### The Final Say On Spending Rule

**March 31, 2015**

**by Laurence B. Siegel**

After decades of focused research, why can’t finance experts decide on a safe withdrawal rate for retirement? It is time to refocus this debate by asking a slightly different question: Is there a spending rule that retirees can use over a fixed time horizon? There is and I call it “the only spending rule you will ever need.”

Ibbotson and Sinquefield documented long-run rates of return on stocks and bonds as early as the 1970s. They came up with generous return projections for diversified portfolios based on this information, but they did not calculate withdrawal rates.^{1} Others used the Ibbotson and Sinquefield data to so do. In the mid-1990s, William Bengen, a trio of authors associated with Trinity University in San Antonio and others coalesced around a safe withdrawal rate of 4%.

No consensus exists among contemporary scholars. Three distinguished writers – David Blanchett, Michael Finke, and Wade Pfau — argue that it’s closer to 3%,^{2} yielding an annual income that is 25% lower than the traditional 4%. The question does not seem that difficult. Why has answering this problem been so contentious?

There are three reasonable possibilities:

- Like string theory, it’s just too hard. Two decades of study are not enough to determine a safe withdrawal rate.
- Market conditions changed, so the safe withdrawal rate changed.
- With risky investments, there is no such thing as a safe withdrawal rate (other than zero).

In a recent *Financial Analysts Journal* piece called “The Only Spending Rule Article You Will Ever Need,” Barton Waring and I argue that the answer is number 3. Here’s our logic. There are three goals that investors pursue:

- A minimum income or withdrawal amount that’s fixed in real terms;
- The possibility of capital growth through risk-taking;
- A guarantee of not running out of money over some time horizon associated with their potential longevity, such as 30 years.

It’s mathematically impossible to achieve all three. Something has to give.

The financial planning community, in proposing withdrawal rates that have less than a 100% chance of success, has given up on the guarantee criterion. In the simulation methods that most planners use, the probability of failure is explicitly calculated and found acceptable. That is one way to make it crystal clear that things might not work out!

By eliminating all investment risk, it’s possible to achieve the other two goals. The real riskless rate (that is, the yield on a risk-free portfolio of TIPS bonds) is currently hovering around zero. If you have a 30-year spend-down period, just spend 1/30 of your initial capital each year. That’s a withdrawal rate of 3.33% of initial capital, and exhausts the portfolio by the end of the period.^{3}

But very few investors will be satisfied with consumption equal to 1/30 of at-retirement capital each year for 30 years. They will want to squeeze more out of the portfolio. The only way to do this, leaving out annuitization for the moment, is to take investment risk, say by buying equities as well as riskless bonds. If the market value of the portfolio fluctuates because you hold equities, as Waring and I demonstrate, then year-to-year consumption also has to fluctuate. Otherwise you will be taking a very real risk of running out of money during the spend-down period.

Put another way, accentuating the positive: If your withdrawal amount is variable and is calculated according to the formula we propose, you will *never* run out of money.

### All right already, what is the magic formula?

It’s not a single formula, but a procedure. The first year’s spending is given by (in ExcelTM notation):

In this equation, 30 is a placeholder for the time horizon in years and $1,000,000 is a placeholder for the initial amount of capital in dollars. The *pmt* (payment) function gives the amount that a fairly priced annuity would pay out in that first year^{4} given the current interest rate on a 30-year riskless Treasury bond, *r0*.

By an “annuity,” we don’t mean a life annuity, but a fixed-term, 30-year annuity. That’s why the investor’s age and gender aren’t inputs; the money just has to last for our retiree’s planning horizon of 30 years, whether he or she is alive or not. In the current environment, most investors use the word “annuity” to mean a *life* annuity (immediate or deferred), offering longevity insurance; but the real meaning of the word is more general and refers to any return of capital to the investor according to a schedule over time. (Insurance companies offer many kinds of annuities that don’t involve longevity insurance including the fixed-term annuity to which we referred above.) We’ll get to life annuities later.

- Full disclosure – I worked on the Ibbotson studies. Yes, I’m that old. I was Ibbotson Associates’ first employee in 1979.
- http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2201323; http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2286146
- In another
*Financial Analysts Journal*article, A Pension Promise to Oneself, Stephen Sexauer and I recommend such an approach mostly as a benchmark or “paper portfolio” designed to measure one’s progress toward an adequate retirement income. In that article, we note that real-life investors are more likely to want to earn a real return of at least 2%, which can only be attained with a good helping of equities, accepting the risk of possible disappointment alongside the hope of doing well. (Why only 2%? If the equity risk premium is 4% – and we have support for that estimate – and if the real riskless interest rate is zero, a 50/50 equity-bond allocation has an expected real return of 2%. Sorry.) - More precisely, it is the amount that the fixed-term annuity would pay out at the
*beginning*of the first year, assuming that the annuity is set up to pay out each year’s cash flow in advance (that is, the payment is for the whole year).

*Exhibit 1*

*30 Years of Spending and Asset Values for Risky Portfolio *

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