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«Abstract: The UK requires individuals with individual accounts to annuitize before the age of 75. Using a time series of annuity prices and ...»

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For Prudential, they represented 6.3 percent of external policies and 1.7 percent of internal policies (by volume, they represented about 10 percent of business).27 For Standard Life, index-linked policies represented about

5.8 percent of policies. For Equitable Life, the share of index-linked policies in the total number of new non-profit annuities in 1997 was close to 38 percent, reflecting Equitable Life’s upmarket clientele. In 1998, however, this fell to 19 percent of total non-profit annuities as more new business went to investment-linked annuities.

• Fifth, until 1999, investment linked annuities on the open market were basically limited to Equitable Life, Prudential and Scottish Widows. In 1997, close to 50 percent of Equitable Life’s new annuities under written According to the Schedule 4 notes for the Prudential regulatory returns, these index-linked annuities include limited price indexation annuities.

were with profits annuities. Business volumes elsewhere were lower, with Scottish Widows reporting a mere 121 contracts of with profits business as opposed to 11,572 non-linked annuities contracts. Norwich Union, Merchant Investors and Sun Life have launched new investment-linked annuities with various designs, including derivative-based hedging for investors. The issues with some of these designs are the heavy capital requirements to reserve against market downswings (see next bullet).

• Sixth, under EU legislation, UK insurers must hold reserves of 104 percent of the mathematical reserves (expected liability) associated with the annuity plus satisfy certain resiliency tests involving declines/increases in equity values and bond yields.28 Unlike US regulations, these regulations are not implemented on a risk-adjusted basis, and are therefore not adept at picking up small probabilities of large events, such as a large improvements in mortality or very large declines in interest rates.29 Since UK insurers underwrite policies involving more risk in the tails, this approach could be a problem; however, in practice, the supervisory authorities insist on large enough margins that more than encompass reasonable risk corrections. Because of mismatching reserves, indexlinked annuities require more reserves and hence are more capital intensive than ordinary non-linked to issue. In addition, because of the relative paucity of corporate index-linked debt, the majority of the insurer’s matching portfolio is likely to be in government bonds, effectively making it more difficult for the insurer to make a profit.

In addition, the discount rate used in valuing liabilities must be less than the yield on matching assets.

The recent Guaranteed Annuity Option problem is an example of such a scenario.

III. Value for Money of Annuities: Theoretical Framework An annuity provides a stream of income until one's death in return for an initial premium. A standard way of evaluating the value for money of such a contract is to compare the expected present discounted value (EPDV) of the future income stream with the initial premium paid. The ratio of the EPDV to the purchase price is known as the money's worth ratio (Friedman and Warshawsky, 1990; Mitchell, Poterba, Warshawsky, and Brown, 1999).

For an individual deciding on which type of annuity to buy, an annuity with a higher money's worth ratio provides greater value for money. In general, the money's worth ratio depends on purchase price, the size of the future income flow, the individual's subjective assessment of mortality risk, and his or her rate of time preference.

More precisely, the EPDV of a single life annuity can be written as:

–  –  –

where At is the payout at time t, St is the probability that the annuitant survives until time t, ij is the one-period rate of time preference at time j, and ∏ (1 + ij) is the discount factor at time t.30 In the analysis that follows, we consider the EPDV from the perspective of the average individual (that is, the individual with the average life expectancy).

The most straightforward component of this calculation is the annuity rate. Annuity rates are available from a number of annuity brokers and are widely quoted in the financial press. For survival probabilities, we consider an individual facing average mortality risk. As an average annuitant tends to live longer than an average member of the population, we examine the EPDV It is fairly straightforward to extend this framework to other types of annuities, such as joint life annuities or those with a minimum guarantee.

from the point of view of both the average person and the average annuitant.

We make two alternative assumptions about the rate of time preference. We first use the term structure of short-term interest rates on UK government bonds. This approach takes the point of view of an individual whose alternative investment is risk-free government bonds. We then consider the term structure of interest rates on corporate bonds. This makes allowance for the fact that annuity payments are not entirely risk-free (insurance companies may go under), and individuals may discount future income flows more heavily than the risk-free return on government assets. All the data used in the analysis are described in further detail in the next section.

The EPDV to purchase price ratio, or the value for money of the annuity, would be equal to one if the annuity were 'actuarially fair'. In practice, we are likely to observe ratios that are less than unity. In other words, for every £ of initial premium, the average individual can expect to receive less than one £'s worth of future income. The difference is accounted for by a number of factors, including the administrative costs of insurance companies, the need to build reserves against various contingencies (such as greater than anticipated mortality improvements among the insured population), company profits, and the costs of adverse selection. We examine these factors in more detail below.





Value for money and adverse selection

As indicated, annuitants tend to have lower mortality than the rest of the population. From the point of view of insurance companies, long-lived individuals are a 'poor' risk, and annuity rates reflect the fact that insurers are pooling mortality experience among a group that has higher survival chances than the population as a whole. In terms of value for money analysis presented above, the EPDV is likely to be lower if population survival rates are used in place of annuitant survival rates. Thus the value for money is likely to be lower for an individual who faces the average mortality risk of the population as a whole rather than the population of annuitants.

