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Calculating The Probability Of Running Out Of Money In Retirement

It is a question on the minds of so many people that are planning for retirement: Will I run out of money? We can take into account all of the income a person expects in retirement as well as their assets and spending needs and give a good idea of how long their funds will last. However, this is a static view of things, and as we all know, investment returns and inflation have been anything but static.

So what is the alternative to a static look at one’s retirement situation? The alternative is Monte Carlo analysis, which is a statistical tool that runs hundreds or thousands of scenarios and gives a person the probability that he or she will never run out of money. It does this by looking at the historical volatility (standard deviation) of the person’s investments as well as the correlation among those assets. We then plug in a reasonable assumed average total return for each investment, either based on history or based on the user’s projection, and the Monte Carlo simulator will shock these returns every year, generating many scenarios and the probability of not running out of money.

Let’s take a look at how this works. I ran a couple’s retirement plan in our retirement planning application. Here were my starting assumptions:

Inflation (CPI)


Current Age of Both People


Age Of Retirement


Age When Both People Have Passed Away


Social Security at age 67 (combined)

$35,000 per year

Average Savings Rate

6% on Income of $100,000

Total Investment Balance Today (all in IRAs)


Recurring Annual Expenses in Retirement


Investment Mix

60% U.S. Value Stocks, 15% Emerging
Market Stocks, 25% Treasuries

Investment Location

50% in taxable accounts, 50% in IRAs

Return Assumption Value Stocks

6% per year

Standard Deviation Value Stocks


Return Assumption Emerging Mkt Stocks

9% per year

Standard Deviation Emerging Mkt Stocks


Return Assumption Treasuries

1.5% per year

Standard Deviation Treasuries


In the static case, I found that this couple would not run out of money before the end of their plan at age 95. In fact, they would have nearly $500,000 (in today’s dollars) left in their plan when they’re 95. However, this is a static look at things where we assume the total returns of their investments do not change from year to year. Using Monte Carlo analysis, we can have the returns shocked from year to year to find the probability that their funds are never depleted.

It turns out that in this case the probability that they never run out of money is only 50%. There are just too many scenarios where the total returns are bad enough to deplete their funds. Part of the problem is the volatility of equities today. The other problem is that this couple is not beating inflation with their treasury investments.

Remember that 25% of this couple’s portfolio is invested in treasuries earning a return well below the rate of inflation. As I pointed out recently here, inflation can simply ruin a portfolio’s value over time. It is incredibly important to at least break even with inflation. So I moved the 25% of treasury funds they own into a 50/50 combination of Treasury-Inflation Protected Securities (TIP) and a portfolio of solid dividend paying stocks with a history of consistent dividend growth, such as Johnson & Johnson (JNJ), Procter & Gamble (PG), Coca-Cola (KO), Exxon (XOM), Intel (INTC), and Wal-Mart (WMT).

I assumed no increase in the prices of these dividend payers, but I did assume they would continue to increase their dividends at their five year growth rate. I also assumed that the dividend payers have a lower volatility than typical U.S. stocks, which is generally true given their steadier returns over time due to dividend payments. I assumed a standard deviation of 12% for them. Here is what I found:

Probability Of Never Running
Out Of Money (Original Case)

Probability Of Never Running
Out Of Money (Funds Shifted From Treasuries To TIPS And Dividend Payers)



The probability of never running out of money increased by a sizable 15%. From here this couple can tweak their plan further by saving more money or retiring later to increase the probability to an even safer number. As an example, if they push out their age of retirement to 67 they would increase the probability that they never run out of money to 75%.

We live in a world of change and nothing is static. Building a retirement plan is fraught with assumptions, even those that use Monte Carlo analysis. But we can give ourselves a more realistic look at how things might pan out of we use statistical tools such as Monte Carlo that give us a more dynamic view of how our plans might unfold.


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