, a probability of 75% has been suggested. By using the initial 10,000 present value scenarios from the CBM model, a 75 percentile risk premium can be determined, and, in turn, an implied cost of capital can be calculated. In this case, the percentile method implies costs of capital of 2.11% for LBM(65,75), 1.75% for LBM(65,90) 2.77% for LBM(75,85), and 2.45% for LBM(75,90).

By using a discount rate of 3.821%, the present value of the coupon payments on the LBM(65,75) bond equals £103.20.

This replaced the Financial Services Authority in April 2013.

The Pensions Regulator in the United Kingdom is responsible for the regulation of occupational trust-based DB and DC schemes and attempts to limit the number of DB schemes needing support from the Pension Protection Fund (which was based on the U.S. Pension Benefit Guaranty Corporation).

Pension Commission (2005, p. 229).

Redressing the Balance—Boosting the Economy and Protecting Pensions, Confederation of British Industry Brief, May 2009.

Antolin and Blommestein (2007).

World Economic Forum (2009).

International Monetary Fund (2012).

Sharing the Load, Project M no. 14, Allianz, April 2013.

Longevity bonds are annuity bonds with the coupon payment involving a return of capital element as well as an interest element. The tax treatment will therefore be more complicated than with a conventional bond.

See Appendix C for further information on the CoC Method.

Dowd (2003, pp. 346–347) makes the same point: “The intergenerational argument is open to the objection that governments have an incentive to put the interests of current voters ahead of those of future voters.” We would argue that the issuance of longevity bonds would help to reduce this incentive. The current generation is getting its longevity risk insurance for free: If longevity bonds were issued, it would have to pay for it!

The conventional methodology for valuing annuities is to calculate the “money's worth” statistic, which will equal 100% when annuity providers have no administrative costs and are making no profits. In practice, the money's worth is typically less than 100% because of the presence of administrative costs, risk charges (in form of cost of capital), and the need for annuity providers to make a “normal profit.” The sum of the costs and normal profit is called the “load factor.”