JWR1945 ***** Legend
Joined: 26 Nov 2002 Posts: 1697 Location: Crestview, Florida

Posted: Tue Jun 22, 2004 8:01 pm Post subject: More about High Risk and 4%? and 5%? 


In a previous post, I showed the risk facing those who might start a 30year retirement with 4% and 5% withdrawals at bubble level valuations. However, there is memory in stock returns and we have captured that effect with the New Tool.
These numbers are for those who actually began their retirements during the bubble. These numbers help you assess how well you are doing as your retirement progresses.
The key is that, if you actually retired in 1997 or later, you have already advanced part way toward a specific outcome. We know what has happened between 1997 and 2004. That has eliminated many of the outcomes that seemed reasonable in 1997. The statistical range has been narrowed down.
It is still early. The New Tool is most accurate at 14 years. The analysis that follows is based on information at year 6. Predictions made from the New Tool do not directly incorporate valuations. The New Tool calculates rates and confidence limits as a function of a portfolio's real, annualized return when there are no withdrawals (and with dividends reinvested and with 0.20% expenses).
Refer to A New Tool from Wed Apr 28, 2004 at 4:41 pm CDT.
http://nofeeboards.com/boards/viewtopic.php?t=2427
The equations for the straight lines that I produced have the form y = mx+b or return0 = slope*HDBR + intercept. Both return0 and HDBR are in percent. I have examined two portfolios, HDBR50 with a 50% stock allocation and HDBR80 with an 80% stock allocation. The Historical Database Rates are for 30 years. Expenses were 0.20% of the portfolio's current balance. Portfolios consisted of stocks and commercial paper with annual rebalancing.
50% Stocks
For a 50% stock portfolio, the relevant information is taken from the returns after 6 years. [Note: I have collected this kind of information at 6, 10 and 14 years. It is possible to calculate similar equations for any specified number of years. It is just that I have not done it.] 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 = 2.6452x9.7732. 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%.
With confidence limits are plus and minus 2.04%, we find that a withdrawal rate of 5.73% has a (very) slight chance of surviving even when the 6year real, annualized total return (return0) of the portfolio is flat (i.e., zero percent). Its chance of survival is close to 50% at a 3.69% withdrawal rate. The safe withdrawal rate, however, would only be 1.65%.
Only when the real, annualized total return (return0) is slightly above 6% [during the first six years] can we rest assured that withdrawing 4% is safe.
We can look at this equation the other way. If the withdrawal rate is 4%, then the Calculated Rate of the real, annualized total return (return0) = y = 2.6452x9.7732 = 0.8076% with confidence limits of plus and minus 5.4%. Adding 5.4% to 0.8076%, we see that a real, annualized total return of 6.2% (or, more precisely, 6.2076%) in the first six years is sufficient to guarantee (a high level of) safety. Subtracting, we see that it takes a real, annualized loss of 4.6% (or, more precisely, 4.5924%) to be assured of failure.
If the withdrawal rate is 5%, then the Calculated Rate of the real, annualized total return (return0) = y = 2.6452x9.7732 = 3.4528% with confidence limits of plus and minus 5.4%. Adding 5.4% to 3.4528%, we see that a real, annualized total return of 8.9% (or, more precisely, 8.8528%) in the first six years would be required to guarantee (a high level of) safety. Subtracting, we find that it takes a real, annualized loss of 1.9% (or, more precisely, 1.9472%) to be assured of failure.
80% Stocks
For an 80% stock portfolio, the relevant information is taken from the returns after 6 years. [Note: I have collected this kind of information at 6, 10 and 14 years. It is possible to calculate similar equations for any specified number of years. It is just that I have not done it.] The equation is y = 2.2778x9.5372, 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 = 2.2778x9.5372. 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%.
With confidence limits are plus and minus 2.98%, we find that a withdrawal rate of 7.17% has a (very) slight chance of surviving even when the 6year real, annualized total return (return0) of the portfolio is flat (i.e., zero percent). Its chance of survival is close to 50% at a 4.19% withdrawal rate. The safe withdrawal rate, however, would only be 1.21%.
Only when the real, annualized total return (return0) is close to 6.5% can we be assured that withdrawing 4% is safe.
We can look at this equation the other way. If the withdrawal rate is 4%, then the Calculated Rate of the real, annualized total return (return0) = y = 2.2778x9.5372= 0.426% with confidence limits of plus and minus 6.8%. Adding 6.8% to 0.426%, we find that a real, annualized total return of 6.4% (or, more precisely, 6.374%) in the first six years is sufficient to guarantee that we can withdraw 4% with (a high level of) safety. Subtracting, we see that it would take an annualized loss of 7.2% (or, more precisely. 7.226%) to be assured of failure.
If the withdrawal rate is 5%, then the Calculated Rate of the annualized total return (return0) = y = 2.2778x9.5372= 1.8518% with confidence limits of plus and minus 6.8%. Adding 6.8% to 1.8518%, we see that a real, annualized total return of 8.7% (or, more precisely, 8.6518%) in the first six years would be required to guarantee (a high level of) safety. Subtracting, we find that it takes a real, annualized loss of 4.9% (or, more precisely, 4.9482%) to be assured of failure.
Remarks
The best Safe Withdrawal Rates predictions are those that incorporate valuations directly. This kind of prediction is different. It allows you to look at possibilities that would not make sense otherwise: cases such as stock prices now having reached a permanent, new, higher plateau (even higher than those of the late 1920s).
Have fun.
John R.

