Okay, what's Optimal? Suppose we define Optimal so that your Total worth (portfolio balance + amount withdrawn) is a maximum, over a twenty year period, from Jan/50 to Jan/00. (Uh ... that may not be your definition, but let's see where it gets us.) For example, the chart on the right shows the Total for our $100K S&P 500 investment (meaning the portfolio PLUS the cumulative withdrawals) which began Jan 1, 1980 and continued to Jan 1, 2000 and we withdrew just the monthly positive gains in our S&P portfolio (as we did above: see Fig. 5). >So why do you say "positive" gains? Ain't "gains" always positive? Uh ... we say positive to avoid somebuddy saying: "What if the gain is negative?" Anyway, let's proceed ...

Fig. 6

Okay, what if we limit our withdrawals: Never take less than 0.5% of the current portfolio balance, each month. (That's like 6% per year.) >To pay the bills, right? Never take more than 0.75% of the current portfolio balance, each month. (That's like 9% per year.) >To buy a new TV, right? Fig. 7 ilustrates the result (with more detail on the final year's withdrawals: Jan/99 to Jan/00). Note that although we talk about 9% per year, we really mean 9%/12 = 0.75% per month, okay? It looks pretty good ... but that's for the S&P 500 and for a particular 20-year period. What about other 20-year periods lying in the interval: 1950 to 2000? Below are charts for certain 20-years intervals. In each case we begin on Jan 1 of the first year indicated, withdrawing monthly at an annual rate between 6% and 9% of the current portfolio. (That's not a fixed amount but varies with the market ... with some flexibility.)

Fig. 7

If the minimum monthly withdrawals seem insufficient to pay the bills, start with $500K instead of $100K ... then you can multiply by 5!

    
      

Of course, since we're talking about withdrawing, we're presumably retired. We'll drop dead in ... what? Thirty years?
>As I write this, I'll be lucky to last another fifteen years
So, let's consider all 30-years periods which begin on the first of each month and lie in the interval Jan 1, 1950 to Jan 1, 2000. The first of these will start Jan 1, 1950 and run to Jan 1, 1980. The next will start Feb 1, 1950 and run till Feb 1, 1980. The last will start Jan 1, 1970 and run until Jan 1, 2000. There's 240 of 'em. For each we'll start with $500K and:

• Withdraw the (positive) gains for the month, or
• 6% (1/12) of the remaining balance if the gains are too small (or negative!), or
• 9% (1/12) of the remaining balance if the gains are too large.

• The gain for the previous month, and
• 6% x $100K (1/12) = $500
• 9% x $100K (1/12) = $750

Fig. 8

Matter of fact, if you withdraw just the (positive) portfolio gains, but at least 10%, and no more than 14%, your portfolio wouldn't even have dropped to 10% of its starting value (which was $500K). That means you'd always have at least $50K left (after thirty years). (See Fig. 8) >Mamma mia! Aah, but would the withdrawals have paid the bills? Well, the minimum withdrawal rate of 10% applied to the minimum portfolio of at least $50,000 would give $5,000 per year. In fact, we'd have done better: The smallest income (over twelve months) would have been $25,471. The largest income (over twelve months) would have been $78,409.

Of course, these withdrawals are before tax.

Further, after thirty years, inflation can kill you! To see the effect of a 2% inflation adjustment, we'll start with Minimum and Maximum Withdrawal Rates of 8% and 10% and increase these, monthly, at the rate of 2% per annum. That'd give (with and without an inflation adjustment) the following charts (starting in Jan/65 and running for thirty years).

     
>Let's see. In '71, when the portfolio wuz about $300K, I'd be withdrawing a Max. of 10% x $300K /12 or about $2,500 ... increased by 'bout five years worth of inflation.
Looks okay to me!

The early, larger monthly withdrawals ($4K) are for travelling, buying that new car, etc. etc.
>... while you're still young enuff to enjoy these things?
The later withdrawals ($1K) are for the nursing home.

Fig. 9

The final portfolio (the $500K, after thirty years of 8% to 10% withdrawals, with 2% inflation, starting in Jan/65) is $70,996 and the final monthly withdrawal is $1060. If we consider starting dates other than Jan/65, what's the final portfolio ... and the final monthly withdrawal? Take a peek at Fig. 9. >There's a moral here, right? Yeah ... retire in 1970.

P.S.
In fact, the thirty period starting in Jan, 1970 had an annualized S&P500 return of 9.8% and you could have withdrawn 10% of the current portfolio with a $2,000 minimum withdrawal, both figures increasing monthly at the annual rate of 2%, and your portfolio would never have gone bust. (Because of this 2%, your monthly withdrawals would have varied between $2000 and $3617.)

On the other hand, had you started on Jan 1, 1965 (withdrawing 10% - $2K minimum - increasing at 2% - etc. etc.) you'd have gone broke in Jan/84; after just nineteen years! (The annualized return, over thirty years, was 5.8%.) However, reducing the minimum from $2000 to $1300, you'd have lasted the thirty years. Notice that withdrawals between 8% and 10% (as we considered above, without specifying any minimum ... to pay the bills) would have resulted in a final withdrawal (after thirty years) of just $1060.

Yeah ... maybe it's time to put this tutorial to bed ... and head off on a trip:

In the meantime, I'll leave you with this ...

This portfolio would have been reduced to ZERO after 25 years.

When 8% x (1/12) = 2/3% of the portfolio is less than $4,000, you'd withdraw the $4,000 minimum.
The monthly withdrawals vary between $4010 and $8252.
If we just withdrew the (inflation-adjusted) $4,000 per monthly (forgetting about the 8%), it'd last thirty years and (surprise!) the withdrawals would vary from $4,000 to $9685!

>A BIGGER maximum withdrawal? Ya gotta be kidding!

That's because, at 8%, we made bigger, early withdrawals. The picture(s) look like so (noting that, at Max = 8%, we ran out of money after 25 years and never got to the BIGGER, later withdrawals of $9685!):