Refer to A New Tool from Wed Apr 28, 2004 at 4:41 pm CDT.

http://nofeeboards.com/boards/viewtopic.php?t=2427

and New Tool errata dated Tue, Jun 22, 2004.

http://nofeeboards.com/boards/viewtopic.php?t=2655

In an earlier post, I showed the risk facing those who might start a 30-year retirement with 4% and 5% withdrawals at bubble level valuations. I have applied the New Tool as well. What I had left undone was to evaluate how those earlier portfolios are progressing. The calculators have actual data through 2002 and dummy values afterwards. We now know how 1994, 1995 and 1996 have performed in the first 6 years.

Unlike calculations based on earnings yield, the New Tool calculations are not based directly on valuations. Instead, they are based on the annualized, real return of a portfolio [with dividends reinvested (and with expenses) but with no deposits or withdrawals] after a specified number of years. This allows us to predict future results that differ from the past in this respect: we can assume that stock valuations have reached a new, permanent, higher plateau.

**Annualized, real rates of return**

For HDBR50, the annualized, real rates of return from 1994, 1995 and 1996:

Code: Select all

`1994 6 years 12.03%`

1994 7 years 9.62%

1994 8 years 7.31%

1995 6 years 11.17%

1995 7 years 8.27%

1996 6 years 6.12%

For HDBR80, the annualized, real rates of return from 1994, 1995 and 1996:

Code: Select all

`1994 6 years 16.22%`

1994 7 years 12.68%

1994 8 years 9.25%

1995 6 years 15.08%

1995 7 years 10.76%

1996 6 years 8.24%

**HDBR50 Progress**

For a 50% stock portfolio, the relevant information is taken from the returns after 6 years. The equation is y = 2.6452x - 9.7732, where y = return0, which is the real, annualized total return with dividends reinvested, no withdrawals and with 0.20% expenses, and x = the Calculated Rate with 50% stocks. The standard deviation for x is 1.24% (or, more precisely, 1.242862%). The standard deviation for y is 3.29% (or, more precisely 3.287619%). The 90% confidence limits are plus and minus 1.64 times the standard deviation away from the Calculated Rates. For x, it is 2.04% (or, more precisely, 2.0382937%). The comparable limits surrounding the real, annualized total return, return0 = y, are plus and minus 5.4% (or, more precisely, 5.3916952%).

Here are some Calculated Rates for various values of y = return0.

1) The equation is y = 2.6452x-9.7732. Solving for x: x = [y+9.7732] / [2.6452].

2) When y = 0, x = 3.69% (the Calculated rate for HDBR50).

3) When y = 2, x = 4.45%.

4) When y = 4, x = 5.21%.

5) When y = 6, x = 5.96%.

6) When y = 8, x = 6.72%.

7) When y = 10, x = 7.48%.

8 ) When y = 11, x = 7.85%.

9) When y = 12, x = 8.23%.

The 1994 return after 6 years was 12.03%. The Calculated Rate (from the formula) is 8.24%. With confidence limits of plus and minus 2.04%, the Safe Withdrawal Rate [with the 2002 estimate] is now 6.20% and the High Risk Rate is 10.28%. Because subsequent years reduced the real, annualized return, we anticipate that the 10-year Calculated Rate will be lower, but it will still be very high.

The 1995 return after 6 years was 11.17%. The Calculated Rate (from the formula) is 7.92%. With confidence limits of plus and minus 2.04%, the Safe Withdrawal Rate [with the 2002 estimate] is 5.88% and the High Risk Rate is 9.96%.

The 1996 return after 6 years was 6.12%. The Calculated Rate (from the formula) is 6.01%. With confidence limits are plus and minus 2.04%, the Safe Withdrawal Rate [with the 2002 estimate] is 3.97% and the High Risk Rate is 8.05%.

**HDBR80 Progress**

For an 80% stock portfolio, the relevant information is taken from the returns after 6 years. The equation is y = 2.2778x-9.5372, where y = return0, which is the real, annualized total return with dividends reinvested, no withdrawals and with 0.20% expenses, and x = the Calculated Rate with 80% stocks. The standard deviation for x is 1.82% (or, more precisely, 1.819669%). The standard deviation for y is 4.14% (or, more precisely 4.144842%). The 90% confidence limits are plus and minus 1.64 times the standard deviation away from the Calculated Rates. For x, it is 2.98% (or, more precisely, 2.9842572%). The comparable limits surrounding the real, annualized total return, return0 = y, are plus and minus 6.8% (or, more precisely, 6.7975409%).

