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Lately I’ve been writing about the case for annuities and my gradual acceptance of their likely role in my own retirement. (See Why an Annuity Could Be in Your Future and A Floor with an Upside: The Best Strategy for Lifetime Income?) Unless you commit to an extremely frugal lifestyle, or build assets into the multiple millions, there is a good probability that you’ll need to employ an annuity too, in some form, to meet your retirement income goals.

An annuity is a contract with an insurance company to pay a stream of income over a set period, possibly for life, in exchange for a lump sum. There are a dizzying number of annuity types and options, and I’m not going to get into those details here. (For a solid primer on annuities see What Is an Annuity and How Does It Work?)

When considering a fixed income annuity, there are at least two critical questions for a potential retiree: How much annuity do I need? And: When should I buy my annuity (or annuities)? To secure lifetime income, you must get both of those questions right.

I’m going to tackle the question of *how much annuity you need* here, and handle the *timing* question in a later article.

But, before we get started, let me redouble my usual **disclaimer **by saying we’re heading into terrain that could well require *professional advice* tailored to your personal situation. There are many variables when discussing retirement income and it’s impossible for me to know and address them all here. However, I do hope to shed light on a few key concepts that will put you on track to designing a good solution, if you’re a technically-minded do-it-yourselfer, or dealing with a financial professional who can do it for you.

### Three Key Ratios

First some background: there are three *rates* or *ratios* that are the key to the entire puzzle. These aren’t complicated in themselves, but it is essential to grasp them each individually before we analyze just how much of an annuity you?ll need. Once you understand these rates, we?ll work through a simple example to see how large an annuity is needed.

**The Sustainable Withdrawal Rate (SWR)**: I’m calling this a "sustainable" withdrawal rate rather than the more conventional "safe" withdrawal rate, which has become so identified with the 4% rule. That rule is under attack because of high current stock market valuations, the anomaly in U.S. vs. international market performance, and the extended length of modern retirements — which could well span 40-50 years. (The 4% rule was originally formulated for a 30-year retirement.) So by "sustainable" rate we are talking about a very conservative annual withdrawal rate, from an investment portfolio of between 40-60% stocks, that most modern experts believe would not risk depleting that portfolio over an indefinite time span. Nobody knows that number for certain, but in today’s world, 4% probably doesn’t cut it. Avant-garde researchers such as Wade Pfau and Jim Otar have argued that a modern sustainable rate could well be more like 3% or even less. Rather than try to prove the un-provable, I’m going to take 3% as a tentative value for our working example and move forward. You can adjust that number as you get more clarity on the economy and your own retirement.

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**Your Withdrawal Rate (WR)**: This is simply the shortfall in what you need to live annually (after pensions or Social Security have been applied against your regular expenses), divided by the total amount of your investment assets. The best way to determine the first part of this ratio is to track your expenses for at least a year. That way you’re using actual numbers and don’t overlook occasional costs such as auto maintenance, travel, or property tax. If you don’t own your house outright, you’ll need to include rent or mortgage interest in your expenses as well. By "investment assets" we mean the money that you can tap to pay for living expenses, via dividends or growth. So, for example, you shouldn’t count home equity. For our working example, let’s say you have a $1 million portfolio and need $40,000/year on top of pensions or Social Security to live. That makes your Withdrawal Rate 40,000/1,000,000 or 4%.

**The Annuity Rate (AR)**: This is simply the annual payout on a fixed income annuity with the features you need, divided by the amount of money you must give the insurance company to purchase the contract. This rate will be a function of your age, the provider, the current state of the bond market and interest rates, and the type of annuity and the options you select. (For a refresher on annuities, see What Is an Annuity and How Does It Work?) If you are married, you’ll need a Joint Life annuity to cover you both with lifetime income, and this will reduce the rate. If you are concerned about inflation, and have no other protection, you’ll need an inflation-adjusted annuity, which will reduce the rate further. Annuity rates fluctuate constantly: right now they are relatively low, in concert with low interest rates. You can get quotes for your specific situation at ImmediateAnnuities.com or Vanguard. For our working example, let’s suppose that a $25,000/year payout with the features you need can be purchased for $500,000. In that case, the annuity rate (AR) for you is 25,000/500,000 or 5%. (Keep in mind this is a hypothetical number: your Annuity Rate will surely be different, depending on your circumstances and when and where you obtain a quote.)

### A Common Scenario

So now we have some basic concepts in place — the three key rates for discussing an optimal annuity mix.

You’ll notice that when I explained the rates above, they appeared in order of **increasing magnitude**. In other words, the Sustainable Withdrawal Rate (SWR) was lowest at 3%, followed by your own Withdrawal Rate (WR) at 4%, followed by the Annuity Rate (AR) at 5%. (And remember that all these numbers, with the possible exception of the first, are purely hypothetical: you must replace them with your own values.)