It is not clear to what extent the difference in mortality experience is due to private information on the part of the annuitants as opposed to their income and wealth background. There are significant differentials in mortality by socio-economic class in the UK. Table 1 provides evidence on mortality by socio-economic class from the latest survey of health inequalities in the UK.31 During 1987-91, men aged 60-64 in classes I-II were nearly 40 percent less likely to die before reaching the age of 65 than men in classes IVV. Although the mortality differential between these two classes declines at higher ages, the fall is gradual and the differential remains above 20 percent till the age of 85. Mortality among women displays similar differences by social class, however the magnitude of the differential is smaller than in the case of men. The report also points to widening inequalities over time, that is, a greater reduction in mortality among the higher social classes. If this were to continue into the future, we can expect greater mortality improvements for these classes than the population as a whole.

In addition to mortality differences by class, there are features of the annuities markets in the UK that encourage higher mortality individuals to opt into separate risk categories. Insurers offer enhanced life annuities with better payouts for those with lower than normal life expectancy.32 As more people take these annuities, the average life expectancy of the remaining pool rises.

See Health Inequalities Decennial Supplement, Office for National Statistics, September 1997. The data are for England and Wales and cover the period 1987-91. Social class is assigned on the basis of occupational status and job sector, with women assigned the same class as their husbands. I is the highest class, V the lowest. For further discussion of class differentials in mortality among the British population, see David Coleman and John Salt, “The British Population”, (Oxford University Press, 1992), Chapter 8. The seminal Whitehall studies on income and mortality experiences within the British Civil Service are discussed in Michael Marmot et. al., "Health Inequalities among British Civil Servants: The Whitehall II study," Lancet, June 8, 1991, pages 1387-93.

There are two types of enhancement, standard and individual. Standard enhancements apply for those who meet certain fixed criteria, such as smokers or diabetics. Individual enhancements may be offered on the basis of the insurance company's assessment of an individual's life expectancy.

Individuals may also act on private information on their mortality prospects. Thus individuals who are sick, or have reason to believe they may not live long, may choose not to annuitize or to delay annuitization. In general, we would expect more limited scope for such behaviour in the compulsory market33 where there is somewhat less of an element of choice.

As discussed previously, annuitization may be delayed (up to the age of 75) but not postponed indefinitely. Even so, individuals may act on private information in a number of ways. They may take a larger proportion of their benefits in the form of a lump sum at maturity (up to the specified legal maximum). Or they may opt for withdrawals from their pension fund (again subject to the legal maximum) until the age at which they can no longer put off annuitization. 34 Compared to the compulsory market, there is greater scope for acting on private information in the market for immediate annuities. As discussed previously, these may be purchased out of the tax-free lump sum. They may also be purchased voluntarily with savings that are not tax-advantaged (unlike pension savings). Individuals with additional savings outside qualified pension plans tend to be richer than average, so their greater longevity may be largely on account of this factor.

Table 2 presents information on the expected mortality of 65-year old males and females drawn from three different populations: the general population, the compulsory market, and the immediate market. As we can see, the combination of socio-economic background and individual behaviour We use the term compulsory market to refer to both open market options and compulsory purchase annuities.

The issue of the optimal annuitization decisions when individuals can invest in equity and try to beat the yields on annuity-backed bonds has been explored by Moshe Arje Milevsky, “Optimal Asset Allocation Towards the End of the Life Cycle: To Annuitize or Not to Annuitize?”, Journal of Risk and Insurance, 65, 3, 401-426. An analysis of the risk pensioners face by delaying annuitization is in: M.

Zaki Khorasanee, Annuity Choices for Pensioners. Journal of Actuarial Practice, 1996, 4(2), pp.229-255.

results in mortality expectations that are lower for the population of annuitants than for the general population. Moreover, immediate annuitants are expected to live longer than compulsory annuitants.

Selection effects may also be evident in the size of the policy and the type of the annuity. Those who buy larger policies tend to live longer than those who buy smaller ones. This can be seen in Table 2, which presents expected mortality weighted both by lives (number of policies) and by amounts. Once again the relative contribution of socio-economic background and individual behaviour to this pattern is not clear. Richer individuals have higher pension savings. At the same time, private information may result in the decision to annuitize later from a smaller, drawn-down pension fund.

In this paper we focus on the compulsory market, considering both single and joint life annuities, by age and sex.35 We examine three types of annuities: level, escalating, and RPI-indexed annuities. A level annuity pays the same nominal sum until the end of the individual's life. Escalating annuities raise the payout at a fixed rate, usually once a year. Annuities that escalate at both 3 percent p.a. and 5 percent p.a. are common in the UK. RPIindexed annuities raise the amount in line with the retail price index, again usually once a year. Compared to level annuities, escalating and RPIindexed annuities provide greater value in the later years of life. Those who expect to live long might thus favour them. We also know that indexed annuities tend to be for larger amounts. Unfortunately, there are no annuitant tables by type of annuity that allow us to examine whether selection is significantly different in these three markets.

We ignore the issues of protected rights annuities by assuming the individual is contracted into SERPS. Because age-related SERPS rebates are capped at 9%, older individuals close to retirement tend to be contracted in so that there are not many people retiring today who need to purchase protected rights annuities.

Our main finding is that on average selection effects account for the majority of the reduction in value for money of annuities. As discussed in further detail below, roughly a half to two-thirds of the reduction in the value for money would appear to be accounted for by selection effects.

IV. Value for Money of Annuities: Evidence from the UK Data Annuity rates: We consider an individual who is contemplating the purchase of a single or joint-life annuity from one of the main life-insurance companies in the UK. Our information on annuity rates is from Investment Intelligence, a financial services company, which provides annuity data by age, gender, market, type of annuity, and policy size.36 The data cover the 15major providers in the market.37 We do not consider rates for enhanced life annuities.



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