Thanks to a new law that went into effect last month, a retirement tool, which uses probability analyses, is now available to the public. It is touted as vastly increasing your chances of creating a reliable retirement plan.

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During World War II, scientists at Los Alamos, N.M., used a sophisticated technique to calculate the probability that the atomic bomb would explode rather than fizzle.

In the 1960s, the same method was used to figure out the probability that Apollo 8, the first manned rocket to orbit the moon, would make it out of the Earth’s atmosphere without disintegrating.

Fast-forward to today: Financial-service companies from T. Rowe Price and Fidelity Investments to small, independent advisory outfits are touting the method, called the Monte Carlo simulation, as the latest, must-have retirement tool. They say it can help investors see whether their portfolios will provide income throughout retirement or dry up too soon.

Thanks to a law that went into effect Feb. 14, brokers, previously barred from running probability analyses to advise their clients, can now use Monte Carlo simulations.

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Independent financial-advisory firms, meanwhile, have been increasingly using Monte Carlo simulations for the past five years as software and computing power have improved.

And there are a number of Web calculators that run a Monte Carlo simulation for free or a minimal charge.

“It’s at the point where you’ve got to wonder why someone doesn’t have it,” says Chris Cordaro, a financial adviser at RegentAtlantic Capital in Chatham, N.J., who was one of the first advisers to use Monte Carlo in the late 1990s.

So what happens when high science meets retirement planning? If used properly, it vastly improves your ability to create a reliable retirement plan. But many advisers familiar with the tool urge caution.

“Everyone is expecting it and demanding it, but even financial planners don’t necessarily know how to use it properly or how to explain the results to their clients,” says Harold Evensky, a financial adviser at Evensky & Katz in Coral Gables, Fla.

Traditional retirement-planning calculators are a snap to use. You plug in an assumed average annual return, along with information about your savings, investment allocation, age and time horizon, and they spit out a yes or no answer as to whether you are ready to retire.

Problem is, if you get a yes, you get the illusion of certainty, when in reality your chance of success is only 50 percent, if you use a fixed, average return. In other words, “Half the time, the market will do better than the average and half the time it won’t,” Cordaro says.

For most people, a 50 percent chance of success is not good enough when the downside is going broke. “They want some level of comfort that under negative scenarios [for financial markets], they can still live comfortably,” Cordaro says.

That’s where a Monte Carlo analysis can help. You or an adviser preprogram the calculator with a range of returns that seem likely for each of your asset classes over, say, 25 years. The calculator then runs through thousands of scenarios within those parameters, with different levels of returns for each year.

Determining odds

For example, stocks might experience a loss of 5 percent one year and gain of 10 percent the next, leaving you worse off than an average gain of 2.5 percent in each year. Based on how each of the many scenarios would affect your investments, the calculator ultimately determines the odds of meeting your income goals.

T. Rowe Price’s Retirement Income Calculator, a free Web calculator at www.troweprice.com, is one of the easiest Monte Carlo simulators to use. Say you have a $2 million nest egg and you would like to live on $8,000 a month for 25 years after retiring at age 65.

The analysis, based on a number of assumptions about market performance and your asset allocation, shows that you have an 80 percent probability of success. If you’re shooting for 90 percent certainty of reaching that goal, you would have to settle for monthly income of about $7,600.

While probability analyses can shed light on many kinds of financial-planning problems, such as how much you should save for your child’s college education or what kind of life-insurance policy is best, so far it has been used most widely to figure out how much income will be available to spend each year in retirement.

“This is such a complex problem because you have multiple sources of income that are taxed at different rates, and some of which is indexed to inflation and some that’s not,” Cordaro says. And the consequences of a serious mistake can be severe, since you’re drawing down your assets permanently.

A wake-up call

For many, a Monte Carlo analysis is a wake-up call. It points out how making a small mistake can derail a retirement plan.

Say you have a $250,000 retirement portfolio invested 60 percent in stocks and 40 percent in bonds. If you withdraw 4 percent a year to live on — $10,000 the first year — there will be a 97 percent probability that your assets will last your lifetime. But if you instead withdraw 6 percent, or $15,000, which is the rate at which most investors say they expect to withdraw income, according to a 2003 Fidelity study, the probability sinks to 61 percent.

