No New Discovery This Time

Normally, I specify a single withdrawal rate. Then I see what happens to portfolio balances. This time, I looked at what happens when you withdraw at each portfolio’s Historical Surviving Withdrawal Rate. I was hoping to find something useful, something to tell us when everything is going OK.

I was hoping to find something new. I didn’t.

Procedure

I collected real balances of HSWR80T2 for years 1 through 30 at each 30-Year Historical Surviving Withdrawal Rate from 1921-1975. The portfolios consisted of 80% stocks (S&P500) and 20% TIPS at a 2% (real) interest rate. I set expenses at 0.20%. All of the balances at Year 30 were positive. In every instance, increasing the withdrawal rate by 0.1% made the Year 30 balance negative.

[There were several instances in which portfolios survived to Years 31 and 32 at the Historical Surviving Withdrawal Rate. But Year 30 was always negative when the rate was 0.1% higher.]

Balances

I started with balances of $100K.

Here is what happens along the way:

At year 5, the balances ranged from $52847 to $193178.
At year 10, the balances ranged from $39396 to $158657.
At year 15, the balances ranged from $33550 to $153829.
At year 20, the balances ranged from $25673 to $126631.
At year 25, the balances ranged from $16898 to $71006.
At year 30, the balances ranged from $98 to $12742.

Withdrawal Rates

I set the withdrawal rate at Year 0 and adjusted withdrawals later to match inflation. Otherwise, the amount withdrawn remained constant. The withdrawal rates were all based upon the initial balance of $100000.

The percentage withdrawal rate along the way varied because the (real) balances varied. The same withdrawal amount became different withdrawal rates.

The percentages varied at Year 0 since I set each year’s withdrawal rate equal to its 30-Year Historical Surviving Withdrawal Rate.

Here is what happened along the way:

At year 0, the withdrawal rate ranged from 3.9% to 10.6%.
At year 5, the withdrawal rate ranged from 4.2% to 12.0%.
At year 10, the withdrawal rate ranged from 4.8% to 12.7%.
At year 15, the withdrawal rate ranged from 5.7% to 15.0%.
At year 20, the withdrawal rate ranged from 7.3% to 18.7%.
At year 25, the withdrawal rate ranged from 13.5% to 26.9%.
At year 30, the withdrawal rate ranged from 40.7% to 6661.7%.

Obvious Patterns

I had been inspired by Rob Bennett’s new discovery about Mean Reversion. Rob discovered that outliers don’t remain outliers. If your year 10 stock market predictions based on P/E10 fail to work out, they will snap back by year 20.

Rob spotted an obvious pattern.

Similarly, in this investigation, I was hoping to spot something obvious. I did not.

Have fun.

John Walter Russell
July 2, 2006