Monte Carlo simulation: will your money last?

Written by the Tactfolio research teamPublished 5 min read

A Monte Carlo simulation tests a plan against thousands of possible futures. This Monte Carlo simulator plays out 10,000 random paths for your savings, one year at a time. It shows how often the money lasts and what might be left at the end. It does not predict the future. It shows the range of results your guesses allow.

  • Each run picks a random return for every year, from the average and volatility you enter.
  • The answer is a chance, like “the money lasted in 70% of runs”, not a promise.
  • Taking $20,000 a year from $500,000 lasted 30 years in about 70% of runs, at a 6% average return.
  • Bad years early on hurt more than bad years later. This is called sequence risk.
  • The result is only as good as your guesses for return, volatility and inflation.

Result

Chance the money lasts
70.1% of 10,000 runs
Middle result at the end, in today's money
$173,023
Bad case: 1 run in 10 ends below
$0
Good case: 1 run in 10 ends above
$937,003

How to use the Monte Carlo simulator#

Type the money you start with, what you take out or add each year, and the number of years. Then set three guesses: the average yearly return, the volatility, and inflation. The simulator shows the chance the money lasts, the middle result, a bad case and a good case.

Withdrawals are in today’s money. They rise with inflation every year, so they buy the same amount each year. The results are in today’s money too.

The starting numbers are examples. They are not advice or a forecast.

How does a Monte Carlo simulation work?#

It runs the same plan many times with different random returns. Then it counts the results.

for each of 10,000 runs:
  start with your money
  each year:
    take out the withdrawal (or add the contribution), raised for inflation
    grow what is left by a random return for that year
  the run succeeds if money is left at the end
chance the money lasts = runs that succeed ÷ 10,000

The random returns follow a bell-shaped curve with the average and spread you choose. Most years land near the average. A few are much better or much worse. Volatility sets how wide the spread is. The curve is a lognormal one, so no single year can lose more than everything.

The bad case is the 10th percentile: 1 run in 10 ends below it. The good case is the 90th percentile: 1 run in 10 ends above it.

A worked example#

Say you retire with $500,000 and take out $20,000 a year, which is 4% of the start. You guess a 6% average return, 12% volatility and 2.5% inflation. You plan for 30 years.

  1. In about 70% of the 10,000 runs, the money lasts all 30 years.
  2. The middle run ends with about $173,000 in today’s money.
  3. In the bad case, the money runs out before year 30.
  4. In the good case, you end with about $937,000.

Now take out $25,000 a year instead. The money lasts in only about 42% of runs. A small change in spending makes a big difference over 30 years.

With no volatility at all, every run would be the same, and the money would always last. The risk comes from the swings, not from the average.

Why does the order of returns matter?#

Say two people get the same yearly returns, in opposite order. One gets the bad years first, while taking money out. They sell more shares when prices are low, so less is left to recover. The other gets the good years first and does fine. This is sequence of returns risk. An average return can’t show it, which is why a simulation helps.

What the simulation leaves out#

  • Extreme years. Real markets have more very bad and very good years than a bell curve.
  • Streaks. Here each year is random on its own. Real markets can have runs of bad years.
  • Taxes and fees. They lower what you keep. Take your fees off the average return.
  • Changing plans. Real people often spend less after a bad year. The simulation keeps spending fixed.

Common mistakes with Monte Carlo results#

  • Guessing a high average return. A guess 2 points higher can turn a failing plan into a safe one on paper. Try lower numbers too.
  • Setting volatility too low. Low volatility makes every plan look safe.
  • Reading 70% as safe. A 30% chance of running out of money is a real risk.
  • Treating the middle result as the plan. Half of the runs end below it.

Try it on Tactfolio#

The simulator makes up returns from your guesses. Tactfolio backtests use real past prices. In the Tactfolio strategy builder you can test a rule on decades of history, and simulated history extends young funds further back, clearly labeled. Real paths include crashes, streaks and slow recoveries that a bell curve misses. Why past results mislead explains what no test can tell you. To turn a start and end value into a yearly rate, try the CAGR calculator. To see how dividends add up, try the dividend calculator. Every tool is on the free trading calculators page.

Common questions#

What is a Monte Carlo simulation in simple terms?#

It is a way to test a plan by running it many times with random inputs. Then you count how often it works. The name comes from the casino town of Monte Carlo, because the method relies on chance.

What is a good success rate for retirement?#

There is no single right number. A higher rate is safer, but aiming for 100% can mean spending far less than you could. Many people pick a level they are comfortable with and plan to cut spending after bad years.

How many runs are enough?#

Thousands. This tool uses 10,000 runs, so the chance it shows barely moves from one set of random draws to the next.

What average return and volatility should I use?#

Use numbers that fit your mix of investments, and test a range. Stocks have had higher returns and bigger swings than bonds. A plan that only works with a hopeful return is not a safe plan.

Is the 4% rule safe?#

The 4% rule says you can take out 4% of your starting savings each year, raised for inflation. It comes from studies of past US returns. It is a rule of thumb, not a promise. Run it here with lower returns to see how it holds up.

Sources

Understand the numbers