In an article called “Retirement: When Your Portfolio Starts Paying You”, we told retirees that less can be more. If you withdraw less from your portfolio in the early years of retirement, you can take out more later. That might seem obvious.

But the less-is-more message this time isn’t so obvious: Retirees may wind up with more money by investing in assets that have lower long-term returns.

This article isn’t a pitch for investing in bonds, though they are an essential part of most retirement portfolios. No, this is a pitch for investments of any type that have lower risks.

I’m not advocating low-risk investing for psychological reasons, though I often do. Right now, I’m advocating it for purely mathematical reasons.

I’m going to show you real-life examples of something many retirees don’t understand: There’s a big difference between the best way to invest before retirement and the best way to invest after retirement.

In the broadest sense, investing can be broken down into two phases: accumulation and distribution. The accumulation stage usually comes before retirement, when an investor is adding assets, not withdrawing them. Growth is the objective; stability is comforting, but it doesn’t affect the math.

The distribution stage usually starts with retirement. That’s when stability starts to matter a great deal – more than most retirees realize.

When we work with clients, we often use a standard retirement portfolio scenario in which an investor retires with $1 million and takes out $60,000 the first year for living expenses, increasing the annual withdrawal by 3.5 percent every year to cover inflation.

Because the scheduled withdrawals go up relentlessly every year, they take an increasing bite out of the portfolio. Withstanding that ever-growing bite requires something new: stability, or the lack of volatility and negative returns. And that, in turn, requires a different kind of asset.

The most important thing we look at in this simulation is not the annualized return. It’s the value of the portfolio from year to year. This measures the most important thing retirees need to know about their finances every year: Are they in danger of running out of money?

Almost every seasoned investor knows, at least in a general way, about the “magic” of compound interest: its ability over many years to turn a small investment into a huge one. And the “magic” of dollar-cost-averaging is also well known.

Much less familiar is a mathematical quirk that should be understood by every retiree: the difference between performance during accumulation and performance during distribution.

When you’re accumulating money, what matters (at least mathematically) is how much you wind up with eventually. If you get to your goal, it doesn’t matter much how you got there. If your portfolio lost 45 percent the first year and then enjoyed an unending run of 14 percent annual gains (this is too good to be true in real life, but it makes the point well), you could be happy. In 16 years, you would nearly quadruple your money.

But here’s something that might surprise you : That very same hypothetical scenario – a serious loss followed by unending 14 percent gains, could spell disaster for a retiree. Those returns seem very favorable. But in a $1 million portfolio from which $60,000 is taken the first year and the withdrawal is raised by 3.5 percent every year, those returns would leave an investor broke after 16 years.

You’ll see this in Table 1, which shows year-by-year results of a portfolio that starts with $1 million and has only one bad year.

Though that example is pure fiction, the same thing happens in the real world.

Table 2 shows the year-by-year results of retiring as described above using real returns from two very different asset classes for 1973 through 1985.

We didn’t choose that period at random. We chose it because during that span of 13 years, the annualized returns of two quite different asset classes – the Standard & Poor's 500 Index and the Lehman Brothers Intermediate Government/Corporate Bond Index – were nearly identical.

From 1973 through 1985, the S&P 500 Index had an annualized return of 9.6 percent; the bond index’s annualized return was 9.5 percent.

For an investor in the accumulation stage, that means the S&P 500 had a (very) slight advantage over the bond index. Each would have turned an initial investment of $10,000 into nearly $33,000.

But for retirees, the stock portfolio was crippled – even though its long-term returns were almost exactly the same as those of the bond index. This is the whole point of Table 2.