There are a lot of moving parts in a retirement plan, however. So while the Monte Carlo simulation can produce a fair idea of your income trajectory, any model’s usefulness depends hugely on the data it’s fed. And remember, too: Even rocket scientists have to watch the weather report.

The basic Web calculators that run the simulations may be a good way to start a retirement plan. But some of them make assumptions that may not match your situation — unless you personalize them.

For example, the T. Rowe Price basic calculator asks you to choose an asset allocation that best matches yours but doesn’t include real estate in its model portfolios. Property owners may want to use a model that adjusts for home equity.

A calculator offered by Principal Financial Group at www.principal.com assumes withdrawals are on a pretax basis. And while most are programmed with assumptions about market returns, standard deviation and inflation rates, some, such as a Web site called www.Moneychimp.com, require you to come up with those assumptions on your own.

In other words, a Monte Carlo simulation is only as good as the assumptions that go into it, and making them takes a depth of knowledge that “even some financial planners may not have,” says Paul Westbrook, a Ridgefield, N.J., financial adviser.

While most of the popular Monte Carlo software that advisers use — such as DecisionPro and DecisionScript by Vanguard Software, Crystal Ball by Decisioneering and various programs by Money Tree — are prepackaged with economic assumptions, you have the option of tweaking them. The bottom line: Choose an adviser who has experience running Monte Carlo simulations and ask questions about what assumptions he or she is making, and why.

Aside from projected average market returns for each asset class in your portfolio, you need to come up with the actual range of returns you expect above and below the average. Then you must factor in how different asset classes will behave in relation to each other.

“If the correlation between asset classes is low, that will cancel out some of the deviation,” Cordaro notes.

“One of the biggest mistakes people make is they assume historic average annual returns when there’s little chance we’ll see those kinds of returns over the next couple of decades, because markets have changed.”

The average annual return for stocks since 1926 was more than 10 percent, Cordaro says, but that reflects the early decades when people were getting dividend yields of 8 percent and were willing to pay a lot more for stocks than they are now. He suggests a more conservative assumed average return of 8 percent.

Personal assumptions

In addition to the “under-the-hood” economic assumptions that go into a Monte Carlo simulation are assumptions about your personal situation, says Michael Harken, an adviser at Principal Financial Group in Des Moines, Iowa.

One of the biggest wild cards is your life expectancy. The Society of Actuaries provides life-expectancy tables — but it’s best to ignore them, says Ron Gebhardtsbauer, a senior pension fellow at the American Academy of Actuaries in Washington, D.C.

“The numbers are averages — so about half of people will live longer,” he says. The average life expectancy for a 65-year-old woman is 23.5 years [to about age 88 ½], according to the tables. But any woman who used that life expectancy in her retirement plan is making a big gamble. “Forty percent of women live longer than 90, and 20 percent live longer than 95. If you’re one of them, you could run out of money,” Gebhardtsbauer says.

The best bet: Make your calculations assuming you’ll live to at least 90. Then factor in anything else relevant to lifespan, for instance, if you come from a long line of centegenarians, tack on another 10 years.

As for what to figure about your spending in retirement, don’t assume they will decline immediately. “Spending doesn’t usually go down until people slow down — usually around age 70,” says Lynn Ballou, a financial adviser in Lafayette, Calif. In fact, in early years of retirement, spending often goes up as people shell out more for travel and entertainment.

Shoot for a probability of 70 percent to 90 percent, Cordaro and other advisers say. Anything lower and you’re gambling too much. Higher, and you’re giving up too much. “Many people may not even be able to retire if they shoot for a 100 percent probability,” Cordaro says.

Adjust portfolio

As market conditions change over the years, keep track of how your portfolio is doing and adjust your spending or allocation accordingly.

Today you may find your retirement plan has an 80 percent probability of success, but after a couple of years of dismal stock-market returns, you may have to make some adjustments to maintain that probability.

In short, while the Monte Carlo model can help future retirees achieve blastoff into the serious-planning phase, this rocket ship is not, Harken says, “a silver bullet.”

On the web

www.troweprice.com

One of the easiest Monte Carlo simulators to use

www.principal.com

Assumes withdrawals are on a pretax bases

www.Moneychimp.com

Requires users to come up with assumptions about market returns, standard deviation and inflation rates on your own