**SWR < WR < AR**

?SWR less than WR less than AR? is a common scenario, and the one for which this article is most valuable, but it’s by no means the only possibility.

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The big wildcard is your Withdrawal Rate, because that is a function of your desired lifestyle (expenses) divided by your savings (investment assets). And we know that for many boomers with insufficient retirement savings, equal to only a few years of living expenses, that ratio is *off the charts* — 30%, or worse.

Then there are those who have saved more than necessary, or are prepared to live a lifestyle of extreme frugality. For them, the Withdrawal Rate might be only a percent or two.

We’ll discuss those boundary cases shortly. But, for now, know that many who have saved diligently over a long career, and led a modest lifestyle, will have Withdrawal Rates **between** the Sustainable Withdrawal Rate and their prevailing Annuity Rate, and that’s the audience that will be most interested in what I have to say next?.

### The Answer in Words

Before we answer the annuity mix question precisely, let’s look at a simple, non-financial example:

What if you mistakenly began filling your car’s gas tank with 86 octane fuel, when the engine really needed 88 octane? You could potentially fix that problem by adding a higher octane, say 90 or 92, to bring the average octane up. It’s the same idea with buying an annuity. If you start with an unsafe Withdrawal Rate, you can move some of your investment funds into a relatively "high octane" annuity, to bring your overall withdrawal in line with a Sustainable Withdrawal Rate.

Back to the question: *How much annuity should you buy?*

Here’s the answer, in words: you need to buy enough annuity so that it pushes your remaining Withdrawal Rate (WR) down to the Sustainable Withdrawal Rate (SWR). Why do you need to do that? Because, if your WR remains *greater* than the SWR, you run a serious risk of depleting your portfolio over a long retirement starting from the current market conditions.

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And how does an annuity fix that problem? Simple: because the Annuity Rate is *higher *than both your Withdrawal Rate and your Sustainable Withdrawal Rate in this example, whatever funds you put into an annuity will give you more income "bang for the buck" than your other funds, thus pushing your remaining WR down towards the SWR.

Annuities can pay more than prevailing interest rates because some of the money is return of principal, plus the insurance company keeps the annuity premiums of those who die early to make the payouts of those who live longer. The cost for that magic is the price of your annuity, because that sum is removed from your investment portfolio, and your estate, and winds up in the insurance company’s coffers.

### The Answer in Numbers

And now for the formula that can apportion your investment funds, telling you just how much annuity to buy.

It’s pretty simple actually, and looks like this:

**Annuity Percent = (WR – SWR) / (AR – SWR)**

Calculating that for our working example we get:

**(4% – 3%) / (5% – 3%) = 1/2** or **50%**

So, if you were to have a $1 million portfolio and need $40,000 annual income to cover retirement living expenses, and you believe the highest Sustainable Withdrawal Rate is 3%, while the quote for your Annuity Rate is 5%, then you’d need to move 50% of your portfolio into an annuity to meet your retirement income objectives.

Let’s back-check this to make sure it works: If you had that $1 million portfolio and used 50% of it to buy an annuity paying out at a 5% rate, then you would be left with $500,000 in your portfolio and an annuity paying $25,000 annually. You could then take the conservative Sustainable Withdrawal Rate of 3% from that $500,000 remaining portfolio indefinitely, for another $15,000 annually in income. Add those two income streams (the $25,000 from the annuity plus the $15,000 from your portfolio) and you get the $40,000 in annual income that you required at the start.

*It works.* The formula produces the retirement income you need by combining a guaranteed lifetime income from an annuity with a very conservative Sustainable Withdrawal Rate from your remaining investment portfolio.

### Boundary Conditions: The Other Scenarios

Before we end, let’s look at the boundary conditions. What happens if your own Withdrawal Rate is *not* within that common range in between the Sustainable Withdrawal Rate and the Annuity Rate? What if it’s *less than* the Sustainable Withdrawal Rate, or *more than* the Annuity Rate?

**WR < SWR** or **AR < WR**

Let’s start with the **happy case**: If your Withdrawal Rate is *less than the Sustainable Withdrawal Rate*, then you can dispense with these calculations and with annuities altogether, if you choose. Because your expenses are so low, or your portfolio is so large, you can rest easy knowing you can withdraw annual living expenses from your portfolio and your assets are likely to survive an indefinite time span, without needing the performance boost of an annuity.

As for the much more common, **unhappy case**: What if your Withdrawal Rate is *greater than the Annuity Rate*? Then the equation above will produce a percentage above 100%. *Not good.* That means to support your lifestyle, you need more money than you have. While buying an annuity could improve your situation, it can’t alone fix it. You are at risk of running out of money in retirement, unless you either cut back on your lifestyle and expenses, or work longer to generate more income.

