More specifically, I am interested in when the High Risk Withdrawal Rate is 4% or 5% over a 30-year time frame.

I have extracted the following from the thread

**From Earnings Yield**dated Thu, Apr 15, 2004.

http://nofeeboards.com/boards/viewtopic.php?t=2368

With the 50% stock portfolio, the Historical Database Rate (HDBR50) equation is HDBR50 = 0.3979x+2.6434%, where x = 100*(E10/P) or 100/[P/E10] = the earnings yield in percent and R squared equals 0.6975. When using this equation, the standard deviation of HDBR50 is 0.6178. The 90% confidence limits are plus and minus 1.01% of the calculated value.

With the 80% stock portfolio, the Historical Database Rate (HDBR80) equation is HDBR80 = 0.6685x+1.6424%, where x = 100*(E10/P) or 100/[P/E10] = the earnings yield in percent and R squared equals 0.7274. The standard deviation of HDBR80 using this formula is 0.9649. The 90% confidence limits are plus and minus 1.58%.

**At 4%**

These days, we refer to the numbers HDBR50 and HDBR80 in the equations as Calculated Rates. Previously, we had referred to them as Zero Balance Rates. In each case, I will solve for x, the earnings yield, when the upper confidence limit equals 4%.

With the 50% stock portfolio, the upper confidence limit is 1.01% above the Calculated Rate. When the upper confidence limit equals 4%, the Calculated Rate is 2.99% (which equals 4.00-1.01). Next we calculate x when HDBR50 is 2.99%. The equation becomes 2.99% = 0.3979x + 2.6434% or 0.3979x = 0.3466% and the earnings yield x = 0.8710731%. The High Risk Withdrawal Rate of a 50% stock portfolio occurs when P/E10 is 115 (or, more precisely, 114.80092).

When the Calculated Rate of the 50% stock portfolio equals 4%, we set HDBR50 = 4% in the equation and solve 4% = HDBR50 = 0.3979x + 2.6434% or 1.3566 = 0.3979x and the earnings yield x = 3.4093993%%. The Calculated Rate of the 50% stock portfolio occurs when P/E10 is 29 (or, more precisely, 29.33068).

With the 80% stock portfolio, the upper confidence limit is 1.58% above the Calculated Rate. When the upper confidence limit equals 4%, the Calculated Rate is 2.42% (which equals 4.00-1.58 ). Next we calculate x when HDBR80 is 2.42%. The equation becomes 2.42% = 0.6685x + 1.6424% or 0.6685x = 0.7776% and the earnings yield x = 1.1632012%. The High Risk Withdrawal Rate of an 80% stock portfolio occurs when P/E10 is 86 (or, more precisely, 85.96965).

When the Calculated Rate of the 80% stock portfolio equals 4%, we set HDBR80 = 4% in the equation and solve 4% = HDBR80 = 0.6685x + 1.6424% or 2.3576 = 0.6685x and the earnings yield x = 3.5267016%. The Calculated Rate of the 80% stock portfolio occurs when P/E10 is 28 (or, more precisely, 28.35511).

**Bubble Valuations and 4%**

P/E10 exceeded 29.0 in February 1997, May 1997 through August 2001 and November 2001 through April 2002. P/E10 peaked just above 44 in December 1999.

Those who started withdrawing 4% of their initial balances during those times still have a chance of reaching 30-years before they deplete their portfolios. In many cases, the odds are almost as good as 50%.

Even at the peak of the bubble, withdrawing 4% was still below the High Risk Withdrawal Rate, above which failure is almost certain to occur.

**At 5%**

Now let us see what happens for those who have started with a 5% withdrawal rate.

With the 50% stock portfolio, the upper confidence limit is 1.01% above the Calculated Rate. When the upper confidence limit equals 5%, the Calculated Rate is 3.99% (which equals 5.00-1.01). Next we calculate x when HDBR50 is 3.99%. The equation becomes 3.99% = 0.3979x + 2.6434% or 0.3979x = 1.3466% and the earnings yield x = 3.3842674%. The High Risk Withdrawal Rate of a 50% stock portfolio occurs when P/E10 is 29.5 (or, more precisely, 29.54849).

When the Calculated Rate of the 50% stock portfolio equals 5%, we set HDBR50 = 5% in the equation and solve 5% = HDBR50 = 0.3979x + 2.6434% or 2.3566 = 0.3979x and the earnings yield x = 5.9225936%. The Calculated Rate of the 50% stock portfolio occurs when P/E10 is 17 (or, more precisely, 16.8845).

With the 80% stock portfolio, the upper confidence limit is 1.58% above the Calculated Rate. When the upper confidence limit equals 5%, the Calculated Rate is 3.42% (which equals 5.00-1.58 ). Next we calculate x when HDBR80 is 3.42%. The equation becomes 3.42% = 0.6685x + 1.6424% or 0.6685x = 1.7776% and the earnings yield x = 2.6590875%. The High Risk Withdrawal Rate of an 80% stock portfolio occurs when P/E10 is 38 (or, more precisely, 37.60689).

When the Calculated Rate of the 80% stock portfolio equals 5%, we set HDBR80 = 5% in the equation and solve 5% = HDBR80 = 0.6685x + 1.6424% or 3.3576 = 0.6685x and the earnings yield x = 5.0225879%. The Calculated Rate of the 80% stock portfolio occurs when P/E10 is 20 (or, more precisely, 19.91006).

**Bubble Valuations and 5%**

P/E10 exceeded 29.5 in May 1997 through August 2001, November 2001 through January 2002 and March 2002.

Those who started withdrawing 5% of their initial balances from a 50% stock portfolio when P/E10 exceeded 29.5 have very little chance of making it to 30-years before they deplete their portfolios.

P/E10 exceeded 38 in July 1997 and in December 1998 through November 2000. P/E10 peaked just above 44 in December 1999.

Those who started withdrawing 5% of their initial balances from an 80% stock portfolio when P/E10 exceeded 38 have very little chance of making it to 30-years before they deplete their portfolios.

**Final Remarks**

This should help balance out the voices of those who have been telling us that 4% is overly conservative. Many who considered withdrawing 5% as taking on a reasonable risk are already in trouble. Taking note of valuations is critically important.

Do not be disturbed that the higher stock allocation has a greater likelihood of surviving with 5% withdrawals. It has a higher growth potential if future returns should turn out favorable. That might allow enough growth to allow for a 5% withdrawal rate.

If your preference is to guarantee safety, you would normalize your comparisons by looking at withdrawal rates in the neighborhood of 4%.

Have fun.

John R.