Retirement and sequence risk

Test the 4% rule against thousands of markets, and see why the order of returns can matter more than the average.

Savings at retirement$1M

First-year withdrawal4.00%, $40K a year

Then the same amount every year, raised with inflation.

Years of retirement30

In stocks60% stocks, 40% bonds

Market model

All figures are after inflation. Stocks: 6.5% a year on average, 17% volatility. Bonds: 2.0%, 7% volatility.

Money lasts the whole time86.5%

Median left at the end$930K

Unluckiest 10% of marketsrun dry

When it fails, typically inyear 26

Median Middle 50% Middle 90% Starting savings

Still has money, year by year

What's left after 30 years

Withdrawing $40,000 a year (4.00% of the start), the money lasted all 30 years in 86.5% of 2,000 simulated markets. The portfolio expects about 4.7% a year after inflation, yet the outcomes range from running dry to ending far richer. The average return doesn't decide the result on its own: the order the returns arrive in does.

Sequence of returns: same returns, different order

Both lines below get exactly the same 30 yearly returns, averaging 3.7%. The only difference is when the three worst years (-19%, -13%, -10%) arrive.

Crash in the first three years$0runs out in year 26

Crash in the last three years$964Klasts the full retirement

Either order, with no withdrawals$2.5Midentical: order can't matter

Bad years first Bad years last

Without withdrawals, multiplying the same returns in any order gives the same answer. With withdrawals, a crash early forces you to sell more shares at low prices, and those shares are not there for the recovery. That is why the first decade of retirement carries most of the risk.

Try this

Find the highest withdrawal rate that still succeeds in at least 90% of markets over 30 years.
Switch to fat tails. Which number moves more: the median ending balance or the success rate?
Set stocks to 0%. Is the all-bond portfolio safer, or does it fail more slowly but more often?

The math

B_{t+1} = \left(B_t - W\right)\left(1 + R_{t+1}\right)

$B_t$: balance at the start of year t
$W$: yearly withdrawal, fixed in today's dollars
$R_{t}$: portfolio return after inflation that year
$B_0 \prod (1+R_t)$: the ending value with no withdrawals, the same in any order

Ask the Loop about this Next: Random walk to Brownian motion