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Wouldn’t it be nice for our retirement planning purposes if stocks consistently gave us eight to 10 percent returns each year? After all, that’s what stock markets have delivered on average over the very long term.

Indeed, between 1935 and 2016 U.S. stocks returned 11.4 percent annually, Canadian stocks returned 9.6 percent annually, and international stocks averaged annual returns of 8.3 percent.

I have an eight percent target in mind when projecting investment returns for my own retirement plan.

The trouble is that stock returns are anything but predictable and so while they may average eight to 10 percent over a 25-or-50-year period, each single year could deliver panic inducing losses, euphoric gains, or something in-between.

Since 1988, the S&P 500 had single-year returns as low as negative 37 percent (2008) and also gained as much as 37.58 percent in a single year (1995). Only in three of those 29 years did the S&P 500 deliver annual returns between eight and 11 percent. The rest of the years are all over the place.

Why does this matter to your retirement planning? Because it’s not enough to just plug “eight percent” into your retirement projections and call it a day.

What happens if stocks plunge by 35 or 40 percent in year one of retirement, as they did to those unlucky enough to retire in 2008?

### Enter the Monte Carlo Simulation

A Monte Carlo Simulation can reveal a wide variety of potential outcomes by taking into account fluctuating market returns. So instead of basing your retirement calculations on just one average rate of return, a Monte Carlo Simulation might generate 5,000 scenarios of what hypothetically might happen to your portfolio as you draw it down and markets fluctuate.

Let’s look at an example of a 60-year-old who retires with \$750,000 invested in a standard balanced portfolio of 60 percent stocks and 40 percent bonds. This retiree wants to know how much is safe to withdraw from the portfolio each year and whether it can last 30, 40, or even 50 years.

We can do this with a Monte Carlo Simulation. I used Vanguard’s retirement nest egg calculator. We’ll start with a safe withdrawal rate of 4 percent per year:

1. How many years should the portfolio last: 30 years
2. What is your portfolio balance today: \$750,000
3. How much do you spend from the portfolio each year: \$30,000

The results: There’s a 93 percent probability that this portfolio lasts 30 years.

When I re-run the simulation using a withdrawal rate of 5.3 percent (spending \$40,000 per year) there’s now just a 74 percent chance the portfolio survives 30 years.

What happens if our retiree lives until 100? We’ll need to make the portfolio last for 40 years instead of 30.

Spending \$40,000 each year means the portfolio has only a 62 percent chance of surviving 40 years. If we go back to our original 4 percent safe withdrawal rate (\$30,000 per year) then our portfolio jumps back up to an 87 percent survival rate.

In one interesting simulation, I increased the stock allocation to 100 percent and changed the annual spending to \$50,000 (or 6.7 percent of the portfolio). The \$750,000 portfolio has a 50 percent chance of lasting 40 years. Not something I’d chance to a coin-flip!

How does a Monte Carlo Simulation work? According to Vanguard, they randomly select the returns from one year of the database for each year of each simulation.