## Tuesday, February 19, 2008

### When Can I Retire?

A major concern for many people is how old they will be when they can retire. This depends on a number of factors such as how much you save, how well your investments perform, how much you spend during retirement, and how long you live.

Retirement calculators can figure this out for you based on a number of assumptions. However, most of them don’t give you a feel for how the final answer would change if your investment returns are volatile instead of perfectly steady.

There was a good post over at the Canadian Financial DIY blog about using Monte Carlo analysis for financial planning. Monte Carlo analysis just means simulating possible outcomes many times to see how the final answer changes.

I decided to use Monte Carlo to see how the mix of stocks and bonds in a portfolio affects when you can retire. I had to make some assumptions:

- Stocks and bonds will have the returns and volatility as reported in the paper Portfolio Optimization by John Norstad (2002-09-11).
- Retirement money has to last until you are 90 years old.
- After retirement you will invest conservatively and get steady returns 3% above inflation.

The simulations were based on the following saving and spending rates:

- You save \$600 per month (rising with inflation) in a retirement account while working.
- You will spend \$4000 per month (in today’s dollars) during retirement.

I ran each simulation until there was enough money to retire. After a million runs, I found the median retirement age as well as the age range that covered 90% of the simulations.

Here are the results if you start saving at age 25:

 Stocks Bonds Retirement Age Median (Range) 0% 100% 75 (65-82) 50% 50% 66 (56-76) 100% 0% 57 (47-72)

The width of these age ranges shows that there is quite a bit of uncertainty. There isn’t much doubt that historically stocks have been better than bonds at giving investors a chance to retire early.

Here are the results if you waited until age 40 to start saving:

 Stocks Bonds Retirement Age Median (Range) 0% 100% 80 (74-84) 50% 50% 75 (68-81) 100% 0% 69 (60-80)

The advantage of stocks is evident here as well. The other thing to note is the power of starting to save earlier. In the all-stock case, the 15-year head start in saving led to retirement about a decade earlier.

It makes sense to use short-term bonds for money that you will need to spend within the next 3 years or so, but I haven’t found a good reason to own bonds for the long term.