Here are some Calculated Rates for various values of y = return0.

1) The equation is y = 2.2778x-9.5372. Solving for x: x = [y+9.5372] / [2.2778].

2) When y = 0, x = 4.19% = the Calculated Rate for HDBR80.

3) When y = 2, x = 5.07%.

4) When y = 4, x = 5.94%.

5) When y = 6, x = 6.82%.

6) When y = 8, x = 7.70%.

7) When y = 10, x = 8.58%.

8 ) When y = 12, x = 9.46%.

9) When y = 14, x = 10.33%.

10) When y = 15, x = 10.77%.

11) When y = 16, x = 11.21%.

The 1994 return after 6 years was 16.22%. The Calculated Rate (from the formula) is 11.31%. With confidence limits of plus and minus 2.98%, the Safe Withdrawal Rate [with the 2002 estimate] is 8.33% and the High Risk Rate is 14.29%. Because subsequent years reduced the real, annualized return, we anticipate that the 10-year Calculated Rate will be lower, but it will still be very high.

The 1995 return after 6 years was 15.08%. The Calculated Rate (from the formula) is 10.81%. With confidence limits of plus and minus 2.98%, the Safe Withdrawal Rate [with the 2002 estimate] is 7.83% and the High Risk Rate is 13.79%.

The 1996 return after 6 years was 8.24%. The Calculated Rate (from the formula) is 7.80%. With confidence limits are plus and minus 2.98%, the Safe Withdrawal Rate [with the 2002 estimate] is 4.82% and the High Risk Rate is 10.78%.

**Comparison with Earnings Yield Calculations**

I recently summarized the Safe, Calculated and High Risk Rates for the last decade based upon earnings yield. We can compare the 1995 and 1996 results from those calculations with our updated 6-year estimates.

Safe, Calculated and High Risk Rates with 50% stocks

Code: Select all

`Year Safe Calculated High Risk`

1995 3.60 4.61 5.62

1996 3.24 4.25 5.26

Safe, Calculated and High Risk Rates with 80% stocks

Code: Select all

`Year Safe Calculated High Risk`

1995 3.37 4.95 6.53

1996 2.76 4.34 5.92

We see that 1995 is turning out to be a lucky sequence. The 2002-updates place the updated Safe Withdrawal Rates higher than the High Risk Rates based on earnings yield calculations.

The 2002 estimates show that 1996 is turning out to be lucky as well, but not nearly as lucky as 1995. The 2002-updates place the Safe Withdrawal Rates close to the Calculated Rates based on earnings yield.

In both 1995 and 1996, the markets have favored higher stock allocations.

**Variations in Calculated Rates**

The New Tool has formulas for 7 and 8 years as well as for 6 years. What I have not calculated are the standard deviations and confidence limits for 7 and 8 years. Here are the Calculated Rates when applied at 6, 7 and 8 years.

For HDBR50, the annualized, real rates of return and Calculated Rates for 1994, 1995 and 1996:

Code: Select all

`1994 6 years 12.03% x = 8.24%`

1994 7 years 9.62% x = 7.17%

1994 8 years 7.31% x = 6.94%

1995 6 years 11.17% x = 7.92%

1995 7 years 8.27% x = 7.31%

1996 6 years 6.12% x = 6.01%

For HDBR80, the annualized, real rates of return and Calculated Rates for 1994, 1995 and 1996:

Code: Select all

`1994 6 years 16.22% x = 11.31%`

1994 7 years 12.68% x = 9.86%

1994 8 years 9.25% x = 8.40%

1995 6 years 15.08% x = 10.81%

1995 7 years 10.76% x = 8.99%

1996 6 years 8.24% x = 7.80%

The 7 and 8 year Calculated Rates for 1994 and 1995 decreased because stocks fell in 2001 and 2002. A 2003 estimate should be higher because stocks went up sharply in 2003, which will increase the real, annualized returns.

We can see the effect of initial valuations in these Calculated Rates. It shows up indirectly. Here, the effect shows up as decreasing real, annualized returns. Those decreases, in turn, correct the Calculated Rates downward.

Have no concern that the Calculated Rates vary with time. We start out with a full range of possible outcomes. This range is narrowed down with each passing year, when we make a new update. At the end of the sequence, the outcome is known and only one rate remains, the Historical Surviving Rate associated with the particular start year. We base each calculation on the information up to a particular year and none thereafter.

Have fun.

John R.