### Stay Tuned

So that?s it. I’ve explained one sound approach to answering the question: *How much annuity do you need?*

The solution, again, is that you need enough to push your Withdrawal Rate down below whatever truly Sustainable Withdrawal Rate is dictated by current economic conditions. This allows the remainder of your portfolio, which wasn’t used to purchase the annuity, to last indefinitely.

The simple equation above, a function of your Withdrawal Rate, the Sustainable Withdrawal Rate, and the Annuity Rate, tells you the actual percentage of your portfolio that must be moved into an annuity.

Stay tuned for more articles on retirement income. There is a lot left to say about choosing and timing annuities to meet the need for secure lifetime income….

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** Credits:** Jim Otar and his book Unveiling The Retirement Myth inspired much of my thinking on this issue. The key insights and some of the terminology here are thanks to Jim, though the presentation is mine. If you’re technically-minded, see his book for a more detailed discussion, along with extensive supporting data and examples. Otherwise see a professional adviser, like Jim, for help with your personal situation.

Very Nice!

Unfortunately, my guess is that a person who can actually read what you have written and understand it has probably positioned themselves to be in the "happy case" boundary value situation anyway. Nonetheless, it is reassuring from a fellow DIYer to have independent confirmation of one's own thinking.

Thanks ERE. I really appreciate that, coming from you!

Yes, this might be my most ambitious post to date. It's a critical topic that I personally wanted to understand and write about. The math is pretty simple, but taken altogether it could be a little overwhelming to some. That's why I recommend consulting an adviser if there is any doubt.

I'll be approaching related annuity topics from some less technical angles in posts to come….

I don't know if you follow Wade Pfau, but here is an interesting blog post vis-a-vis annuities. I would be interested in your impression of his analysis.

http://wpfau.blogspot.com/2012/09/an-efficient-frontier-for-retirement.html

Darrow,

I also appreciate your writing on this topic. I'm not sure, but I hope that we will not need an annuity. My concerns: a) the risk that the insurance company will be viable for 40-50 years, b) interest rates will eventually increase, and then the AR rates and bond yields will go up, so I'd be leaving money on the table by buying an annuity sooner than later.

Regardless, I think you hit the nail on the head about determining ones WR: record everything for at least a year to fully understand where your money is going. Simple advice but my sense is that it's not followed much. Too much effort for most as well as a desire to keep ones head in the sand.

Regards,

Barry

Thanks for the comment Barry. I share your concerns on insurance company viability and interest rates. Those are prime examples of the uncertainty in retirement planning that we really can't escape. By contrast, we have a lot more control over our living expenses, so that's a good starting point. Though often ignored, as you say.

ERE: thanks for the pointer to Pfau's excellent efficient frontier article. (I do follow his site but hadn't gotten to this one yet.) I'll read the original paper when I get time, but on first look this is invaluable research from Wade. He seems to be extending and improving on results from others (Milevsky and Otar).

I did pose a question on his blog: Very interesting to look at annuities as "super bonds," then leave bonds out of the investment portfolio altogether. But that leaves a question: how can we consider 100% stocks as a buffer/emergency reserve? They don't really satisfy that objective, due to volatility. We'll see what he says.

I also note that he, like most advisers, warns that these results are not "one-size-fits all." You have to run the numbers for each retirement scenario they say….

Thank you for the post. But i feel that it does not adequately address inflation. Concur that SWD, by definition, does account for inflation. But, Fix'd pensions are not inflation adjusted. So, subtracting fix'd pensions from your retirement expense shortfall, understates your inflation adjusted shortfall. Moreover, the AR is fixed and therefore the Annuity payouts are also not inflation adjusted.

Citing your working example, assuming no SS and no pension, results in half of your income being inflation adjusted (WD portion), while the other half on your income would not be inflation adjusted (Annuity portion). To me, without making this point clear, it grossly overstates the benefits of annuities. Perhaps more importantly, I feel this point fundamentally undermines the entire point of the blog post. Am I missing something here? What do you think? Thank you for your time.

Thanks JSM. Sometimes it's necessary to simplify a discussion in order to focus on the essential points. In this post, I was focusing on how to mix an annuity with an investment portfolio. So inflation wasn't the primary concern. That doesn't mean inflation is not important in general, so I appreciate your comment. And I could have been clearer about the issues with mixing inflation-adjusted and non-inflation-adjusted income streams.

Note it isn't exactly the case that fixed annuities are not inflation adjusted. That's a feature that can be added to some annuities, for a cost. I did note in my post that "If you are concerned about inflation, and have no other protection, you'll need an inflation-adjusted annuity, which will reduce the rate further." In that case, the example math is in real, inflation-adjusted terms.

Though the concept of inflation-adjusted retirement income is appealing, it's not a slam dunk that an inflation-adjusted annuity always makes sense.

For some thoughts on current cost considerations for inflation-adjusted annuities from a leading researcher see Update on Retirement Income Market Conditions. For my own thoughts on why inflation may not always be the bugaboo it's alleged to be, see What is Your Personal Rate of Inflation?