Calculating the cost of retirement

Around the World, individuals are living longer than ever before and the burden of supporting growing numbers of retirees is falling on a declining working population. The lucky retirees have generous defined benefit (DB) final salary pensions to support them, sponsored by solvent employers. The less fortunate have worthless DB promises from failing employers and dwindling state pensions to rely on. Increasing numbers have defined contribution (DC) pension schemes and take their luck with interest rate, investment and longevity risk in providing for their own retirement.

Against this background, Moshe Milevsky's new book 'The calculus of retirement income' presents readers with a range of tools for use in the retirement saving problem. Milevsky notes that the book is intended as a textbook for applied courses on wealth management and retirement planning and can serve as a reference text for quantitatively minded financial planners.

Part one of the book - the first eight chapters - provides the underlying mathematical models of retirement saving and investment. Each chapter concludes with suggestions for further reading and a short set of problems. In terms of coverage, chapter one provides some interesting background statistics on dependency ratios and longevity trends, while chapter two considers modelling the human financial lifecycle and presents a deterministic model for calculating required savings rates. Models of human mortality provide the topic for chapter three which looks at mortality rates and tables. Chapter four reviews continuously compounded interest rates and the term structure of interest rates. Models of risky financial instruments, such as equities, are presented in chapter five, including consideration of the differences between arithmetic and geometric returns. Chapter six covers models of pension life annuities, with a good discussion of the basics of annuity pricing. Chapter seven covers models of life insurance, while chapter eight covers models of DB and DC pensions, presenting a DC accumulation model and a model for valuing DB pensions promises.

Part two (chapters nine and 10) covers wealth management applications. Chapter nine looks at sustainable spending rates in retirement, while chapter 10 covers longevity insurance and the individual's decision about whether to annuitise. The final section of the book is titled "Advanced Topics" and presents a discussion of options with variable annuities (chapter 11) and of the utility of annuitisation, including the optimal timing of annuitisation and the option to defer (chapter 12).

Milevsky uses the book for the graduate class he teaches at York University in Toronto and it appears highly suitable for actuarial students and others interested in learning about the quantitative end of life and pensions modelling work. The topic coverage is comprehensive, although most of the material is squarely in the North American context. Some discussion of institutional differences across geographies and the impact that has on modelling may have improved the relevance of the book for non-US readers.

While the mathematics used in the book is not highly complex, equations occupy many pages and may prove intimidating for individuals, even financial professionals, who do not use these modelling techniques on a regular basis. Milevsky encourages us to 'read around the equations' and has worked hard to write clearly and provide us with the intuition of the material. Nonetheless, this is still a book for the mathematically-inclined and may not be to wider tastes.

What is missing from the book? This is a book about personal financial planning issues and we know that individuals, and many of the financial planners they seek advice from, use heuristics and rules of thumb to solve the complex problems of saving and investment (and this text shows us just how complex some of the problems are.) The book is very much in the camp of rational, optimisation-based approaches and has little to say about these rules of thumb. It would be interesting to know whether and how these rules fit with the more theoretical financial economics presented in Milevsky's book. Perhaps that is another book rather than this one, but it is certainly something we should know more about.

- Alistair Byrne CFA, University of Strathclyde and The Pensions Institute.

Title: The calculus of retirement income

Authors: Moshe A Milevsky

Publisher: Cambridge University Press

Price: £25.00

ISBN: 0521842581.