And bond investing is likely to remain challenging for years to come. Investors may face a double-whammy — low yields now and the prospect of significant losses as yields rise. On Friday, after the Labor Department reported that the unemployment rate edged up to 7.6 percent from 7.5 percent, yields rose further, amid uncertainty about the Fed's intentions.
Despite this market instability, bonds tend to be the investment of choice as people retire, because they throw off steady income. But as the projections from Bernstein Global Wealth Management suggest, over-reliance on bonds leads to financial quandaries.
These projections, based on proprietary market and economic forecasts and portfolio analyses, as well as on standard actuarial and tax data, estimate future probabilities for investors. That's a quixotic task at best, intended to illustrate possible outcomes rather than to provide precise forecasts, said Mr. Masters at Bernstein.
Still, they are worrisome. Consider again the 65-year-old couple who are starting to draw down $1 million in savings this year: if they withdrew 3 percent, or $30,000, a year, rather than that standard rate of 4 percent, inflation-adjusted, there is still a one-in-three chance that they will outlive their money, under current market conditions.
There are ways to improve these outcomes, but they have their own hazards. Adding stocks to a portfolio is an obvious counterbalance. And there is now a broad consensus among asset managers and academics that stocks have an unusually high likelihood of outperforming bonds over the next decade. That was the finding of a recent study by two economists at the Federal Reserve Bank of New York.
The Bernstein projections concur that adding stocks to a portfolio reduces the risk of outliving your savings. But it also increases the risk of big losses.
Assume, for example, a diversified portfolio that is 80 percent invested in stocks and 20 percent in bonds — a much higher stock-to-bond ratio than advisers typically suggest for someone near retirement. In that situation, under current market conditions and at a 4 percent withdrawal rate, the probability of running out of money drops to 14 percent. That's mainly because of higher expected returns for stocks. At a 3 percent withdrawal rate, the probability of outliving the portfolio is only 4 percent.
But then stock market risk comes into play. Over the long term, stocks tend to outperform bonds, but typically fluctuate much more wildly. There's a good chance that at some point, stock investments will produce major losses that many people simply can't tolerate.
"We find that people tend to think of losses in their portfolios based on the peak value they've ever had," Mr. Masters said. So Bernstein calculates the probability of what it calls a "peak-to-trough loss" of at least 20 percent in its sample portfolios.
For those with an 80/20 mix of stocks and bonds, it found a 60 percent probability of such a loss over the investors' lifetime. And, of course, some market declines far exceed 20 percent.
"Large losses may not be something that people are willing to live with, even if they are associated with higher returns over the long term," Mr. Masters said. "Which is why we'd recommend holding some stocks, but not as much as 80 percent, for most people."
Bonds would fare better in an economic environment more typical of the past, with higher interest rates, among other factors, Bernstein projections show. Should those conditions return one day, investment choices would be less stark. Under "normal" conditions, Bernstein projects, at a 4 percent withdrawal rate, inflation-adjusted, a portfolio 100 percent invested in bonds would have a 38 percent chance of running out in an investor's lifetime; at a 3 percent withdrawal rate, the chances drop to 14 percent.
Other investment companies modeling similar problems come up with different numbers, although the broad implications are reasonably close. "We're operating in the same ballpark," said Ms. Bruno at Vanguard.
T. Rowe Price projections — which don't differentiate between current conditions and a historically normal environment — include different stock and bond indexes, and don't include the effect of taxes. That outlook finds that a 65-year-old couple who invested entirely in bonds have a 21 percent chance of outliving their portfolio. That's much more favorable than the Bernstein projections.
Still, Jim Tzitzouris, quantitative analyst at the asset allocation group of T. Rowe Price, said, "In the current environment, it's worth being quite concerned about the effects of low interest rates on a retirement portfolio."