The reviewed book introduces the benefits of life annuities and why it would be a good retirement income product and provides a comprehensive review of the literature life annuities. It is written such that people without prior knowledge of life annuities can easily understand the product and its features.
Chapter one discusses the institutional details of life annuities. It provides a comprehensive overview of the features of the product and the history of the product. Many readers will be surprised to find out that the first recorded life annuity transaction was four millennia ago in Egypt! The historic overview also provides examples of market failure where inadequate pricing and reserving has affected the issuer of life annuities. When looking at product innovations today it is good to keep in mind this historical perspective. It also deals with taxation and default risk from a North American perspective. Unfortunately, for readers interested in the global context, this is missing. An overview of the market is given for North America, where eight companies have total life annuities reserves of over $100 billion. Interestingly, shopping around for annuities can pay off. The monthly income for an annuity can differ by as much as 10% between insurance companies with the same credit rating. As expected, the higher the credit rating of an insurer, the lower monthly income you can expect. However, as the book shows, a lower monthly income does not imply that the credit rating has to be better. The chapter concludes by discussing variable annuities. Although these are popular annuity products, it is not the focus of the book and thus not much detail is provided.
Chapter two discusses ten formulas. The first four formulas relate to mortality tables and annuity pricing. It goes step by step from mortality rate to survival probability to constructing a life table. The book starts with providing the definition of the mortality rate. Technically literate readers might get confused by the definition of mortality rate as it uses rates and probabilities interchangeably. However, given that mortality probabilities are relatively small, they are approximately the same. It then continues by providing the equations for the survival probabilities given mortality probabilities and the construction of a mortality table given the Gompertz law. The Gompertz law was introduced in the 19th century and has stood the test of time, it is still applicable today. The nice feature of the Gompertz law is that based on only two parameters, a modal age at death parameter and a dispersion parameter, a mortality table can be constructed. This indeed would be a useful tool for financial planners in order to easily create individual survival curves for their clients based on their subjective life expectation. Those clients could be surprised to see their probability of living to advanced ages and would value financial advice for retirement even more. The last step is the construction of the price of a life annuity, assuming a time independent interest rate. The book also provides a pricing formula for annuities when mortality follows the Gompertz law, which then could easily be used when determining the money's worth for individuals given their subjective survival beliefs. The book also provides the formula for the money's worth of annuities. The closer to one the money's worth of annuities is, the fairer the price is. The author shows that the literature has found that the money's worth of annuities has been close to one for those who buy them, but only around 0.9 for the average person.
In retirement an individual can manage their risk of outliving their financial assets by purchasing a life annuity. Alternatively, one can set up an investment strategy themselves and hope that it will fund their spending needs until you pass away. Then there is a probability that at some point in time you cannot afford your lifetime anymore and run out of money. The book provides this lifetime ruin probability given constant consumption level for different spending rates and investment portfolios. Probably surprising to many is that with a very moderate spending of only 5% of your initial retirement wealth you will have a chance of at least 1 out of 4 to run out of money in retirement.
Given that without annuities the probability of running out of money is substantial; it might be worthwhile to include annuities in your asset portfolio. The book introduces the implied longevity yield, which is the annualized return when one would buy an annuity and in a number of years would sell the annuity. Alternatively, it can be seen as the annual return a portfolio needs in order for it to outperform postponing the purchase of an annuity. This concept is valuable for individuals who have decided to purchase an annuity at some point in their retirement, but consider postponing doing so. Of course, the older you are, the higher your mortality probabilities are and thus the higher your implied longevity yield would be. A reason why consumers, especially nowadays, might want to postpone the purchase of an annuity is the hope for a better deal in the future due to rising interest rates. The book provides the interest rate sensitivity for annuities and argues that it is low for people in their 70s. Given that the implied longevity yield is high at those ages, it is probably better not to postpone purchasing a life annuity at those ages.
The final part of the second chapter discusses tontine products, also known as group self-annuity products. This is a kind of life annuity product, but the risks are borne by the group of buyers of the product. The defined benefit pension in the Netherlands, with its soft rights, could be seen as a tontine product rather than a life annuity.
The third chapter provides a literature review of the academic papers relating to life annuities. It starts with the papers which investigate the role of annuities in portfolios in a life cycle model. Not only does the chapter discuss the seminal paper by Yaari, but also papers which investigate the role of bequests and pre-annuitized wealth on the annuitizing decision. Next it discusses the papers relating to when to purchase a life annuity and what type of life annuity. Generally, most papers find that the optimal age at which one should purchase a life annuity is in their 70s. Before that the equity premium is too high relative to the implied longevity yield to make annuities preferable. Given that life annuities are utility enhancing, it is a puzzle why relatively few people actually buy them. The book discusses numerous reasons from the literature as to why people do not annuitize. These include rational reasons, such as bequest and pre-annuitized wealth. More interestingly, it also discusses behavior reasons, such as default options and peer effects. Next, it summarizes the empirical studies on the money's worth of annuities around the world. Generally, life annuity prices include a loading, but it is not too large. The chapter concludes by discussing policy and institutional settings. This includes the move from defined benefit pensions to defined contribution and arrangements.
The final short chapter provides a summary of the book, the takeaways and a discussion of the future of life annuities. The book provides a valuable introduction to life annuities, which is an especially good read for retirement financial planners.
