## Saturday, September 14, 2013

### Withdrawal rate confusion

Zouk’s post provides the opportunity to clarify a bit of personal finance that usually gets messed up in the newspapers.

In this discussion, I will ignore taxes, investment returns, and inflation in order to show the point simply.

Zouk is correct. Suppose you start with \$50,000 and withdraw 10% each year. You won’t run out of money, but each year you will withdraw less. Here’s what happens for the first 15 years:

\$ 5,000 \$ 4,500 \$ 4,050 \$ 3,645 \$ 3,281 \$ 2,952 \$ 2,657 \$ 2,391 \$ 2,152 \$ 1,937 \$ 1,743 \$ 1,569 \$ 1,412 \$ 1,271 \$ 1,144

In that 15th year, your 10% withdrawal is only getting you \$1,144 – a lot less than \$5,000 but not zero.

What they really mean isn’t what they say.

When financial planners make assumptions about withdrawal rates, they are making the hidden assumption that once you calculate how much you can withdraw at a rate, you continue to pull THAT AMOUNT, NOT THAT PERCENTAGE out.  So, if you start with \$50,000 and withdraw 10% in the first year, that means you needed \$5,000 and will continue to need \$5,000 in successive years.

Here’s what happens to that after 15 years:

\$ 5,000 \$ 5,000 \$ 5,000 \$ 5,000 \$ 5,000 \$ 5,000 \$ 5,000 \$ 5,000 \$ 5,000 \$ 5,000 \$0 \$0 \$0 \$0 \$0

You run out after 10 years; the last five years you have nothing.

The reason for this hidden assumption is clear: if you needed \$5,000 the first year, you probably needed just as much in actual dollars each year after that.  But expressing this as a percentage can confuse the issue. If you pull out \$5,000 each year, the actual percentage you take in each subsequent years is higher:

10.0%11.1%12.5%14.3%16.7%20.0%25.0%33.3%50.0%100.0% and then of course 0% 0% 0% 0% 0% because there’s no money left.

The 4% rule

The 4% rule is the typical rule of thumb for retirement.  You figure 4% of your nest egg can with withdrawn in the first year (\$2,000 on that \$50,000 nest egg), and then increase that amount each year by the rate of inflation. The idea is that with historical rates of investment return, taxation, and inflation, this should avoid running amount of money before you die.  It’s not a guarantee, of course, since nobody knows for sure what investment returns, taxation, or inflation are going to be.

But if we look backwards and imagine we’d used these rules beginning in 1972, here’s what would result:

The 6% line goes to zero because of the reasons outlined above: It’s not 6% each year (of a decreasing amount).  You figure 6% of the initial amount is withdrawn, and then that larger amount, plus inflation, is next year’s withdrawal.  The 4% line in this case shows an increase over time, but then the last 40 years have been, overall, very good years for stocks and bonds which we aren’t likely to see in the near future.