Governments around the world are moving their pension plans away from pay-as-you-go financing towards individual saving plans, in a large part due to increased longevity and the progressive deterioration of the old-age dependency ratio. Defined benefit plans are progressively being replaced by defined contribution plans that transfer longevity and investments risks from employers to individual workers. As saving built up during the accumulation phase may need to last for a long time, the purchase of an annuity could be an attractive option for a retired worker to eliminate the risk of running out of funds in old age. This book provides an overview of annuity markets and current issues, and it also offers a survey of research on annuities, ambitiously summarizing results from actuarial science, demography, economics, finance, and insurance, with particular emphasis on the UK, the world's largest annuity market.
After an introductory chapter that demonstrates that demographic forces are likely to increase the future demand for annuities, the authors define numerous types of annuities available to retirees, provide illustrative annuity prices, and demonstrate using British data that changes of annuity prices over time are mostly a function of prevailing interest rates. They then go on to outline the historical development of annuity markets, primarily in the UK. The next two chapters summarize in the simplest possible way (sometimes at the price of lack of mathematical rigor) the mathematical models used by actuaries to price annuities, describe mortality patterns, and extrapolate mortality. Readers with some knowledge of actuarial models may wish to skip Chapter 4, as it seems designed to introduce non-actuaries to issues in modeling such as select periods, period vs. cohort life tables, and mortality and survival fan charts. The first part of the book ends with a brief overview of annuity markets in eight countries worldwide.
The latter half of the book is devoted to current research topics. One question addressed is how good a deal is the purchaser of an annuity getting? This is explored through the concept of money's worth, defined as the actuarial present value of all annuity payments divided by the price of the annuity. A money's worth of 1 means that the annuity is actuarially fair: the annuitant's expected monthly payments equal the full value of the purchase. The introduction of expense and profit loadings in annuity issuers' calculations in most cases reduces the money's worth to less than one – the price an annuitant has to pay for peace of mind, the elimination of longevity and investment risks. Several authors have calculated the money's worth of annuities in many countries, a difficult exercise which requires assumptions about future mortality rates specific to annuitants and the shape of the yield curve. Observed values consistently range between 0.85 and 1, leading to the conclusion that annuities generally offer good values to consumers, systematically higher than the values offered by other insurance products. Another measure of the value of an annuity to the purchaser, the internal rate of return implied by the annuity payments, has not been explored much, despite its significant advantage that it does not require assumptions about future spot rates.
The authors then study in more detail the economic theory of demand for annuities. A simple example (assuming no inflation, pensioners that can only live one or two more periods, no bequest motive, only bonds and annuities available for investment) illustrates Yaari's main result that risk-averse individuals faced with uncertain duration of life should fully annuitize their portfolio, if annuities are sold at actuarially fair prices in a perfect annuity market – a market where a full set of assets with life-contingent returns is available for every maturity without transaction costs. Readers unfamiliar with Yaari's result may regret that no formal proof of the theorem is provided. This main theorem may have little value in practice given the facts that perfect annuity markets do not exist (temporary and deferred annuities are rarely sold), and that annuities prices include expense and profit loadings.
The concept of money's worth, interesting as it is, fails to take into account annuitants' aversion to risk and spending preferences as a function of time. To incorporate these elements in the reasoning, models based on utility theory are introduced to show the value of annuities using different assumptions of preferences. They also show the limitations of utility theory, particularly in the case of time-additive separability and geometric discounting. For one thing, Yaari's theorem suggests that demand for annuities should be high, even if some assumptions are not realistic. In practice, annuity markets around the world are fairly small. Explanations for this discrepancy between theory and observations (“the annuity puzzle”) include: there may be valid reasons to spend more early in retirement than later; annuities are usually backed by bonds that earn low rates of return compared with equities; most governments provide a basic survival annuity to all retirees; adverse selection; bequests; and lack of financial knowledge from potential annuity purchasers.
The book concludes with a summary of international research presenting evidence of adverse selection, and on the type of annuities purchased. There is also a discussion on the supply of annuities, with major issues being the small number of providers, the inadequate supply of long-term government bonds, and the modest development of markets to pool longevity risks.
This book is a good, self-contained, overview of annuity markets and issues at a basic level. Mathematically-inclined readers may wish to consult some of the referenced papers for more advanced topics; actuarial and financial techniques, in particular, are only briefly sketched. There is, for instance, little discussion of the hedging role of annuities in insurance markets. The book could be used as a text for a one-semester introductory undergraduate course on pensions or annuities. A large number of chapters and results are British-specific, which may limit the adoption of the book in other countries. Also a sizable number of imprecise or incorrect mathematical statements may preclude this book from inclusion in actuarial examinations.
