When I turned 60, my wife and I still had a few years of asset accumulation ahead of us. But we started thinking about our decumulation, or drawdown, years. We are aware that a couple in good health has roughly a 50/50 chance that at least one of the two will survive beyond age 90. We had some idea of what our financial goals were — they were the typical ones of supporting a lifestyle and leaving bequests — but had not made any serious projections about the probability or means of achieving them. We knew that my familiarity with matters related to investment and longevity was grossly insufficient to enable us to plan well; our ignorance of personal, gift, and estate taxation, for example, could have a much greater negative impact on our planning than the positive impact our limited knowledge would provide. So, we found a financial planner supported by a team of specialists, and we have made what appear to us to be adequate arrangements, although the need to monitor the ongoing appropriateness of those arrangements will never cease.

My intellectual curiosity remained unsatisfied in one aspect. Should we buy a lifetime income annuity to lock in our proposed spending pattern? If not, why not? If so, at what age, or in what circumstances, should we buy it? I thought about these questions and searched the relevant literature. I concluded that most people probably need a lifetime income annuity. My wife and I are fortunate enough not to need one yet. And some people will never need one. This article explains why.

Why having annuities available is beneficial  
Have you come across the concept of “annuity-equivalent wealth”? Briefly, here’s what it means.

Imagine two societies, A and N (A for available lifetime annuities and N for not available). You and your spouse live in Society A. You’ve worked out your desired postretirement spending pattern. And you have just enough money to lock in that spending pattern by buying an annuity. Buying that annuity gives you a certain amount of utility. (That’s economist’s jargon for how good you feel.)

Your twin and your twin’s spouse live in Society N, and they have exactly the same desired lifestyle and exactly the same amount of money as you. But they don’t have annuities available to them. So, they’re exposed to longevity risk. What do they do? Being sensible, they set aside some money each year against the chance that they’ll live past 90. Thus, they spend less than you and have less utility than you. Depending on what exactly delivers utility — or, as an economist would put it, depending on the shape of the utility function — their utility might be 80 percent or 90 percent of yours; certainly, it will be less than 100 percent because, unlike you, they cannot live their desired lifestyle.

How much more money would they need to raise their utility to your level? That’s what annuity-equivalent wealth measures. It’s expressed as a ratio — 1.2 or 1.45 or whatever — and is always bigger than 1.0, of course, because no pooling mechanism exists for longevity risk. That’s why you’re better off living in Society A than in Society N. (Admittedly, I’m ignoring the fact that your twin will be able to leave a bequest, and you won’t. But the utility from a bequest is typically much smaller than that from living comfortably yourself.)

Buy a lifetime annuity early or late?
Annuity-equivalent wealth has an interesting corollary related to age. If you look at calculations of annuity-equivalent wealth, you’ll find that it increases with age. The reason why is simple. The longevity curve — which shows how many people are likely to die at each age in any defined group of people — flattens as the age increases. Mathematically, the standard deviation of your life expectancy is a bigger proportion of your life expectancy the higher your age. For example, for U.S. males aged 60, life expectancy is 22 years, with a standard deviation of 9 years, which is about 40 percent of the expectancy. At age 75, the life expectancy is about 10.5 years, with a standard deviation of 6 years, or about 60 percent of the expectancy.

Therefore, in Society N, as you get older, you’ll have to set aside a bigger proportion of your remaining wealth every year to hedge your longevity risk; so, annuity-equivalent wealth increases with age. In other words, the benefit to you of an annuity to hedge your longevity risk increases as you age.

This fact has an important consequence. We know that lifetime annuities cost less the older we are. And now we know that their value as a hedge increases with age. So, if you put off buying a lifetime annuity, its price goes down as its value goes up. Therefore, postpone buying an annuity as long as you can!

But that conclusion leads to two obvious questions: How long can you postpone buying an annuity? And shouldn’t everybody buy a lifetime annuity?

Should everybody buy a lifetime annuity?
Quite simply, no. In my discussion of annuity-equivalent wealth, I specified that you must have exactly enough wealth to buy the desired annuity. But what if you’re Warren Buffett or Bill Gates? In that case, you have so much money that you never actually decumulate; even in retirement (which, given their passion for what they do, is a theoretical concept for them anyway), you’re still accumulating. You simply don’t have a financial exposure to longevity risk.

So, if you have, at most, enough money to buy your desired lifetime annuity, buy it, because doing so maximizes your utility. But if you have more than enough for the annuity, you have the luxury of focusing on wealth management first and longevity protection only in certain circumstances.

More wealth, more choices
I have found it useful to think of the amount of one’s wealth as levels of a house, each level providing more freedom than the one below it.

To start with, all of us have some pre-annuitized wealth, in the form of Social Security or perhaps from some other source (e.g., a defined-benefit plan). Although we tend not to include the present value of the likely cash flow from these sources in our financial assets, they are nevertheless valuable because they directly reduce our financial risk from longevity. Think of this level as the foundation of the house, below the ground but anchoring the whole structure.

The first level above ground is the “essentials zone.” Its ceiling is the amount required to buy a lifetime annuity that, in addition to pre-annuitized wealth, will provide enough income to meet essential needs every year. A family that cannot fill the essentials zone hasn’t enough money to guarantee the essentials of life for the rest of their lives. Their best strategy is probably to keep an emergency cash reserve and rely on social assistance for longevity protection.

The next level is the “lifestyle zone.” Its ceiling is the additional amount required to buy a lifetime annuity that will provide enough income to meet the family’s desired lifestyle each year. This zone, therefore, provides enough money to lock in essentials but not enough to lock in the full lifestyle. The amount of wealth to annuitize here depends on the strength of the family’s bequest motive. The weaker the bequest motive, the more inclined the family will be to buy an annuity and secure as much of their lifestyle as possible. The stronger the bequest motive, the more inclined the family will be to lock in a portion of their desired lifestyle and take some risk by investing the rest for a bequest.

Most people’s wealth will probably not fill the lifestyle zone. For them, longevity protection is more important than worrying about investing, and the only question is how much of their lifestyle to lock in with an annuity.

The next level is the “bequest zone.” Here, the family finally has enough to satisfy their lifestyle, as well as a surplus to invest for a bequest. But it’s important to monitor that surplus. The last few months have shown us how quickly it can evaporate and take us back to the lifestyle zone. Dynamic hedging becomes particularly important for these families.

Finally, the top floor is the “endowed zone,” where live those families that never decumulate because the investment return on their wealth is sufficient both to live on and to enhance their wealth. They have the luxury of focusing solely on investing for bequests.

To sum up, financial exposure to longevity risk is dominant until wealth increases sufficiently to be able to buy a lifetime annuity that locks in a desired lifestyle. Above that level of wealth, buying an annuity to lock in some or all of a lifestyle is a risk-minimizing choice; postponing the annuity purchase results in lower cost and higher value from the longevity hedge.

This article is based on ideas in a forthcoming book, The Retirement Plan Solution: The Reinvention of Defined Contribution, by Don Ezra, Bob Collie, and Matthew X. Smith, to be published in 2009 by John Wiley & Sons, Inc.