These retirement saving 'rules' just don't add up

For years, financial advisors have tried to keep retirement planning simple. You can count on the stock market returning roughly 7 percent a year over the long run, according to the conventional wisdom, and expect to withdraw about 4 percent from your nest egg every year once you're retired.

Unfortunately, those two little numbers just don't add up any more. This week, one of our readers asks why. (Tweet This)

Please explain, when the stock market has earned an [average annual] return in the range of 7 percent over the long term, how a 4 percent withdrawal rate from a retirement fund will exhaust funds in about 30 years. It must be related to the fluctuations coupled with the steady annual withdrawal. — Perry W.

It sounds like the math should work: if you can get a 7 percent return over the long term and you're only withdrawing 4 percent, why wouldn't your savings last forever? Unfortunately, the conventional wisdom overlooks two big problems with that assumption. Let's take the 7 percent return first.

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Every week, the world of business and finance brings news that seems designed to confuse most of us. So CNBC Explains wants to hear from you. Each week, we'll answer as many of your questions as we can. (Like most readers, we'd also like to know your first name and where you're from. We may also edit your questions for space.) Any question is fair game.

It's true that, when you average out the stock market's ups and downs, the investment return for the Standard & Poor's 500 index over the long term (back to 1928) has been about 7.5 percent. Adjusted for inflation, though, that long-term return has been more like 4.4 percent. Add back in the return from reinvesting dividends, adjust for inflation again and the return goes back up to 8.6 percent. (We're using a simple compound average. Your estimates may vary.)

Those long-term averages help explain why it's a good idea to invest in stocks if you're young and have a long time to build up your retirement savings. If the market drops, you still have plenty of time to make up those losses in good years. (The simplest way is with a low-cost index fund; if you invest in a managed fund, you will typically pay more in investment fees. Compounded over decades, those fees add up.)

But once you're retired, your horizon shrinks considerably, so you may not have time to make up for those down years—especially if the stock market hits a lengthy slump. There have been plenty of 10-year periods when average annual returns were much less than the long-term average. During the 1960s and 1970s, for example, the inflation-adjusted S&P 500 index fell by an average 1.6 percent a year. So your nest egg would have shrunk even if you'd made no withdrawals at all.

The latest 30-year period has been an unusually good one for stock investors now nearing retirement. With dividends reinvested, you would have generated inflation-adjusted annual returns of nearly 10 percent. That timeline started with the strong bull markets of the 1980s and 1990s and low inflation–both of which helped generate those generous inflation-adjusted returns.

Compare that with that 20-year stretch between 1961 to 1981 when the economy slid in and out of recession four times and inflation soared to double digits. If you were trying to live off a nest egg in those days, inflation wiped out any investment gains from the stock market.

It's possible the latest run of good times will keep rolling for decades to come. But you can't count on it. If you're going to live off your savings for the next 30 years there's a reasonable chance of another long stretch of disappointing stock returns.

So you may want to put some of your money in safer investments. But with interest rates far lower than historical averages, returns on low-risk investments like Treasury bonds have all but dried up. After adjusting for inflation, you get little or no return at all.

That brings us to the so-called 4 percent rule, which is now generally considered out of date. It may have worked when stock returns were above average and interest rates were higher. But recent studies have demonstrated the perils of relying on a 4 percent annual withdrawal.

Read MoreThe 4 percent rule no longer applies for most retirees

A 2013 study by Michael Finke at Texas Tech and co-authors, for example, plotted the "failure rate" (meaning you'll run out of money) of a retirement account over 30 years, using various annual rates of withdrawal.

Even with a high-risk portfolio of all stocks, the authors estimate a 40 percent failure rate over 30 years if you withdraw 4 percent a year. If you try to play it safe and stick with zero stocks, your odds of running out of money are 99 percent. If you withdraw just 3 percent a year, with a portfolio of half stocks and half cash or bonds, your odds of running out of money drop to about 1 in 5.

The 4 percent rule no longer works for two main reasons. One is that those outsized stock market returns of the last three decades probably won't hold up. The other is that "safer" investments—like bonds—are paying much less than historical averages.

Read MoreShould you dump your bonds now?

Low interest rates not only mean you're getting less return on savings stashed in bonds. You also risk losing money when rates go back to historical norms because rising interest rates push bond prices lower. And that cuts into your overall return.

"If today's bond rates return to their historical average after either five or 10 years," the authors wrote, "(we) find that failure rates are much higher—18 percent and 32 percent, respectively for a 50 percent stock allocation—than many retirees may be willing to accept."

That means you'll have to save a little more or count on spending a little less, or both, if you want to make the retirement numbers add up.

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