Practical analysis for investment professionals
20 February 2014

Book Review: Life Annuities

Life Annuities: An Optimal Product for Retirement Income. 2013. Moshe A. Milevsky.

The origin of life annuities dates back thousands of years. In Life Annuities: An Optimal Product for Retirement Income, Moshe A. Milevsky of York University notes that the concept behind modern annuities can be traced to English astronomer Edmond Halley. In 1693, Halley devised a formula for exchanging a lump sum for a lifetime stream of income based on the annuitant’s age.

Few other financial contracts are as simple and useful as the immediate life annuity, which guarantees annuitants income that lasts as long as they do. Yet, immediate annuities are often seen as the financial equivalent of the kid who gets sand kicked in his face (for those of us old enough to remember the Charles Atlas ads).

Annuities remain unloved and unpopular as a destination for retirement assets. Fewer annuities are purchased than rational economic expectations would suggest, especially in a world of financial uncertainty and increasing longevity, both of which should enhance the products’ attractiveness. This “annuity puzzle” has engaged academics and practitioners in vigorous debate for several decades.

Milevsky is a frequently published leader of the “pro-annuity” camp. Many financial advisers and some academics have taken the opposite tack. They maintain that there is no annuity puzzle because there are rational explanations for why consumers decide not to annuitize.

In this book, Milevsky provides a comprehensive review of life annuities, detailing their origins and history; the mechanics of how they work; and their uses, benefits, and risks. He touches on the numerous variations on the “annuity theme,” but his primary focus is the basics (i.e., the single-premium immediate annuity in North America).

The book includes rigorous analysis and an organized review of the academic literature. Milevsky’s work is detailed enough for the needs of any student or professional practitioner, and he structures the content as a series of questions and answers so that readers seeking specific topics can find them easily. Although not explicitly aiming at the annuity puzzle debate, Milevsky provides a central repository of ammunition for pro-annuity arguments.

In the first section, Milevsky starts with definitions and a brief history of life annuities, from the origins of the annuity concept to their modern usage, including the link to today’s defined benefit pensions. This section includes a clear explanation of the impact of age and gender on annuity pricing, as well as the impact of interest rates (historically low at present) and changes in mortality (longevity). That explanation sets the stage for a discussion of the economics of today’s annuity market, covering taxation, investment policy, and the impact of the creditworthiness of the insurers offering the policies. He concludes the section with a look at today’s market, including what sells and why.

The key observation is that although the market for retirement income is very large if Social Security plus public and private defined benefit pensions are included, the market for “voluntary” fixed immediate annuities is very small (the annuity puzzle). Milevsky notes that the majority of sales of so-called annuity products in the United States are variable annuities, or VAs ($151 billion in sales for the year ending June 2012, compared with $9 billion for fixed immediate annuities). He observes that VAs are essentially mutual funds with some guarantees attached and few are ever used to provide an annuity income in retirement.

The book’s second section is designed for the mathematically inclined. Milevsky presents and explains his top 10 list of “Formulas to Know” for understanding and applying annuity concepts. Some of these are the basic building blocks: What are mortality rates, and how are they used to derive survival probabilities? Others focus on addressing user-oriented issues, such as

  • whether to wait to annuitize,
  • the chance of ruin without an annuity, and
  • the mechanics of such variations as variable immediate annuities (which are typically available today) and tontines (more of historic interest).

The core of this section, however, deals with the critical formulas for understanding annuity construction and pricing (the Gompertz law of mortality and the annuity pricing model) and for assessing the value of an annuity (the money’s worth ratio). Unlike television host David Letterman’s top 10 lists, Milevsky’s list places these key elements in the middle, avoiding the drumroll crescendo of “and the most important formula is. . . .” No doubt this ordering emphasizes the different priorities of actuarial science and show business.

In the third section, Milevsky tackles the immense task of reviewing and filtering the scholarly literature on the subject. From the more than 2,000 papers published in the last half-century, he has winnowed the list down to around 200, in five broad topic areas plus a catchall “other” category. As well as inspiring respect for the sheer scope of this task, this section will be helpful to readers in tracking down topic-specific references. For this reviewer, the most interesting categories are those on the annuity puzzle and the money’s worth ratio (MWR). Milevsky effectively summarizes the accumulating body of research illuminating the annuity puzzle. The review of MWR touches on an intriguing aspect of annuities: the degree to which design, pricing, and popularity vary across countries. In an otherwise North American–focused book, this section opens a window to a topic of global interest.

This thorough and thoughtful book provides some new ideas on a very old topic, the immediate annuity. More importantly, it provides a central reference point for readers interested in the past, present, and future of the annuity industry. The author notes that the work’s primary focus is North American immediate annuities. There is plenty within that topic to keep the reader engaged, but Milevsky periodically opens a window to other related topics that deserve more attention, possibly in future research publications. These include

  • longevity insurance (also known as advance life deferred annuities),
  • annuities within pension plans (an especially important topic given the accelerating move away from defined benefit to defined contribution plans), and
  • differences in annuity design, pricing, and popularity across world markets.

A key theme that runs throughout the book (and indeed, that is central to the debate over the annuity puzzle) is the extent to which rational influences dominate behavioral ones. Behavioral finance has been prominent in recent years, seeking to explain most or all of consumers’ actions. In contrast, Milevsky’s formulaic definitions and citations of the academic literature seek to explain consumers’ actions through economic theory and empirical studies. Behavioral motivations are thus the residual, the unexplained “leftovers.” As such, the author concludes the annuity puzzle section of the literature review by observing that this puzzle “is not as perplexing as it was 45 years ago.” Life Annuities makes a significant contribution in that context.

More book reviews are available on the CFA Institute website or in the Financial Analysts Journal.

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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.


About the Author(s)
Barry M. Gillman, CFA

Barry M. Gillman, CFA, is a principal at Longevity Financial Consulting, Fort Lee, New Jersey.

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